Etalon, etalon device, etalon control method, and refractive index determination method

Abstract

An etalon (10) according to the present invention allows light to be incident from a direction different from the direction perpendicular to an incident surface, and to be emitted from an emission surface facing the incident surface, and comprises: a first end surface provided on the incident surface side; and a second end surface provided on the emission surface side and facing the first end surface, wherein a dielectric substance, in which the distribution of refractive indices is set so that the lateral displacement of the light is smaller compared to an etalon (20) having uniform refractive index distribution under a condition in which the optical path lengths of the light are the same, is provided between the first end surface and the second end surface.　Consequently, the etalon according to the present invention can provide excellent wavelength controllability.

Description

[Technical field]

[0001] The present invention relates to an etalon having excellent wavelength controllability, an etalon device, an etalon control method, and a method for determining a refractive index. [Background technology]

[0002] Etalons, which are optical elements, are used as optical filters in fields such as wavelength division multiplexing (WDM) transmission optical communications and precision measurement, as wavelength selection filters, and as interference filters for narrowing wavelength bands. Laser light is incident on an etalon, and wavelength-selected light or wavelength-narrowed light is emitted. A typical etalon has a uniform refractive index and operates using the interference of light between the entrance surface and exit surface (reflection surface) (Non-Patent Document 1).

[0003] When inserting an etalon so that it passes through the optical axis in the laser resonator to select the resonant wavelength, if the angle of incidence of light to the etalon (the angle between the optical axis and the normal vector of the etalon's incidence surface) is set to 0 degrees, an unnecessary resonator will be formed by the light reflected from the etalon's incidence surface, and the laser oscillation wavelength may not be the desired one.

[0004] Therefore, normally, the angle of incidence on the etalon is not set to 0 degrees, and it is necessary to make the light incident at a predetermined angle. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Pierre Jacquinot, “The Luminosity of Spectrometers with Prisms, Gratings, or Fabry-Perot Etalons,” Journal of the Optical Society of America, Vol. 44, Issue 10, pp. 761-765, 1954. Summary of the Invention [Problem to be solved by the invention]

[0006] However, if the incident angle is too large, the optical axis is shifted due to the lateral shift of the light beam that is multiple-reflected inside the etalon, and the wavelength controllability is lost due to the change in the optical path length inside the laser resonator. In order to suppress this loss of wavelength controllability, it becomes necessary to fine-tune the arrangement of the optical components inside the laser resonator, which requires effort, time, and cost. Therefore, it is necessary to suppress the lateral shift of the light beam that is multiple-reflected inside the etalon and suppress the loss of the wavelength stability and controllability of the etalon. [Means for solving the problem]

[0007] In order to solve the above-mentioned problems, an etalon according to the present invention is an etalon in which light is incident from a direction different from a perpendicular direction to an incident surface and exits from an exit surface opposed to the incident surface, the etalon having a first end face on the incident surface side and a second end face on the exit surface side opposed to the first end face, and including a dielectric material having a refractive index distribution set so that lateral deviation of the light is smaller between the first end face and the second end face as compared to a uniform refractive index distribution etalon under a condition in which the optical path length of the light is equivalent. When the distance from the first end face to the second end face in a direction perpendicular to the first end face is defined as x, the refractive index of the dielectric changes as a quadratic function of x, and the minimum value of the refractive index in the direction perpendicular to the first end face is n 0 , the refractive index is n 0 The value of x is x 0 , the coefficient of the refractive index distribution is β, the optical path length is L, the thickness of the etalon is d, and the incident angle of the light to the incident surface is θ′. i Then, equation (41) is satisfied.

[0009] The etalon according to the present invention is Is, A dielectric material having a refractive index that changes with application of a voltage from the first end face to the second end face. Good .

[0010] Furthermore, a method for controlling an etalon according to the present invention is a method for controlling an etalon in which light is incident from a direction different from a perpendicular direction to an incident surface and exits from an exit surface opposite the incident surface, the etalon comprising a dielectric having a first end face on the incident surface side and a second end face on the exit surface side opposite the first end face, and a voltage is applied between the first end face and the second end face to change the refractive index of the dielectric between the first end face and the second end face, thereby reducing the distance between a point on the exit surface from which the light exits and a point on the exit surface from which light is incident from a direction perpendicular to the incident surface and exits.

[0011] Furthermore, a method for determining a refractive index according to the present invention is a method for determining a refractive index of a first dielectric in a first etalon, in which light is incident from a direction different from a perpendicular direction to an incident surface and exits from an exit surface opposite to the incident surface, and includes the steps of: converting the refractive index of a second dielectric of a second etalon having a uniform refractive index distribution so that the optical path length of the second etalon is equivalent to the optical path length of the first etalon; deriving a lateral shift of the second etalon using the converted refractive index; deriving a lateral shift of the first etalon; comparing the lateral shift of the first etalon with the lateral shift of the second etalon; and deriving the refractive index of the first dielectric so that the lateral shift of the first etalon is smaller than the lateral shift of the second etalon. Effect of the Invention

[0012] According to the present invention, it is possible to provide an etalon having excellent wavelength controllability, an etalon device, an etalon control method, and a refractive index determination method. [Brief description of the drawings]

[0013] [Figure 1] FIG. 1 is a schematic side view of an etalon according to a first embodiment of the present invention and a diagram showing a refractive index distribution. [Diagram 2] FIG. 2 is a schematic side view of an etalon having a uniform refractive index distribution and a diagram showing the refractive index distribution. [Figure 3A]FIG. 3A is a diagram for explaining the effect of the etalon according to the first embodiment of the present invention. [Figure 3B] FIG. 3B is a diagram for explaining the effect of the etalon according to the first embodiment of the present invention. [Figure 3C] FIG. 3C is a diagram for explaining the effect of the etalon according to the first embodiment of the present invention. [Figure 3D] FIG. 3D is a diagram for explaining the effect of the etalon according to the first embodiment of the present invention. [Figure 4A] FIG. 4A is a diagram for explaining the effect of the etalon according to the first embodiment of the present invention. [Figure 4B] FIG. 4B is a diagram for explaining the effect of the etalon according to the first embodiment of the present invention. [Figure 5A] FIG. 5A is a schematic side view showing the configuration of an etalon according to a second embodiment of the present invention. [Figure 5B] FIG. 5B is a perspective view showing the configuration of an etalon according to the second embodiment of the present invention. [Figure 5C] FIG. 5C is a schematic side view showing the configuration of an etalon according to the third embodiment of the present invention. [Figure 5D] FIG. 5D is a perspective view showing the configuration of an etalon according to the third embodiment of the present invention. [Figure 5E] FIG. 5E is a schematic side cross-sectional view showing the configuration of an etalon according to the fourth embodiment of the present invention. [Figure 6] FIG. 6 is a diagram for explaining the operation of the etalons according to the second to fourth embodiments of the present invention. [Figure 7A] FIG. 7A is a diagram for explaining the effects of the etalons according to the second to fourth embodiments of the present invention. [Figure 7B] FIG. 7B is a diagram for explaining the effect of the etalons according to the second to fourth embodiments of the present invention. [Figure 7C] FIG. 7C is a diagram for explaining the effect of the etalons according to the second to fourth embodiments of the present invention. [Figure 7D]FIG. 7D is a diagram for explaining the effect of the etalons according to the second to fourth embodiments of the present invention. [Figure 8] FIG. 8 is a diagram for explaining the effects of the etalons according to the second to fourth embodiments of the present invention. [Figure 9A] FIG. 9A is a diagram for explaining the effects of the etalons according to the second to fourth embodiments of the present invention. [Figure 9B] FIG. 9B is a diagram for explaining the effect of the etalons according to the second to fourth embodiments of the present invention. [Figure 9C] FIG. 9C is a diagram for explaining the effect of the etalons according to the second to fourth embodiments of the present invention. [Figure 9D] FIG. 9D is a diagram for explaining the effect of the etalons according to the second to fourth embodiments of the present invention. [Figure 10A] FIG. 10A is a diagram for explaining the effects of the etalons according to the second to fourth embodiments of the present invention. [Figure 10B] FIG. 10B is a diagram for explaining the effect of the etalons according to the second to fourth embodiments of the present invention. [Figure 10C] FIG. 10C is a diagram for explaining the effect of the etalons according to the second to fourth embodiments of the present invention. [Figure 11] FIG. 11 is a schematic diagram showing a configuration of an etalon device according to the fifth embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] <First embodiment> An etalon according to a first embodiment of the present invention will be described with reference to FIGS. 1 to 4B.

