Notch filter

Abstract

To provide a notch filter that has a wider free filter area.SOLUTION: A notch filter 1 has: a free filter area that is a wavelength region transmitting light; and one or more block bands that are arranged between a lower limit of the free filter area and an upper limit thereof, and suppress transmission of the light of a prescribed wavelength region. The notch filter 1 comprises: a base material 2; and an optical multilayer film 4 that is directly or indirectly formed relative to a base material surface M being a surface of the base material 2. The optical multilayer film 4 is formed based on a basic filter repeated structure that has a low refractive index material-made low refractive index layer L and a high refractive index material-made high refractive index layer H alternately arranged. A film thickness of each layer in the optical multilayer film 4 corresponds to a sequence row of a modulation film thickness adding a modulation in a cycle different from a basic cycle based on the number of layers of the basic filter structure relative to a sequence row of the basic film thickness having a film thickness of each layer lined in order from the base material 2.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a notch filter that suppresses the transmission of light in a relatively narrow wavelength range (stopband) within a free filter region which is a predetermined wavelength range, while transmitting light in other wavelength ranges. [Background technology]

[0002] A notch filter (also called a negative filter or bandstop filter) is known, as described in Patent Document 1 (Japanese Patent Publication No. 4575052). In this notch filter, for example, as described as (d) in

[0019] , the design reference wavelength, i.e., the design wavelength λ = 500 nm, is (0.65H 0.35L) 10 An alternating repeating structure of high-refractive-index and low-refractive-index layers is observed, realizing a reflection band centered on the design wavelength λ, and preventing transmission in the reflection band. Here, "0.65H" indicates a high-refractive-index layer with an optical film thickness of 0.65 times the design wavelength λ, and "0.35L" indicates a low-refractive-index layer with an optical film thickness of 0.35 times the design wavelength λ. The "10" in the upper right corner of the parentheses indicates that the structure inside the parentheses is repeated 10 times. Note that the first 0.65H is closest to the substrate. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Patent No. 4575052 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] Recently, there has been a demand for notch filters with wider free filtering ranges, such as between 400nm and 1200nm, or between 400nm and 1800nm. For example, in fields such as medicine or biotechnology, attempts are being made to non-destructively analyze the characteristics of an object by irradiating it with a laser and capturing and analyzing the weak signal light that is secondarily generated by an image sensor (spectroscopic analysis). To achieve better analysis, a notch filter with a stopband at the laser wavelength is placed in the optical path to the image sensor. This suppresses the arrival of relatively strong laser light that would interfere with the analysis, while allowing light in a wide range of wavelengths necessary for analysis to pass through. Furthermore, to achieve even better analysis, the adoption of image sensors with a wider sensitivity wavelength is expected. For example, the sensitivity wavelength of an image sensor using a silicon photodiode is approximately 400 nm to 1200 nm. Also, the sensitivity wavelength of an image sensor using both a silicon photodiode and an InGaAs (indium gallium arsenide) photodiode is approximately 400 nm to 1800 nm. However, in the notch filter described in Patent Document 1, a stopband is formed on the wavelength shorter than the design wavelength λ due to the monotonous repeating structure of high-refractive-index and low-refractive-index layers. Therefore, in this notch filter, it is not possible to have only the stopband centered on the wavelength of a laser having a relatively long wavelength (e.g., 1064, 1550 nm) in a wider free filter region. In this notch filter, for example, if a stopband centered on 1550 nm is provided (design wavelength λ = 1550 nm), then in the region between 400 nm and 1800 nm, a stopband centered on 1550 × 1 / 2.5 = 620 nm and a stopband centered on 1550 × 1 / 3.5 ≈ 442.9 nm will be generated together. Such stopbands other than those centered on the design wavelength λ prevent light in that wavelength band from reaching the image sensor, degrading the quality of the analysis.

[0005] On the other hand, when two materials with a small difference in refractive index are used, the conventional {(b / 2)L aH (b / 2)L} cEven in the case of the design, by setting the optical film thickness ratio to H:L = 1:1 (a = b), the appearance of the stop band is suppressed up to a wavelength of 1 / 3 of the design wavelength. Here, "H" represents a high refractive index layer having an optical film thickness of 1 / 4 (0.25) times the design wavelength λ, "aH" represents a high refractive index layer having an optical film thickness of a × 0.25 × λ, "L" represents a low refractive index layer having an optical film thickness of 0.25 times the design wavelength λ, and "(b / 2)L" represents a low refractive index layer having an optical film thickness of (b / 2) × 0.25 × λ. Also, the "c" on the right shoulder of the parentheses indicates that the structure inside the parentheses is repeated c times. Note that the first (b / 2)L located on the leftmost side is the one closest to the substrate side. Hereinafter, unless otherwise specified, the film structure is shown in the same manner as this. However, in order to form a stop band with an even narrower wavelength width (the size between the upper and lower limits of the wavelength) and improve the quality of the analysis by imaging the signal light at wavelengths adjacent to the laser wavelength as much as possible, when the optical film thickness ratio is shifted (a > b or a < b), a stop band is formed at 1 / 2 of the design wavelength like the notch filter of Patent Document 1 described above, and a notch filter with a wide free filter region on the shorter wavelength side than the design wavelength λ cannot be obtained.

[0006] One of the main objects of the present disclosure is to provide a notch filter having a wider free filter region. Another one of the main objects of the present disclosure is to provide a notch filter having a stop band with a narrower wavelength width.

Means for Solving the Problems

[0007] This specification discloses a notch filter. The notch filter has a free filter region which is a wavelength range that transmits light, and a plurality of stop bands which are arranged between the lower and upper limits of the free filter region and which suppress the transmission of light in a predetermined wavelength range. The notch filter also comprises a substrate and an optical multilayer film which is formed directly or indirectly on the surface of the substrate. The optical multilayer film is formed based on a basic filter repeat structure which is a multiple repetition of a basic filter structure in which a low refractive index layer made of a low refractive index material and a high refractive index layer made of a high refractive index material are alternately arranged. The film thickness of each layer in the optical multilayer film is determined by the basic film thickness sequence obtained by arranging the film thickness of each layer in the basic filter repeat structure in order from the substrate side, and the basic filter structure Based on the number of layers This corresponds to a sequence of modulated film thicknesses with modulation applied at a period different from the fundamental period. Multiple modulation periods exist. The free filter region includes a wavelength range of 400 nm to 1200 nm. The basic filter repeat structure is one of the following: a first basic filter repeat structure which repeats the basic filter structure having a basic period of 6; a second basic filter repeat structure which repeats the basic filter structure having a basic period of 14; or a third basic filter repeat structure which repeats the basic filter structure having a basic period of 10. [Effects of the Invention]

[0008] One of the main effects of this disclosure is that it provides a notch filter having a wider free filter area. Another key effect of this disclosure is that it provides a notch filter with a narrower wavelength stopband. [Brief explanation of the drawing]

[0009] [Figure 1] This is a schematic cross-sectional view of the notch filter according to the present invention. [Figure 2] This graph shows the spectral transmittance exhibited by the first basic filter repeating structure when the number of repetitions q = 50. [Figure 3] This graph shows the spectral transmittance exhibited by the second basic filter repeating structure when the number of repetitions r = 40. [Figure 4] This graph shows the spectral transmittance exhibited by the third basic filter repeating structure when the number of repetitions s = 40. [Figure 5] This graph shows the relationship between the modulation period Λ1 and the center wavelength of the stopband. [Figure 6] This graph shows the relationship between the modulation amplitude a1 and the wavelength width of the stopband. [Figure 7] This graph shows the discrete Fourier transform spectrum of the film thickness sequence for the first basic filter repeating structure (number of repetitions q=50) and the period corresponding to the number m. [Figure 8] This graph shows the discrete Fourier transform spectrum of the film thickness sequence for the second basic filter repeating structure (number of repetitions r=40) and the period corresponding to the number m. [Figure 9] This graph shows the discrete Fourier transform spectrum of the film thickness sequence for the third basic filter repeating structure (number of repetitions s=40) and the period corresponding to the number m. [Figure 10] Figure 1 is a flowchart showing an example of a design method for optical multilayer films. [Figure 11] This graph shows the spectral transmittance exhibited by Example 1. [Figure 12] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 1 and the period corresponding to the number m. [Figure 13] This graph shows the spectral transmittance exhibited by Example 2. [Figure 14] This is a graph showing the discrete Fourier transform spectrum of the film thickness sequence in Example 2 and the period corresponding to the number m. [Figure 15] This graph shows the spectral transmittance exhibited by Example 3. [Figure 16] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 3 and the period corresponding to the number m. [Figure 17] This graph shows the spectral transmittance exhibited by Example 4. [Figure 18] This is a graph showing the discrete Fourier transform spectrum of the film thickness sequence in Example 4 and the period corresponding to the number m. [Figure 19] This graph shows the spectral transmittance exhibited by Example 5. [Figure 20] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 5 and the period corresponding to the number m. [Figure 21] This graph shows the spectral transmittance exhibited by Example 6. [Figure 22] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 6 and the period corresponding to the number m. [Figure 23] This graph shows the spectral transmittance exhibited by Example 7. [Figure 24] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 7 and the period corresponding to the number m. [Figure 25] This graph shows the spectral transmittance exhibited by Example 8. [Figure 26] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 8 and the period corresponding to the number m. [Figure 27] This graph shows the spectral transmittance exhibited by Example 9. [Figure 28] This is a graph showing the discrete Fourier transform spectrum of the film thickness sequence in Example 9 and the period corresponding to the number m. [Figure 29] This graph shows the spectral transmittance exhibited by Example 10. [Figure 30] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 10 and the period corresponding to the number m. [Figure 31] This graph shows the spectral transmittance exhibited by Example 11. [Figure 32] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 11 and the period corresponding to the number m. [Figure 33] This graph shows the spectral transmittance exhibited by Comparative Example 1. [Figure 34] This graph shows the discrete Fourier transform spectrum of the film thickness sequence for Comparative Example 1 and the period corresponding to the number m. [Figure 35] This graph shows the spectral transmittance exhibited by Comparative Example 2. [Figure 36] This is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Comparative Example 2 and the period corresponding to the number m. [Figure 37]This graph shows the spectral transmittance exhibited by Example 12. [Figure 38] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 12 and the period corresponding to the number m. [Figure 39] This graph shows the spectral transmittance exhibited by Example 13. [Figure 40] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 13 and the period corresponding to the number m. [Figure 41] This graph shows the spectral transmittance exhibited by Example 14. [Figure 42] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 14 and the period corresponding to the number m. [Figure 43] This graph shows the spectral transmittance exhibited by Example 15. [Figure 44] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 15 and the period corresponding to the number m. [Figure 45] This graph shows the spectral transmittance exhibited by Example 16. [Figure 46] This graph shows the discrete Fourier transform spectrum of the film thickness sequence in Example 16 and the period corresponding to the number m. [Figure 47] This graph shows the spectral transmittance exhibited by Example 17. [Figure 48] This is a graph showing the discrete Fourier transform spectrum of the film thickness sequence in Example 17 and the period corresponding to the number m. [Modes for carrying out the invention]

[0010] Examples of embodiments of the present invention will be described below with reference to the drawings as appropriate. However, the embodiments of the present invention are not limited to these examples.

[0011] [Configuration, etc.] As shown in Figure 1, the notch filter 1 according to the present invention comprises a substrate 2 and an optical multilayer film 4. The substrate 2 has a substrate surface M on which an optical multilayer film 4 is directly deposited. The notch filter 1 transmits light in the wavelength range related to the free filter region and suppresses the transmission of light in the wavelength range related to the stopband, from the light that has passed through the medium (e.g., air) in the optical multilayer film 4 laminated on the substrate surface M. The stopband is positioned between the upper and lower limits of the free filter region. The size (wavelength width) of the space between the upper and lower limits of the stopband is smaller than the wavelength width of the free filter region. The average transmittance of the free filter region (excluding the stopband) is preferably 85% or higher, and more preferably 90% or higher. The free filter region may be defined in terms of spectral transmittance (for example, as the wavelength range where the transmittance is 85% or higher), or in terms of design (specifications, predetermined range) (for example, as the wavelength range of 400 nm to 1200 nm or 400 nm to 1800 nm). Furthermore, the optical multilayer film 4 may be formed indirectly on the substrate surface M, which is the surface of the substrate 2, via another film such as an adhesion film for the optical multilayer film 4. In addition, another type of film, such as a protective film, may be placed on the outside of the optical multilayer film 4 (medium side, anti-substrate side). The other film and the other type of film may be single-layer films or multilayer films. The configuration of the optical multilayer film 4 may include at least one of the other film and the other type of film.

[0012] Substrate 2 is transparent to light in at least the free filter region. The material of the base material 2 is not particularly limited and may be, for example, a non-metallic material such as glass, crystal, ceramic, or resin. The shape of the base material 2 is not particularly limited and is, for example, a parallel plate.

[0013] The optical multilayer film 4 is an inorganic multilayer film using two or more dielectric materials, and is a dielectric multilayer film. The optical multilayer film 4 is formed on part or all of at least one surface of the substrate 2. The optical multilayer film 4 includes a plurality of low refractive index layers L and a plurality of high refractive index layers H. In the optical multilayer film 4, the low refractive index layers L and the high refractive index layers H are preferably arranged alternately. The design of the optical multilayer film 4 is modified by changing design elements such as the selection of the number and material of the high refractive index layer H and the low refractive index layer L, and increasing or decreasing the thickness of each layer (physical film thickness or optical film thickness related to the layer). In the design of the optical multilayer film 4, the film thickness of each high refractive index layer H is determined based on the optical film thickness; therefore, any high refractive index material may be used as long as it satisfies that optical film thickness. Similarly, the film thickness of each low refractive index layer L is determined based on the optical film thickness; therefore, any low refractive index material may be used as long as it satisfies that optical film thickness. Furthermore, to facilitate manufacturing, it is preferable that at least one of the high refractive index material and the low refractive index material in the optical multilayer film 4 be of a single type.

[0014] The high refractive index layer H is formed from a high refractive index material such as zirconium oxide (ZrO2), titanium oxide (TiO2), tantalum oxide (Ta2O5), niobium oxide (Nb2O5), hafnium oxide (HfO2), lanthanum oxide (La2O3), silicon (Si), or praseodymium oxide (Pr2O3), or a mixture of two or more of these. Furthermore, the low refractive index layer L is formed from low refractive index materials such as silicon dioxide (SiO2), aluminum oxide (Al2O3), calcium fluoride (CaF2), magnesium fluoride (MgF2), a combination of aluminum oxide and praseodymium oxide (Al2O3-Pr2O3), a combination of aluminum oxide and lanthanum oxide (Al2O3-La2O3), a combination of aluminum oxide and tantalum oxide (Al2O3-Ta2O5), or a mixture of two or more of these. Furthermore, the relative refractive indices of the high refractive index layer H and the low refractive index layer L are relative, and the optical multilayer film 4 can be formed from at least two materials with different refractive indices.

[0015] The low refractive index layer L and high refractive index layer H of the optical multilayer film 4 are formed, for example, by physical vapor deposition, and more specifically by vacuum deposition, ion-assisted deposition, ion plating, sputtering, etc. The optical multilayer film 4 may be formed on multiple surfaces of the substrate 2. That is, the substrate 2 may have multiple substrate surfaces M on which the optical multilayer film 4 is formed. For example, the optical multilayer film 4 may be formed on both the front and back surfaces of a parallel plate substrate 2.

[0016] The structure of the optical multilayer film 4 is based on a repeating basic filter structure, which is a basic filter structure repeated multiple times. The following membrane structures are as described above, unless otherwise specified (aL bH) c It is shown as appropriate in the format shown. The design wavelength λ is, for example, 500 nm.

[0017] For example, the first basic filter structure is: 1.17L 0.32H 0.32L 2.31H 0.32L 0.32H 1.17L And, The first basic filter repeat structure is: (1.17L 0.32H 0.32L 2.31H 0.32L 0.32H 1.17L) q Here, q is the number of repetitions. In the first basic filter repeating structure, the lowest refractive index layer L (hereinafter referred to as the 1st layer) on the medium side of the first basic filter structure B1, which is closest to the substrate 2, and the lowest refractive index layer L on the substrate 2 side of the adjacent second basic filter structure B2, form a single lowest refractive index layer L (1.17L + 1.17L = 2.34L; the 7th layer). Similarly, at the boundary between odd-numbered and even-numbered basic filter structures, the lowest refractive index layers L are connected as one. Therefore, in the first basic filter repeating structure, the basic period p, which is the period in which the same film thickness appears based on the basic filter structure, is 6. Also, in the first basic filter repeating structure, the total number of layers is q × p + 1. The +1 here is based on the fact that the lowest refractive index layers L at both ends are not shared. For example, when q = 50, the number of film layers is 50 × 6 + 1 = 301.

[0018] Figure 2 shows the spectral transmittance exhibited by the first basic filter repeating structure when q=50. In this first basic repeating filter structure, a stopband is formed in the wavelength range of approximately 1330 nm to 1660 nm where the transmittance is close to zero, and a free filter region is formed in the wavelength range of approximately 305 nm to less than 1330 nm, with large ripples (around 370 and 500 nm) present in between. This first basic filter repeating structure generally has a free filter region between 400 nm and 1200 nm.

[0019] Furthermore, the second basic filter structure is: 1.10L 0.14H 0.48L 0.30H 0.28L 0.50H 0.12L 2.16H 0.12L 0.50H 0.28L 0.30H 0.48L 0.14H 1.10L And, The second basic filter repeat structure is: (1.10L 0.14H 0.48L 0.30H 0.28L 0.50H 0.12L 2.16H 0.12L 0.50H 0.28L 0.30H 0.48L 0.14H 1.10L) r Here, r is the number of repetitions. In the second basic filter repeat structure, 1 Similar to the basic repeating filter structure, a predetermined low refractive index layer L is linked together. In the second basic repeating filter structure, the basic period p for which the same film thickness appears is 14. Also, in the second basic repeating filter structure, when r=40, the number of film layers is 40 × 14 + 1 = 561.

[0020] Figure 3 shows the spectral transmittance exhibited by the second basic filter repeating structure when r=40. In this second basic repeating filter structure, a stopband is formed in the wavelength range of approximately 1800 nm to 2230 nm where the transmittance is close to zero, while a free filter region is formed in the wavelength range of approximately 300 nm to less than 1800 nm, with large ripples (around 320, 400, 500, 680, and 1000 nm) present. This second basic filter repeating structure generally has a free filter region between 400 nm and 1800 nm.

[0021] Furthermore, the third basic filter structure is: 1.26L 0.22H 0.51L 0.52H 0.21L 2.53H 0.21L 0.52H 0.51L 0.22H 1.26L And, The third basic filter repeat structure is: (1.26L 0.22H 0.51L 0.52H 0.21L 2.53H 0.21L 0.52H 0.51L 0.22H 1.26L) s Here, s is the number of repetitions. In the third basic filter repeat structure, 1 Similar to the basic repeating filter structure, a predetermined low refractive index layer L is linked together. In the third basic repeating filter structure, the basic period p for which the same film thickness appears is 10. Also, in the third basic repeating filter structure, when s=40, the number of film layers is 40 × 10 + 1 = 401.

[0022] Figure 4 shows the spectral transmittance exhibited by the third basic filter repeating structure when s=40. In this third basic repeating filter structure, a stopband is formed in the wavelength range of approximately 1800 nm to 2230 nm where the transmittance is close to zero, while a free filter region is formed in the wavelength range of approximately 300 nm to less than 1800 nm, with large ripples (around 320, 400, 680, and 1000 nm) present. This third basic filter repeating structure generally has a free filter region between 400 nm and 1800 nm.

[0023] The structure of the optical multilayer film 4 is fundamentally one in which each optical film thickness in the basic filter repeat structure is modulated. That is, by adding a corresponding modulation component to each term in a sequence of numbers obtained by arranging the optical film thicknesses of each layer in the basic filter repeat structure in order from the first layer (sequence of optical film thicknesses in the basic filter repeat structure; basic optical film thickness sequence), a sequence of numbers obtained by arranging the optical film thicknesses of each layer in the optical multilayer film 4 in order from the first layer (sequence of optical film thicknesses in the optical multilayer film 4; modulated optical film thickness sequence). Furthermore, even when the optical film thickness is converted to other film thicknesses such as physical film thickness, the same results can be obtained for the basic film thickness sequence, the modulation, and each film thickness of the optical multilayer film 4 (modulated film thickness sequence).

