Two-dimensional photonic crystal laser

Abstract

A two-dimensional photonic crystal laser (10) is provided with: a pair of electrodes (171, 172); an active layer (11) that is provided between the pair of electrodes and that generates light of a predetermined wavelength by injecting a current from the electrodes; and a two-dimensional photonic crystal layer (12) that is provided between one of the pair of electrodes and the active layer, and that has a plate-shaped base material (121) and a plurality of different refractive index regions (122) that are disposed on the base material and have a refractive index different from that of the base material. The plurality of different refractive index regions are disposed so as to be offset from each lattice point of a two-dimensional lattice, which is periodically disposed in the base material at an in-plane period corresponding to the prescribed wavelength, by a different amount of positional offset, or / and the plurality of different refractive index regions are disposed so as to be offset from each lattice point at a different amount of positional offset. Each of the plurality of different refractive index regions is disposed at each lattice point or at a position deviated from the lattice point by the positional deviation amount at an area that differs from a predetermined reference area by an area deviation amount, and each of the plurality of different refractive index regions is disposed at a position deviated from the lattice point by the positional deviation amount or / and the area deviation amount. The modulation value is determined in a different refractive index region in which the modulation value, which is determined by a composite period in which a plurality of mutually different in-plane periods overlap, is a value between a prescribed upper limit value and a prescribed lower limit value at a lattice point in which the different refractive index region is disposed. The upper limit value is in the different refractive index region in which the modulation value exceeds the upper limit value, and the lower limit value is in the different refractive index region in which the modulation value is smaller than the lower limit value.

Description

Technical Field

[0001] The present invention relates to a two-dimensional photonic crystal laser (also referred to as a "two-dimensional photonic crystal surface emitting laser") that amplifies light using a two-dimensional photonic crystal. Background Art

[0002] The two-dimensional photonic crystal laser comprises an active layer and a two-dimensional photonic crystal layer, and a pair of electrodes arranged in a manner sandwiching them. The active layer generates light of a specific luminous wavelength band by injecting carriers (holes, electrons) from the electrode pair. The two-dimensional photonic crystal layer has a structure in which different refractive index regions having different refractive indexes are periodically arranged two-dimensionally on a plate-like base material. The different refractive index regions are composed of holes (air) formed in the base material or components of a material different from that of the base material. In such a two-dimensional photonic crystal laser, only light of a specified wavelength corresponding to the period length of the arrangement of the different refractive index regions among the light generated in the active layer is amplified in the two-dimensional photonic crystal layer to perform laser oscillation, and a laser beam is emitted from the surface of the two-dimensional photonic crystal layer.

[0003] In a typical two-dimensional photonic crystal laser, regions with different refractive indexes having the same planar shape are arranged at lattice points of a two-dimensional lattice such as a square lattice, a rectangular lattice, or a triangular lattice, and the laser beam is emitted in a direction perpendicular to the two-dimensional photonic crystal layer.

[0004] In contrast, Patent Documents 1 and 2 describe two-dimensional photonic crystal lasers having a two-dimensional photonic crystal layer in which, at each lattice point of a two-dimensional lattice, different refractive index regions are arranged at different offsets from the lattice point or / and the different refractive index regions are arranged with different areas. Here, the offset is the quantity of a vector within a plane parallel to the two-dimensional photonic crystal layer (i.e., a quantity having both magnitude and direction). "Different offsets" also include cases where the magnitude of the offset is the same but only the direction of the offset is different. These offsets or / and areas vary with a specified period (longer than the period of the lattice point arrangement) along a specified direction parallel to the two-dimensional photonic crystal layer. The period of this variation in offset or / and area is referred to as the "modulation period," and the offset or / and area in each different refractive index region modulated within this modulation period is referred to as the "modulation phase." Such a two-dimensional photonic crystal laser is tilted from the direction perpendicular to the two-dimensional photonic crystal layer by an angle corresponding to the modulation period (tilt angle), and emits two laser beams with azimuth angles in the above-mentioned predetermined directions and 180° apart from each other.

[0005] In addition, Patent Document 3 describes a two-dimensional photonic crystal laser comprising a two-dimensional photonic crystal layer in which different refractive index regions are arranged at each lattice point of the two-dimensional lattice or at positions deviated from each lattice point, according to the deviation amount and / or area modulated by a composite period formed by overlapping N different modulation periods (N is an integer greater than or equal to 2). Such a two-dimensional photonic crystal laser emits 2N (or more than 4) laser beams from the two-dimensional photonic crystal layer, each of which has an inclination angle and azimuth angle corresponding to each modulation period overlapping in the composite period. In fields such as LIDAR (Laser Imaging Detection And Ranging), which is a sensor for remote sensing, a laser light source that emits multiple laser beams is required, and the two-dimensional photonic crystal laser described in Patent Document 3 is suitable for such applications.