[0015] The etalon 10 according to the present embodiment suppresses lateral shift of light passing through the etalon by changing the refractive index of the dielectric material used in the etalon. Here, "lateral shift" refers to the distance between the exit point on the exit surface and the intersection point of the exit surface and a line passing through the entrance point on the entrance surface and perpendicular to the entrance surface, when light is incident on the entrance surface of the etalon at a predetermined angle (not including the direction perpendicular to the entrance surface) and exits from the exit surface.

[0016] Here, the distribution of the refractive index of the dielectric is set so that the lateral shift of the etalon 10, whose refractive index varies, is smaller than the lateral shift of the etalon with a uniform refractive index (hereinafter, "uniform refractive index distribution etalon").

[0017] At this time, the optical path of the light passing through the etalon is set to be equal between the etalon 10 and the uniform refractive index distribution etalon. Also, the lateral shift of the etalon 10 and the lateral shift of the uniform refractive index distribution etalon are represented by the incidence angle from the outside of the light passing through the etalon.

[0018] In the present embodiment, as an example of the refractive index distribution of the dielectric material in the etalon 10, a case in which the refractive index varies as a quadratic function of the distance x in the direction perpendicular to the incidence surface will be described in detail below.

[0019] 1 shows a schematic side view 11 and a refractive index distribution 12 of an etalon 10 according to the first embodiment. The schematic top view 11 shows an optical path 1 of light incident on the etalon 10.

[0020] The etalon 10 comprises a material (dielectric) that transmits light, and a semi-reflective film (semi-reflective mirror) formed on the surface where light is incident and exits. The refractive index inside the etalon 10 varies in the x-axis direction, but is constant and does not vary in the y-axis direction. The refractive index n inside the etalon 10 is expressed as a quadratic function of x, as shown in equation (1).

[0021]

number

[0022] Here, n0 is the minimum value of n, and x0 is the position in the x-axis direction where n is the minimum value. β is the coefficient of the refractive index distribution (hereinafter referred to as the "refractive index distribution coefficient") and is a positive real number.

[0023] For reference, the formula commonly used to define a lens is given below.

[0024]

number

[0025] Here, B is the convergence coefficient. When B>0, and parallel light is transmitted in the y-axis direction, the etalon 10 becomes a convex lens with a maximum refractive index at x0, and converges (collects) the parallel light traveling in the y-axis direction. The refractive index distribution constant √A used in graded-index (GRIN) lenses and B are related by equation (2). However, B must be in the range of B>0.

[0026]

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[0027] First, a description will be given of the optical path length of light passing through the etalon 10. The optical path length L inside the etalon 10 shown in FIG.

[0028]

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[0029] The line element ds in equation (3) is expressed by equation (4).

[0030]

number

[0031] Here, y'=dy / dx. From equations (3) and (4) and the integration range in the x-axis direction being 0 to d, equation (5) can be obtained, where d is the thickness of the etalon.

[0032]

number

[0033] g = n√(1 + y' 2 ), according to Fermat's principle, g is the function that minimizes the optical path length L. Since g is a function of x, y, and y', it is known that the function g that minimizes L satisfies Euler's equation in formula (6) using the calculus of variations.

[0034]

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[0035] On the left side of equation (6), g = n√(1 + y' 2 ) to obtain equation (7).

[0036]

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[0037] When light is incident on the etalon 10 nearly parallel to the x-axis (θ is close to 0), y'<<1 (so y' 2 <<1, so √(1+y' 2 )~1, and y' / √(1+y' 2 )~y', so equation (7) can be expressed as equation (8).

[0038]

number

[0039] Substituting equation (1) into equation (8) gives equation (9).

[0040]

number

[0041] Here, y'=dy / dx, y''=d 2 y / dx 2 (=d / dx(dy / dx)). The solution to the differential equation (9) is equation (10).

[0042]

number

[0043] Here, C1 and C2 are constants, and C1 and C2 will be calculated below.

[0044] As shown in FIG. 1, the angle of incidence (inside the etalon 10) at the incidence position x=0 on the etalon 10 is θ i Then, y'| x=0 = tan θ i Therefore, C1 is expressed by equation (11). However, η'| ξ=a indicates the result of substituting a for ξ in the differential equation of η with respect to ξ. However, θ i For θ< i <π / 2, and cosθ i =√(1-sin 2 θ i ) and transformed into

[0045]

number

[0046] Furthermore, as shown in FIG. 1, when x=0, y=0. From equations (10) and (11), C2 is expressed by equation (12).

[0047]

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[0048] From equations (10), (11), and (12), the optical path y is given by equation (13).

[0049]

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[0050] Here, if equation (14) holds, equation (15) can be obtained from equation (13).

[0051]

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[0052]

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[0053] The optical path length L of this optical path y is expressed by equation (16) by substituting equations (1) and (10) into equation (5).

[0054]

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[0055] The optical path length L in equation (16) is expressed as a linear sum of the first kind elliptic integral EllipticF(Φ,m) and the second kind elliptic integral EllipticE(Φ,m) as shown in equation (16').

[0056]

number

[0057] In order to simplify the optical path length L, the optical path length L is approximated by an elementary function. First, equation (17) is set as a condition.

[0058]

number

[0059] In this case, [1+β(x-x0) 2 ] 2~1+2β(x-x0) 2 Therefore, equation (16) can be approximated to equation (18).