[0024] First, the case where a single barrier is formed will be explained. In the basic filter repeating structure, the nth term of the film thickness sequence (the film thickness of the nth layer) is D n Assuming (with the total number of terms (total number of layers) being L0 (where L0 is a natural number), and n=1,2,...,L0), and the modulation amplitude, period, and phase being a1, Λ1, and φ1 respectively, the nth term (thickness of the nth layer) of the thickness sequence of the basic optical multilayer film 4 is d n This can be expressed by the following equation (1).

[0025]

number

[0026] In optical multilayer films 4 with such a film thickness structure, the center wavelength and wavelength width of the stopband are adjusted from those in the basic filter repeat structure. Generally, adjusting the modulation amplitude a1 adjusts the wavelength width of the stopband (the larger the amplitude a1, the wider the wavelength width); adjusting the modulation period Λ1 adjusts the center wavelength of the stopband (the larger the period Λ1, the longer the center wavelength); and adjusting the modulation phase φ1 adjusts the ripple in the transmittance distribution.

[0027] Next, the case of forming a plurality of stop bands will be described. In this case, since one modulation period corresponds to the formation of one stop band, modulations with different modulation periods are added by the number of stop bands. That is, when the amplitude, period, and phase of the modulation related to the k-th stop band are a k , Λ k , φ k respectively (where k = 1, 2, ···, u with the number of stop bands to be formed being u (u is a natural number)), the n-th term d n of the film thickness sequence of the basic optical multilayer film 4 is represented by the following formula (2). In order to form each stop band more clearly, the modulation period Λ k is preferably larger than the basic period p in each case, and is preferably different from an integer multiple of the basic period p. The above formula (1) is equivalent to the case where k = 1 in the above formula (2). The above formula (2) includes the above formula (1).

[0028]

Equation

[0029] FIG. 5 is a graph showing an example of the relationship between the modulation period Λ1 and the center wavelength of the stop band. According to FIG. 5, it can be seen that in the basic optical multilayer film 4 based on any basic filter repeating structure, the center wavelength of the stop band monotonically increases with an increase in the modulation period Λ1. The center wavelength of the stop band is a function of the modulation period Λ1, and this function can be obtained by, for example, repeatedly performing simulations by varying the modulation period Λ1 variously and appropriately calculating a fitting curve (refer to the three fitting curves (polynomials) in FIG. 5).

[0030] FIG. 6 is a graph showing an example of the relationship between the modulation amplitude a1 and the wavelength width of the stop band. As shown in Figure 6, when the modulation amplitude a1 applied to the basic optical multilayer film 4 based on the first basic filter repeat structure (number of repetitions q=50) increases from 0.1 to 0.2, the wavelength width of the stopband around 1064 nm widens. The modulation period Λ1 here is 15.6.

[0031] Further adjustments can be made to such a basic sequence of optical multilayer film thicknesses 4 to partially or fully achieve various objectives, including mitigating ripple in the transmittance distribution in the free filter region, thereby forming an adjusted optical multilayer film 4. Such adjustments may be performed by a designer based on know-how, automatically by a computer equipped with a design program, or by a combination of both. The design program may also include an AI (artificial intelligence) processing unit. Even with the adjusted optical multilayer film 4, the periodicity related to the fundamental period p and the modulation period Λ1 remains in the film thickness sequence. These periodicities can be found by Fourier analysis of the film thickness sequence. Since this is an analysis of periodicity, the film thickness can be the optical film thickness, the physical film thickness, or any other film thickness.

[0032] [Analysis of the configuration, etc.] Thus, the structure of the optical multilayer film 4 can be determined by Fourier analysis of the film thickness sequence. For example, if a discrete Fourier transform is applied to a sequence of film thicknesses of a certain optical multilayer film, and the spectrum contains maximum values ​​(peaks) corresponding to the fundamental period p and the modulation period Λ1, then it can be determined that it is a basic or tuned optical multilayer film 4 because it exhibits periodicity related to the fundamental period p and the modulation period Λ1. More specifically, if the discrete Fourier transform number is m (m=1,2,···,L0 / 2), then the intensity P of the discrete Fourier transform spectrum... mThis is given by equations (3) to (5) below. Note that the division by P1 in equation (3) is performed for normalization. The reason why the upper limit of the number m is set to L0 / 2 is that half of that analysis is sufficient to grasp the overall periodicity (see sampling theorem). If L0 / 2 is not a natural number (i.e., L0 is odd), the fraction is truncated to make it a natural number.

[0033]

number

[0034] And the period Λ' of the trigonometric function corresponding to the Fourier coefficient at number m m This is given by equation (6) below.

[0035]

number

[0036] Therefore, if there is one stopband, in the discrete Fourier transform spectrum, Λ' m’ A peak exists at or around the number m' where =p, and Λ' m” If a peak exists at or around the number m'' where =Λ1, then the optical multilayer film can be said to be the basic or modified optical multilayer film 4 described above. Here, Λ' m’ The range of the number m' or its surroundings for which =p is defined, for example, as follows: namely, the spectral number m', the spectral numbers immediately preceding and succeeding it m'-1, m'+1, and the numbers on either side of them m'-2, m'+2. Also, Λ' m”The range of the number m'' or its surroundings that equals Λ1 can be defined, for example, as follows: namely, the spectral number m'' and the spectral numbers m''-1 and m''+1, which are the one number before and one number after it. Furthermore, since there may be basic or tuned optical multilayer films 4 that exhibit the property of having multiple types of fundamental periods p, it is also possible to confirm that corresponding peaks exist for multiple fundamental periods p (e.g., p=6, 14, 10). Similarly, since there may be basic or tuned optical multilayer films 4 that exhibit the property of having multiple types of modulation periods determined by the fundamental period p and the center wavelength of the stopband, it is also possible to confirm that corresponding peaks exist for spectral numbers corresponding to multiple modulation periods. In the case of modulation periods, the range of spectral numbers may be from the smallest to the largest spectral number among the spectral numbers corresponding to multiple modulation periods. If multiple stopbands exist, the above Λ' m” Except for the fact that the confirmation of the existence of peaks at indices m", m"-1, m"+1 where =Λ1 is obtained is extended from once (k=1) to the number of times equal to the number of stopbands (k=1, 2, ..., u), the applicability of the basic or tuned optical multilayer film 4 can be confirmed in the same way as when there is one stopband.

[0037] For reference, Figures 7-9 show the discrete Fourier transform spectra and periods corresponding to the number m in the first to third basic filter repeat structures for each of the aforementioned number of repetitions. In the discrete Fourier transform spectra (Figure 7) for the first basic filter repeat structure (number of repetitions q=50), the peak with the smallest number m among the three peaks is m=50, and from equation (6) above, Λ' 50 =(301-1) / 50=6.0. Thus, the first basic filter repeating structure has a period Λ'. 50 It can be seen that it has a periodicity of =6.0. In fact, as mentioned above, the fundamental period p=6 of the first fundamental filter repeating structure. In the discrete Fourier transform spectra (Figure 8) for the second basic filter repeating structure (number of repetitions r=40), the peak with the smallest number m among the seven peaks is m=40, and from equation (6) above, Λ' 40 =(561-1) / 40=14.0. Thus, the second basic filter repeating structure has a period Λ'. 40 It can be seen that it has a periodicity of =14. In fact, as mentioned above, the fundamental period p=14 is the fundamental period of the second fundamental filter repeating structure. In the discrete Fourier transform spectra (Figure 9) for the third basic filter repeat structure (number of repetitions s=40), the peak with the smallest number m among the five peaks is m=40, and from equation (6) above, Λ' 40 =(401-1) / 40=10.0. Therefore, Third The basic repeating filter structure is period Λ' 40 It can be seen that it has a periodicity of =10. In fact, as mentioned above, the fundamental period p=10 is the fundamental period of the third fundamental filter repeating structure.

[0038] [Design of optical multilayer films, etc.] Figure 10 is a flowchart showing an example of a design method for the optical multilayer film 4. In designing the optical multilayer film 4, the designer first obtains a basic filter structure (step S1), and then obtains a repeating basic filter structure (step S2).

[0039] Next, the designer modulates the film thickness sequence of the basic filter repeating structure using equation (2) above (step S3). By step S3, a basic optical multilayer film 4 (and its related film thickness sequence) is obtained.

[0040] Next, the designer adjusts the film thickness of one or more layers in the basic optical multilayer film 4 (the value of one or more terms in the film thickness sequence) as needed (step S4). Step S4 yields the adjusted optical multilayer film 4 (and the sequence of film thicknesses related thereto). [Examples]

[0041] Next, examples relating to the above embodiments of the present invention, and comparative examples outside the scope of the present invention are shown. However, the examples provided are not intended to limit the scope of the present invention. Furthermore, depending on how the present invention is interpreted, the examples may become substantial comparative examples, or the comparative examples may become substantial examples that fall within the scope of the present invention.

[0042] [Example 1] In Example 1, a notch filter having a basic optical multilayer film 4 was formed by simulation on one side (substrate surface M) of a parallel plate substrate 2 (substrate). The substrate is made of quartz glass, has a refractive index of 1.453, and a thickness of 1 millimeter. Note that various values ​​related to the substrate can be changed. The optical multilayer film 4 of Example 1 is designed with in mind a state in which the wavelength range of the stopband includes 1064 nm (preferably with a central wavelength of 1064 nm) and a free filter region is formed in a wavelength range including 400 nm to 1200 nm. The optical multilayer film 4 of Example 1 is designed by applying the modulation of equation (1) above to the first basic filter repeating structure (number of repetitions q=50, L0=301). Here, the amplitude a1=0.1, the period Λ1=15.7, and the phase φ1=0.

[0043] The film structure of the optical multilayer film 4 in Example 1 is shown below. Here, "H" simply indicates a high refractive index layer, and its coefficient (the number before H) indicates the physical film thickness (nm) of that layer, and "L" simply indicates a low refractive index layer, and its coefficient (the number before L) indicates the physical film thickness (nm) of that layer. The leftmost layer (109.25L) is closest to the substrate. Hereafter, the notation format for the film structure related to such coefficients, etc., will be called the physical film thickness format. Furthermore, in Example 1, the following values ​​are taken into consideration: namely, the design wavelength λ0 = 500 nm, and the refractive index n of the low refractive index material at λ0. L = 1.475, refractive index n of high refractive index materialH =2.18, and the refractive index of the medium n0 = 1. Note that these values ​​are merely examples and can be changed in various ways. Furthermore, these values ​​are the same in subsequent examples unless otherwise specified. 109.25L 19.85H 28.64L 137.42H 26.7L 17.42H 183.98L 16.46H 24.11L 120.74H 25.03L 17.62H 200.43L 19.03H 28.86L 145.37H 29.44L 19.75H 210.67L 18.63H 26.38L 125.69H 24.6L 16.4H 179.1L 16.66H 25.29L 130.12H 27.34L 19.22H 215.47L 19.97H 29.38L 143.26H 28.13L 18.41H 193.34L 17.05H 24.43L 119.43H 24.22L 16.79H 189.64L 18.05H 27.65L 141.47H 29.2L 19.99H 217.23L 19.49H 27.85L 132.76H 25.76L 16.88H 180.2L 16.36H 24.33L 123.58H 25.86L 18.27H 207.29L 19.54H 29.32L 145.85H 29.15L 19.33H 204.33L 17.98H 25.47L 122.15H 24.19L 16.38H 181.61L 17.11H 26.17L 134.87H 28.23L 19.68H 218.11L 19.96H 28.99L 139.79H 27.23L 17.76H 186.94L 16.62H 24.13L 119.81H 24.66L 17.29H 196.46L 18.7H 28.49L 144.39H 29.45L 19.9H 213.57L 18.97H 26.91L 128.08H 24.95L 16.52H 178.78L 16.49H 24.88L 127.58H 26.81L 18.9H 213.04L 19.88H 29.46L 144.62H 28.57L 18.77H 197.25L 17.35H 24.73L 119.96H 24.12L 16.58H 186.3L 17.69H 27.13L 139.33H 28.93L 19.94H 218.25L 19.72H 28.31L 135.39H 26.27L 17.16H 182.03L 16.39H 24.17L 121.83H 25.38L 17.9H 203.56L 19.28H 29.1L 145.79H 29.35L 19.59H 208L 18.34H 25.96L 123.98H 24.38L 16.36H 179.92L 16.83H 25.66L 132.23H 27.75L 19.44H 216.94L 19.99H 29.25L 141.86H 27.75L 18.12H 190.36L 16.83H 24.26L 119.39H 24.38L 16.99H 192.58L 18.34H 28.04L 142.94H 29.35L 19.98H 215.88L 19.28H 27.44L 130.64H 25.38L 16.7H 179.26L 16.39H 24.54L 125.24H 26.27L 18.56H 210.03L 19.72H 29.42L 145.51H 28.93L 19.1H 201.22L 17.69H 25.12L 120.99H 24.12L 16.44H 183.46L 17.35H 26.59L 136.93H 28.57L 19.82H 218.49L 19.88H 28.72L 137.92H 26.81L 17.49H 184.53L 16.49H 24.1L 120.52H 24.95L 17.55H 199.64L 18.97H 28.79L 145.21H 29.45L 19.79H 211.29L 18.7H 26.49L 126.15H 24.66L 16.42H 178.97L 16.62H 25.2L 129.6H 27.23L 19.16H 215.04L 19.96H 29.4L 143.57H 28.23L 18.48H 194.11L 17.11H 24.48L 119.49H 24.19L 16.74H 188.94L 17.98H 27.55L 141.07H 29.15L 19.99H 217.5L 19.54H 27.95L 133.29H 25.86L 16.94H 180.51L 16.36H 24.29L 123.2H 25.76L 18.19H 206.57L 19.49H 29.29L 145.88H 29.2L 19.39H 205.08L 18.05H 25.57L 122.49H 24.22L 16.37H 181.21L 17.05H 26.07L 134.35H 28.13L 19.63H 217.94L 19.97H 29.05L 140.23H 27.34L 17.83H 187.59L 16.66H 24.15L 119.68H 24.6L 17.23H 195.67L 18.63H 28.4L 144.13H 29.44L 19.92H 107.04L.

[0044] Figure 11 is a graph showing the spectral transmittance exhibited by Example 1. As shown in Figure 11, in Example 1, a stopband with a central wavelength of 1064 nm is formed, and a free filter region is formed in a wavelength range including the wavelength range from 400 nm to 1200 nm. Moreover, the wavelength width of the stopband is sufficiently narrow, at about 20 nm (approximately 1050 nm to 1070 nm).

[0045] Figure 12 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 1 and the period corresponding to the number m. In Figure 12, compared to before modulation (the first basic filter repeat structure when the number of repetitions q=50; Figure 7), the number of peaks in the discrete Fourier transform spectrum increases by one at the point m=19. This peak is Λ', according to equation (6) above. 19 =(301-1) / 19=15.8, which corresponds to the period Λ1=15.7. Furthermore, in Figure 12, as before modulation, m=50(Λ') corresponds to the fundamental period p=6. 50 A peak exists at =6.0. Thus, in Example 1, the discrete Fourier transform spectrum contains peaks corresponding to the fundamental period p and period Λ1, respectively.

[0046] [Example 2] Example 2 has a modified optical multilayer film 4, which is designed by adjusting the values ​​of appropriate terms in the film thickness sequence of the basic optical multilayer film 4 of Example 1, with the aim of reducing ripple in the transmittance distribution in the free filter region.

[0047] The film structure of the optical multilayer film 4 in Example 2 is shown below in terms of physical film thickness. 126.36L 21.28H 31.13L 142.72H 26.6L 21.23H 196.22L 18.38H 27.22L 136.35H 30.93L 19.21H 219.15L 20.04H 31.47L 139.66H 27.34L 18.76H 178.01L 16.31H 27.05L 125.1H 27.04L 17.95H 197.95L 19.59H 29.77L 146.13H 29.61L 21.34H 208.12L 19.96H 24.75L 112.94H 22.37L 19.94H 187.2L 18.29H 24.02L 126.85H 28.6L 19.89H 217.93L 20.59H 32.02L 144.16H 30.77L 17.96H 165.26L 14.61H 29.38L 129.26H 30.05L 14.23H 169.3L 18.14H 30.03L 145.59H 31.17L 21.27H 218.4L 19.61H 29.98L 124.06H 22.85L 17.72H 186.26L 20.15H 21.88L 105.32H 23.3L 21.2H 208.32L 21.69H 29.28L 151.92H 28.85L 22.21H 201.71L 19.07H 25.25L 110.11H 23.26L 18.62H 175.49L 16.35H 24.48L 129.46H 31L 18.9H 221.22L 20.15H 33.18L 144.16H 29.15L 19.29H 170.66L 14.37H 26.48L 128.4H 32.46L 13.14H 155.13L 17.39H 30.73L 144.99H 32.29L 21.29H 224.76L 18.68H 32.99L 131.76H 26.16L 14.52H 171.27L 18.3H 23.5L 107.65H 22.67L 19.79H 204.71L 22.41H 27.9L 154.25H 28.9L 22.57H 206.24L 19.93H 25.42L 107.89H 22.11L 18.73H 182.45L 17.86H 21.07L 122.23H 29.83L 18.56H 217.54L 20.71H 33L 147.66H 26.82L 21.38H 183.88L 15.57H 23.17L 122.42H 29.57L 14.11H 154.92L 16.4H 30.66L 142.35H 33.32L 20.19H 228.35L 18.7H 33.97L 136.86H 29.89L 14.76H 156.59L 15.9H 27.24L 115.35H 22.37L 17.63H 197.18L 22.14H 27.35L 152.61H 29.47L 22.23H 211.92L 19.39H 27.14L 112.75H 21.14L 18.19H 185.54L 19.18H 19.88L 115H 27.83L 19.16H 214.37L 21.36H 31.74L 150.81H 26.63L 22.31H 192.73L 17.91H 21.07L 115.62H 26.67L 15.8H 161.85L 15.79H 29.21L 139.22H 32.79L 19.78H 228.34L 19.15H 32.94L 139.78H 30.53L 15.59H 155.78L 14.68H 29.12L 120.95H 23.51L 16.21H 191.17L 21.36H 27.43L 150.16H 30.16L 21.52H 215.33L 18.97H 27.91L 117.21H 21.81L 17.42H 184.65L 18.87H 20.22L 116.26H 27.46L 19.25H 214.9L 21.45H 31.15L 148.96H 27.56L 20.99H 189.75L 16.63H 23.85L 122.27H 28.08L 14.82H 164.48L 16.3H 29.66L 141.41H 32.41L 20.27H 222.06L 20.72H 29.41L 135.82H 26.75L 16.37H 177.82L 18.13H 23.72L 113.93H 23.13L 19.05H 203.89L 21.83H 28.66L 149.04H 31.76L 20.16H 205.99L 18.2H 25.83L 120.91H 25.11L 17.36H 177L 16.8H 26.78L 135.8H 31L 19.82H 222.74L 19.32H 33.44L 140.88H 30.08L 17.34H 175.59L 15.43H 28.79L 136.17H 32.74L 17.83H 217.13L 20.95H 30.05L 137.14H 21.43L 23.95H 94.67L.

[0048] Figure 13 is a graph showing the spectral transmittance exhibited by Example 2. As shown in Figure 13, Example 2 has the same free filter region and stopband as Example 1, but the ripple in the transmittance distribution in the free filter region is suppressed.

[0049] Figure 14 shows the discrete Fourier transform spectrum of the film thickness sequence in Example 2 and a graph showing the period corresponding to the number m. In Figure 14, even in Example 2 (after adjusting the values ​​of appropriate terms in the film thickness sequence), the modulation period Λ1 corresponds to m=19(Λ'), similar to Example 1 (Figure 12). 19 The peak of =15.8) and m=50(Λ') corresponding to the fundamental period p. 50 There is a peak at =6.0.