[0006] Prior art literature

[0007] Patent Literature

[0008] Patent Document 1: International Publication No. WO2014 / 136607

[0009] Patent Document 2: U.S. Patent Publication No. US2016 / 0248224

[0010] Patent Document 3: International Publication No. WO2022 / 181723 Summary of the Invention

[0011] Problems to be solved by the invention

[0012] The inventors of the present application have studied the two-dimensional photonic crystal laser described in Patent Document 3 and have discovered that, in addition to the 2N laser beams corresponding to the recombination period (referred to as the "original laser beams"), multiple unnecessary laser beams with weaker intensities are also emitted. While the intensities of these unnecessary laser beams are negligible when the original laser beams have intensities similar to those shown in the examples of Patent Document 3, if the intensity of the original laser beams is increased by increasing the current injected into the active layer, the intensities of the unnecessary laser beams also increase and become non-negligible.

[0013] An object of the present invention is to provide a two-dimensional photonic crystal laser that suppresses the emission of unnecessary laser beams and emits a plurality of (four or more) laser beams.

[0014] Solutions for solving problems

[0015] The two-dimensional photonic crystal laser of the present invention, which has been developed to solve the above-mentioned problems, is characterized by comprising:

[0016] a) a pair of electrodes;

[0017] b) an active layer provided between the pair of electrodes and generating light of a predetermined wavelength by injection of current from the electrodes; and

[0018] c) a two-dimensional photonic crystal layer disposed between one of the pair of electrodes and the active layer, comprising a plate-shaped base material and a plurality of different refractive index regions disposed on the base material and having a refractive index different from that of the base material;

[0019] The plurality of different refractive index regions are arranged at different positional deviations from each lattice point of the two-dimensional lattice periodically arranged at an in-plane period corresponding to the predetermined wavelength, or / and are arranged at each lattice point or at a position deviated from the lattice point by the positional deviation with an area different from a predetermined reference area, i.e., an area deviation amount.

[0020] For the position deviation and / or area deviation of each of the aforementioned multiple different refractive index regions, the modulation value determined by the composite period formed by overlapping multiple different in-plane periods is a value between a specified upper limit value and a specified lower limit value at the lattice point where the different refractive index region is configured is the modulation value, the upper limit value is the different refractive index region where the modulation value exceeds the upper limit value, and the lower limit value is the different refractive index region where the modulation value is less than the lower limit value.

[0021] Here, the term "composite period formed by overlapping multiple different in-plane periods" may also include overlapping modulations formed with multiple different period lengths along one direction (the same direction) parallel to the two-dimensional photonic crystal layer, overlapping modulations formed with one period length (which may be the same period length in each direction or different period lengths) in multiple directions parallel to the two-dimensional photonic crystal layer, and combinations thereof (combinations of modulations formed with multiple different period lengths along the multiple directions). "Position deviation" includes the distance from the lattice point, the size of the azimuth angle of the deviation, and a combination of these distances and azimuth angles.

[0022] As a premise for explaining the two-dimensional photonic crystal laser of the present invention, first, the two-dimensional photonic crystal laser described in Patent Document 3 will be further explained.

[0023] In the two-dimensional photonic crystal laser described in Patent Document 3, the positional deviation and / or area deviation of the different refractive index regions at each lattice point of the two-dimensional lattice are modulated with a composite period formed by overlapping multiple different periods, and the modulation phase Ψ(r↑) using the vector r↑ representing the position of each lattice point is given by

[0024]

[0025] Here, A n and exp(iα n ) are the amplitude and phase determined for each n respectively. Vector k n ↑ is achieved by having different tilt angles θ n and / or azimuth The wave number vector is determined by the combination of the inclination angle and azimuth angle of each of the N laser beams (N is an integer greater than 2, and n is an arbitrary value from 1 to N). In fact, 2N laser beams with azimuth angles that differ by 180° are emitted for each value of n. For example, when the two-dimensional lattice is a square lattice with a period length a, the vector k n ↑ By

[0026]

[0027] Using the modulation phase Ψ(r↑), the position deviation Δd(r↑) and area deviation ΔS(r↑) at each lattice point are expressed by

[0028]

[0029] express.