[0060]

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[0061] Furthermore, if the refractive index at the center of the etalon 10 in the x-axis direction is minimum, then equation (19) holds, and the optical path length L can be obtained by equation (20).

[0062]

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[0063]

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[0064] A feature of the etalon 10 according to this embodiment is that the refractive index of the dielectric material used in the etalon is changed to suppress lateral shift of light that enters the entrance surface of the etalon at a predetermined angle (excluding 0°) and exits.

[0065] To demonstrate this, the difference between the exit position of an etalon 20 with a uniform internal refractive index (hereinafter referred to as a "uniform refractive index distribution etalon") and the exit position of an etalon according to this embodiment (hereinafter referred to as a "quadratic function refractive index distribution etalon") 10 is calculated under the condition that the free spectral range (FSR) of the uniform refractive index distribution etalon 20 and the quadratic function refractive index distribution etalon 10 are equivalent, i.e., the optical path lengths are equivalent.

[0066] Here, the lateral deviation of the beam refers to the deviation in the y-axis direction in Fig. 1. For example, when the incident position is (x, y) = (0, 0) and the exit position is (x, y) = (d, y0), the deviation amount is y0.

[0067] First, the amount of lateral deviation of the beam in the uniform refractive index distribution etalon 20 will be described. Fig. 2 shows the optical path 2 and the refractive index distribution 22 in the uniform refractive index distribution etalon 20. The refractive index is constant in the x-axis direction, and its value is n u Here, the refractive index is also constant in the y direction (not shown). At this time, the optical path 2 becomes a straight line.

[0068] The lateral shift y of the uniform refractive index distribution etalon 20 shown in FIG. u0 is expressed by equation (21).

[0069]

number

[0070] Here, θ ui is the angle of incidence inside the uniform refractive index distribution etalon 20 at (x, y) = (0, 0). The angle of incidence from the outside of the uniform refractive index distribution etalon 20 is θ' ui Then, from Snell's law, θ ui and θ' ui The relationship is expressed by equation (22).

[0071]

number

[0072] Therefore, n u Once is found, θ' ui By determining the amount of lateral shift y of the beam due to the uniform refractive index distribution etalon 20, u0 Then, n u is set (converted) so that the optical path lengths of the uniform refractive index distribution etalon 20 and the quadratic function refractive index distribution etalon 10 are equal to each other, and the lateral shift amount y u0 Calculate.

[0073] The physical length of the optical path inside the uniform refractive index distribution etalon 20 is d / cosθ ui Therefore, the optical path length L u is expressed by equation (23).ui 0<θ ui <π / 2, and cosθ ui =√(1-sin 2 θ ui ) and transforms into

[0074]

number

[0075] By substituting equation (22) into equation (23), we obtain equation (24).

[0076]

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[0077] If we square both sides of equation (24), we get n u Equation (25) is obtained as a polynomial of

[0078]

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[0079] n u >0, so we change equation (25) to n u 2 As a quadratic equation of n u 2 Solving for n u Solving for this, we obtain equation (27).

[0080]

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[0081] When "±" in the formula (26) is "-", the incident angle θ' to the uniform refractive index distribution etalon 20 ui When n = 0, the right hand side of equation (26) is 0, that is, u = 0, which has no physical meaning, so only the "+" in equation (26) is valid. Therefore, n u becomes equation (27).

[0082]

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[0083] The uniform refractive index distribution etalon 20 and the quadratic refractive index distribution etalon 10 have the same FSR, that is, the optical path length is the same. Therefore, L u = L. So, n u is expressed by equation (28).

[0084]

number

[0085] Here, L is expressed by equation (18). If equation (19) holds, that is, if the refractive index at the center in the x-axis direction of the etalon 10 is minimum (if x0=d / 2), L is expressed by equation (20).

[0086] From the formulas (21), (22), and (28), the lateral shift amount y u0 is expressed by equation (29).

[0087]

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[0088] Next, the lateral shift amount y0 of the etalon according to this embodiment, that is, the quadratic function refractive index distribution etalon 10 will be described.

[0089] The optical path in the quadratic function refractive index distribution etalon 10 is expressed by equation (13). By substituting d, which is the thickness of the etalon, for x in equation (13), the position of the emission position in the y-axis direction, that is, the lateral shift amount y0, can be calculated.

[0090] Here, in equation (13), θ i (the incident angle inside the etalon 10 at the incident position (x, y) = (0, 0)) is used. However, θi Since it is difficult to determine (measure) the lateral deviation y0, it is difficult to calculate the lateral deviation y0 from equation (13).

[0091] On the other hand, the incident angle θ′ outside the etalon 10 at the incident position (x, y)=(0, 0) i can be easily determined (measured). Therefore, θ i Instead of θ' i If the above formula is used, the lateral deviation amount y0 can be easily calculated from formula (13). Therefore, as shown below, formula (13) is changed to θ' i It is expressed as:

[0092] According to Snell's law, θ' i and θ i The relationship between is expressed by equation (30).

[0093]

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[0094] However, n | x=0 is n when x = 0. From equation (1), n ​​= n0 · [1 + β · (x-x0) 2 ], so n| x=0 is expressed by equation (31).

[0095]

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[0096] Therefore, equation (30) can be expressed as equation (32).

[0097]

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[0098] From equation (32) and equation (13), the optical path of the quadratic function refractive index distribution etalon 10 is expressed by equation (33). Here, θ i 0<θ i <π / 2, and cosθi =√(1-sin 2 θ i ) and transforms into

[0099]

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[0100] Here, if equation (34) holds, equation (33) can be expressed as equation (35).

[0101]

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[0102]

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[0103] By substituting d for x in equation (33), the lateral shift amount y0 of the quadratic function refractive index distribution etalon 10 is obtained as equation (36).

[0104]

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[0105] Here, if equation (37), in which x in equation (34) is changed to d, holds, equation (36) can be expressed as equation (38).

[0106]

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[0107]

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[0108] In this embodiment, in order for the quadratic function refractive index distribution etalon 10 to be effective, the lateral shift amount y0 of the quadratic function refractive index distribution etalon 10 must be greater than the lateral shift amount y of the uniform refractive index distribution etalon 20. u0Therefore, equation (39) needs to be satisfied.

[0109]

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[0110] Equation (39) can be expressed by equation (40) from equation (36) and equation (29). Here, the incident angle θ′ from the outside on the uniform refractive index distribution etalon 20 is ui and the incident angle θ' from the outside on the quadratic refractive index distribution etalon 10 i In order to satisfy the condition that θ' in equation (29) must be the same, ui θ' i has been replaced with.

[0111]

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[0112] Here, if expression (37) is satisfied, condition expression (39) can be expressed by expression (41) based on expressions (38) and (29).

[0113]

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[0114] From the above, when formula (40) or formula (41) is satisfied, the quadratic function refractive index distribution etalon 10 according to this embodiment has a smaller lateral shift of light that is incident on the etalon's incident surface at a predetermined angle (excluding 0°) and exits than the uniform refractive index distribution etalon 20.