[0050] [Example 3] As Example 3, a structure similar to that of Example 1 was formed, except that the basic optical multilayer film 4 was designed based on a second basic filter repeating structure instead of the first basic filter repeating structure. The optical multilayer film 4 of Example 3 is designed with in mind a state in which the wavelength range of the stopband includes 1550 nm (preferably with a central wavelength of 1550 nm) and a free filter region is formed in a wavelength range including 400 nm to 1800 nm. The optical multilayer film 4 of Example 3 is designed by applying the modulation of equation (1) above to the second basic filter repeat structure (number of repetitions r=40, L0=561). Here, the amplitude a1=0.1, the period Λ1=50, and the phase φ1=0.

[0051] The film structure of the optical multilayer film 4 in Example 3 is shown below. 1.21L .154H .527L .328H .305L .54H .129L 2.298H .126L .521H .289L .306H .483L .139H 2.159L .136H .46L .284H .262L .464H. .282L .306H .495L .146H 2.318L .149H .515L .324H .305L .547H .132L 2.374H .132L .55H .307L .328H .522L .151H 2.36L .149H .506L .313H .289L .509H .121L 2.147H .118L .484H .268L .284H .449L .13H 2.022L .128H .435L .271H .252L .45H .108L 1.951H .109L .456H 257L 278H 449L 133H 2.106L 136H 471L 298H 282L 509H 124L 2.252H 126L 532H 3L 324H 522L 153H 2.413L 154H 528L 33H 307L 547H 131L 2.335H 129L 532H 295L 313H 495L 143H 2.214L 139H 471L 291H 268L 473H 112L 2.002H 11L 456H 254L 271H 432L 126H 1.982L 126H 435L 274H 257L 464H 112L 2.044H 115L 484H 275L 298H 483L 143H 2.268L 146H 506L 319H 3L 54H 131L 2.361H 132L 55H 308L 33H 527L 153H 2.393L 151H 515L 319H 295L 521H 124L 2.2H .121L .497H .275L .291H .46L .133H 2.06L .13H .441L .274H .254L .452H .108L 1.944H .108L .452H .254L .274H .441L .13H 2.06L .133H .46L .291H .275L .497H .121L 2.2H .124L .521H .295L .319H .515L .151H 2.393L .153H .527L .33H .308L .55H .132L 2.361H .131L .54H .3L .319H .506L .146H 2.268L .143H .483L .298H .275L .484H .115L 2.044H .112L .464H .257L .274H .435L .126H 1.982L .126H .432L .271H .254L .456H .11L 2.002H .112L .473H .268L .291H .471L .139H 2.214L .143H .495L .313H .295L .532H .129L 2.335H .131L .547H 307L 33H 528L 154H 2.413L 153H 522L 324H 3L 532H 126L 2.252H 124L 509H 282L 298H 471L 136H 2.106L 133H 449L 278H 257L 456H 109L 1.951H 108L 45H 252L 271H 435L 128H 2.022L 13H 449L 284H 268L 484H 118L 2.147H .121L .509H .289L .313H .506L .149H 2.36L .151H .522L .328H .307L .55H .132L 2.374H .132L .547H .305L .324H .515L .149H 2.318L .146H .495L .306H .282L .497H .118L 2.093H .115L .473H .262L .278H .441L .128H 1.995L .126H .432L .27H .252L .452H .109L 1.971H .11L .464H .262L .284H .46L .136H 2.159L .139H .483L .306H .289L .521H .126L 2.298H .129L .54H .305L .328H .527L .154H 2.42L .154H .527L .328H .305L .54H .129L 2.298H .126L .521H .289L .306H .483L .139H 2.159L .136H .46L .284H .262L .464H .11L 1.971H .109L .452H .252L .27H .432L .126H 1.995L .128H .441L .278H .262L .473H .115L 2.093H .118L .497H .282L .306H .495L .146H 2.318L .149H .515L .324H .305L .547H .132L 2.374H .132L .55H .307L .328H .522L .151H 2.36L .149H .506L .313H .289L .509H .121L 2.147H .118L .484H .268L .284H .449L .13H 2.022L .128H .435L .271H .252L .45H .108L 1.951H .109L .456H .257L .278H .449L .133H 2.106L .136H .471L .298H .282L .509H .124L 2.252H .126L .532H .3L .324H .522L .153H 2.413L .154H .528L .33H .307L .547H .131L 2.335H .129L .532H .295L .313H .495L .143H 2.214L .139H .471L .291H .268L .473H .112L 2.002H .11L .456H .254L .271H .432L .126H 1.982L .126H .435L .274H .257L .464H .112L 2.044H .115L .484H .275L .298H .483L .143H 2.268L .146H .506L .319H .3L .54H .131L 2.361H .132L .55H .308L .33H .527L .153H 2.393L .151H .515L .319H .295L .521H .124L 2.2H .121L .497H .275L .291H .46L .133H 2.06L .13H .441L .274H .254L .452H .108L 1.944H .108L .452H .254L .274H .441L .13H 2.06L .133H .46L .291H .275L .497H .121L 2.2H .124L .521H .295L .319H .515L .151H 2.393L .153H .527L .33H .308L .55H .132L 2.361H .131L .54H .3L .319H .506L .146H 1.134L.

[0052] Figure 15 is a graph showing the spectral transmittance exhibited by Example 3. As shown in Figure 15, in Example 3, a stopband with a central wavelength of 1550 nm is formed, and a free filter region is formed in a wavelength range that includes the wavelength range from 400 nm to 1800 nm. Moreover, the wavelength width of the stopband is sufficiently narrow, at about 60 nm (approximately 1520 nm to 1580 nm).

[0053] Figure 16 shows the discrete Fourier transform spectrum of the film thickness sequence in Example 3 and a graph showing the period corresponding to the number m. In Figure 16, compared to before modulation (the second basic filter repeat structure with s=40 iterations; Figure 8), the number of peaks in the discrete Fourier transform spectrum increases by one at the point m=11. This peak is Λ', according to equation (6) above. 11 =(561-1) / 11=50.9, which corresponds to a period Λ1=50. Furthermore, in Figure 16, as before modulation, m=40(Λ') corresponds to the fundamental period p=14. 40 A peak exists at =14.0. Thus, in Example 3, the discrete Fourier transform spectrum contains peaks corresponding to the fundamental period p and period Λ1, respectively.

[0054] [Example 4] Example 4 has a modified optical multilayer film 4, which is designed by adjusting the values ​​of appropriate terms in the film thickness sequence of the basic optical multilayer film 4 of Example 3, with the aim of reducing ripple in the transmittance distribution in the free filter region.

[0055] The film structure of the optical multilayer film 4 in Example 4 is shown below. 1.198L .125H .521L .311H .301L .498H .114L 2.077H .111L .445H .245L .287H .468L .137H 2.24L .145H .479L .318H .26L .499H .106L 2.221H .123L .531H .305L .327H .523L .137H 2.415L .138H .534L .337H .317L .544H .127L 2.315H .117L .57H .307L .344H .519L .14H 2.16L .121H .49L .283H .276L .455H .116L 2.069H .116L .445H .253L .266H .448L .123H 2.064L .121H .454L .273H .254L .437H .112L 2.085H .124L .446H .255L .258H .449L .129H 2.232L .144H .49L .323H .265L .499H .107L 2.228H .123L .535H .311L .333H .536L .138H 2.379L .131H .57L .339H .322L .538H .117L 2.107H .108L .513H .279L .305H .475L .126H 2.137L .128H .448L .267H .249L .443H .114L 1.991H .104L .448H .261L .278H .449L .116H 2.061L .137H .461L .28H .217L .393H .111L 2.133H .123L .409H .234L .27H .472L .136H 2.203L .119H .482L .289H .311L .521H .133L 2.344H .125L .563H .329L .34H .557L .135H 2.349L .131H .546L .328H .307L .52H .113L 2.076H .108L .479H .264L .292H .463L .129H 2.118L .127H .438L .261H .239L .424H .112L 2.015H .114L .42H .23L .249H .418L .13H 2.137L .139H .432L .254H .215L .409H .119L 2.116H .117L .434H .251L .28H .472L .133H 2.242L .131H .512L .319H .303L .531H .123L 2.331H .126L .586H .34L .348H .571L .131H 2.286L .124H .536L .319H .307L .516H .113L 2.055H .109L .47H .26L .28H .447L .126H 2.125L .133H .423L .241H .225L .413H .121L 2.066H .127L .431H .256L .227H .402L .113H 2.105L .141H .424L .23H .206L .404H .133L 2.157H .116L .43H .249L .288H .485L .136H 2.27L .133H .527L .329H .314L .552H .125L 2.365H .13L .573H .337L .34H .56L .13H 2.267L .126H .524L .317H .295L .503H .108L 2.038H .112L .462H .258L .272H .442L .124H 2.108L .136H .428L .242H .209L .387H .123L 2.109H .131L .393H .204L .222H .41L .138H 2.156L .137H .416L .234H .221L .419H .13L 2.155H .12L .448H .26L .286H .485L .136H 2.345L .15H .554L .372H .307L .579H .107L 2.235H .115L .583H .319L .359H .556L .14H 2.264L .122H .495L .291H .289L .48H .117L 2.089H .12L .447H .249L .248H .419L .126H 2.138L .139H .415L .228H .204L .393H .127L 2.11H .128L .397H .213L .231H .42L .135H 2.124L .127H .447L .277H .253L .456H .11L 2.069H .113L .51H .301L .316H .531L .126H 2.288L .128H .561L .336H .343L .574H .135L 2.384H .125L .546H .308L .322H .514L .133H 2.277L .142H .491L .3H .235L .414H .109L 2.149H .132L .396H .204L .236H .43L .141H 2.112L .122H .434L .266H .247L .432H .108L 2.002H .11L .429H .24L .272H .451L .129H 2.099L .123H .486L .31H .285L .512H .107L 2.091H .116L .561H .336L .347H .595L .13H 2.439L .143H .541L .338H .315L .535H .127L 2.343H .127L .495H .276L .281H .455L .136H 2.273L .147H .464L .257H .205L .388H .131L 2.193H .132L .388H .209L .239H .436L .137H 2.124L .131H .452L .282H .241L .433H .108L 2.084H .117L .459H .264L .291H .488L .135H 2.335L .15H .551L .369H .308L .58H .112L 2.338H .123L .606H .336L .373H .582L .145H 2.365L .127H .508L .292H .295L .486H .127L 2.205H .133L .452H .251L .24H .423L .133H 2.223L .146H .432L .235H .215L .418H .136L 2.182H .114L .43H .247L .3H .495L .142H 2.315L .139H .538L .342H .316L .565H .125L 2.444H .134L .615H .354L .369H .598L .142H 2.389L .129H .532L .313H .307L .51H .122L 2.174H .126L .471H .271L .267H .45L .126H 2.189L .14H .456L .27H .238L .435H .122L 2.147H .11L .447H .252L .307H .494L .142H 2.31L .131H .541L .342H .321L .579H .122L 2.529H .136L .618H .357L .382H .601L .149H 2.369L .124H .521L .296H .305L .483H .126L 1.912H .106L .472H .243L .261H .41L .118H .953L.

[0056] Figure 17 is a graph showing the spectral transmittance exhibited by Example 4. As shown in Figure 17, Example 4 has a free filter region and stopband similar to Example 3, while suppressing ripple in the transmittance distribution in the free filter region.

[0057] Figure 18 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence in Example 4 and the period corresponding to the number m. In Figure 18, even in Example 4 (after adjusting the values ​​of appropriate terms in the film thickness sequence), the modulation period Λ1 corresponds to m=11(Λ'), similar to Example 3 (Figure 16). 11 The peak of =50.9) and m=40(Λ') corresponding to the fundamental period p. 40 There is a peak at m=14.0. Also, by adjusting the film thickness sequence, m=10(Λ' 10 The value of m=11(Λ' =56.0) is 11 The peak now exhibits a similar spectral intensity to the peak at =50.9).

[0058] [Example 5] As Example 5, a device similar to that of Example 3 was formed, except that the phase φ1 in the modulation of equation (1) above was changed from 0 to π / 2.

[0059] The film structure of the optical multilayer film 4 in Example 5 is shown below. 1.1L .142H .492L .311H .293L .529H .128L 2.326H .13L .545H .307L .329H .528L .154H 2.416L .153H .523L .325H .302L .534H .127L 2.264H .124L .512H .284L .3H .474L .137H 2.119L .133H .452L .279H .258L .458H .109L 1.955H .108L .45H .252L .27H .434L .127H 2.014L .129H .447L .282H .267L .482H .117L 2.133H .12L .506H .287L .311H .503L .148H 2.351L .151H .52L .327H .307L .549H .132L 2.376H .132L .548H .305L .325H .517L .15H 2.329L .147H .498L .307H .284L .5H .118L 2.106H .116L .476H .263L .279H .443L .128H 2.001L .127H .433L .27H .252L .451H .109L 1.965H .11L .461H .261L .282H .457L .135H 2.145L .138H .48L .304H .287L .518H .126L 2.287H .128L .539H .304L .327H .526L .154H 2.42L .154H .527L .329H .305L .542H .129L 2.308H.127L .524H .29L .307H .486L .14H 2.172L .137H .462L .285H .263L .466H .111L 1.978H .109L .452H .253L .27H .432L .126H 1.991L .127H .439L .277H .261L .471H .114L 2.08H .117L .494H .28L .304H .492L .145H 2.306L .148H .513L .323H .304L .545H .131L 2.372H .132L .55H .308L .329H .523L .152H 2.37L .15H .508L .314H .29L .512H .122L 2.16H .118L .488H .27L .285H .452L .13H 2.031L .128H .437L .272H .253L .45H .108L 1.948H .109L .455H .256L .277H .447L .132H 2.094L .135H .468L .296H .28L .506H .123L 2.239H .126L .529H .299L .323H .52L .153H .2.409L .154H .528L .33H .308L .548H .131L 2.342H .129L .534H .296L .314H .498L .144H 2.228L .14H .474L .292H .27L .476H .113L 2.012H .111L .458H .255L .272H .433L .126H 1.98L .126H .434L .273H .256L .461H .112L 2.033H.114L .482H .273L .296H .48L .142H 2.255L .145H .503L .318H .299L .539H .13L 2.355H .131L .549H .308L .33H .527L .153H 2.399L .152H .517L .321H .296L .524H .124L 2.214H .122L .5H .276L .292H .462L .133H 2.071L .13H .443L .275H .255L .452H .108L 1.944H .108L .451H .253L .273H .439L .129H 2.049L .132H .457L .289H .273L .494H .12L 2.187H .123L .518H .293L .318H .513L .151H 2.386L .153H .526L .329H .308L .55H .132L 2.365H .131L .542H .302L .321H .508L .147H 2.281L .144H .486L .3H .276L .488H .116L 2.056H .113L .466H .258L .275H .437L .127H 1.984L .126H .432L .27H .253L .455H .11L 1.994H .112L .471H .267L .289H .468L .138H 2.2L .142H .492L .311H .293L .529H .128L 2.326H .13L .545H .307L .329H .528L .154H 2.416L .153H .523L .325H .302L .534H .127L 2.264H .124L .512H .284L .3H .474L .137H 2.119L .133H .452L .279H .258L .458H .109L 1.955H .108L .45H .252L .27H .434L .127H 2.014L .129H .447L .282H .267L .482H .117L 2.133H .12L .506H .287L .311H .503L .148H 2.351L .151H .52L .327H .307L .549H .132L 2.376H 132L 548H 305L 325H 517L 15H 2.329L 147H 498L 307H 284L 5H 118L 2.106H 116L 476H 263L 279H 443L 128H 2.001L 127H 433L 27H 252L 451H 109L 1.965H 11L 461H 261L 282H 457L 135H 2.145L 138H 48L 304H 287L 518H 126L 2.287H .128L .539H .304L .327H .526L .154H 2.42L .154H .527L .329H .305L .542H .129L 2.308H .127L .524H .29L .307H .486L .14H 2.172L .137H .462L .285H .263L .466H .111L 1.978H .109L .452H .253L .27H .432L .126H 1.991L .127H .439L .277H .261L .471H .114L 2.08H .117L .494H .28L .304H .492L .145H 2.306L .148H .513L .323H .304L .545H .131L 2.372H .132L .55H .308L .329H .523L .152H 2.37L .15H .508L .314H .29L .512H .122L 2.16H .118L .488H .27L .285H .452L .13H 2.031L .128H .437L .272H .253L .45H .108L 1.948H .109L .455H .256L .277H .447L .132H 2.094L .135H .468L .296H .28L .506H .123L 2.239H .126L .529H .299L .323H .52L .153H 1.205L.

[0060] Figure 19 is a graph showing the spectral transmittance exhibited by Example 5. According to Figure 19, the spectral transmittance of Example 5 is the same as that of Example 3.

[0061] Figure 20 shows the discrete Fourier transform spectrum of the film thickness sequence in Example 5 and a graph showing the period corresponding to the number m. According to Figure 20, the discrete Fourier transform spectrum of Example 5 is the same as that of Example 3. In other words, in Example 5 as well, there are peaks in the discrete Fourier transform spectrum corresponding to the fundamental period p and period Λ1, respectively (Λ' 40 =14.0=p,Λ' 11 =50.9≈Λ1).

[0062] [Example 6] As Example 6, a device similar to that of Example 3 was formed, except that the amplitude a1 in the modulation of equation (1) above was changed from 0.1 to 0.3 and the period Λ1 was changed from 50 to 15.7.

[0063] The film structure of the optical multilayer film 4 in Example 6 is shown below. 1.43L .179H .58L .333H .278L .437H .093L 1.549H .084L .366H .225L .273H .493L .16H 2.713L .18H .623L .378H .331L .537H .115L 1.821H .091L .354H .197L .225H .4L .132H 2.338L .164H .602L .389H .362L .62H .138L 2.244H .11L .407H .206L .211H .342L .108H 1.901L .137H .527L .36H .356L .65H .154L 2.63H .134L .502H .248L .236H .346L .098H 1.597L .111H .431L .305H .317L .613H .154L 2.806H .152L .596H .304L .29H .41L .107H 1.562L .098H .356L .247H .261L .525H .139L 2.695H .155L .647H .349L .349H .504L .13H 1.811L .104H .337L .213H .214L .427H .116L 2.345H .143L .633H .364L .385H .588L .158H 2.233L .126H .382L .218H .196L .361H .094L 1.914H .12L .56H .341L .384H .624L .178H 2.64L .154H .47L .259H .216L .357H .084L 1.591H .098L .46H .291L .345H .595L .181H 2.852L .176H .563L .319H .264L .416H .09L 1.523H .085L .378H .236L .287H .516L .166H 2.773L .182H .618L .37H .32L .513H .109L 1.737H .088L .35H .201L .234H .42L .139H 2.439L .169H .613L .39H .357L .604H .133L 2.141H .105L .389H .201L .21H .351L .113H 1.999L .144H .548L .37H .361L .649H .151L 2.552H .129L .478H .236L .227H .339L .099H 1.648L .117H .453L .319H .328L .627H .156L 2.789H .149L .576H .291L .276H .391L .103H 1.543L .1H .37L .259H .274L .549H .144L 2.746H .156L .64H .341L .336H .481L .124H 1.731L .101H .336L .218H .223L .449H .122L 2.442H .147L .642H .364L .38H .572L .152H 2.128L .119H .366L .213H .197L .371H .099L 2.012H .126L .581H .349L .388H .621L .175H 2.556L .147H .447L .247H .208L .351H .085L 1.648H .102L .484H .304L .357H .608L .182H 2.826L .172H .543L .305H .251L .398H .087L 1.512H .087L .393H .248L .301H .537L .17H 2.818L .182H .61L .36H .307L .49H .104L 1.664H .086L .351H .206L .244H .442L .145H 2.534L .174H .62L .389H .351L .586H .128L 2.038H.1L .375H .197L .212H .363L .118H 2.101L .15H .567L .378H .363L .644H .148L 2.465H .123L .454H .225L .219H .336L .1H 1.713L .122H .476L .333H .339L .638H .156L 2.757H .145L .554H .278L .262H .374L .1H 1.541L .102H .386L .273H .288L .571H .148L 2.783H .156L .63H .331L .322H .458L .118H 1.663L .099H .338L .225H .233L .472H .128L 2.531H .15L .648H .362L .372H .553L .145H 2.024L .114H .354L .211H .2L .385H .104L 2.115H .132L .6H .356L .39H .615L .17H 2.463L .14H .425L .236H .202L .35H .087L 1.718H .108L .508H .317L .368H .617L .182H 2.785L .167H .521L .29H .239L .382H .085L 1.518H .089L .412H .261L .315H .558L .175H 2.847L .181H .599L .349H .294L .466H .099L 1.604H .084L .355H .214L .256H .464L .152H 2.62L .177H .624L .385H .343L .565H .122L 1.938H 0.95L 363H 196L 216H 378L 124H 2.207L 157H 584L 384H 364L 636H 144L 2.37H 118L 432H 216L 214H 337L 103H 1.79L 129H 499L 345H 347L 646H 156L 2.709H 141L 531H 264L 25H 36L 0.99H 1.556L 106H 405L 287H 301L 591H .151L 2.803H .155L .617H .32L .308H .436L .113H 1.609L .098H .344L .234H .245L .495H .133L 2.611H .153L .65H .357L .363H .532L .139H 1.925L .109H .344L .21H .205L .402H .109L 2.218H .137L .617H .361L .389H .605L .166H 2.363L .134H .405L .227H .198L .352H .09L 1.799H .113L .531H .328L .376H .622L .181H 2.729L .161H .499L .276H .228L .368H .084L 1.541H .093L .432H .274L .329H .576L .178H 2.859L .179H .584L .336H .281L .443H .094L 1.558H .084L .363H .223L .269H .487L .158H 2.696L .18H .624L .38H .333L .543H .116L 1.844H .092L .355H .197L .223H .395L .13H 2.312L .163H .599L .388H .362L .624H .139L 2.27H .112L .412H .208L .211H .341L .107H .939L.