[0030] Here, Δd and ΔS are constants, and Δd(r↑) and ΔS(r↑) are functions of the variable r↑. The values ​​of Δd and ΔS can basically be determined arbitrarily. However, if Δd is too small, the position deviation Δd(r↑) becomes so small that it can be ignored. Therefore, the constant Δd is appropriately determined so that the value of Δd(r↑) at the position where Δd(r↑)≠0 becomes a non-negligible value (for example, 0.1nm or more). Similarly, ΔS is determined so that the value of ΔS(r↑) at the position where ΔS(r↑)≠0 becomes a non-negligible value (for example, 0.1nm or more). 2 The above) method is appropriately determined.

[0031] The following description will be given with reference to the position deviation amount Δd(r↑), but the description is also applicable to the area deviation amount ΔS(r↑).

[0032] The position deviation Δd(r↑) expressed by equation (3) uses the general complex number C.

[0033] sin[arg C]=Im(C) / |C|…(5)

[0034] (Here, Im(C) is the imaginary part of C),

[0035] Depend on

[0036]

[0037] It is considered that the second term of the denominator of formula (6) is

[0038]

[0039] With vector (k m ↑-k m' ↑) is the emission of the two-dimensional photonic crystal laser described in Patent Document 3 except for the vector k m ↑ (m is any one of 1 to N) The cause of unnecessary laser beams other than the corresponding 2N laser beams.

[0040] Therefore, in the two-dimensional photonic crystal laser of the present invention, the second term in the denominator of equation (6) is ignored and the modulation value Δd'(r↑) determined by the recombination period is defined as

[0041]

[0042] However, in formula (3), the maximum value that Δd(r↑) can take is the constant Δd. In contrast, ignoring the second term in the denominator of formula (6) may cause a lattice point where the modulation value Δd'(r↑) in formula (8) becomes too large. Therefore, in the two-dimensional photonic crystal laser of the present invention, the modulation value Δd'(r↑) obtained by formula (8) is a predetermined upper limit value Δd. max Compared with the specified lower limit value Δd min At the lattice point with a value between Δd and Δd, the modulation value Δd'(r↑) is set as the position deviation amount Δd(r↑). When the modulation value Δd'(r↑) exceeds the upper limit Δd max At the lattice point of max Assume that the position deviation is Δd(r↑), when the modulation value Δd'(r↑) is less than the lower limit value Δd min At the lattice point of min The upper limit value Δd is defined as the position deviation amount Δd (r↑). max Typically, it is Δd, but it is also allowed to change between 0.25Δd and 4.0Δd. In addition, the lower limit Δd min It is typically -Δd, but a change between -4.0Δd and -0.25Δd is also permitted.

[0043] As mentioned above, the above description of the position deviation Δd(r↑) is also applicable to the area deviation ΔS(r↑). Therefore, the modulation value ΔS'(r↑) determined by the composite period for the area deviation is given by

[0044]

[0045] Regulation.

[0046] The modulation value ΔS'(r↑) obtained by equation (9) is the upper limit value ΔS max Compared with the specified lower limit ΔS min At the lattice point with a value between ΔS and ΔS, the modulation value ΔS'(r↑) is set as the area deviation ΔS(r↑). When the modulation value ΔS'(r↑) exceeds the upper limit ΔS max At the lattice point, the upper limit ΔS max Assuming the area deviation ΔS(r↑), when the modulation value ΔS'(r↑) is less than the lower limit ΔS min At the lattice point, the lower limit ΔS min Let the area deviation be ΔS (r↑). Upper limit ΔS max Typically, it is ΔS, but it is also allowed to change between 0.25ΔS and 4.0ΔS. In addition, the lower limit ΔS min Typically, it is -ΔS, but it is also allowed to change between -4.0ΔS and -0.25ΔS. In addition, the lower limit value ΔS min And / or the reference area is the reference area and the lower limit value ΔS min The sum is set in a non-negative way.

[0047] By using these modulation values, upper limit value and lower limit value to define the position deviation amount Δd(r↑) and the area deviation amount ΔS(r↑), the two-dimensional photonic crystal laser of the present invention can emit light corresponding to the vector k n ↑ (n is any one of 1 to N) corresponding to 2N laser beams, but does not include the two-dimensional photonic crystal laser described in Patent Document 3 with vector (k m ↑-k m' ↑) caused by the unwanted laser beam.

[0048] In the two-dimensional photonic crystal laser of the present invention, the following configuration can be adopted:

[0049] The aforementioned two-dimensional lattice is a first square lattice belonging to the square lattice,

[0050] The plurality of different refractive index regions are arranged so as not to deviate from a first lattice point, which is a lattice point of the first square lattice, and each has an area determined by the area deviation amount.

[0051] Furthermore, the two-dimensional photonic crystal laser comprises a plurality of second different-refractive-index regions having a refractive index different from that of the base material.