[0115] That is, when formula (40) or formula (41) is satisfied, the quadratic function refractive index distribution etalon 10 according to this embodiment can suppress lateral shift of light.

[0116] In this way, the etalon 10 according to the present embodiment is set so that the refractive index distribution has smaller lateral deviation than a uniform refractive index distribution etalon under the condition that the optical path length of light passing through the etalon is equivalent.

[0117] In addition, when comparing the lateral shift, the lateral shift of the etalon 10 and the lateral shift of the uniform refractive index distribution etalon are expressed by the incident angle of light transmitted through the etalon from the outside.

[0118] <Etalon effect> As an example of the effect of the quadratic function refractive index distribution etalon 10 according to the present embodiment, when the position x0 where the refractive index is minimum is the center of the etalon 10 in the x-axis direction, that is, when the thickness of the etalon 10 is d and the etalon 10 is located from 0 to d on the x-axis and x0=d / 2, the incident angle θ′ from the outside of the etalon 10 is i We present the calculation results for the lateral shift of the beam when changing the

[0119] The parameters used in the calculation are as follows:

[0120] ·Refractive index distribution constant β:120000m -2 Etalon thickness d: 1mm (0.001m) Minimum refractive index position x0: 0.5mm (0.0005m) Incident angle from outside the etalon θ' i :0~10° Minimum refractive index n0:1.5

[0121] The refractive index distribution 31 in the x-axis direction is a refractive index distribution according to a downward convex quadratic function with a minimum refractive index of 1.5 at x0=0.5 mm, as shown in Fig. 3A. The refractive index distribution in the y-axis direction is constant.

[0122] 3B shows an optical path (solid line) 32 in the quadratic function refractive index distribution etalon 10, and an angle (dashed line) 33 between the tangent to the optical path 32 and the x-axis. i was set to 10°. Although the optical path 32 is approximately a straight line, the angle 33 of the tangent to the optical path is not constant but changes, which indicates that the optical path 32 is a curve.

[0123] FIG. 3C shows the position y0 at which light incident at (x, y)=(0, 0) with an incident angle of 10° exits the quadratic function refractive index distribution etalon 10, relative to the incident angle θ' i For comparison, the uniform refractive index distribution etalon 20 has a plot 34 of the exit position y u0 A plot 35 of the above is also shown. Since the light is incident at (x,y)=(0,0), the exit position in the y-axis direction (the value on the vertical axis in FIG. 3C) is the amount of lateral shift caused by the etalon.

[0124] FIG. 3D shows the output position y0 of the quadratic function refractive index distribution etalon 10 and the output position y of the uniform refractive index distribution etalon 20 in FIG. 3C. u0 Difference in lateral deviation between u0 Plot 36 of θ' is shown. i At any value between 0 and 10°, y0-y u0 is a negative quantity, and y0 <y u0 That is, the amount of lateral deviation is smaller in the quadratic function refractive index distribution etalon 10.

[0125] The optical path tangent angle shown in the graph of FIG. 3B is calculated by equation (42).

[0126]

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[0127] As a next example, the incident angle θ' from the outside of the etalon 10 i The calculation results of the beam deviation when the refractive index minimum position x0 is changed while keeping is constant are described below.

[0128] The parameters used in the calculation are as follows:

[0129] ·Refractive index distribution constant β: 120000m -2 Etalon thickness d: 1mm (0.001m) Refractive index minimum position x0: 0~0.5mm (0~0.0005m) - Incident angle θ' from outside the etalon i :10° Minimum refractive index n0:1.5

[0130] 4A shows a plot 41 of the position y0 at which light incident at (x, y) = (0, 0) with an incident angle of 10° emerges from the quadratic function refractive index distribution etalon 10, against the minimum refractive index position x0. Since the light is incident at (x, y) = (0, 0), the emergence position in the y-axis direction (the value on the vertical axis in FIG. 4A) is the lateral displacement of the etalon.

[0131] For comparison, the exit position y u0 Also shown is a plot 42 of u0 was calculated by converting the refractive index so that the optical path in the uniform refractive index distribution etalon 20 becomes equivalent to the optical path in the quadratic function refractive index distribution etalon 10. In this calculation process, the position where the refractive index is minimum was plotted as x0.

[0132] FIG. 4B shows the output position y0 of the quadratic function refractive index distribution etalon 10 in FIG. 4A and the output position y u0 Difference in lateral deviation between u0 The plot 43 shows the relationship between y0-y u0 is a negative quantity, and y0 <y u0 That is, the amount of lateral deviation is smaller in the quadratic function refractive index distribution etalon 10.

[0133] The above calculation results show that if the refractive index distribution constant β and the etalon thickness d of the quadratic refractive index distribution etalon 10 are set so as to satisfy equation (40) or equation (41), the lateral shift of light passing through the etalon can be suppressed within a specified range of incident angles (0 to 10°) or at any minimum refractive index position x0.

[0134] <Second embodiment> Next, an etalon according to a second embodiment of the present invention will be described with reference to FIGS. 5A and 5B.

[0135] <Etalon configuration> The medium material through which the etalon transmits light (having a quadratic refractive index distribution) is potassium tantalate niobate (KTN, KTa x Nb 1-x We will discuss an example using O3) crystals.

[0136] KTN crystals have a quadratic electro-optic effect (the refractive index changes in proportion to the square of the electric field), and charges (electrons) can be injected or trapped inside the KTN crystal. Using this characteristic, we can realize a refractive index distribution that can be expressed by a quadratic function as shown in Figure 1, as described later.

[0137] 5A and 5B show an example of the structure of an etalon having a quadratic function refractive index distribution using a KTN crystal (hereinafter referred to as a "KTN crystal quadratic function refractive index distribution etalon") 50. Fig. 5A is a side view of the etalon 50, and Fig. 5B is a perspective view of the etalon 50.

[0138] A pair of opposing two faces of a rectangular parallelepiped KTN crystal 501 is mirror-polished, and transparent electrodes 502 and 503 are formed on each of the two faces, respectively. Electrodes 504 and 505 and semi-reflecting mirrors 506 and 507 are formed on the transparent electrodes 502 and 503 so as not to overlap.

[0139] When the charge injected from the electrode into the KTN crystal 501 is an electron, in order for the transparent electrodes 502 and 503 to form an ohmic contact with the KTN crystal 501, it is desirable for the work function to be 5.0 eV or less (Patent Document 1). One example of a transparent electrode that satisfies this requirement is In2O3:Sn (ITO), which has a work function of 4.5 to 4.7 eV (Patent Publication No. 6440169).

[0140] A good example of the semi-reflecting mirrors 506 and 507 is a dielectric multilayer film, which realizes a reflectance of 98% to 99%. An example of the electrodes is one in which titanium (Ti), platinum (Pt), and gold (Au) are laminated in this order on the transparent electrodes 502 and 503.

[0141] As shown in Figure 5A, the origin of the xy coordinate system is located on the interface between the transparent electrode 502 and the KTN crystal 501, the axis that passes through the origin and is perpendicular to the interface between the transparent electrode 502 and the KTN crystal 501 is defined as the x-axis 508, and the axis that is perpendicular to the x-axis, parallel to the side surface, and passes through the origin is defined as the y-axis.