[0064] Figure 21 is a graph showing the spectral transmittance exhibited by Example 6. According to Figure 21, in Example 6, a stopband with a central wavelength of 1064 nm is formed, and a free filter region is formed in a wavelength range including the wavelength range from 400 nm to 1800 nm. Moreover, the wavelength width of the stopband is sufficiently narrow, at approximately 40 nm (approximately 1040 nm to 1080 nm).

[0065] Figure 22 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 6 and the period corresponding to the number m. In Figure 22, peaks in the discrete Fourier transform spectrum are located at indices m=36 and m=40. Of these, the peak at m=36 is Λ' according to equation (6) above. 36 =(561-1) / 36=15.6, which corresponds to the period Λ1=15.7. Furthermore, the peak at m=40 is given by Λ' from equation (6) above. 40 =(561-1) / 40=14.0, which corresponds to the fundamental period p=14. Thus, in Example 6, the discrete Fourier transform spectrum contains peaks corresponding to the fundamental period p and period Λ1, respectively.

[0066] [Example 7] Example 7 has a modified optical multilayer film 4, which is designed by adjusting the values ​​of appropriate terms in the film thickness sequence of the basic optical multilayer film 4 of Example 6, with the aim of reducing ripple in the transmittance distribution in the free filter region.

[0067] The film structure of the optical multilayer film 4 in Example 7 is shown below. 1.308L .215H .566L .403H .336L .529H .113L 1.874H .102L .442H .196L .33H .475L .193H 2.704L .147H .647L .385H .383L .624H .132L 2.074H .11L .361H .182L .272H .447L .16H 2.442L .146H .604L .343H .367L .552H .153L 2.207H .126L .397H .244L .228H .414L .107H 2.122L .151H .611L .388H .375L .63H .152L 2.246H .14L .43H .257L .191H .363L .109H 1.911L .11H .521L .356H .362L .656H .153L 2.597H .144L .482H .29L .235H .496L .087H 1.46L .1H .431L .232H .309L .542H .15L 2.74H .126L .666H .324L .331H .442L .106H 1.848L .114H .334L .217H .212L .372H .116L 2.476H .141L .737H .345L .454H .571L .156H 1.874L .128H .38L .184H .194L .425H .11L 1.964H .146L .647H .409L .433H .654L .199H 2.339L .125H .381L .278H .196L .296H .068L 1.812H .097L .455H .352L .344H .698L .146H 2.805L .142H .514L .308H .214L .446H .073L 1.385H .071L .346H .206L .347H .567L .134H 2.914L .147H .675L .339H .321L .416H .088L 1.798H .071L .284H .18L .216H .34L .137H 2.525L .188H .679L .393H .432L .598H .161L 1.966H .104L .356H .163L .183H .37L .116H 2.019L .174H .579L .448H .379L .69H .183L 2.411H .104L .387H .232L .21H .288L .08H 1.832L .095H .367L .316H .309L .679H .126L 3.008H .121L .556H .31L .223H .368L .084H 1.458L .088H .425L .21H .238L .458H .117L 2.891H .126L .755H .303L .407H .477L .114H 1.775L .082H .272L .194H .25L .363H .099L 2.336H .178L .676H .407L .46H .617L .184H 2.152L .097H .337L .181H .161L .337H .115L 1.942H .153L .566H .423L .375H .699L .188H 2.665L .146H .379L .2H .171L .425H .07L 1.486H 0.83L 3.92H 2.96L 3.22H 6.17L 1.147H 3.363L 1.139H 4.95L 3.28H 2.04L 3.52H 0.71L 1.225H 0.7L 4.44H 2.01L 2.92H 4.35L 1.138H 3.178L 1.147H 7.11L 3.27H 3.72L 4.85H 0.85L 1.585H 0.69L 3.22H 167L 2.224H 3.58L 1.44H 2.497L 2.21H 6.56L 4.26H 4.25L 6.29H .154L 2.038H .094L .363H .16L .172H .343L .121H 2.092L .182H .568L .457H .38L .696H .179L 2.494H .122L .368H .23L .18H .272L .081H 1.683L .099H .471L .385H .314L .745H .126L 2.983H .118L .501H .268L .213H .418L .081H 1.418L .083H .37L .221H .302L .554H .12L 2.992H .126L .731H .308L .341H .371L .096H 1.817L .08H .274L .182H .226L .382H .126L 2.521H .179L .722H .371L .45H .576L .17H 1.987L .131H .359L .171H .167L .412H .089L 1.969H .159L .64H .431L .43H .663L .206H 2.406L .115H .344L .249H .2L .284H .071L 1.7H .09L .502H .383L .341H .727L .147H 2.883L .135H .516L .313H .194L .408H .069L 1.403H .072L .337H .211L .342H .553L .141H 3.02L .147H .646L .346H .309L .377H .08L 1.702H .068L .352H .174L .234H .376L .151H 2.546L .189H .673L .404H .415L .605H .147L 1.939H .116L .357H .159L .207H .423L .116H 1.936L .182H .584L .465H .356L .723H .155L 2.4H .116L .359H .217L .198H .277L .102H 1.863L .104H .447L .342H .32L .686H .126L 2.762H .139L .56H .32L .237H .422L .093H 1.389L .089H .49L .232H .275L .482H .139L 2.637H .147L .682H .358L .373H .521L .112H 1.863L .097H .308L .192H .291L .447H .115L 2.115H .152L .661H .393L .402H .639L .162H 2.156L .106H .4L .201H .216L .377H .13L 1.987H .136L .527H .378L .347H .663L .139H 2.526L .14H .439L .253H .229L .416H .109L 1.457H .101L .585H .323L .381H .622L .146H 2.593L .147H .547L .323H .275L .446H .101L 1.761H .075L .428H .24L .342H .517L .157H 2.546L .163H .588L .392H .308L .536H .093L 1.766H .086L .439H .216L .326H .459L .158H 2.45L .15H .62L .414H .333L .657H .101L 1.907H .111L .43H .197L .27H .477L .158H 2.401L .147H .554L .314H .312L .542H .136L 2.166H .111L .407H .238L .21H .337L .129H 1.136L.

[0068] Figure 23 is a graph showing the spectral transmittance exhibited by Example 7. As shown in Figure 23, Example 7 has a free filter region and stopband similar to Example 6, while suppressing ripple in the transmittance distribution in the free filter region.

[0069] Figure 24 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence in Example 7 and the period corresponding to the number m. In Figure 24, even in Example 7 (after adjusting the values ​​of appropriate terms in the film thickness sequence), the modulation period Λ1 corresponds to m=36(Λ'), similar to Example 6 (Figure 22). 36 The peak of =15.6) and m=40(Λ') corresponding to the fundamental period p. 40 There is a peak at =14.0.

[0070] [Example 8] As Example 8, a structure similar to Example 3 (second basic filter repeating structure (basic period p=14, number of repetitions r=40), L0=561) was formed, except that the modulation of equation (2) (number of stopbands u=2) was used instead of equation (1) above. Here, the amplitude a1=0.3, a2=0.1, the period Λ1=15.7, Λ2=50, and the phase φ1=0, φ2=0.

[0071] The film structure of the optical multilayer film 4 in Example 8 is shown below. 1.54L .193H .627L .36H .302L .478H .102L 1.687H .091L .387H .234L .278H .496L .159H 2.672L .176H .603L .362H .313L .501H .105L 1.632H .08L .305H .17L .195H .352L .118H 2.133L .152H .563L .367H .344L .593H .133L 2.177H .108L .404H .208L .216H .357L .114H 2.019L .146H .562L .384H .381L .696H .165L 2.844H .146L .551H .275L .264H .388L .109H 1.758L .12H .456L .317H .325L .622H .155L 2.792H .15L .58H .292L .274H .379L .097H 1.384L .086H .312L .218H .233L .475H .128L 2.486H .144L .603H .327L .327H .474L .123H 1.717L .1H .328L .211H .215L .436H .12L 2.437H .149L .665H .384L .41H .63L .171H 2.446L .14H .43L .248H .223L .407H .105L 2.088H .129L .592H .356L .397H .639L .181H 2.654L .153H .461L .25H .204L .33H .077L 1.434H .088L .416H .265L .317H .548L .167H 2.633L .162H .518L .292H .241L .38H .082L 1.407H .08L .363H .231L .285H .519L .168H 2.841L .188H .644L .389H .34L .554H .12L 1.938H .099L .4H .229L .263H .466L .152H 2.632L .181H .648L .409H .372L .626H .137L 2.181H .106L .386H .196L .201H .331L .105H 1.858L .134H .509L .344H .335L .6H .139L 2.336H .117L .429H .21L .201H .301L .088H 1.508L .109H .432L .31H .323L .624H .156L 2.83H .153L .597H .306L .295H .426L .114H 1.736L .113H .416L .289H .302L .598H .156L 2.947H .166L .681H .361L .355H .507L .13H 1.799L .104H .339L .216H .217L .433H .117L 2.326H .139L .606H .341L .354H .527L .138H 1.909L .106H .319L .184H .171L .328H .089L 1.855H .118L .554H .337L .379H .612L .174H 2.57L .15H .462L .26H .223L .383H .094L 1.823H .113L .53H .331L .387H .656L .196H 3.04L .185H .585L .329H .272L .43H .094L 1.604H .09L .403H .25L .299H .528L .166H 2.724L .174H .58L .338H .285L .446H .093L 1.455H .074L .301H .179L .215H .397L .133H 2.356L .163H .589L .373H .339L .57H .125L 2.024H 101L 384H 206L 225H 389L 127H 2.262L 162H 609L 406H 39L 694H 16L 2.679H 135L 501H 25L 244H 371L 109H 1.831L 128H 491L 338H 34L 635H 154L 2.69H 14L 528H 26L 241H 335L 088H 1.337L 089H 338L 243H 26L 522H 137L 2.594H .146L .594H .313L .306H .438L .114H 1.622L .098H .341L .23H .242L .493H .134L 2.669H .159L .689H .386L .4H .599L .159H 2.244L .128H .4L .238H .224L .426H .112L 2.252H .138L .621H .365L .396H .618L .17H 2.422L .136H .405L .22H .184L .314H .077L 1.529H.097L .459H .289L .338H .569L .168H 2.581L .155H .482L .268H .221L .355H .08L 1.452H .087L .408H .263L .321H .573L .181H 2.965L .19H .634L .373H .319L .512H .11L 1.819H .096L .405H .241L .284H .506L .163H 2.781L .186H .649L .398H .352L .575H .123L 1.924H .093L .348H .184L .2H .347L .114H 2.029L .144H .54L .355H .336L .586H .132L 2.161H .106L .388H .193L .192H .306L .096H 1.696L .125H .49L .344H .349L .655H .159L 2.801H .147L .563H .284L .274H .402L .112H 1.769L .12H .453L .316H .328L .637H .162L 2.978H .163L .648H .335L .321H .451L .115H 1.623L .097H .335L .224H .233L .469H .125L 2.454H .143L .606H .331L .334H .485L .125H 1.707L .095H .3L .184H .182L .366H .101L 2.103H .132L .601H .356L .388H .608L .168H 2.431L .14H .43L .246H .218L .393H .1L 2H .125L .581H .356L .406H .669L .194H 2.922L .172H .534L .295H .243L .39H .088L 1.581H .093L .429H .269L .32H .556L .171H 2.719L .169H .546L .31H .255L .394H .082L 1.342H .072L .315H .197L .243H .448L .148H 2.556L .172H .603L .371H .328L .54H .117L 1.884H .095L .376H .212L .242H .43L .142H 2.505L .176H .645L .418H .39L .673H .151L 2.471H .122L .452H .228L .23H .367L .113H .973L.

[0072] Figure 25 is a graph showing the spectral transmittance exhibited by Example 8. According to Figure 25, in Example 8, a first stopband with a center wavelength of 1064 nm and a second stopband with a center wavelength of 1550 nm are formed, and a free filter region is formed in a wavelength range including the wavelength range of 400 nm to 1800 nm. Moreover, the wavelength widths of these stopbands are approximately 20 nm (approximately 1050 nm to 1070 nm) for the first stopband and approximately 60 nm (approximately 1520 nm to 1580 nm) for the second stopband, both of which are sufficiently narrow.

[0073] Figure 26 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence in Example 8 and the period corresponding to the number m. In Figure 26, peaks in the discrete Fourier transform spectrum are present at m=11, 36, and 40. Of these peaks, the peak at m=11 is Λ' from equation (6) above. 11 =(561-1) / 11=50.9, which corresponds to a period Λ²=50. Furthermore, the peak at m=36 is given by Λ' from equation (6) above. 36 =(561-1) / 36=15.6, which corresponds to the period Λ1=15.7. Furthermore, the peak at m=40 is given by Λ' from equation (6) above. 40 =(561-1) / 40=14.0, which corresponds to the fundamental period p=14. Thus, in Example 8, the discrete Fourier transform spectrum contains peaks corresponding to the fundamental period p and periods Λ1 and Λ2, respectively.

[0074] [Example 9] Example 9 has a modified optical multilayer film 4, which is designed by adjusting the values ​​of appropriate terms in the film thickness sequence of the basic optical multilayer film 4 of Example 8, with the aim of reducing ripple in the transmittance distribution in the free filter region.

[0075] The film structure of the optical multilayer film 4 in Example 9 is shown below. 1.01L .174H .457L .392H .246L .587H .1L 2.442H .133L .566H .342L .407H .576L .161H 2.813L .212H .563L .495H .343L .729H .154L 2.389H .104L .437H .204L .285H .416L .142H 2.149L .16H .531L .394H .296L .608H .114L 2.283H .124L .463H .232L .204H .351L .12H 1.829L .096H .452L .308H .293L .588H .108L 2.734H .122L .658H .334L .358H .516L .105H 2.047L .171H .575L .464H .321L .74H .135L 2.709H .151L .499H .345L .18H .351L .063H 1.5L .098H .457L .253H .25L .447H .12L 2.522H .128L .671H .348L .367H .568L .091H .1.616L .08H .308L .192H .269L .36H .096L 2.139H .219L .561H .522L .334H .741L .144H 2.311L .1H .42L .245H .215L .326H .117L 2.433H .188L .712H .381L .531H .574L .252H 2.271L .1H .302L .268H .227L .33H .05L 1.788H .121L .508H .388L .348H .702L .15H 2.573L .159H .34L .225H .191L .415H .057L 1.407H .052L .339H .158L .226H .34L .165H 2.482L .203H .66L .408H .44L .588H .175L 2.1H .071L .262H .186L .332H .525L .121H 2.935L .127H .868L .268H .545L .552H .164L 1.679H.127L .404H .167L .177H .436L .115H 1.989L .137H .693L .358H .48L .601H .204L 2.151H .087L .315H .234L .173H .295L .092H 1.41L .076H .428L .203H .261L .485H .125L 2.709H .122L .725H .298L .431H .51L .155H 1.679L .074H .421L .246H .282L .491H .108L 4.065H .109L .53H .28L .233H .356L .085H 1.591L .111H .406L .25H .218L .447H .114L 2.738H .101L .73H .303L .372H .423L .091H 1.774L .086H .239L .219H .199L .231H .087L 1.518H .078L .587H .399L .328H .77L .114H 2.758L .144H .491L .253H .185L .376H .113L 1.292H .074L .517H .282L .314H .567L .128H 4.076L .121H .503L .323H .197L .318H .065L 1.709H .107L .482H .351L .316H .653L .125H 2.9L .114H .498L .306H .195L .292H .061L 1.588H .088L .243H .151L .221H .322L .102H 2.107L .221H .548L .515H .324L .727H .13L 1.972H .093L .454H .169L .158H .322L .152H 1.795L .159H .508L .512H .259L .84H .128L 3.191H .089L .464H .28L .206H .284L .088H 2.148L .188H .573L .441H .393L .651H .198L 2.346H .092L .346H .244L .217H .237L .058H 1.795L .058H .28L .238H .234L .343H .093L 2.456H .166L .684H .381L .385H .555L .114H 1.795L .064H .244L .197H .276L .324H .088L 2.208H .233L .551H .565L .337H .741L .188H 2.579L .149H .391L .17H .154L .375H .126L 2.343H .159L .706H .344L .525H .558L .231H 2.283L .13H .266L .236H .181L .306H .053L 1.577H 0.78L 427H 282L 283H 534L 11H 2.651L 119H 639L 337H 253L 271H 0.78L 1.691H 0.57L 37H 172L 222H 376L 15H 2.443L 245H 592L 467H 394L 657H 162L 2.244H 0.63L 35H 237L 332H 519L 12H 2.902L 122H 746L 313H 438L 569H 12L 1.713H .133L .344H .135L .187H .416L .109H 1.968L .171H .569L .439H .316L .655H .106L 2.094H .127L .44H .223L .172H .35L .114H 1.689L .082H .381L .225H .281L .516H .117L 2.579H .137L .648H .327L .401H .544L .16H 2.215L .138H .504L .401H .293L 705H 106L 2.794H 144L 567H 328L 223H 342L 092H 1.841L 105H 405L 211H 207L 374H 148L 2.429H 161L 527H 284L 264H 436L 136H 2.028L 094H 39L 206H 213L 345H 139L 2.006H 087L 467H 303L 371H 624L 149H 2.616L 155H 532L .337H .262L .478H .105L 2.224H .14L .617H .371L .396H .64L .166H 2.494L .164H .467L .316H .226L .446H .078L 1.708H .094L .519H .261L .342H .502L .155H 2.37L .156H .494L .364H .235L .483H .063L 1.792H .082L .377H .203L .341H .506L .172H 2.422L .155H .555L .364H .323L .6H .126L 2.406H .116L .537H .302L .354H .581L .161H 2.543L .136H .543L .274H .313L .477H .167L 2.243H .08L .297H .206L .276H .24L .076H 1.039L.

[0076] Figure 27 is a graph showing the spectral transmittance exhibited by Example 9. As shown in Figure 27, Example 9 has a free filter region and two stopbands within that region, similar to Example 8, while suppressing ripple in the transmittance distribution in the free filter region.

[0077] Figure 28 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 9 and the period corresponding to the number m. In Figure 28, even in Example 9 (after adjusting the values ​​of appropriate terms in the film thickness sequence), the modulation period Λ2, Λ1 corresponds to m=12(Λ' 12 =46.7),m=36(Λ' 36 The peak of =15.6) and m=40(Λ') corresponding to the fundamental period p. 40 A peak at m=14.0 exists. Furthermore, by adjusting the film thickness sequence, the m=11(Λ') in Example 8 is obtained. 11 The peak at m=50.9 is replaced by the peak at m=12 in Example 9. Furthermore, in Example 9, the spectral intensity at the m=11 peak is only slightly lower than that at the m=12 peak.