[0052] The plurality of second different refractive index regions are arranged so as not to deviate from second lattice points that are lattice points of a second square lattice having the same period length as the first square lattice and arranged at positions different from those of the first square lattice.

[0053] The area of ​​the aforementioned second refractive index region at each second lattice point is a value that deviates from the specified second reference area by a second area deviation amount, and the second area deviation amount is the modulation value in the refractive index region where the aforementioned modulation value at the second lattice point is between the specified second upper limit value and the specified second lower limit value, the second upper limit value in the refractive index region where the modulation value exceeds the second upper limit value, and the second lower limit value in the refractive index region where the modulation value is less than the second lower limit value.

[0054] When a modified refractive index region is provided only at a first lattice point, if the modified refractive index region is arranged so as not to deviate from the first lattice point (i.e., the positional deviation is set to 0) and only the area deviation is modulated, the position of the node of the standing wave of the electric field formed within the two-dimensional photonic crystal layer coincides with the position of the modified refractive index region, and the intensity of the laser beam emitted from the two-dimensional photonic crystal layer is weakened. Therefore, by arranging a second modified refractive index region having an area determined by a second reference area and a second area deviation at a second lattice point of a second square lattice arranged at a different position from the first square lattice, so as not to deviate from the second lattice point, the second modified refractive index region is located at a position other than the node of the standing wave of the electric field, thereby enhancing the intensity of the laser beam.

[0055] To enhance the intensity of the laser beam through the aforementioned effects, it is ideal to arrange the different-refractive-index regions in both the first and second square lattices so that they do not deviate from the lattice points. However, it is also acceptable to arrange the different-refractive-index regions in one of the first and second square lattices so that they deviate from the lattice points, with modulation applied to the amount of positional deviation limited by upper and lower limits. Furthermore, other additional modulations may be applied as long as the modulation amount is small enough to have little effect on the characteristics of the laser beam.

[0056] Alternatively, in the two-dimensional photonic crystal laser of the present invention, the following structure may be adopted:

[0057] The aforementioned two-dimensional lattice is a first square lattice belonging to the square lattice,

[0058] The plurality of different refractive index regions are arranged so as to be deviated from the first lattice point, which is the lattice point of the first square lattice, by the positional deviation amount, and each has an area determined by the area deviation amount.

[0059] Furthermore, the two-dimensional photonic crystal laser comprises a plurality of second different-refractive-index regions having a refractive index different from that of the base material.

[0060] The multiple second different refractive index regions are arranged in a manner that does not deviate from the second lattice points that are lattice points of the second square lattice, and each has the same area. The second square lattice is a square lattice having the same period length as the aforementioned first square lattice and arranged at a position different from the first square lattice.

[0061] In a structure where both the position and area of ​​the different-refractive-index region are modulated at the first lattice point, increasing the area of ​​the laser oscillation region can degrade the laser beam quality due to, for example, oscillation in higher-order modes. Therefore, by arranging a second different-refractive-index region that does not modulate the position and area at a second lattice point of a second square lattice located at a different position from that of the first square lattice, the laser beam quality can be maintained. Alternatively, if the modulation amount is small enough to have little effect on the laser beam characteristics, the second different-refractive-index region can also be additionally modulated in position and / or area.

[0062] The second reference area, second upper limit and second lower limit can be set to the same values ​​as the reference area, upper limit and lower limit in the different refractive index region configured in the first square lattice, or some or all of them can be set to values ​​different from those of the different refractive index region.

[0063] In the structure including the second different-refractive-index region, the second square lattice is preferably arranged so as to be offset in the same direction as one of the two fundamental translation vectors of the first square lattice by a period within a range of 0.4 to 0.6 periods (more preferably 0.5 periods). Thus, by arranging the second different-refractive-index region near the antinode of the standing wave formed by the periodicity of the different-refractive-index region arranged at the first lattice point, the intensity of the laser beam emitted from the two-dimensional photonic crystal layer can be enhanced.

[0064] In the two-dimensional photonic crystal laser of the present invention, the position deviation and / or area deviation of each of the aforementioned multiple different refractive index regions can be represented by a function that takes the position of the aforementioned lattice point as a variable and saturates at the aforementioned upper limit and lower limit, respectively.

[0065] For example, the following σ is represented by a vector r↑ indicating the position of each lattice point.

[0066]

[0067] (k n ↑ and α n As described above, the function Δd(σ) of the position deviation amount and the function ΔS(σ) of the area deviation amount can be expressed as follows (with σ as a variable).