[0142] Light that enters etalon 50 from the left side in Figure 5A and passes through the origin of the xy coordinates via semi-reflecting mirror 506 and transparent electrode 502 travels according to the quadratic function refractive index distribution in KTN crystal 501, exits from (x, y) = (d, y0) on the surface of KTN crystal 501 on the right side of Figure 5A, and exits outside etalon 50 through transparent electrode 503 and semi-reflecting mirror 507.

[0143] In this case, y0 is the amount of beam deviation. However, it is assumed that the optical path 5 of the light incident on the etalon 50 is on the xy plane.

[0144] The crystal structure of the KTN crystal 501 changes depending on the temperature, but in this embodiment, the temperature is kept constant at a temperature several degrees (about 2 to 3 degrees Celsius) higher than the Curie temperature to make it a cubic crystal in the paraelectric phase. Therefore, the temperature control of the KTN crystal 501 is required.

[0145] In the KTN crystal quadratic refractive index distribution etalon 50 according to the present embodiment, in order to change the refractive index of the KTN crystal 501 in a quadratic function manner, electric charges are injected from the electrodes into the KTN crystal 501. In order to inject the electric charges, a direct current (DC) voltage or an alternating current (AC) voltage of about 20 kHz or less is applied from the outside.

[0146] <Third embodiment> Next, an etalon according to a third embodiment of the present invention will be described with reference to FIGS. 5C and 5D.

[0147] In the second embodiment, a direct current (DC) voltage or an alternating current (AC) voltage of about 20 kHz or less is applied from the outside in order to inject electric charges from the electrodes into the KTN crystal 501. In this embodiment, in order to change the refractive index minimum position x0, in addition to the above-mentioned DC voltage and AC voltage (about 20 kHz or less), a voltage with a frequency higher than about 20 kHz is applied.

[0148] When an AC voltage of about 20 kHz or less is applied to the etalon, the etalon generates heat due to vibration of the etalon and the carrier inside the etalon, so a structure for controlling the temperature of the etalon is required.

[0149] <Etalon configuration> As shown in FIGS. 5C and 5D, the etalon 51 according to this embodiment includes a KTN crystal quadratic refractive index distribution etalon 50, and a configuration for temperature control including a thermistor 511 and a Peltier element 512 as temperature sensors.

[0150] A metal block 513, a Peltier element 512, and a heat sink (a metal block, a metal block with fins, etc.) 514 are arranged on one side of the light exit / entrance surface of the etalon 50, and the etalon 50 and the metal block 513, the metal block 513 and the Peltier element 512, and the Peltier element 512 and the heat sink 514 are bonded together with an adhesive having high thermal conductivity.

[0151] In addition, a thermistor (sensor) 511 for measuring temperature is fixed in a hole in the metal block 513. Thermistor (sensor) 511 may be fixed to the surface of the metal block 513.

[0152] Metal block 513, Peltier element 512, and heat sink 514 are formed with holes 515 for allowing light to pass therethrough, as shown by dashed lines in FIGS. 5C and 5D.

[0153] Voltage application to the etalon 50 may be performed by bonding lead wires to the two electrodes 504, 505 of the etalon 50 and applying a voltage to each lead wire, or voltage may be applied to one side of the etalon 50 via a metal block 513 to which the electrodes 504, 505 are in contact. Possible materials for the metal block 513 include aluminum, copper, copper tungsten, etc. <Fourth embodiment> Next, an etalon according to a fourth embodiment of the present invention will be described with reference to FIG. 5E.

[0154] <Etalon configuration> Etalon 52 according to this embodiment is equipped with a configuration for controlling temperature, as shown in Fig. 5E. Etalon 50 is sandwiched between metal blocks 513 and 522 via conductive buffer sheet 521. Conductive buffer sheet 521 is made of a material that has good thermal conductivity, is conductive, and is soft like a cushion, so that it returns to its original shape when pressed.

[0155] Furthermore, the etalon 51 includes a cap 523 , a spacer 524 , a bolt 525 , and a spring 526 for tightly attaching the etalon 50 and the two conductive buffer sheets 521 .

[0156] In the etalon 51, a screw hole is formed in the metal block 513, and a bolt 525 is inserted through a hole formed in the metal block 522. The bolt 525 is tightened to sandwich the etalon 50 between the metal blocks 513 and 522 and the conductive interference sheet 521 and fix the etalon 50.

[0157] Spring 526 is inserted and locked or attached to bolt 525 and adjusted so that an appropriate pressure of about several N (1 to 2 N) is applied to conductive buffer sheet 521 and metal blocks 513 and 522 .

[0158] Cap 523 is disposed between metal block 513 and the head of bolt 525 to protect spring 526. The thickness of cap 523 is an indicator of the length of spring 526 required to obtain an appropriate repulsive force when bolt 525 is tightened.

[0159] Spacers 524 are disposed to sandwich the etalon 50 in order to fix the etalon 50 in the y direction, and are fixed by bolts 525 .

[0160] The size of the spacer in the lateral direction (x direction, etalon thickness direction) is slightly (by several tens of μm, about 10 μm to 50 μm) smaller than the size of the etalon 50 in the lateral direction (x direction). This is to avoid impeding the contraction of the conductive buffer sheet 521 when pressed against the etalon 50.

[0161] On the one semi-reflecting mirror 507 side of the etalon 50, a hole 515 (indicated by a dashed line in FIG. 5E) for passing light is formed in the conductive buffer sheet 521, the metal block 513, the Peltier element 512, and the heat sink 514. Similarly, on the other semi-reflecting mirror 506 side of the etalon 50, a hole 527 (indicated by a dashed line in FIG. 5E) for passing light is formed in the conductive buffer sheet 521, the metal block 513, and the cap 523.

[0162] The metal block 513, the Peltier element 512, and the heat sink 514 are bonded together with an adhesive having good thermal conductivity. The other members are not bonded together.

[0163] Voltage application to the etalon 50 may be performed by bonding (fixing) lead wires to the two electrodes 504 and 505 of the etalon 50 and applying a voltage to each of the lead wires. Alternatively, voltage may be applied via the metal blocks 513 and 522.

[0164] The material of the conductive buffer sheet 521 is graphite, carbon, conductive rubber, indium, etc. The material of the bolt 525 is plastic, etc. The material of the metal block 513 is aluminum, copper, copper tungsten, etc.

[0165] <Etalon Operation> (Action) An example of the refractive index distribution when charges (electrons) are injected into the KTN crystal and an electric field is applied from outside the KTN crystal is shown in Figure 6. The x-axis in the figure is the same as the x-axis in Figure 5A.

[0166] When the density of electric charges (electrons) is uniformly distributed with respect to x (601 in FIG. 6), the electric field (602 in FIG. 6) expressed by equation (43) is generated from the electric charge distribution and Gauss's law. However, the electric field is constant within the KTN crystal in FIG. 5A and within a plane parallel to the planes of the transparent electrodes 502 and 503 (within a plane including the y-axis and an axis perpendicular to the xy plane and within a plane parallel to that plane).