[0078] [Example 10] As Example 10, a structure similar to that of Example 1 was formed, except that the basic optical multilayer film 4 was designed based on a third basic filter repeating structure instead of the first basic filter repeating structure. The optical multilayer film 4 of Example 10 is designed with in mind a state in which the wavelength range of the stopband includes 1550 nm (preferably with a central wavelength of 1550 nm) and a free filter region is formed in a wavelength range including 400 nm to 1800 nm. The optical multilayer film 4 of Example 10 is designed by applying the modulation of equation (1) above to the third basic filter repeat structure (number of repetitions s=40, L0=401). Here, the amplitude a1=0.1, the period Λ1=36, and the phase φ1=0.

[0079] The film structure of the optical multilayer film 4 in Example 10 is shown below. 1.386L .242H .558L .565H .226L 2.693H .221L .538H .519L .22H 2.476L .212H .485L .487H .194L 2.311H .19L .469H .459L .198H 2.283L .201H .471L .487H .2L 2.444H .206L .52H .519L .228H 2.646L .234H .549L .565H .23L 2.779H .231L .571H .558L .239H 2.713L .234H .535L .538H .214L 2.53H .206L .502H .485L .206H 2.327L .201H .462L .469H .189L 2.281H .19L .475H .471L .206H 2.394L .212H .501L .52H .214L 2.617H .221L .553H .549L .239H 2.757L .242H .561L .571H .23L 2.749H .226L .553H .535L .228H 2.564L .22H .501L .502H .2L 2.367H .194L .475H .462L .198H 2.268L .198H .462L .475H .194L 2.367H .2L .502H .501L .22H 2.564L .228H .535L .553H .226L 2.749H .23L .571H .561L .242H 2.757L .239H .549L .553H .221L 2.617H .214L .52H .501L .212H 2.394L .206H .471L .475H .19L 2.281H .189L .469H .462L .201H 2.327L .206H .485L .502H .206L 2.53H .214L .538H .535L .234H 2.713L .239H .558L .571H .231L 2.779H .23L .565H .549L .234H 2.646L .228H .519L .52H .206L 2.444H .2L .487H .471L .201H 2.283L .198H .459L .469H .19L 2.311H .194L .487H .485L .212H 2.476L .22H .519L .538H .221L 2.693H .226L .565H .558L .242H 2.772L .242H .558L .565H .226L 2.693H .221L .538H .519L .22H 2.476L .212H .485L .487H .194L 2.311H .19L .469H .459L .198H 2.283L .201H .471L .487H .2L 2.444H .206L .52H .519L .228H 2.646L .234H .549L .565H .23L 2.779H .231L .571H .558L .239H 2.713L .234H .535L .538H .214L 2.53H .206L .502H .485L .206H 2.327L .201H .462L .469H .189L 2.281H .19L .475H .471L .206H 2.394L .212H .501L .52H .214L 2.617H .221L .553H .549L .239H 2.757L .242H .561L .571H .23L 2.749H .226L .553H .535L .228H 2.564L .22H .501L .502H .2L 2.367H .194L .475H .462L .198H 2.268L .198H .462L .475H .194L 2.367H .2L .502H .501L .22H 2.564L .228H .535L .553H .226L 2.749H .23L .571H .561L .242H 2.757L .239H .549L .553H .221L 2.617H .214L .52H .501L .212H 2.394L .206H .471L .475H .19L 2.281H .189L .469H .462L .201H 2.327L .206H .485L .502H .206L 2.53H .214L .538H .535L .234H 2.713L .239H .558L .571H .231L 2.779H .23L .565H .549L .234H 2.646L .228H .519L .52H .206L 2.444H .2L .487H .471L .201H 2.283L .198H .459L .469H .19L 2.311H .194L .487H .485L .212H 2.476L .22H .519L .538H .221L 2.693H .226L .565H .558L .242H 2.772L .242H .558L .565H .226L 2.693H .221L .538H .519L .22H 2.476L .212H .485L .487H .194L 2.311H .19L .469H .459L .198H 2.283L .201H .471L .487H .2L 2.444H .206L .52H .519L .228H 2.646L .234H .549L .565H .23L 2.779H .231L .571H .558L .239H 1.357L.

[0080] Figure 29 is a graph showing the spectral transmittance exhibited by Example 10. As shown in Figure 29, in Example 10, a stopband with a central wavelength of 1550 nm is formed, and a free filter region is formed in a wavelength range that includes the wavelength range from 400 nm to 1800 nm. Moreover, the wavelength width of the stopband is sufficiently narrow, at about 60 nm (approximately 1520 nm to 1580 nm).

[0081] Figure 30 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 10 and the period corresponding to the number m. In Figure 30, compared to before modulation (the third basic filter repeat structure with r=40 iterations; Figure 9), the number of peaks in the discrete Fourier transform spectrum increases by one at the number m=11. This peak is Λ', according to equation (6) above. 11 =(401-1) / 11=36.3, which corresponds to the period Λ1=36. Furthermore, in Figure 30, as before modulation, m=40(Λ') corresponds to the fundamental period p=10. 40 A peak exists at (=10.0). Thus, in Example 10, the discrete Fourier transform spectrum contains peaks corresponding to the fundamental period p and period Λ1, respectively.

[0082] [Example 11] Example 11 has a modified optical multilayer film 4, which is designed by adjusting the values ​​of appropriate terms in the film thickness sequence of the basic optical multilayer film 4 of Example 10, with the aim of reducing ripple in the transmittance distribution in the free filter region.

[0083] The film structure of the optical multilayer film 4 in Example 11 is shown below. 1.388L .23H .516L .532H .227L 2.463H .222L .499H .509L .203H 2.333L .193H .506L .499H .213L 2.541H .229L .522H .561L .2H 2.669L .246H .543L .545H .223L 2.749H .208L .59H .51L .265H 2.655L .188H .594L .507H .247L 2.539H .22L .498H .508L .189H 2.21L .173H .508L .468H .224L 2.387H .206L .477H .483L .189H 2.372L .203H .517L .52H .205L 2.626H .243L .517H .56L .199H 2.72L .232H .548L .549H .244L 2.645H .203L .583H .517L .252H 2.546L .217H .524L .519H .201L 2.287H .194L .472H .46L .209H 2.35L .221H .474L .497H .186L 2.17H .188L .493H .484L .214H 2.46L .229H .512L .545H .211L 2.571H .238L .532H .545L .234H 2.647L .192H .607L .484H .285L 2.577H .168L .649H .465L .286H 2.566L .177H .584L .52H .223L 2.461H .244L .446H .519L .155H 2.064L .161H .48L .468H .207L 2.426H .206L .514H .537L .185H 2.554L .267H .473L .612H .173L 2.637H .255L .522H .569L .217H 2.696L .189H .601L .496H .263L 2.64H .187L .566H .509L .226H 2.498L .216H .469L .506H .169L 2.195H .18L .471H .457L .194H 2.324L .187H .501L .5H .199L 2.517H .248L .474H .611L .162H 2.606L .277H .471L .59H .168L 2.87H .22L .538H .518L .232H 2.703L .18H .568L .485H .239L 2.556H .189L .512H .485L .203H 2.33L .195H .481L .475H .195L 2.281H .187L .47H .473L .198H 2.441L .228H .485L .569H .173L 2.594H .259L .463H .559L .166H 2.961L .23H .513L .524H .222L 2.832H .18L .559H .48L .247H 2.58L .187H .536L .487H .21L 2.353H .187L .484H .457L .209H 2.325L .206H .469L .487H .187L 2.336H .209L .491H .526L .188H 2.597L .252H .473L .579H .178L 2.767H .22L .526H .512L .231H 2.917L .177H .562L .473H .263L 2.58H .175L .58H .481L .231H 2.487L .195H .477L .479H .19L 2.314H .197L .465H .475L .186H 2.238L .183H .512L .487H .213L 2.543H .242L .491H .588L .183H 2.677L .244H .512L .578H 207L 2.746H 193L 585H 503L 265H 2.619L 179H 595L 486H 25L 2.542H 199L 498H 509L 195H 2.358L 213H 462L 498H 168L 2.118H 152L 511H 444L 24H 2.5L 221H 527L 571H 194L 2.638H 255L 505H 613L 186H 2.711L 226H 556L 557H .236L 2.631H .215L .574H .529L .246H 2.542L .23H .505L .534H .193L 2.286H .183L .484H .463L .213H 2.38L .211H .467L .487H .19L 2.31H .209L .515H .528L .204H 2.598L .248H .506L .589H .188L 2.734H .226L .56H .549L .239H 2.661L .205H .616L .516H .267L 2.569H .236L .57H .549L .222H 2.533L .255H .44L .526H .152L 2.151H .197L .528H .519L .206H 2.599L .265H .481L .612H .159L 2.702H .274L .49H .574L .206H 2.881L .188H .598L .453H .299L 2.569H .169L .651H .407L .307H 1.213L.

[0084] Figure 31 is a graph showing the spectral transmittance exhibited by Example 11. As shown in Figure 31, Example 11 has the same free filter region and stopband as Example 10, but the ripple in the transmittance distribution in the free filter region is suppressed.

[0085] Figure 32 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 11 and the period corresponding to the number m. In Figure 32, even in Example 11 (after adjusting the values ​​of appropriate terms in the film thickness sequence), the modulation period Λ1 corresponds to m=11(Λ'), similar to Example 10 (Figure 30). 11 The peak of =36.3) and m=40(Λ') corresponding to the fundamental period p. 40 There is a peak at =10.0.

[0086] [Comparative Example 1] As Comparative Example 1, a notch filter was formed that was the same as in Example 1 except for the film structure of the optical multilayer film 4. The optical multilayer film 4 of Comparative Example 1 is designed with the assumption that the center wavelength of the stopband is 500 nm and that a free filter region is formed in a wavelength range including the wavelength range from 400 nm to 1800 nm. The film structure of the optical multilayer film 4 in Comparative Example 1 is (0.90L 0.20H 0.90L) 30 That is the case.

[0087] Figure 33 is a graph showing the spectral transmittance exhibited by Comparative Example 1. According to Figure 33, in Comparative Example 1, the center wavelength of the stopband is 500 nm, and a free filter region is formed in a wavelength range that includes the wavelength range from 400 nm to 1800 nm.

[0088] Figure 34 shows the discrete Fourier transform spectrum of the film thickness sequence for Comparative Example 1 and a graph showing the period corresponding to the number m. According to Figure 34, there are no peaks in the discrete Fourier transform spectrum of the film thickness sequence for Comparative Example 1, and the maximum value is m=30(Λ'). 30 At (61-1) / 30=2.0), it appears as a representation of a double period.

[0089] [Comparative Example 2] As Comparative Example 2, a notch filter was formed that was the same as in Comparative Example 1 except for the film structure of the optical multilayer film 4. The optical multilayer film 4 of Comparative Example 2 is designed with the assumption that the center wavelengths of the two stopbands are 532 and 1064 nm, and that a free filter region is formed in a wavelength range including the wavelength range from 400 nm to 1800 nm. The film structure of the optical multilayer film 4 in Comparative Example 2 is (0.95L 0.10H 0.95L) 70 That is the case.

[0090] Figure 35 is a graph showing the spectral transmittance exhibited by Comparative Example 2. According to Figure 35, in Comparative Example 2, the center wavelengths of each stopband are 532 and 1064 nm, respectively, and a free filter region is formed in a wavelength range that includes the wavelength range from 400 nm to 1800 nm.

[0091] Figure 36 shows the discrete Fourier transform spectrum of the film thickness sequence for Comparative Example 2 and a graph showing the period corresponding to the number m. According to Figure 36, there are no peaks in the discrete Fourier transform spectrum of the film thickness sequence for Comparative Example 2, and the maximum value is m=70(Λ'). 70 At (141-1) / 70=2.0), it appears as a representation of a double period.

[0092] [Example 12] As Example 12, the refractive index n of a high refractive index material H A product similar to that of Example 3 was formed, except that part 2.18 was replaced with part 2.4.

[0093] The film structure of the optical multilayer film 4 in Example 12 is shown below in terms of physical film thickness. 102.54L 8.02H 44.62L 17.08H 25.81L 28.15H 10.91L 119.67H 10.71L 27.15H 24.46L 15.92H 40.93L 7.25H 182.95L 7.07H 38.95L 14.79H 22.22L 24.14H 9.35L 102.64H 9.22L 23.52H 21.37L 14.06H 36.64L 6.59H 169.11L 6.65H 37.39L 14.49H 22.22L 24.65H 9.74L 109.02H 9.98L 25.88H 23.88L 15.92H 41.93L 7.6H 196.43L 7.76H 43.64L 16.89H 25.81L 28.46H 11.15L 123.66H 11.19L 28.63H 26.03L 17.08H 44.24L 7.88H 200.03L 7.76H 42.86L 16.29H 24.46L 26.53H 10.23L 111.79H 9.98L 25.24H 22.72L 14.79H 38.09L 6.76H 171.36L 6.65H 36.9L 14.11H 21.37L 23.44H 9.16L 101.6H 9.22L 23.76H 21.81L 14.49H 38.09L 6.9H 178.5L 7.07H 39.92L 15.53H 23.88L 26.53H 10.48L 117.29H 10.71L 27.7H 25.46L 16.89H 44.24L 7.97H 204.5L 8.02H 44.75L 17.18H 26.03L 28.46H 11.06L 121.6H 10.91L 27.7H 25L 16.29H 41.93L 7.43H 187.61L 7.25H 39.92L 15.14H 22.72L 24.65H 9.52L 104.3H 9.35L 23.76H 21.52L 14.11H 36.64L 6.56H 167.94L 6.59H 36.9L 14.26H 21.81L 24.14H 9.52L 106.47H 9.74L 25.24H 23.28L 15.53H 40.93L 7.43H 192.2L 7.6H 42.86L 16.62H 25.46L 28.15H 11.06L 122.96H 11.15L 28.63H 26.1L 17.18H 44.62L 7.97H 202.78L 7.88H 43.64L 16.62H 25L 27.15H 10.48L 114.61H 10.23L 25.88H 23.28L 15.14H 38.95L 6.9H 174.56L 6.76H 37.39L 14.26H 21.52L 23.52H 9.16L 101.25H 9.16L 23.52H 21.52L 14.26H 37.39L 6.76H 174.56L 6.9H 38.95L 15.14H 23.28L 25.88H 10.23L 114.61H 10.48L 27.15H 25L 16.62H 43.64L 7.88H 202.78L 7.97H 44.62L 17.18H 26.1L 28.63H 11.15L 122.96H 11.06L 28.15H 25.46L 16.62H 42.86L 7.6H 192.2L 7.43H 40.93L 15.53H 23.28L 25.24H 9.74L 106.47H 9.52L 24.14H 21.81L 14.26H 36.9L 6.59H 167.94L 6.56H 36.64L 14.11H 21.52L 23.76H 9.35L 104.3H 9.52L 24.65H 22.72L 15.14H 39.92L 7.25H 187.61L 7.43H 41.93L 16.29H 25L 27.7H 10.91L 121.6H 11.06L 28.46H 26.03L 17.18H 44.75L 8.02H 204.5L 7.97H 44.24L 16.89H 25.46L 27.7H 10.71L 117.29H 10.48L 26.53H 23.88L 15.53H 39.92L 7.07H 178.5L 6.9H 38.09L 14.49H 21.81L 23.76H 9.22L 101.6H 9.16L 23.44H 21.37L 14.11H 36.9L 6.65H 171.36L 6.76H 38.09L 14.79H 22.72L 25.24H 9.98L 111.79H 10.23L 26.53H 24.46L 16.29H 42.86L 7.76H 200.03L 7.88H 44.24L 17.08H 26.03L 28.63H 11.19L 123.66H 11.15L 28.46H 25.81L 16.89H 43.64L 7.76H 196.43L 7.6H 41.93L 15.92H 23.88L 25.88H 9.98L 109.02H 9.74L 24.65H 22.22L 14.49H 37.39L 6.65H 169.11L 6.59H 36.64L 14.06H 21.37L 23.52H 9.22L 102.64H 9.35L 24.14H 22.22L 14.79H 38.95L 7.07H 182.95L 7.25H 40.93L 15.92H 24.46L 27.15H 10.71L 119.67H 10.91L 28.15H 25.81L 17.08H 44.62L 8.02H 205.08L 8.02H 44.62L 17.08H 25.81L 28.15H 10.91L 119.67H 10.71L 27.15H 24.46L 15.92H 40.93L 7.25H 182.95L 7.07H 38.95L 14.79H 22.22L 24.14H 9.35L 102.64H 9.22L 23.52H 21.37L 14.06H 36.64L 6.59H 169.11L 6.65H 37.39L 14.49H 22.22L 24.65H 9.74L 109.02H 9.98L 25.88H 23.88L 15.92H 41.93L 7.6H 196.43L 7.76H 43.64L 16.89H 25.81L 28.46H 11.15L 123.66H 11.19L 28.63H 26.03L 17.08H 44.24L 7.88H 200.03L 7.76H 42.86L 16.29H 24.46L 26.53H 10.23L 111.79H 9.98L 25.24H 22.72L 14.79H 38.09L 6.76H 171.36L 6.65H 36.9L 14.11H 21.37L 23.44H 9.16L 101.6H 9.22L 23.76H 21.81L 14.49H 38.09L 6.9H 178.5L 7.07H 39.92L 15.53H 23.88L 26.53H 10.48L 117.29H 10.71L 27.7H 25.46L 16.89H 44.24L 7.97H 204.5L 8.02H 44.75L 17.18H 26.03L 28.46H 11.06L 121.6H 10.91L 27.7H 25L 16.29H 41.93L 7.43H 187.61L 7.25H 39.92L 15.14H 22.72L 24.65H 9.52L 104.3H 9.35L 23.76H 21.52L 14.11H 36.64L 6.56H 167.94L 6.59H 36.9L 14.26H 21.81L 24.14H 9.52L 106.47H 9.74L 25.24H 23.28L 15.53H 40.93L 7.43H 192.2L 7.6H 42.86L 16.62H 25.46L 28.15H 11.06L 122.96H 11.15L 28.63H 26.1L 17.18H 44.62L 7.97H 202.78L 7.88H 43.64L 16.62H 25L 27.15H 10.48L 114.61H 10.23L 25.88H 23.28L 15.14H 38.95L 6.9H 174.56L 6.76H 37.39L 14.26H 21.52L 23.52H 9.16L 101.25H 9.16L 23.52H 21.52L 14.26H 37.39L 6.76H 174.56L 6.9H 38.95L 15.14H 23.28L 25.88H 10.23L 114.61H 10.48L 27.15H 25L 16.62H 43.64L 7.88H 202.78L 7.97H 44.62L 17.18H 26.1L 28.63H 11.15L 122.96H 11.06L 28.15H 25.46L 16.62H 42.86L 7.6H 96.1L.

[0094] Figure 37 is a graph showing the spectral transmittance exhibited by Example 12. According to Figure 37, the spectral transmittance of Example 12 is the same as that of Example 3.

[0095] Figure 38 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 12 and the period corresponding to the number m. According to Figure 38, the discrete Fourier transform spectrum of Example 12 is the same as that of Example 3. In other words, in Example 12 as well, there are peaks in the discrete Fourier transform spectrum corresponding to the fundamental period p and period Λ1, respectively (Λ' 40 =14.0=p,Λ' 11 =50.9≈Λ1).

[0096] Furthermore, from the viewpoint of making it easier to design with modulation of the film thickness sequence, the refractive index n of high refractive index materials H It is preferable that the refractive index is between 2.0 and 3.0. For example, the refractive index of Ta2O5 (at a wavelength of 500 nm, the same applies hereinafter) is 2.18, the refractive index of TiO2 and Nb2O5 is 2.4, and the refractive index of HfO2, ZrO2 and La x Ti y O z The refractive index of is 2.0. In addition, the refractive index n of low refractive index materials L It is preferable that the refractive index is between 1.4 and 1.5. For example, the refractive index of SiO2 is 1.475.