[0068]

[0069] Here, t is an arbitrary constant. Δd and ΔS are constants as described above. Furthermore, Δd(σ) and ΔS(σ) are functions of the variable σ, but since σ is represented by r↑, they are also functions of the variable r↑. These functions Δd(σ) and ΔS(σ) saturate at their lower limits -Δd and -ΔS, respectively, as σ approaches negative infinity, and saturate at their upper limits Δd and ΔS, respectively, as σ approaches positive infinity.

[0070] Effects of the Invention

[0071] According to the present invention, it is possible to obtain a two-dimensional photonic crystal laser that suppresses the emission of unnecessary laser beams and emits a plurality of (four or more) laser beams. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 1 and 2. (a) A perspective view showing a first embodiment of a two-dimensional photonic crystal laser according to the present invention, and (b) a partial plan view of a two-dimensional photonic crystal layer included in the two-dimensional photonic crystal laser.

[0073] Figure 2 This is a partial plan view showing a modification of the two-dimensional photonic crystal layer in the two-dimensional photonic crystal laser of the first embodiment, and an example in which the positions of the different refractive index regions are shifted in different directions from the lattice points.

[0074] Figure 3 This is a partial plan view showing a modification of the two-dimensional photonic crystal layer in the two-dimensional photonic crystal laser of the first embodiment, and shows an example in which only the position of the different refractive index region is modulated.

[0075] Figure 4 This is a modified example of the two-dimensional photonic crystal layer in the two-dimensional photonic crystal laser of the first embodiment, and is a partial plan view showing an example in which only the area of ​​the planar shape of the different refractive index region is modulated.

[0076] Figure 5 This is a diagram for explaining the tilt angle and azimuth angle of a laser beam emitted in an example of the two-dimensional photonic crystal laser according to the first embodiment.

[0077] Figure 6 This is a diagram showing the results of calculations to determine the intensity of the spot of the laser beam emitted from an example of the two-dimensional photonic crystal laser according to the first embodiment.

[0078] Figure 7 This is a diagram showing the results of calculations of the intensity of the spot of the laser beam emitted from the two-dimensional photonic crystal laser of the comparative example.

[0079] Figure 8 1 is a diagram showing an example of modulating the angle ξ indicating the direction in which the position at which the different refractive index region is arranged deviates from the lattice point.

[0080] Figure 9 1 and 2. (a) A perspective view showing a second embodiment of a two-dimensional photonic crystal laser according to the present invention, and (b) a partial plan view of a two-dimensional photonic crystal layer included in the two-dimensional photonic crystal laser.

[0081] Figure 10 This is a diagram showing the results of calculations to determine the intensity of the spot of the laser beam emitted from an example of the two-dimensional photonic crystal laser according to the second embodiment.

[0082] Figure 11 The diagram shows the results of calculation of the electric field distribution within the two-dimensional photonic crystal layer in an example (a) of the two-dimensional photonic crystal laser of the second embodiment and an example (b) of the two-dimensional photonic crystal laser of the first embodiment in which only the area is modulated.

[0083] Figure 12 This is a partial plan view showing a modified example of the two-dimensional photonic crystal layer in the two-dimensional photonic crystal laser according to the second embodiment.

[0084] Figure 13 This is a photograph showing a far-field image formed by a laser beam using the two-dimensional photonic crystal laser according to the third embodiment.

[0085] Figure 14 It means to form Figure 13 The far-field images shown are graphs showing experimental results of the relationship between peak optical output power and current for the third embodiment and a conventional two-dimensional photonic crystal laser.

[0086] Figure 15 This is a graph showing an example of a function of the area deviation amount ΔS(σ) in an example of the two-dimensional photonic crystal laser according to the fourth embodiment.

[0087] Figure 16 Is to express Figure 15 A graph showing an example of a change in the area deviation amount ΔS(σ) according to σ in an example of the two-dimensional photonic crystal laser according to the first embodiment, which is approximated by the function of .

[0088] Figure 17 This is a diagram showing the results of calculations to determine the intensity of the spot of the laser beam emitted from an example of the two-dimensional photonic crystal laser according to the fourth embodiment. DETAILED DESCRIPTION

[0089] use Figures 1 to 17 An embodiment of the two-dimensional photonic crystal laser of the present invention will be described.