[0167]

number

[0168] where ρ is the charge density, ε r is the relative dielectric constant of the KTN crystal, ε0 is the dielectric constant of a vacuum (also called the electric constant), and d is the thickness of the KTN crystal (the distance between the transparent electrodes).

[0169] When a voltage (KTN crystal applied voltage) V is applied between the electrodes of the KTN crystal, an electric field (603 in Figure 6) expressed by equation (44) is generated inside the KTN crystal.

[0170]

number

[0171] The electric field E (604 in FIG. 6) generated inside the KTN crystal is E in (x) and E ex (x) is added, and is expressed by equation (45).

[0172]

number

[0173] Since KTN crystals have the Kerr effect, the refractive index change Δn is proportional to the square of the electric field, as shown in equation (46), where Δn(x) is the refractive index change Δn. (Jun Miyazu, Tadayuki Imai, Seiji Toyoda, Masahiro Sasaura, Shogo Yagi, Kazutoshi Kato, Yuzo Sasaki, and Kazuo Fujiura, “New Beam Scanning Model for High-Speed ​​Operation Using KTa1-xNbxO3 Crystals,” Applied Physics Express, Vol. 4, pp. 111501-1-111501-3, 2011.)

[0174]

number

[0175] Here, n0 is the refractive index when no electric field is applied (V=0). Also, g 12 is an electro-optic constant, which is a quantity that affects the direction of the electric field of light perpendicular to the direction of the electric field applied to the crystal.

[0176] In FIG. 5A, since the light travels almost in the x-axis direction, the direction of the electric field E(x) is almost perpendicular to the x-axis direction. However, an electric field occurs in the KTN crystal in the x-axis direction, so Δn is g 12 (E(x)) 2 is proportional to.

[0177] In addition, since the electric field of the light is perpendicular to the traveling direction of the light, in the configuration of FIG. 5A, the refractive index distribution does not depend on the polarization of the light (it is polarization independent).

[0178] The refractive index distribution n(x) of the KTN crystal is obtained by adding n0 to this Δn, and is expressed by equation (47).

[0179]

number

[0180] In this way, when the KTN crystal is used in Fig. 5A, it becomes an etalon with a refractive index distribution that is a quadratic function of x with respect to the x axis. Comparing with equation (1), equation (48) is obtained.

[0181]

number

[0182] <Etalon effect> Next, the lateral deviation of the beam in the KTN crystal quadratic function refractive index distribution etalon 50 according to the second to fourth embodiments will be described with reference to FIGS. 7A to 10C.

[0183] In the KTN crystal quadratic refractive index distribution etalon 50, the applied voltage V between the electrodes of the KTN crystal is set to 0, and the incident angle θ' from the outside of the etalon is i By changing the refractive index distribution inside the KTN crystal, the optical path inside the KTN crystal, and the beam exit position were calculated.

[0184] For comparison, a similar calculation was performed for a uniform gradient index etalon. Here, the uniform gradient index etalon has the same FSR as the KTN crystal quadratic gradient index etalon 50, i.e., the optical path length inside the etalon is equal to that of the KTN crystal quadratic gradient index etalon 50.

[0185] ·Charge density ρ:-80Cm -3 ·Dielectric constant ε of KTN crystal r :17500 · Dielectric constant of vacuum (electric constant) ε0: 8.8541878129×10-12 Fm-1 · Thickness of KTN crystal (distance between transparent electrodes) d: 0.38 mm (0.00038 m) The refractive index of KTN crystal when no electric field is applied (V=0): n0: 2.18 Electro-optic constant g 12 :-0.038 C 4 m -2 Voltage between electrodes of KTN crystal: 0 V - Incident angle θ' from outside the etalon i :0~10°

[0186] In this case, β = 577.8918m -2 , x0=1.9×10-4-5.0969831×10 -6 ×V=1.9×10 -4 It becomes m.

[0187] In the refractive index distribution 71 shown in FIG. 7A, V=0, so x0=d / 2=1.9×10 -4 mm. Therefore, from equation (45), we obtain a downward convex quadratic function whose center in the x-axis direction of the KTN crystal is the minimum refractive index value n0 = 2.18. The refractive index distribution in the y-axis direction is constant.

[0188] 7B shows an optical path (solid line) 72 in the KTN crystal quadratic refractive index distribution etalon 50, and an angle (dashed line) 73 between the tangent to the optical path 72 and the x-axis. i The calculation was performed assuming that the angle is 10°. Although the optical path 72 is approximately a straight line, the angle 73 of the tangent to the optical path is not constant but changes, which indicates that the optical path 72 is a curve.

[0189] FIG. 7C shows the position y0 at which light incident at (x, y)=(0, 0) with an incident angle of 10° exits the KTN crystal quadratic refractive index distribution etalon 50, relative to the incident angle θ' i 7C is a plot of the amount of lateral shift caused by the etalon. Since the light is incident at (x,y)=(0,0), the exit position in the y-axis direction (the value on the vertical axis in FIG. 7C) is the amount of lateral shift caused by the etalon. For comparison, the exit position y u0 Plot 75 is also shown.

[0190] FIG. 7D shows the output position y0 of the KTN crystal quadratic refractive index distribution etalon 50 in FIG. 7C and the output position y u0 Difference in lateral deviation between u0 θ' i At any value between 0 and 10°, y0-y u0 is a negative quantity, and y0 <y u0 That is, the lateral deviation amount is smaller in the KTN crystal quadratic refractive index distribution etalon 50.

[0191] The optical path tangent angle shown in the graph of FIG. 7B is calculated by equation (42).

[0192] Next, the incident angle θ' from outside the etalon i The calculation results of the lateral shift of the beam when the minimum refractive index position x0 is changed by changing the voltage (applied voltage) V between the electrodes of the KTN crystal while keeping constant are described below. The following parameters were used for the calculation.

[0193] ·Charge density ρ:-80Cm-3 ·Dielectric constant ε of KTN crystal r :17500 · Dielectric constant of vacuum (electric constant) ε0: 8.8541878129×10-12 Fm-1 · Thickness of KTN crystal (distance between transparent electrodes) d: 0.38 mm (0.00038 m) The refractive index of KTN crystal when no electric field is applied (V=0): n0: 2.18 Electro-optic constant g 12 :-0.038 C 4 m -2 KTN crystal interelectrode voltage (AC): -200 to +200 - Incident angle θ' from outside the etalon i :10°

[0194] In this case, β = 577.8918m -2 , x0=1.9×10-4-5.0969831×10 -6 ×V=-8.29396623×10 -4 ~+1.20939662×10 -3 It becomes m.

[0195] Figure 8 shows the position x of the minimum refractive index with the change in the voltage between the KTN crystal electrodes (voltage applied to the KTN crystal) V, obtained from equation (48). x0 changes linearly with respect to V. The positive slope of the graph in Figure 8 is due to ρ<0.