[0097] [Example 13] Example 13 has a modified optical multilayer film 4, which is designed by adjusting the values ​​of appropriate terms in the film thickness sequence of the basic optical multilayer film 4 of Example 12, with the aim of reducing ripple in the transmittance distribution in the free filter region.

[0098] The film structure of the optical multilayer film 4 in Example 13 is shown below in terms of physical film thickness. 124.07L 7.87H 50.01L 17.89H 31.23L 29.88H 12.28L 118.47H 9.07L 26.88H 23.38L 16.65H 43.41L 6.9H 184.21L 6.26H 38.89L 14.39H 24.93L 26.1H 10.83L 117.46H 10.57L 25.81H 25.29L 16.06H 44.33L 6.84H 204.62L 7.22H 45.24L 17.53H 26.89L 28.4H 10.61L 120.6H 9.89L 30.6H 27.26L 18.02H 46.27L 6.76H 187.92L 6.29H 43.74L 16.27H 25.55L 26.62H 9.36L 102.94H 9.06L 25.29H 23.26L 15.22H 39.75L 6.38H 177.66L 6.29H 39.01L 14.32H 23.06L 24.6H 9.96L 105.33H 8.08L 24.99H 22.69L 17.13H 43.39L 7.12H 190.63L 7.05H 42.7L 17H 24.77L 27.99H 9.57L 117.12H 10.3L 27.9H 26.39L 17.47H 45.69L 7.2H 199.6L 6.78H 47.64L 17.59H 27.03L 28.4H 9.55L 108.19H 8.69L 27.42H 24.56L 16.73H 42.86L 6.46H 175.45L 6.5H 40.7L 15.28H 22.08L 23.55H 8.96L 106.09H 10.12L 22.86H 20.53L 13.58H 37.65L 6.94H 183.61L 6.66H 37.64L 13.8H 22.49L 24.77H 10.54L 112.19H 9.6L 24.42H 23.48L 16.26H 43.58L 7.13H 200.23L 7.28H 44.3L 17.26H 26.16L 28H 10.51L 121.2H 10.54L 30.26H 28.17L 17.5H 46.59L 6.43H 184.6L 6.16H 44.04L 16.19H 25.82L 27.09H 9.47L 103.14H 9.03L 24.95H 22.69L 15.13H 39.43L 6.46H 176.36L 6.65H 39.71L 15.41H 21.48L 23.83H 8.49L 101.5H 8.84L 24.86H 23.37L 15.54H 41.56L 6.26H 176.59L 6.07H 42.53L 16.01H 25.83L 27.46H 9.85L 114.79H 10.22L 27.11H 26.04L 17.12H 45.24L 7.05H 206.11L 7.19H 47.13L 18.32H 27.61L 29.61H 10L 113.23H 9.21L 28.09H 25.44L 17.03H 43.98L 6.49H 178.6L 6.46H 41L 15.38H 22.55L 23.6H 9.03L 106.01H 10.01L 22.89H 20.62L 13.46H 37.12L 6.79H 179.35L 6.14H 35.29L 12.58H 23.05L 24.47H 10.84L 105.99H 7.94L 24.27H 22.43L 16.98H 43.16L 7.02H 189.22L 6.82H 44.02L 17.07H 26.04L 28.43H 10.05L 119.95H 10.54L 29.34H 27.49L 18.06H 47.1L 7.2H 198.96L 6.57H 46.36L 16.85H 26.61L 27.63H 9.78L 106.51H 8.96L 26.71H 24.06L 16.38H 41.74L 6.5H 174.41L 6.46H 39.74L 15.16H 21.48L 22.85H 8.68L 106.37H 10.74L 22.27H 19.93L 12.58H 36.39L 6.87H 182.67L 6.59H 37.07L 13.47H 22.37L 24.46H 10.66L 112.18H 9.64L 25.44H 24.38L 16.41H 44.47L 6.83H 198.33L 7.05H 46.09L 17.77H 27.44L 29.19H 10.69L 122.68H 10.67L 29.7H 27.81L 17.19H 45.92L 6.48H 183.01L 6.38H 43.66L 16.18H 25.5L 26.91H 9.41L 102.54H 9.03L 24.74H 22.84L 14.98H 39.22L 6.29H 174.14L 6.3H 39.51L 15.14H 22.42L 24.64H 8.59L 98.98H 7.89L 24.95H 22.44L 16.35H 41.41L 6.66H 179.09L 6.28H 42.6L 16.21H 25.27L 27.37H 9.53L 111.9H 9.72L 28.73H 26.86L 17.9H 47.13L 7.14H 205.2L 7.02H 48.75L 17.97H 28.03L 29.43H 10.29L 113.11H 9.26L 27.41H 25.06L 16.77H 43.8L 6.54H 180.37L 6.5H 40.51L 15.43H 22.68L 24.43H 8.84L 102.67H 9.12L 24.68H 23.49L 14.9H 40.28L 5.87H 170.42L 6.37H 41.82L 16.77H 23.3L 26.76H 7.57L 95.59H 8.1L 27.09H 24L 17.01H 43.51L 6.7H 188.15L 7.01H 44.92L 17.52H 25.77L 28.11H 9.67L 118.63H 10.47L 30.17H 28.22L 18.25H 48.37L 7.06H 198.04L 6.74H 45.68L 16.98H 25.96L 27.54H 9.43L 107.08H 9.06L 25.77H 23.51L 15.62H 40.45L 6.38H 178.77L 6.78H 40.27L 15.75H 21.39L 23.8H 8.29L 102.96H 9.58L 24.25H 23.14L 14.46H 39.53L 6.06H 174.46L 6.09H 40.46L 15.03H 24.12L 25.47H 9.71L 108.84H 9.52L 27.04H 25.56L 16.83H 45.29L 6.76H 196.55L 7.07H 47.85L 18.06H 27.86L 29.9H 10.38L 118.51H 9.86L 28.69H 26.17L 17.47H 45.41L 6.86H 187.41L 6.5H 42.56L 16.01H 24.33L 26H 9.08L 103.37H 8.84L 25.7H 23.96L 15.59H 41.3L 6.02H 172.5L 6.37H 42.05L 16.73H 23.74L 27.18H 7.71L 95.13H 8.35L 27.41H 24.86L 16.53H 43.01L 6.16H 177.6L 6.33H 44.54L 16.91H 26.04L 28.21H 9.43L 111.95H 9.6L 29.55H 27.07L 18.52H 48.08L 7.35H 204.12L 7.18H 47.38L 17.94H 26.55L 28.68H 9.5L 109.82H 9.26L 27.04H 24.67L 16.38H 42.41L 6.46H 182.18L 6.75H 41.6L 16.11H 22.37L 24.45H 8.49L 105.36H 9.67L 24.62H 22.68L 14.61H 39.22L 6.5H 183.62L 7.01H 40.41L 15.59H 21.98L 24.43H 9.26L 111.33H 10.24L 26.79H 26.04L 16.27H 45.12L 6.51H 199.86L 7.3H 47.13L 18.32H 27.85L 30.01H 10.45L 121.27H 9.95L 30.49H 27.05L 18.55H 47.27L 7.25H 187.95L 6.46H 43.73L 15.6H 25.41L 25.83H 9.51L 99.6H 8.96L 23.93H 20.62L 13.54H 34.72L 6.16H 81.75L.

[0099] Figure 39 is a graph showing the spectral transmittance exhibited by Example 13. As shown in Figure 39, Example 13 has a free filter region and stopband similar to Example 12, while suppressing ripple in the transmittance distribution in the free filter region.

[0100] Figure 40 shows the discrete Fourier transform spectrum of the film thickness sequence for Example 13 and a graph showing the period corresponding to the number m. In Figure 40, even in Example 13 (after adjusting the values ​​of appropriate terms in the film thickness sequence), the modulation period Λ1 corresponds to m=11(Λ'), similar to Example 12 (Figure 38). 11 The peak of =50.9) and m=40(Λ') corresponding to the fundamental period p. 40 There is a peak at =14.0.

[0101] [Example 14] As Example 14, a structure similar to that of Example 3 was formed, except that the total number of layers L0 was changed from 561 to 551. In other words, the layer structure of Example 14 is the same as the layer structure of Example 3, but with the 10 layers on the medium side removed.

[0102] The film structure of the optical multilayer film 4 in Example 14 is shown below. 1.21L .154H .527L .328H .305L .54H .129L 2.298H .126L .521H .289L .306H .483L .139H 2.159L .136H .46L .284H .262L .464H. .282L .306H .495L .146H 2.318L .149H .515L .324H .305L .547H .132L 2.374H .132L .55H .307L .328H .522L .151H 2.36L .149H .506L .313H .289L .509H .121L 2.147H .118L .484H .268L .284H .449L .13H 2.022L .128H .435L .271H .252L .45H .108L 1.951H .109L .456H 257L 278H 449L 133H 2.106L 136H 471L 298H 282L 509H 124L 2.252H 126L 532H 3L 324H 522L 153H 2.413L 154H 528L 33H 307L 547H 131L 2.335H 129L 532H 295L 313H 495L 143H 2.214L 139H 471L 291H 268L 473H 112L 2.002H 11L 456H 254L 271H 432L 126H 1.982L 126H 435L 274H 257L 464H 112L 2.044H 115L 484H 275L 298H 483L 143H 2.268L 146H 506L 319H 3L 54H 131L 2.361H 132L 55H 308L 33H 527L 153H 2.393L 151H 515L 319H 295L 521H 124L 2.2H .121L .497H .275L .291H .46L .133H 2.06L .13H .441L .274H .254L .452H .108L 1.944H .108L .452H .254L .274H .441L .13H 2.06L .133H .46L .291H .275L .497H .121L 2.2H .124L .521H .295L .319H .515L .151H 2.393L .153H .527L .33H .308L .55H .132L 2.361H .131L .54H .3L .319H .506L .146H 2.268L .143H .483L .298H .275L .484H .115L 2.044H .112L .464H .257L .274H .435L .126H 1.982L .126H .432L .271H .254L .456H .11L 2.002H .112L .473H .268L .291H .471L .139H 2.214L .143H .495L .313H .295L .532H .129L 2.335H .131L .547H 307L 33H 528L 154H 2.413L 153H 522L 324H 3L 532H 126L 2.252H 124L 509H 282L 298H 471L 136H 2.106L 133H 449L 278H 257L 456H 109L 1.951H 108L 45H 252L 271H 435L 128H 2.022L 13H 449L 284H 268L 484H 118L 2.147H .121L .509H .289L .313H .506L .149H 2.36L .151H .522L .328H .307L .55H .132L 2.374H .132L .547H .305L .324H .515L .149H 2.318L .146H .495L .306H .282L .497H .118L 2.093H .115L .473H .262L .278H .441L .128H 1.995L .126H .432L .27H .252L .452H .109L 1.971H .11L .464H .262L .284H .46L .136H 2.159L .139H .483L .306H .289L .521H .126L 2.298H .129L .54H .305L .328H .527L .154H 2.42L .154H .527L .328H .305L .54H .129L 2.298H .126L .521H .289L .306H .483L .139H 2.159L .136H .46L .284H .262L .464H .11L 1.971H .109L .452H .252L .27H .432L .126H 1.995L .128H .441L .278H .262L .473H .115L 2.093H .118L .497H .282L .306H .495L .146H 2.318L .149H .515L .324H .305L .547H .132L 2.374H .132L .55H .307L .328H .522L .151H 2.36L .149H .506L .313H .289L .509H .121L 2.147H .118L .484H .268L .284H .449L .13H 2.022L .128H .435L .271H .252L .45H .108L 1.951H .109L .456H .257L .278H .449L .133H 2.106L .136H .471L .298H .282L .509H .124L 2.252H .126L .532H .3L .324H .522L .153H 2.413L .154H .528L .33H .307L .547H .131L 2.335H .129L .532H .295L .313H .495L .143H 2.214L .139H .471L .291H .268L .473H .112L 2.002H .11L .456H .254L .271H .432L .126H 1.982L .126H .435L .274H .257L .464H .112L 2.044H .115L .484H .275L .298H .483L .143H 2.268L .146H .506L .319H .3L .54H .131L 2.361H .132L .55H .308L .33H .527L .153H 2.393L .151H .515L .319H .295L .521H .124L 2.2H .121L .497H .275L .291H .46L .133H 2.06L .13H .441L .274H .254L .452H .108L 1.944H .108L .452H .254L .274H .441L .13H 2.06L .133H .46L .291H .275L .497H .121L 2.2H .124L .521H .295L .319H .515L .151H 2.393L .153H .527L .33H .308L.

[0103] Figure 41 is a graph showing the spectral transmittance exhibited by Example 14. As shown in Figure 41, the spectral transmittance of Example 14 is similar to that of Example 3 in general terms, including the stopband and free filter region, although a relatively large amount of ripple appears. In Example 14, unlike the other examples, the average transmittance in the free filter region (400 nm to 1800 nm) is less than 85% due to the omission of some film structures compared to the film structure of Example 3 (reducing the periodicity of the film structure).

[0104] Figure 42 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 14 and the period corresponding to the number m. As shown in Figure 42, the discrete Fourier transform spectrum of Example 14 differs slightly from that of Example 3 due to the decrease in periodicity of the film structure, but it has discrete Fourier transform spectral peaks corresponding to the fundamental period p and period Λ1, respectively (Λ' 39 =14.1≒p,Λ' 11 =50.9≈Λ1). As in the film structure of Example 14, even if a part of the film structure is not a basic filter structure, if the other parts are repetitions of the basic filter, then the film structure can be said to have a basic filter repeat structure. In this case, due to the repetition of the basic filter, a peak is located at number m, which corresponds to the basic period, in the discrete Fourier transform spectrum of the film thickness sequence.

[0105] [Example 15] Example 15 has a modified optical multilayer film 4, which is designed by adjusting the values ​​of appropriate terms in the film thickness sequence of the optical multilayer film 4 of Example 14, with the aim of reducing ripple in the transmittance distribution in the free filter region.

[0106] The film structure of the optical multilayer film 4 in Example 15 is shown below. .965L .112H .597L .314H .373L .546H .148L 2.248H .112L .465H .248L .299H .469L .146H 2.287L .154H .491L .322H .239L .449H .104L 2.222H .138L .513H .316L .295H .52L .128H 2.423L .153H .592L .392H .327L .616H .106L 2.09H .11L .602H .338L .36H .592L .121H 1.928L .102H .588L .344H .338L .604H .097L 1.729H .11L .539H .291L .28H .438L .117H 2.113L .124H .404L .234H .267L .473H .127L 1.944H .099L .521H .31L .313H .521L .103H 2.032L .135H .535L .355H .286L .529H .093L 2.152H .137L .57H .359L .324H .574L .115H 2.281L .134H .59L .373H .338L .629H .107L 1.813H .095L .631H .334L .365H .601L .112H 1.782L .106H .583L .344H .316L .568H .087L 1.702H .094L .516H .283L .317H .511L .114H 1.844L .103H .533L .329H .303L .544H .086L 1.786H .103L .484H .256L .298H .467L .137H 2.202L .126H .474L .284H .294L .508H .132L 2.31H .13L .545H .325L .332H .554L .136H 2.419L .151H .56L .372H .294L .544H .093L 2.056H .125L .503H .291L .273H .453L .118H 2.116L .127H .454L .294H .268L .514H .099L 1.712H .1L .558H .331L .305H .528L .083H 1.863L .133H .475L .293H .234L .423H .104L 1.949H .095L .476H .276L .318H .508L .122H 2.079L .121H .535L .333H .314L .552H .112L 2.196H .122L .585H .34L .357H .585L .136H 2.308L .115H .546L .309H .34L .542H .132L 2.089H.101L .519H .306L .326H .551L .11H 1.804L .105H .552L .333H .3L .524H .083L 1.844H .12L .455H .26L .25H .432L .117H 1.987L .112H .463L .29H .274L .473H .099L 1.957H .119L .474H .281L .272H .467L .118H 2.102L .11H .494L .285H .328L .53H .141L 2.39H .142L .565H .351L .325H .565L .125H 2.36L .145H .565L .373H .305L .58H .091L 1.846H .093L .521H .264L .323H .474L .138H 2.143L .132H .447L .292H .254L .486H .096L 1.753H .097L .519H .293L .289H .456L .103H 2.02L .133H .43L .254H .236L .441H .117L 1.967H .106L .525H .339L .323H .635L .099H 1.57L .102H .655L .334H .371L .582H .13L 2.238H .113L .588H .326L .374H .582L .148H 2.388L .125H .524L .301H .316L .516H .131L 2.12H .102L .485H .284L .319H .526L .117H 1.859L .104H .544L .337H .302L .55H .079L 1.78H .117L .444H .228L .25H .425L .138H 2.046L .105H .467L .306H .307L .592H .102L 1.479H .091L .62H .301L .347H .521L .124H 2.105L .116H .519L .305H .323L .536H .132L 2.36H .139L .571H .35L .332H .57L .126H 2.339L .141H .563L .368H .308L .58H .093L 1.867H .103L .529H .283L .305H .467L .124H 2.131L .141H .447L .284H .231L .444H .101L 1.846H .1L .517H .321L .304H .552L .086H 1.741L .116H .516L .315H .276L .482H .094L 1.925H .114L .512H .324L .304H .557L .1H 1.851L .098H .591L .318H .365L .571H .135L 2.272H .113L .572H .317L .367H .569L .148H 2.375L .128H .508L .291H .302L .498H .132L 2.131H .096L .445H .248L .324H .497L .137H 2.001L .105H .509L .325H .306L .577H .09L 1.608H .098L .542H .293L .305H .483L .11H 1.95L .114H .491L .311H .285L .51H .095L 1.888H .109L .515H .298L .305H .5L .119H 2.199L .134H .534L .334H .307L .541H .119L 2.334H .141L .578H .365L .327H .582L .112H 2.137L .118H .565L .34H .327L .566H .105L 1.907H .104L .528H .29L .299H .464L .118H 2.13L .138H .418L .225H .23L .434H .135L 1.993H .09L .483H .288L .321H .524L .109H 1.95L .128H .532L .353H .279L .513H .082L 2.05H .139L .532H .337L .288H .512L .113H 2.358L .153H .601L .404H .335L .657H .108L 1.93H .087L .665H .31L .423H .593L .161H 2.374L .125H .461L .281H .322L .559H .139L 2.569H .198L .576H .475L .324H .76L .137H 2.55L .09H .812L .195H .182L.

[0107] Figure 43 is a graph showing the spectral transmittance exhibited by Example 15. As shown in Figure 43, Example 15 has the same free filter region and stopband as Example 14, but the ripple in the transmittance distribution in the free filter region is suppressed. Furthermore, the average transmittance in the free filter region (400nm to 1800nm) is 85% or higher.

[0108] Figure 44 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 15 and the period corresponding to the number m. In Figure 44, even in Example 15 (after adjusting the values ​​of appropriate terms in the film thickness sequence), the modulation period Λ1 corresponds to m=10(Λ'), similar to Example 14 (Figure 42). 11 The peak of =55) and m=39(Λ') corresponding to the fundamental period p. 40 There is a peak at =14.1).

[0109] [Example 16] If we increase the portion that is not part of the basic filter structure relative to the basic filter repeating structure and apply modulation using equation (2) above, or if we apply greater adjustments to the film thickness of an arbitrary layer to the film structure after modulation, thereby making larger changes to the layer structure of the basic optical multilayer film 4, the periodicity of the film thickness sequence will be more significantly disrupted. As a result, the modified film structure will approach the film structure related to the film thickness sequence that is not modulated. Therefore, the modified film structure will deviate further from the ideal spectral transmittance shape required for a notch filter, such as an increase in ripple in the free filter region or larger ripple (smaller minimum value of transmittance). Examples 16 and 17 below deliberately incorporate such modifications without considering the reduction of ripple in the free filter region as much as possible.

[0110] As Example 16, a structure similar to Example 3 was formed, except that the total number of layers L0 was changed from 561 to 433 (the number of repetitions r was changed from 40 to 31), and the film thickness was further adjusted to a greater extent. In the second basic filter repeating structure (basic period p=14), the center wavelength of the stopband is set to 1550 nm, so the modulation period is Λ1=50.