[0090] (1) First embodiment

[0091] like Figure 1 As shown in (a), the two-dimensional photonic crystal laser 10 of the first embodiment has a structure in which a first electrode 171, a first cladding layer 141, a two-dimensional photonic crystal layer 12, a spacer layer 13, an active layer 11, a second cladding layer 142, a substrate 16, and a second electrode 172 are stacked in this order. However, the order of the active layer 11 and the two-dimensional photonic crystal layer 12 can also be reversed to the above order. Figure 1 In (a), for convenience, the first electrode 171 is shown as the lower side and the second electrode 172 is shown as the upper side, but the orientation of the two-dimensional photonic crystal laser 10 during use is not limited to the orientation shown in the figure. The following describes the configuration of each layer and electrode.

[0092] The active layer 11 emits light in a predetermined wavelength band due to charge injection from the first electrode 171 and the second electrode 172. The material of the active layer 11 can be, for example, InGaAs / AlGaAs multiple quantum wells (emission wavelength band: 935 to 945 nm).

[0093] like Figure 1 As shown in (b), the two-dimensional photonic crystal layer 12 is configured with a different refractive index region 122 having a different refractive index from each lattice point of the two-dimensional lattice on a plate-shaped base material 121. Figure 1 In (b), only a portion of the two-dimensional photonic crystal layer 12 is magnified. In the actual two-dimensional photonic crystal layer 12, a plurality of different refractive index regions 122 are arranged within a range that is the same as the outer edge of the planar shape of the second electrode 172. The material of the base material 121 can be, for example, p-type GaAs (p-type semiconductor). In the different refractive index regions 122, holes are typically used, but a member having a refractive index different from that of the base material 121 can also be used instead of the holes. The position where the different refractive index regions 122 are arranged and the planar shape of the different refractive index regions 122 will be described in detail later.

[0094] The first cladding layer 141 and the second cladding layer 142 have the function of injecting charges from the first electrode 171 and the second electrode 172, and have the function of suppressing the leakage of the in-plane guided light guided parallel to the two-dimensional photonic crystal layer 12 from the layer. In order to achieve the former function, a p-type semiconductor (e.g., p-type Al 0.37 Ga 0.63 As), an n-type semiconductor (e.g., n-type Al 0.37 Ga 0.63 As) (Note that the reason for using the base material 121 of the two-dimensional photonic crystal layer 12 as a p-type semiconductor is the same as this).

[0095] The spacer layer 13 is provided to allow holes injected from the first electrode 171 to pass through and be introduced into the active layer 11, while suppressing electrons injected from the second electrode 172 from passing through the active layer 11 (thereby, combining with holes closer to the first electrode 171 than the active layer 11). The material of the spacer layer 13 can be, for example, p-type Al 0.45 Ga 0.55 As.

[0096] The substrate 16 is sufficiently thicker than other layers in order to maintain the mechanical strength of the entire two-dimensional photonic crystal laser 10. For the same reason as the second cladding layer 142, an n-type semiconductor is used as the material of the substrate 16.

[0097] In the first embodiment, the first electrode 171 is formed of a square metal plate-like member. In the first embodiment, the second electrode 172 is formed by hollowing out a square metal plate-like member having a side length longer than that of the first electrode 171. The hollowed-out portion of the plate-like member of the second electrode 172 is referred to as a window portion 1722, and the portion where the plate-like member remains is referred to as a frame portion 1721. As described later, the window portion 1722 is provided to allow the laser beam oscillating from the two-dimensional photonic crystal layer 12 to pass through. In addition, Figure 1 In (a), the first electrode 171 and the first cladding layer 141 are shown separately to illustrate the shape of the first electrode 171 , but the first electrode 171 is actually in contact with the first cladding layer 141 .

[0098] The materials of the various layers described so far are examples, and other materials may also be used. Furthermore, the shapes of the first electrode 171 and the second electrode 172 are not limited to those described above, and electrodes of other shapes may also be used (e.g., a first electrode formed of a circular metal plate-like member and a second electrode formed of a circular metal plate-like member having a diameter greater than that of the first electrode, with the center hollowed out to form a circular shape).

[0099] Hereinafter, the position where the different refractive index region 122 is arranged in the two-dimensional photonic crystal layer 12 and the planar shape of the different refractive index region 122 will be described in detail.

[0100] exist Figure 1In the example shown in (b), the center of gravity G of the planar shape of the different refractive index region 122 is located at a position deviated from the y direction by a predetermined position deviation amount from the lattice point of the intersection of the single-point dashed line extending along the x direction (the horizontal direction of the figure) and the single-point dashed line extending along the y direction (the vertical direction of the figure) in the square lattice represented by the single-point dashed line in the figure. The position deviation amount is different for each different refractive index region 122 (lattice point) as described later. The planar shape of each different refractive index region 122 is an ellipse with the x direction as the major axis, and its area (area deviation amount described later) is also different for each different refractive index region 122. In addition, the lattice point period (length) a of the square lattice is appropriately determined according to the material of the base material 121 and the light-emitting wavelength band in the active layer 11. In addition, other two-dimensional lattices such as rectangular lattices and triangular lattices can also be used instead of the square lattice. The planar shape including the positional deviation amount and / or area of ​​the different refractive index region 122 can be modified in various ways, and examples of these modifications will be described later.