[0196] Here, the length of the KTN crystal 501 in the x-axis direction corresponds to the range of 0 to 0.38 mm on the vertical axis of Fig. 8. Furthermore, the position of x0 can be set by V outside the range of the KTN crystal (a range longer than 0.38 mm on the vertical axis of Fig. 8).

[0197] 9A shows a plot 91 of the position y0 at which light incident at (x, y) = (0, 0) with an incident angle of 10° emerges from the KTN crystal quadratic refractive index distribution etalon 50, relative to the minimum refractive index position x0. Since the light is incident at (x, y) = (0, 0), the emergence position in the y-axis direction (the value on the vertical axis in FIG. 9A) is the lateral displacement of the etalon.

[0198] For comparison, the exit position y u0 Plot 92 is also shown. Here, the exit position y u0 was calculated by converting the refractive index so that the optical path in the uniform refractive index distribution etalon becomes equivalent to the optical path in the quadratic function refractive index distribution etalon 50. In this calculation process, the position where the refractive index is minimum is plotted as x0.

[0199] FIG. 9B shows the output position y0 of the KTN crystal quadratic refractive index distribution etalon 50 in FIG. 9A and the output position y u0 Difference in lateral deviation between u0 According to equation (46), when the AC voltage V changes from -200 to +200 V, x0 is -8.29396623×10 -4 ~+1.20939662×10 -3 m. In any range of x0, y0-y u0 is a negative quantity, and y0 <y u0 That is, the lateral deviation amount of the KTN crystal quadratic refractive index distribution etalon 50 is smaller.

[0200] 9C and 9D are graphs in which the minimum refractive index position x0 on the horizontal axis of FIGS. 9A and 9B is replaced with the KTN applied voltage V. FIG. 9C shows a plot 94 of the output position y0 in the KTN crystal quadratic refractive index distribution etalon 50 and a plot 95 of the output position y0 in the uniform refractive index distribution etalon. u0 FIG. 9D shows a plot 95 of the difference in lateral displacement y0-y u0 As mentioned above, when V is in the range of -200 to +200 V, y0 <y u0That is, the lateral deviation amount of the KTN crystal quadratic refractive index distribution etalon 50 is smaller.

[0201] The above calculation results show that by using a KTN crystal, it is possible to realize a refractive index profile that suppresses the lateral shift of light passing through the etalon by applying a voltage to the KTN crystal.

[0202] Next, a description will be given of the calculation results regarding the change in the filter characteristic (wavelength change) of the KTN crystal quadratic refractive index distribution etalon 50 due to the change in the applied voltage V to the KTN. The calculation was performed based on equation (49).

[0203]

number

[0204] When the AC voltage V applied to the KTN is changed in the range of -200 to +200 V, the optical path length in the etalon changes as shown in Fig. 10A. With the change in the optical path length, the FSR changes as shown in Fig. 10B, and the frequency of the longitudinal mode, i.e., the wavelength, changes as shown in Fig. 10C. Here, the longitudinal mode frequency is the frequency of (one) longitudinal mode of the qth order (1073th order).

[0205] In this way, in the KTN crystal quadratic refractive index distribution etalon 50, the filter characteristics (longitudinal mode frequency) of the etalon can be changed by changing the voltage applied to the KTN.

[0206] In other words, in an etalon using a KTN crystal with a refractive index distribution that suppresses the lateral shift of light passing through the etalon, the filter characteristics of the etalon (longitudinal mode frequency) can be changed by changing the voltage applied to the KTN, so it can be used as a voltage-driven tunable filter or wavelength sweep filter.

[0207] For example, when a direct current (DC) or a low-frequency (10 to 20 kHz or less) AC voltage is applied, but a high-frequency AC voltage is not applied, the refractive index minimum position x0 does not change, and the optical path does not change either. Therefore, the wavelength does not fluctuate with time, and it can be used as a wavelength tunable filter.

[0208] For example, when a high-frequency AC voltage of more than 10 to 20 kHz is applied in addition to a direct current (DC) or low-frequency AC voltage (10 to 20 kHz or less), the minimum refractive index position x0 changes and the optical path also changes. Therefore, the wavelength can be continuously changed (swept) over time, and the device can be used as a wavelength sweep filter.

[0209] In this way, a wavelength tunable filter or a wavelength sweep filter using the KTN crystal quadratic refractive index distribution etalon 50 has good wavelength stability (controllability).

[0210] Here, the (1073th order) longitudinal mode shown in Fig. 10(c) represents the longitudinal mode order corresponding to a wavelength of 1550 nm, which is the wavelength used in LiDAR and the like.

[0211] In this embodiment, an example has been shown in which a KTN crystal is used as a material having a quadratic refractive index distribution of the etalon. 1-y L y Ta x Nb 1-x O3) may also be used.

[0212] <Fifth embodiment> Next, an etalon device according to a fifth embodiment of the present invention will be described with reference to FIG.

[0213] 11, the etalon device 53 according to the present embodiment includes the etalon 51 according to the second embodiment, a driving power supply 531, and a light irradiation mechanism. The etalon 51 according to the second embodiment includes the KTN crystal quadratic refractive index distribution etalon 50 as described above.

[0214] The light source 532 in the light irradiation mechanism is an LED (Light Emitting Diode) with an emission wavelength of 405 nm (3.06 eV). LEDs with this wavelength are inexpensive and commercially available, so the light irradiation mechanism can be manufactured inexpensively. In addition to the light source 532, optical components such as lenses and filters may be used in the light irradiation mechanism.

[0215] When the KTN crystal quadratic refractive index distribution etalon 50 is operated by injecting electric charges (electrons), a direct current (DC) or a low-frequency (10 to 20 kHz or less) AC voltage is applied between the electrodes of the KTN crystal by the driving power supply 531. However, if the electric charges (electrons) are not injected into the KTN crystal and are accumulated near the negative electrode, the etalon does not operate well.

[0216] In the etalon device 53 according to the present embodiment, the light source 532 irradiates the KTN crystal with light having a wavelength having a photon energy close to the band gap 3.18 eV of the KTN crystal, and excites the charges (electrons) trapped in the trap levels in the KTN crystal to transition to the conduction band, thereby making it possible to inject the charges (electrons) up to the vicinity of the positive electrode.

[0217] Here, the irradiation light from the light source 532 is irradiated with the same optical axis 530 as the light incident on the etalon 50. The irradiation light may be irradiated by passing through a hole 515 formed in the etalon 51. The irradiation light is not limited to this, and may be irradiated from a direction different from the optical axis of the incident light, as long as it is irradiated on the etalon.

[0218] Here, the charge (electron) density ρ in the KTN crystal changes depending on the power density irradiated from the light source 531. In detail, when the LED irradiation light power density is large, the absolute value of ρ is small, and when the power density is small, the absolute value of ρ is large. The power density irradiated from the light source 531 is 1 mW / mm 2 ~20mW / mm 2 A degree is desirable.