[0111] The film structure of the optical multilayer film 4 in Example 16 is shown below in terms of physical film thickness. 98.29L 11.4H 43.9L 27.73H 19.67L 143.52H 15.51L 31.33H 41.45L 13.17H 197.2L 5.49H 27.16L 10.93H 32.07L 31.04H 14.83L 145.4H 19.27L 29.79H 44.96L 12.78H 221.92L 7.61H 58.49L 21.8H 32.69L 38.55H 10.66L 105.9H 5.91L 39.81H 24.98L 24.81H 50.25L 9.25H 186.22L 5.25H 35.63L 14.79H 27.51L 28.81H 10.62L 117.38H 14.43L 29.45H 39.31L 13.01H 205.82L 11.47H 44.45L 30.24H 16.96L 141.66H 19.29L 27.44H 46.36L 10.13H 202.77L 10.11H 40.26L 20.62H 20.62L 30.46H 7.5L 125.93H 10.38L 31.81H 27.86L 20.03H 50.16L 7.52H 191.95L 4.86H 39.91L 13.75H 32.65L 30.24H 14.89L 140.38H 17.52L 29.2H 44.55L 11.27H 203.94L 12.75H 38.1L 28.66H 14.48L 118.41H 9.7L 25.71H 20.66L 13.24H 32.24L 7.53H 196.32L 11.56H 41.1L 29.27H 16.04L 140.45H 18.34L 27.58H 43.31L 11.1H 207.42L 8.96H 48.41L 23.46H 25.26L 35.87H 7.71L 110.9H 7.38L 37.8H 25.98L 23.66H 50.11L 9.15H 214.44L 11.96H 43.03L 28.93H 18.04L 140.37H 17.01L 28.5H 41.81L 11.01H 194.11L 10.68H 38.43L 26.37H 15.86L 132.66H 16.74L 27.7H 42.29L 10.74H 201.67L 12.31H 38.05L 27.96H 14.69L 124.83H 8.11L 31.07H 25.61L 19.07H 46.59L 7.41H 190.96L 7.16H 50.93L 19.4H 29.99L 32.89H 11.27L 122.8H 6.86L 33.55H 23.83L 22.62H 46.54L 9.58H 209.1L 10.88H 44.29L 27.5H 18.74L 139.09H 16.9L 28.63H 43.05L 11.08H 199.56L 11.94H 37.89L 27.39H 14.78L 126.79H 14.41L 28.53H 38.39L 12.35H 204.31L 11.98H 41.49L 30.24H 15.95L 143.38H 18.84L 29.04H 44.58L 11.79H 219.64L 9.01H 52.08L 24.39H 28.63L 40.95H 9.11L 88.34H 7.37L 43.47H 25.08L 25.4H 48.12L 9.54H 203.68L 10.97H 40.95L 27.13H 17.4L 136.42H 16.15L 28.47H 41.62L 11.27H 199.26L 11.79H 38.52L 27.39H 14.47L 128.44H 15.15L 28H 39.95L 11.89H 205.83L 12.31H 41.58L 30.83H 15.83L 143.4H 19.16L 29.1H 44.49L 11.96H 221.38L 8.74H 52.12L 23.53H 28.41L 38.47H 8.33L 102.07H 7.12L 39.4H 24.98L 23.8H 47.39L 8.76H 198.49L 10.56H 40.21L 25.99H 17.59L 134.9H 15.6L 28.93H 41.24L 11.38H 194.52L 11.29H 38.35L 27.65H 15.08L 128.28H 18.1L 25.5H 39.95L 10.57H 192.2L 5.74H 53.57L 17.05H 32.71L 32.12H 12.37L 133.74H 20.36L 27.18H 43.13L 12.18H 202.65L 6.84H 53.36L 19.14H 31.72L 33.74H 12.29L 141.34H 17.23L 29.88H 41.69L 12.82H 210.48L 11.2H 43.99L 28.79H 18.01L 137.33H 18.18L 26.37H 41.32L 9.87H 183.05L 9.6H 41.51L 26.06H 18.24L 136.79H 18.04L 28.33H 44.25L 10.71H 206.65L 12.52H 39.58L 28.52H 16.13L 136.5H 11.44L 34.28H 32.33L 19.45H 56.43L 6.42H 217.22L 13.63H 41.69L 30.26H 17.9L 145.95H 16.05L 31.3H 41.35L 13.33H 209.47L 11.35H 43.38L 28.58H 17.46L 134.31H 16.9L 26.97H 39.83L 10.98H 196.08L 11.18H 41.28L 28.64H 16.69L 136.33H 18.14L 27.04H 41.54L 10.52H 193.55L 7.52H 45.62L 20.75H 25.16L 33.21H 7.98L 117.34H 8.75L 35.97H 28.97L 22.28H 52.77L 8.34H 220.21L 12.56H 43.55L 29.59H 18.59L 144.73H 16.54L 30.91H 41.69L 12.96H 206.24L 11.84H 41.64L 27.97H 16.6L 131H 16.06L 27.46H 40.73L 11.69H 202.02L 12.54H 41.38L 30.62H 15.91L 142.34H 20.11L 27.31H 46.14L 10.41H 221.12L 10.26H 49.06L 24.22H 27.13L 37.39H 8.79L 129H 8.21L 33.8H 24.53L 22.69H 43.3L 9.74H 184.35L 6.9H 43.22L 17.26H 23.85L 27.4H 8.9L 118.37H 12.58L 28.61H 31.82L 15.51H 51.22L 4.65H 105.93L.

[0112] Figure 45 is a graph showing the spectral transmittance exhibited by Example 16. According to Figure 45, the spectral transmittance of Example 16 is similar to that of Example 3 in general terms, including the stopband and free filter region.

[0113] Figure 46 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 16 and the period corresponding to the number m. As shown in Figure 46, the discrete Fourier transform spectrum of Example 16 is slightly different from that of Example 3, but it has discrete Fourier transform spectral peaks corresponding to the fundamental period p and period Λ1, respectively (Λ' 29 =(433-1) / 29=14.9≒p,Λ'8=(433-1) / 8=54.0≒Λ1)。 As shown in the film structure of Example 16, even if relatively large adjustments are made from the basic filter repeating structure, if peaks corresponding to the fundamental period p and period Λ1 appear in the discrete Fourier transform spectrum, the periodicity of the fundamental period p and the modulation period Λ1 is maintained, and the characteristics required for a notch filter are sufficiently obtained.

[0114] [Example 17] As Example 17, a structure similar to Example 3 was formed, except that the total number of layers L0 was changed from 561 to 343 (the number of repetitions r from 40 to 24), and the film thickness was adjusted more significantly. In Example 17, six additional layers were added to the medium side of the second basic filter repeating structure for the number of repetitions r=24. In other words, in Example 17, eight layers on the medium side were removed from the second basic filter repeating structure for the number of repetitions r=25. In the second basic filter repeating structure (basic period p=14), the center wavelength of the stopband is set to 1550 nm, so the modulation period is Λ1=50.

[0115] The film structure of the optical multilayer film 4 in Example 17 is shown below in terms of physical film thickness. 97.85L 14.01H 38.9L 30.45H 16.62L 145.58H 17.92L 29.61H 40.77L 13.63H 1472.77L 13.47H 41.7L 29.28H 19.73L 146.55H 15.28L 32.87H 39.92L 14.62H 211.96L 11.61H 45.91L 29.33H 17.91L 141.91H 23.92L 21.58H 288.26L 17.62H 33.8L 38.03H 10.89L 140.6H 28.2L 19.58H 300.26L 15.13H 39.7L 32.4H 16.31L 150.86H 16.9L 31.17H 43.41L 12.64H 214.6L 11.81H 44.99L 29.26H 17.6L 142.63H 24.85L 20.53H 282.57L 19.66H 26.89L 142.07H 14.93L 31.63H 42.33L 12.93H 210.74L 13H 43.2L 32.01H 15.33L 147.48H 20.92L 28.97H 45.17L 12.23H 218.1L 12.04H 47.05L 28.74H 20.84L 149.27H 13.56L 34.96H 36.88L 16.72H 287.06L 20.82H 24.27L 140.21H 16.67L 28.03H 42.15L 11.25H 191.7L 10.33H 40.4L 25.92H 17.44L 137.8H 16.98L 28.92H 45.2L 11.99H 205.73L 12.51H 42.25L 30.58H 16.44L 143.22H 16.73L 31.26H 39.33L 13.62H 286.36L 14.2H 38.33L 30.89H 17.06L 142.35H 16.88L 30.06H 43.79L 11.98H 210.51L 13.47H 40.52L 32.27H 13.66L 142.98H 28.03L 19.28H 202.82L 10.07H 49.12L 28.2H 19.71L 142.25H 19.12L 29.14H 45.8L 10.55H 216.95L 14.72H 39.16L 32.95H 14.2L 152.3H 20.05L 28.12H 44.13L 12.21H 236.04L 10.95H 45.54L 27.46H 21.9L 143.66H 15.64L 32.41H 40.84L 13.33H 215.42L 12.29H 42.38L 31.04H 14.89L 143.54H 26.34L 19.19H 204.77L 10.29H 47.82L 27.69H 20.21L 140.8H 20.54L 28.42H 47.33L 10.86H 211.03L 14.56H 39.29L 32.53H 14.62L 145.05H 17.98L 28.77H 38.69L 13.39H 285.24L 12.77H 39.05L 30.11H 16.35L 140.86H 16.14L 31.18H 40.72L 11.78H 202.15L 11.93H 40.4L 26.37H 16.24L 128.66H 14.5L 29.16H 39.89L 11.78H 202.75L 13.59H 39.33L 31.1H 13.95L 146.29H 25.2L 20.04H 289.74L 15.94H 36.41L 34.5H 12.68L 154.95H 17.59L 30.42H 43.53L 13.3H 213.65L 10.97H 47.47L 28.15H 20.69L 146.85H 15.31L 32.82H 40.64L 13.76H 208.22L 13.47H 41.33L 32.25H 14.09L 140.65H 28.06L 18.5H 206.62L 11.35H 44.14L 30.28H 17.41L 144.6H 18.71L 28.99H 48.54L 11.36H 209.75L 13.79H 42.81L 30.7H 17.28L 151.74H 15.58L 33.35H 37.24L 16.89H 304.42L 14.12H 41.04L 32.47H 16.88L 142.1H 17.96L 30.26H 43.38L 13.03H 639.07L 12.12H 42.36L 30.02H 17.65L 145.45H 17.58L 28.57H 44.33L 11.57H 215.09L 14.13H 39.67L 31.32H 15.93L 141.96H 17.83L 28.75H 38.91L 12.28H 278.12L 13.25H 39.22L 29.74H 17.25L 147.63H 14.53L 32.73H 40.54L 13.53H 213.56L 10.44H 46.34L 28.08H 19.18L 137.98H 17.18L 27.25H 41.22L 11.18H 193.57L 10.36H 44.21L 26.98H 19.31L 138.03H 20.99L 27.02H 44.87L 11.45H 221.33L 14.32H 40.48L 31.42H 18.06L 148.76H 16.12L 34.37H 37.97L 17.28H 299.72L 16.22H 38.25L 33.2H 15.49L 145.51H 19.48L 28.07H 43.6L 12.22H 534L.

[0116] Figure 47 is a graph showing the spectral transmittance exhibited by Example 17. As shown in Figure 47, the spectral transmittance of Example 17 is similar to that of Example 3 in terms of the overall structure, such as the stopband and free filter region, although the ripple is relatively large and appears more frequently due to the relatively small total number of layers L0 being 343.

[0117] Figure 48 is a graph showing the discrete Fourier transform spectrum of the film thickness sequence for Example 17 and the period corresponding to the number m. As shown in Figure 48, the discrete Fourier transform spectrum of Example 17 differs from that of Example 3, but has discrete Fourier transform spectral peaks corresponding to the fundamental period p and period Λ1, respectively (Λ' 35 =(343-1) / 35=9.8≒p,Λ'9=(343-1) / 9=38.0≒Λ1). However, with respect to the modulation period Λ1, a relatively large adjustment was made to make the center wavelength of the stopband 1550nm in the third basic filter repeating structure (basic period p=10), so the modulation period Λ1=35 corresponds more accurately. Examples 17As with the film structure shown, even if relatively large adjustments are made to the basic filter repeating structure, if peaks corresponding to the fundamental period p and period Λ1 appear in the discrete Fourier transform spectrum, the periodicity of the fundamental period p and the modulation period Λ1 is maintained, and the characteristics required for a notch filter are obtained.

[0118] [Examples of periodicity criteria: 400~1200nm] A notch filter can achieve better performance if it meets the following conditions. (1-1) The free filter region includes a wavelength range of 400 nm to 1200 nm. (1-2) The stopband is formed in the wavelength range of 600 nm to 1200 nm. (1-3) The average transmittance in the free filter region is 85% or higher. Note that the transmittance in the stopband is not considered in the calculation of the average transmittance in the free filter region. The wavelength range of the stopband may be the wavelength range between each adjacent ripple (minimum transmittance) on both sides of it. (1-4) In the discrete Fourier transform spectra of the film thickness sequence, the following peaks exist for each fundamental period p of the first fundamental filter structure (fundamental period p=6), the second fundamental filter structure (fundamental period p=14), and the third fundamental filter structure (fundamental period p=10). That is, spectral number m best corresponds to period 6. f1 and its number m f1 Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one. f1 -2,m f1 -1,m f1 +1,m f1 The spectral number m best corresponds to +2 and period 14. f2 and its number m f2 Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one. f2 -2,m f2 -1,m f2 +1,m f2 The spectral number m best corresponds to +2 and period 10. f3 and its number m f3 Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one.f3 -2, m f3 -1, m f3 +1, m f3 There is a peak at least in any of +2. It may be an additional condition that the spectral intensity of the peak is greater than the spectral intensity at spectral number m = 1, that is, the spectral intensity when showing vibrations over all layer numbers and not showing periodicity. Hereinafter, "m f1 -1, m f1 +1" is expressed as "m f1 ±1", and "m f1 -2, m f1 +2" may be expressed as "m f1 ±2", and may be expressed similarly for other spectral numbers. (1 - 5) In the discrete Fourier transform spectrum of the film thickness sequence, the following peaks exist with respect to the modulation period Λ k . That is, the spectral numbers m k that best correspond to the modulation period Λ m1 , m m2 , m m3 determined according to the periods (three types of 6, 14, 10) and the center wavelength of the stop band, and the spectral numbers m m1 , m m2 , m m3 one before and one after each of these numbers m m1 ±1, m m2 ±1, m m3 ±1, among which there is a peak in the spectral numbers between the smallest number m min and the largest number m max . It may be an additional condition that the spectral intensity of the peak is greater than the spectral intensity at spectral number m = 1.

[0119] The application of the above conditions to the above-described examples is shown in the following Table 1. Also, the application of the above conditions to the above-described comparative examples is shown in the following Table 2. In Table 2, (1 - 1) is omitted, and the conditions (1 - 2) to (1 - 5) are described as (2) to (5) in order.

[0120]

Table 1

[0121] [Table 2]

[0122] First, (1-1) Examples 1 and 2 and Comparative Examples 1 and 2 have a free filter region that includes a wavelength range of 400 nm to 1200 nm. Cases where the free filter region includes a wavelength range of 400 nm to 1800 nm will be described later.

[0123] Next, in all of Examples 1 and 2 and Comparative Examples 1 and 2, (1-2) the stopband is formed within a wavelength range of 600 nm to 1200 nm (OK).

[0124] Next, in all of Examples 1 and 2 and Comparative Examples 1 and 2, (1-3) the average transmittance in the free filter region is 85% or higher (OK).

[0125] On the other hand, in Examples 1 and 2, (1-4) there is a peak related to the fundamental period p (OK), and (1-5) the modulation period Λ k A peak exists related to (OK). The spectral intensities of these peaks are all greater than the spectral intensity of number m=1 (all additional conditions OK). In contrast, in comparative examples 1 and 2, (1-4) there is no peak related to the fundamental period p (×), and (1-5) the modulation period Λ k There is no peak related to this (×). In Comparative Example 2, there are two stopbands and two corresponding modulation periods Λ1 and Λ2, therefore the spectral number m m2 There can be two (m m2a ,m m2b ), and spectral number m m3 There can be two (m m3a ,m m3b ).

[0126] [Examples of periodicity criteria: 400~1800nm] A notch filter can achieve better performance if it meets the following conditions. (2-1) The free filter region includes a wavelength range of 400 nm to 1800 nm. (2-2) The stopband is formed in the wavelength range of 600 nm to 1800 nm. (2-3) The average transmittance in the free filter region is 85% or higher. Note that the transmittance in the stopband is not considered in the calculation of the average transmittance in the free filter region. The wavelength range of the stopband may be the wavelength range between each adjacent ripple (minimum transmittance) on both sides of it. (2-4) In the discrete Fourier transform spectra of the film thickness sequence, the following peaks exist for each fundamental period p of the second fundamental filter structure (fundamental period p=14) and the third fundamental filter structure (fundamental period p=10). That is, spectral number m best corresponds to period 14. f2 and its number m f2 Spectral numbers m of ±1, ±2 f2 ±1,m f2 The spectral number m best corresponds to ±2 and period 10. f3 and its number m f3 Spectral numbers m of ±1, ±2 f3 ±1,m f3 A peak exists at least one of ±2. An additional condition may be that the spectral intensity of this peak is greater than the spectral intensity at spectral number m=1. (2-5) In the discrete Fourier transform spectrum of the film thickness sequence, the modulation period Λ k The following peaks exist in relation to this: namely, the modulation period Λ, which is determined by the fundamental period p (two types: 14 and 10) and the center wavelength of the stopband. k The corresponding spectral number m m2 ,m m3 and each of its numbers m m2 ,m m3 The spectral number m of ±1 m2 ±1,m m3 The smallest number among ±1 is m min and the largest number m max A peak exists at spectral indices between m=1 and m=1. An additional condition may be that the spectral intensity of this peak is greater than the spectral intensity at spectral indice m=1.

[0127] The fitting of the above conditions to the above embodiments is shown in Tables 3-5 below.

[0128]

Table 3

[0129]

Table 4

[0130]

Table 5

[0131] First, in Examples 3 to 17, the free filter region includes a wavelength range of 400 nm or more and 1800 nm or less.

[0132] Next, in any of Examples 3 to 17, (2-2) a stop band is formed within a wavelength range of 600 nm or more and 1800 nm or less (OK).

[0133] Subsequently, in Examples 3 to 17, except for Example 14, (2-3) the average transmittance in the free filter region is 85% or more (OK). In Example 14, the average transmittance in the free filter region is 84.7%, slightly less than 85% (△).

[0134] On the other hand, in Examples 3 to 17, (2-4) there is a peak regarding the basic period p (OK), and (2-5) there is a peak regarding the modulation period Λ k (OK). The spectral intensities of these peaks are all greater than the spectral intensity of spectrum number m = 1, except for Example 17 (each additional condition OK). In Example 17, the spectral intensity of the peak of spectrum number m = 8 is smaller than the spectral intensity of spectrum number m = 1 ((2-5) additional condition ×). In Examples 8 and 9, there are two stop bands and two corresponding modulation periods Λ1 and Λ2 exist, so the spectrum number mm2 There can be two (m m2a ,m m2b ), and spectral number m m3 There can be two (m m3a ,m m3b ). The smallest number m min and the largest number m max is, m m2a ,m m2b ,m m3a ,m m3b All m m* (* represents any symbol) is taken into consideration when making the decision.