[0101] Here, the positional deviation amount at each lattice point represented by the position vector r↑ of each lattice point is determined based on the introduction of the following value σ. σ is given by

[0102]

[0103] Here, k n ↑As mentioned above, the inclination angles θ are different from each other. n and / or azimuth The wave number vector is determined by the combination of the tilt angle and azimuth angle of each of the N laser beams (N is an integer greater than 2, and n is an arbitrary value from 1 to N). In the first embodiment, a square lattice is used, so it is expressed by formula (2). In the first embodiment, the position deviation Δd (r↑) at each lattice point is set to

[0104]

[0105] On the right side of the first row of equation (12), in the modulation amount Δd'(r↑) determined by the composite period shown in equation (8), the amplitude A is set to n It is set to 1. In addition, the amplitude A is set to n The fact that the value 1 is not a necessary condition of the present invention is merely an example of the present invention. In the second and third lines of formula (12), the upper limit of the position deviation Δd(r↑) is defined as a constant +Δd, and the lower limit is defined as a constant -Δd. In addition, on the right side of the first line of formula (12), when σ is set to the upper limit of the formula in the first line, that is, N 1 / 2 And the lower limit is -N 1 / 2When , the values ​​of Δd(r↑) become +Δd and -Δd, respectively, which are consistent with the values ​​of the second and third rows, respectively.

[0106] Thus, in the first embodiment, an upper limit value Δd is set for the position deviation amount determined by the composite period. max =Δd and lower limit Δd inx =-Δd, so that positional deviation outside the range between the upper limit and the lower limit does not occur. In the first embodiment, since the different refractive index region 122 is deviated in the y direction, the positive or negative sign of Δd(r↑) indicates the positive or negative sign in the y direction.

[0107] The area S(r↑) of the planar shape of the different refractive index region 122 is the sum of a predetermined reference area S0 that is independent of the position of the lattice point and an area deviation ΔS(r↑) representing the deviation from the reference area S0.

[0108] S(r↑)=S0+ΔS(r↑)…(13)

[0109] The area deviation ΔS(r↑) is expressed in the same way as the position deviation Δd(r↑).

[0110]

[0111] . Thus, the area deviation ΔS(r↑) is also determined by the modulation amount, which is determined by the composite period of the linear sum of the sine functions of σ in the first row on the right side of equation (14), the upper limit +ΔS, and the lower limit -ΔS, so that no area deviation exceeding the upper limit occurs. Furthermore, the reference area S0 is set to a value larger than ΔS so that no different-refractive-index regions 122 with negative S(r↑) values ​​occur. On the other hand, if the reference area S0 is too large, adjacent different-refractive-index regions 122 overlap, so the reference area S0 is determined so that no such overlap occurs.

[0112] The position deviation Δd(r↑) shown in formula (12) and the area deviation ΔS(r↑) shown in formula (14) are defined by the same σ and therefore have the same compound period. Figure 1 As shown in (b), the area deviation ΔS(r↑) of the different-refractive-index region 1221 located at the lattice point (Δd(r↑)=0) is also 0 (therefore, the area S is S0), the area deviation ΔS(r↑) of the different-refractive-index region 1222 that is configured to deviate in the positive direction in the y direction compared to the lattice point (Δd(r↑)>0) is positive (S>S0), and the area deviation ΔS(r↑) of the different-refractive-index region 1223 that is configured to deviate in the negative direction in the y direction compared to the lattice point (Δd(r↑)<0) is negative (S <S0)。

[0113] In the example shown above, the position of the different refractive index region 122 is modulated so as to be deviated from the lattice point in the y direction, but the position of the different refractive index region 122 may be modulated so as to be deviated in other directions. Figure 2 In the example shown, the major axis of the ellipse of the different refractive index region 122 is Figure 1 (b) is also oriented in the x direction, and the direction of the position deviation is set to the x direction. Figure 3 As shown, it is also possible to not modulate the area of ​​the planar shape (using the different refractive index regions 122 of the same area) and only modulate the position deviation. Figure 4 As shown, instead of modulating the amount of positional deviation (arranging the different refractive index regions 122 at lattice points), only the area of ​​the planar shape may be modulated.