[0219] When the etalon device 53 according to this embodiment is used in a wavelength tunable filter and the wavelength is not varied over time, a DC voltage can be continuously applied to the KTN crystal while irradiating it with light having a photon energy close to 3.18 eV (for example, a wavelength of 405 nm).

[0220] In addition, when the etalon device 53 according to the present embodiment is used in a wavelength sweep filter and is operated by continuously changing (sweeping) the wavelength over time, a voltage in which an alternating current (AC) voltage is superimposed on a DC voltage can be applied to the KTN crystal while irradiating it with light having a photon energy close to 3.18 eV (for example, a wavelength of 405 nm). In this case, the frequency of the AC voltage is preferably high frequency (10 kHz or higher) that does not cause charge injection into the KTN crystal.

[0221] In this embodiment, the light source has an emission wavelength of 405 nm, but the wavelength is not limited to this and may be other wavelengths as long as the wavelength can excite the charges (electrons) trapped in the trap level in the KTN crystal to the conduction band.

[0222] In this embodiment, etalon 51 according to the second embodiment is used, but etalon 52 according to the second embodiment may be used. In this case, irradiation light is irradiated by passing through hole 515 or hole 527 formed in etalon 52.

[0223] In the embodiment of the present invention, an example using a semi-reflecting mirror has been shown, but the present invention is not limited to this, and a semi-reflecting mirror may not be used. Even if a semi-reflecting mirror is not used, if the refractive index of the etalon is different from the refractive index of the surroundings of the etalon, for example, the air, Fresnel reflection occurs on the etalon surface, and the same effect can be achieved.

[0224] In the embodiment of the present invention, an example in which the refractive index of the dielectric material used in the etalon changes according to a quadratic function has been shown, but the present invention is not limited thereto. It is sufficient that the refractive index distribution of the dielectric material used in the etalon according to the embodiment of the present invention is set so that the lateral shift is smaller than that of a uniform refractive index distribution etalon under the condition that the optical path length of light passing through the etalon is the same.

[0225] Furthermore, when comparing the lateral shift, the lateral shift of the etalon according to the embodiment of the present invention and the lateral shift of the uniform refractive index distribution etalon may be expressed in terms of the incident angle of light transmitted through the etalon from the outside.

[0226] For example, the refractive index may change so as to be convex downward in the refractive index distribution. For example, the refractive index may decrease from one end face of the dielectric material used in the etalon toward the inside of the dielectric material and increase from an arbitrary point inside the dielectric material to the other end face. In addition, the change in the refractive index of the dielectric material may be a monotonous decrease or increase.

[0227] In the embodiment of the present invention, an example has been shown in which the refractive index inside the etalon varies in the x-axis direction and is constant in the y-axis direction, but is not limited to this. It may vary in the y-axis direction.

[0228] In the embodiment of the present invention, the dielectric material used in the etalon is a KTN crystal, but this is not limited to this. Barium titanate (BaTiO3:BT), potassium tantalate (KTaO3:KT), and strontium titanate (SrTiO3:ST) may also be used as a material having the Kerr effect, which is an electro-optic effect.

[0229] Furthermore, the dielectric material used in the etalon may be a material having the Pockels effect, in which the refractive index changes in proportion to the applied voltage. Lithium niobate (LiNbO3, hereafter referred to as "LN") may be used as the material having the Pockels effect, and lead lanthanum zirconate titanate (Pb 1-x La x )(Zr y Ti 1-y ) 1-x / 4O3:PLZT) may also be used.

[0230] In the embodiment of the present invention, an example has been shown in which a KTN crystal is used for the etalon and a voltage is applied from the outside to change the refractive index, but this is not limiting. The refractive index may be changed by changing the components and composition in the dielectric. In this case, in addition to the above-mentioned materials, SiOx , SiN x , SiO x N y etc., or the compositions x and y may be changed.

[0231] In the embodiment of the present invention, examples of the structure, dimensions, materials, etc. of each component in the configuration and manufacturing method of the etalon and etalon device are shown, but the present invention is not limited to these. Anything that can exert the function and effect of the etalon and etalon device may be used. [Industrial Applicability]

[0232] The present invention can be applied as an optical filter in the fields of wavelength division multiplexing (WDM) transmission optical communications, precision measurement, and the like, as a wavelength selection filter or an interference filter for narrowing wavelength bands. [Explanation of symbols]

[0233] 10 Etalon 20 Uniform refractive index distribution etalon

Claims

1. An etalon in which light is incident from a direction different from a perpendicular direction to an incident surface and exits from an exit surface opposite to the incident surface, the etalon has a first end face on the incident surface side and a second end face on the exit surface side opposite the first end face, and is provided between the first end face and the second end face with a dielectric material having a refractive index distribution set so that lateral shift of the light is smaller than that of a uniform refractive index distribution etalon under a condition in which the optical path length of the light is equivalent; a refractive index of the dielectric changes as a quadratic function of x, where x is a distance from the first end face to the second end face in a direction perpendicular to the first end face; In a direction perpendicular to the first end face, the minimum value of the refractive index is n ０ , the refractive index is n ０ The value of x is x ０ , the coefficient of the refractive index distribution is β, the optical path length is L, the thickness of the etalon is d, and the incident angle of the light to the incident surface is θ′. ｉ The etalon satisfies the following formula (A): [0010]

2. The refractive index of the dielectric material changes from the first end face to the second end face when a voltage is applied. The etalon of claim 1 , comprising:

3. The etalon according to claim 1 , further comprising a temperature adjustment mechanism.

4. An etalon according to any one of claims 1 to 3; A driving power source; a light source; an etalon device in which the light from the light source is irradiated onto the etalon;

5. A method for controlling an etalon in which light is incident from a direction different from a perpendicular direction to an incident surface and exits from an exit surface opposite to the incident surface, comprising the steps of: the etalon comprises a dielectric having a first end face on the incident surface side and a second end face on the exit surface side opposite the first end face, Applying a voltage between the first end surface and the second end surface, changing a refractive index of the dielectric material between the first end face and the second end face; A method for controlling an etalon that reduces a distance between a point on the exit surface from which the light exits and a point on the exit surface where the light enters from a direction perpendicular to the entrance surface and exits.

6. 6. The method for controlling an etalon according to claim 5, further comprising irradiating the etalon with irradiation light.

7. A method for determining a refractive index of a first dielectric in a first etalon in which light is incident from a direction different from a perpendicular direction to an incident surface and exits from an exit surface opposite to the incident surface, comprising the steps of: converting the refractive index of a second dielectric of a second etalon having a uniform refractive index distribution so that the optical path length of the second etalon is equal to the optical path length of the first etalon; deriving a lateral shift of the second etalon using the transformed refractive index; Deriving a lateral shift of the first etalon; comparing a lateral shift of the first etalon with a lateral shift of the second etalon; deriving a refractive index of the first dielectric material such that a lateral shift of the first etalon is smaller than a lateral shift of the second etalon; A method for determining a refractive index comprising:

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