[0135] For reference, the application of the conditions to Example 16 will be explained in more detail. As in Example 16, when the center wavelength of the stopband is set to 1550 nm, the second basic filter repeating structure (basic period p=14) is modulated with a period of 50, and the third basic filter repeating structure (basic period p=10) is modulated with a period of 35. Therefore, in Example 16, first, as shown in (2-4), the number m that best corresponds to the fundamental period p=14 is determined. f2 =31(Λ' 31 =(433-1) / 31=13.9), and that number m f2 A peak in spectral intensity exists at one of the spectral numbers 29, 30, 32, or 33 in ±1 or ±2 (a peak exists at number m=29; Λ'). 29 =(433-1) / 29=14.9), which maintains the periodicity of the basic period p=14, and is preferable for improving the characteristics of the notch filter. Furthermore, in Example 16, as shown in (2-5), the spectral number m best corresponds to the modulation period of 50. m2 =9(Λ'9=(433-1) / 9=48), and the m on both sides of it m2 ±1 = 8, 10, and spectral number m corresponding to the modulation period of 35. m3 =12, and the m on both sides m3 The smallest number among ±1=11,13 is m min =8(=m m2 -1) and the largest number m max =13(=mm3 Between +1) there are peaks in spectral intensity (peaks at numbers m=8,10,12; Λ'8=(433-1) / 8=54.0,Λ' 10 =(433-1) / 10=43.2,Λ' 12 =(433-1) / 12=36.0), which is preferable as it provides better periodicity in the film thickness sequence. In Example 16, since there is periodicity related to the modulation period 50, the periodicity related to the modulation period 35 may be small or even absent. In fact, in Example 16, the condition (2-5) related to the modulation period 35, i.e., the spectral number m corresponding to the modulation period 35, is met. m3 =12, and the m on both sides m3 In the case of ±1=11,13, although a peak in spectral intensity exists at number m=12, its spectral intensity is smaller than that of number m=1. Furthermore, it is acceptable to observe only the periodicity related to the modulation period of 35, or to strongly observe both the periodicity related to the modulation periods of 50 and 35.

[0136] [Summary of Examples, etc.] Examples 1 to 17 are notch filters having a free filter region which is a wavelength range in which light is transmitted, and one or more stopbands which are arranged between the lower and upper limits of the free filter region and suppress the transmission of light in a predetermined wavelength range, and comprising a substrate 2 and an optical multilayer film 4 which is formed directly or indirectly on the substrate surface M which is the surface of the substrate 2. The optical multilayer film 4 is formed based on a basic filter repeat structure which is obtained by repeating a basic filter structure in which a low refractive index layer L made of a low refractive index material and a high refractive index layer H made of a high refractive index material are arranged alternately multiple times, and the film thickness of each layer in the optical multilayer film 4 corresponds to a modulated film thickness sequence obtained by adding modulation at a period different from the basic period based on the number of layers of the basic filter structure to a basic film thickness sequence obtained by arranging the film thickness of each layer in the basic filter repeat structure in order from the substrate 2 side. Therefore, Examples 1 to 17 have a wider free filter region. Also, Examples 1 to 17 have a narrower wavelength stopband.

[0137] Furthermore, in Examples 8 and 9, there are multiple modulation periods. Therefore, Examples 8 and 9 have multiple stopbands with narrower wavelengths. Furthermore, in Examples 1 to 17, the value d is the nth term of the modulated film thickness sequence corresponding to the film thickness of the nth layer counted from the substrate 2 side in the optical multilayer film 4. n In the basic filter repeating structure, the nth term of the basic film thickness sequence, which corresponds to the film thickness of the nth layer counted from the substrate 2 side, is D. n (With L0 as the total number of terms, n=1,2,...,L0), and the amplitude, period, and phase of the modulation related to the k-th stopband are a in order. k , Λ k , φ k If this is the case (where k=1,2,···,u is the number of stopbands formed), it can be expressed by equation (2) above. Therefore, modulation is performed more appropriately.

[0138] In addition, in Examples 2, 4, 7, 9, 11, 13, and 15-17, the film thickness of each layer in the optical multilayer film 4 follows an adjusted modulated film thickness sequence obtained by adjusting the values ​​of one or more terms in the modulated film thickness sequence. Thus, a notch filter is provided in which adjustments such as ripple reduction in the free filter region have been made. Furthermore, in Examples 1 to 17, the modulation period corresponds to the center wavelength of the stopband. Therefore, the modulation period can be set more appropriately, and the design becomes easier.

[0139] Furthermore, in Examples 1 and 2, the free filter region includes a wavelength range of 400 nm to 1200 nm, and the basic filter repeat structure is one of the following: a first basic filter repeat structure which repeats a basic filter structure with a basic period of 6, a second basic filter repeat structure which repeats a basic filter structure with a basic period of 14, or a third basic filter repeat structure which repeats a basic filter structure with a basic period of 10. In addition, the basic filter structure with a basic period of 6 has an optical film thickness of 0.25 times the original, with the first layer being a low refractive index layer, starting from the substrate 2 side, in the order of "1.17 0.32 0.32 2.31 0.32 0.32 1.17". Furthermore, the basic filter structure with a fundamental period of 14 has an optical film thickness of 0.25 times the original value, with the first layer being a low refractive index layer, starting from the substrate 2 side, and the layers being "1.10 0.14 0.48 0.30 0.28 0.50 0.12 2.16 0.12 0.50 0.28 0.30 0.48 0.14 1.10". Moreover, the basic filter structure with a fundamental period of 10 has an optical film thickness of 0.25 times the original value, with the first layer being a low refractive index layer, starting from the substrate 2 side, and the layers being "1.26 0.22 0.51 0.52 0.21 2.53 0.21 0.52 0.51 0.22 1.26". Therefore, designing notch filters becomes easier.

[0140] Furthermore, in Examples 3 to 17, the free filter region includes a wavelength range of 400 nm to 1800 nm, and the basic filter repeat structure is either a second basic filter repeat structure which repeats a basic filter structure with a basic period of 14, or a third basic filter repeat structure which repeats a basic filter structure with a basic period of 10. In addition, the basic filter structure with a basic period of 14 has an optical film thickness of 0.25 times the following values, with the first layer being a low refractive index layer, starting from the substrate 2 side: "1.10 0.14 0.48 0.30 0.28 0.50 0.12 2.16 0.12 0.50 0.28 0.30 0.48 0.14 1.10". Furthermore, the basic filter structure with a fundamental period of 10 has optical film thicknesses of 0.25 times the values ​​of "1.26 0.22 0.51 0.52 0.21 2.53 0.21 0.52 0.51 0.22 1.26", with the first layer being a low refractive index layer, starting from the substrate 2 side. Therefore, designing notch filters becomes easier.

[0141] In addition, Examples 1 and 2 have a free filter region which is a wavelength range in which light is transmitted, and one or more stopbands which are arranged between the lower and upper limits of the free filter region and suppress the transmission of light in a predetermined wavelength range, and comprise a substrate 2 and an optical multilayer film 4 which is formed directly or indirectly on the substrate surface M which is the surface of the substrate 2. The optical multilayer film 4 alternates between a low refractive index layer L made of a low refractive index material and a high refractive index layer H made of a high refractive index material, and satisfies all of the following conditions. (1-1) The free filter region includes a wavelength range of 400 nm to 1200 nm. (1-2) The stopband is formed in the wavelength range of 600 nm to 1200 nm. (1-3) The average transmittance in the free filter region is 85% or higher. (1-4) In the discrete Fourier transform spectrum of the film thickness sequence obtained by arranging the film thickness of each layer in the optical multilayer film 4 in order from the substrate 2 side, the spectral number m that best corresponds to period 6 f1 and its number m f1 Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one.f1 -2,m f1 -1,m f1 +1,m f1 The spectral number m best corresponds to +2 and period 14. f2 and its number m f2 Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one. f2 -2,m f2 -1,m f2 +1,m f2 The spectral number m best corresponds to +2 and period 10. f3 and its number m f3 Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one. f3 -2,m f3 -1,m f3 +1,m f3 There is a peak at least at +2. (1-5) The spectral number m that best corresponds to the modulation period determined by the three types of periods 6, 14, and 10 and the center wavelength of the stopband in the discrete Fourier transform spectrum. m1 ,m m2 ,m m3 and each of its numbers m m1 ,m m2 ,m m3 The spectral number m of the one preceding and one succeeding one. m1 -1,m m1 +1,m m2 -1,m m2 +1,m m3 -1,m m3 The smallest number among +1, m min and the largest number m max A peak exists in the spectral number between [the specified range]. Therefore, Examples 1 and 2 have a wider free filter region. Also, Examples 1 and 2 have a narrower wavelength stopband.

[0142] Furthermore, in Examples 1 and 2, the additional condition that the peak spectral intensity is greater than the spectral intensity at spectral number m=1 is also satisfied under conditions (1-4) and (1-5). Therefore, better periodicity of the film thickness sequence is obtained, and at least one of a wider free filter region and a narrower wavelength stopband is obtained.

[0143] Furthermore, Examples 3-13 and 15-17 have a free filter region which is a wavelength range that transmits light, and one or more stopbands which are arranged between the lower and upper limits of the free filter region and suppress the transmission of light in a predetermined wavelength range, and comprise a substrate 2 and an optical multilayer film 4 which is formed directly or indirectly on the substrate surface M which is the surface of the substrate 2. The optical multilayer film 4 alternates between a low refractive index layer L made of a low refractive index material and a high refractive index layer H made of a high refractive index material, and satisfies all of the following conditions. (2-1) The free filter region includes a wavelength range of 400 nm to 1800 nm. (2-2) The stopband is formed in the wavelength range of 600 nm to 1800 nm. (2-3) The average transmittance in the free filter region is 85% or higher. (2-4) In the discrete Fourier transform spectrum of the film thickness sequence obtained by arranging the film thickness of each layer in the optical multilayer film 4 in order from the substrate 2 side, the spectral number m that best corresponds to period 14 f2 and its number m f2 Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one. f2 -2,m f2 -1,m f2 +1,m f2 The spectral number m best corresponds to +2 and period 10. f3 and its number m f3 Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one. f3 -2,m f3 -1,m f3 +1,m f3 There is a peak at least at +2. (2-5) In the discrete Fourier transform spectrum, the spectral number m best corresponds to the modulation period determined by the two types of periods, 14 and 10, and the center wavelength of the stopband. m2 ,m m3 and each of its numbers m m2 ,m m3 The spectral number m of the one preceding and one succeeding one. m2 -1,m m2 +1,m m3 -1,m m3The smallest number among +1, m min and the largest number m max A peak exists in the spectral number between [the specified range]. Therefore, Examples 3-13 and 15-17 have a wider free filter area. 3~13,15~17 It has a narrower wavelength stopband.

[0144] Furthermore, Examples 3 to 16 also satisfy the additional condition that, under conditions (2-4) and (2-5), the spectral intensity of the peak is greater than the spectral intensity at spectral number m=1. Also, Example 17 also satisfies the additional condition that, under condition (2-4), the spectral intensity of the peak is greater than the spectral intensity at spectral number m=1. Therefore, better periodicity of the film thickness sequence is obtained, resulting in at least one of a wider free filter region and a narrower stopband. [Explanation of symbols]

[0145] 1. Notch filter, 2. Substrate, 4. Optical multilayer film, B1. First basic filter structure (closest to the substrate), B2. Second basic filter structure, H. High refractive index layer, L. Low refractive index layer, M. Substrate surface.

Claims

1. A notch filter having a free filter region which is a wavelength range that transmits light, and a plurality of stopbands which are arranged between the lower and upper limits of the free filter region and suppress the transmission of light in a predetermined wavelength range, Substrate and An optical multilayer film formed directly or indirectly on the substrate surface, which is the surface of the substrate, It is equipped with, The optical multilayer film is formed based on a repeating basic filter structure, which is obtained by repeating a basic filter structure multiple times, in which a low refractive index layer made of a low refractive index material and a high refractive index layer made of a high refractive index material are alternately arranged. The film thickness of each layer in the optical multilayer film corresponds to a modulated film thickness sequence obtained by modulating a basic film thickness sequence, which is obtained by arranging the film thicknesses of each layer in the basic filter repeating structure in order from the substrate side, with a modulation period different from the basic period based on the number of layers in the basic filter structure. Multiple modulation periods exist. The aforementioned free filter region includes a wavelength range of 400 nm to 1200 nm. The basic filter repeating structure is one of the following: a first basic filter repeating structure which repeats the basic filter structure having a basic period of 6; a second basic filter repeating structure which repeats the basic filter structure having a basic period of 14; or a third basic filter repeating structure which repeats the basic filter structure having a basic period of 10. A notch filter characterized by the following features.

2. The basic filter structure, having a basic period of 6, has the following optical film thicknesses, starting from the substrate side, with the first layer being the low refractive index layer and the next layer being 0.25 times the original thickness. １．１７ ０．３２ ０．３２ ２．３１ ０．３２ ０．３２ １．１７ The notch filter according to feature 1.

3. A notch filter having a free filter region which is a wavelength range that transmits light, and a plurality of stopbands which are arranged between the lower and upper limits of the free filter region and suppress the transmission of light in a predetermined wavelength range, Substrate and An optical multilayer film formed directly or indirectly on the substrate surface, which is the surface of the substrate, It is equipped with, The optical multilayer film is formed based on a repeating basic filter structure, which is obtained by repeating a basic filter structure multiple times, in which a low refractive index layer made of a low refractive index material and a high refractive index layer made of a high refractive index material are alternately arranged. The film thickness of each layer in the optical multilayer film corresponds to a modulated film thickness sequence obtained by modulating a basic film thickness sequence, which is obtained by arranging the film thicknesses of each layer in the basic filter repeating structure in order from the substrate side, with a modulation period different from the basic period based on the number of layers in the basic filter structure. Multiple modulation periods exist. The aforementioned free filter region includes a wavelength range of 400 nm to 1800 nm. The aforementioned basic filter repeating structure is either a second basic filter repeating structure obtained by repeating the aforementioned basic filter structure having a basic period of 14, or a third basic filter repeating structure obtained by repeating the aforementioned basic filter structure having a basic period of 10. A notch filter characterized by the following features.

4. The basic filter structure, having a basic period of 14, has the following optical film thicknesses, starting from the substrate side, with the first layer being the low refractive index layer and the next layer being 0.25 times the original thickness. １．１０ ０．１４ ０．４８ ０．３０ ０．２８ ０．５０ ０．１２ ２．１６ ０．１２ ０．５０ ０．２８ ０．３０ ０．４８ ０．１４ １．１０ A notch filter according to any one of claims 1 to 3.

5. The basic filter structure, having a basic period of 10, has the following optical film thicknesses, starting from the substrate side, with the first layer being the low refractive index layer and the next layer being 0.25 times the original thickness. １．２６ ０．２２ ０．５１ ０．５２ ０．２１ ２．５３ ０．２１ ０．５２ ０．５１ ０．２２ １．２６ A notch filter according to any one of claims 1 to 4.

6. The value d of the nth term in the modulated film thickness sequence, which corresponds to the film thickness of the nth layer from the substrate side in the optical multilayer film. ｎ The nth term of the basic film thickness sequence, which corresponds to the film thickness of the nth layer counted from the substrate side in the basic filter repeating structure, is D ｎ (The total number of terms is L ０ Let n = 1, 2, ..., L ０ ), the amplitude, period, and phase of the modulation related to the k-th stopband are a in order. ｋ , Λ ｋ , φ ｋ If this is the case (where u is the number of barriers formed, k = 1, 2, ..., u), then it is expressed by the following equation (A), where u is 2 or more. [Math 1] A notch filter according to any one of claims 1 to 5.

7. The film thickness of each layer in the optical multilayer film is determined according to an adjusted modulated film thickness sequence obtained by adjusting the values ​​of one or more terms in the modulated film thickness sequence. A notch filter according to any one of claims 1 to 6.

8. The modulation period corresponds to the central wavelength of the stopband. A notch filter according to any one of claims 1 to 7.

9. A notch filter having a free filter region which is a wavelength range that transmits light, and one or more stopbands which are arranged between the lower and upper limits of the free filter region and which suppress the transmission of light in a predetermined wavelength range, Substrate and An optical multilayer film formed directly or indirectly on the substrate surface, which is the surface of the substrate, It is equipped with, The optical multilayer film has alternating low-refractive-index layers made of low-refractive-index material and high-refractive-index layers made of high-refractive-index material, and satisfies all of the following conditions: (1-1) The free filter region includes the entire wavelength range of 400 nm to 1200 nm. (1-2) The stopband is formed in a wavelength range of 600 nm to 1200 nm. (1-3) The average transmittance in the free filter region is 85% or more. (1-4) In the discrete Fourier transform spectrum of the film thickness sequence in which the film thicknesses of the respective layers in the optical multilayer film are arranged in order from the substrate side, the spectrum number m that best corresponds to the period 6 ｆ１ and its number m ｆ１ for the spectrum numbers m two before, one before, one after, and two after ｆ１ -2, m ｆ１ -1, m ｆ１ +1, m ｆ１ +2, the spectrum number m that best corresponds to the period 14 ｆ２ and its number m ｆ２ for the spectrum numbers m two before, one before, one after, and two after ｆ２ -2, m ｆ２ -1, m ｆ２ +1, m ｆ２ +2, and the spectrum number m that best corresponds to the period 10 ｆ３ and its number m ｆ３ for the spectrum numbers m two before, one before, one after, and two after ｆ３ -2, m ｆ３ -1, m ｆ３ +1, m ｆ３ +2, there is a peak in at least any one of them (1-5) The spectral number m that best corresponds to the modulation period determined in the discrete Fourier transform spectrum according to the three periods 6, 14, and 10 and the center wavelength of the stopband. ｍ１ ,m ｍ２ ,m ｍ３ and each of its numbers m ｍ１ ,m ｍ２ ,m ｍ３ The spectral number m of the one preceding and one succeeding one. ｍ１ -1, m ｍ１ +1,m ｍ２ -1, m ｍ２ +1,m ｍ３ -1, m ｍ３ The smallest number among +1, m ｍｉｎ and the largest number m ｍａｘ A peak exists in the spectral number between [the specified range]. A notch filter characterized by the following features.

10. The conditions in (1-4) above have an additional condition that the spectral intensity of the peak is greater than the spectral intensity at spectral number m=1. The notch filter according to feature 9.

11. The conditions in (1-5) above have an additional condition that the spectral intensity of the peak is greater than the spectral intensity at spectral number m=1. The notch filter according to claim 9 or 10, characterized in that it is a notch filter.

12. A notch filter having a free filter region which is a wavelength range that transmits light, and one or more stopbands which are arranged between the lower and upper limits of the free filter region and which suppress the transmission of light in a predetermined wavelength range, Substrate and An optical multilayer film formed directly or indirectly on the substrate surface, which is the surface of the substrate, It is equipped with, The optical multilayer film has alternating low-refractive-index layers made of low-refractive-index material and high-refractive-index layers made of high-refractive-index material, and satisfies all of the following conditions: (2-1) The free filter region includes the entire wavelength range of 400 nm to 1800 nm. (2-2) The stopband is formed in a wavelength range of 600 nm to 1800 nm. (2-3) The average transmittance in the free filter region is 85% or more. (2-4) In the discrete Fourier transform spectrum of the film thickness sequence obtained by arranging the film thickness of each layer in the optical multilayer film in order from the substrate side, the spectral number m that best corresponds to period 14 ｆ２ and its number m ｆ２ Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one. ｆ２ -2,m ｆ２ -1, m ｆ２ +1,m ｆ２ The spectral number m best corresponds to +2 and period 10. ｆ３ and its number m ｆ３ Spectral numbers m two steps prior, one step prior, one step after, and two steps after the previous one. ｆ３ -2,m ｆ３ -1, m ｆ３ +1,m ｆ３ A peak exists at least in one of the following locations: +2. (2-5) The spectral number m that best corresponds to the modulation period determined in the discrete Fourier transform spectrum, which is determined according to the two types of periods, 14 and 10, and the center wavelength of the stopband. ｍ２ ,m ｍ３ and each of its numbers m ｍ２ ,m ｍ３ The spectral number m of the one preceding and one succeeding one. ｍ２ -1, m ｍ２ +1,m ｍ３ -1, m ｍ３ The smallest number among +1, m ｍｉｎ and the largest number m ｍａｘ A peak exists in the spectral number between [the specified range]. A notch filter characterized by the following features.

13. The condition in (2-4) above has an additional condition that the spectral intensity of the peak is greater than the spectral intensity at spectral number m=1. The notch filter according to feature 12.

14. The condition in (2-5) above has an additional condition that the spectral intensity of the peak is greater than the spectral intensity at spectral number m=1. The notch filter according to claim 12 or 13.

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