[0114] Next, the results of calculating the intensity of the laser beam emitted by the two-dimensional photonic crystal laser 10 of the first embodiment are shown. In this calculation example, the intensity of the laser beam spot incident on a surface parallel to the two-dimensional photonic crystal layer 12 and at a predetermined distance from the second electrode 172 in a direction perpendicular to the layer is calculated. In this calculation example, θ in equation (2) is set to n and combination of They are (5°, 0°), (5°, 45°), (5°, 90°), (5°, 135°), (10°, 0°), (10°, 22.5°), (10°, 45°), (10°, 67.5°), (10°, 90°), (10°, 112.5°), (10°, 135°), (10°, 157.5°), (15°, 9°), (15°, 27 °), (15°, 45°), (15°, 63°), (15°, 81°), (15°, 99°), (15°, 117°), (15°, 135°), (15°, 153°), (15°, 171°), (20°, 6.4°), (20°, 19.3°), (20°, 32.1°), (20°, 45°), (20°, 57.9°), (2 0°,70.7°)、(20°,83.6°)、(20°,96.4°)、(20°,109.3°)、(20°,122.1°)、(20°,135°)、(20°,147.9°)、(20°,160.7°)、(20°,173.6°)、(25°,6.4°)、(25°,19.3°)、(25°,32.1°)、( 50 (N=50) vectors k including (25°,45°), (25°,57.9°), (25°,70.7°), (25°,83.6°), (25°,96.4°), (25°,109.3°), (25°,122.1°), (25°,135°), (25°,147.9°), (25°,160.7°), and (25°,173.6°) n ↑. Figure 5 As shown, these vectors k n ↑ works as follows: the tilt angle θ n =5° laser beam at an azimuth angle of A total of 8 lines are injected, and θ n =10° laser beam per A total of 16 lines are injected, and θ n =15° laser beam per A total of 20 shots are injected, and θ n = 20° laser beam per A total of 28 shots were emitted, and θ n = 25° laser beam per A total of 28 beams are emitted. The total number of emitted laser beams is 100 (=2N).

[0115] When these vectors k nWhen applied to equation (11), σ is represented by the linear sum of sine functions with N = 50 terms. In this calculation example, equations (12) and (14) are calculated with Δd = 0.08a (i.e., the upper limit of the positional deviation is 8% of the lattice constant a of the square lattice), S0 = 0.095a 2 (i.e. S0 is the area of ​​the unit cell of the square lattice a 2 9.5%), ΔS=0.03a 2 (That is, the upper limit of the area deviation is the area a of the unit cell of the square lattice 2 3% of ) for calculation.

[0116] As a comparative example, the same 50 vectors k as in the above calculation example are set. n ↑, set S0 = 0.095a 2 On the basis of the above, the intensity of the laser beam spot was also calculated by applying composite modulation without setting the upper limit +Δd and lower limit -Δd of the position deviation, and the upper limit +ΔS and lower limit -ΔS of the area deviation. This comparative example is equivalent to the two-dimensional photonic crystal laser of Patent Document 3. However, in this calculation, the injected current was increased compared to the calculation performed in Patent Document 3, thereby increasing the intensity of the laser beam. In the calculation of the first embodiment, the current was also set to the same magnitude as in the comparative example.

[0117] Figure 6 The calculation results of the first embodiment are shown. Figure 7 The calculation results of the comparative example are shown in Figure 2. Figure 5 In addition to the original spot position of the laser beam shown in FIG, multiple spots of laser beams weaker than the original spot are observed. For these weak laser beams, the injection current is increased, and as a result, unnecessary laser beams weak enough to be ignored become prominent in Patent Document 3. In contrast, in Figure 6 In the figure, almost no unnecessary laser beam is observed, and it can be seen that the first embodiment can suppress the emission of such unnecessary laser beam.

[0118] It should be noted that, in the first embodiment, Figure 6 A negligibly weak unnecessary laser beam is also emitted. If expressed as the ratio of the sum of the intensities of the unnecessary laser beams to the sum of the intensities of all laser beams (the sum of the original laser beams and the unnecessary laser beams), the comparative example is 23.9%, whereas the first embodiment is 8.5%, confirming that the first embodiment also suppresses the emission of unnecessary laser beams based on the calculated values.

[0119] The two-dimensional photonic crystal laser of the first embodiment has Figures 2 to 4In addition to the modified example of changing the periodic structure of the two-dimensional photonic crystal layer shown, various modifications can be made. For example, in the above embodiment, the planar shape of the different refractive index region is set to be an ellipse, but it can also be set to various shapes such as an equilateral triangle, a triangle other than this, a polygon with a quadrilateral or larger, a circle, an irregular shape, etc. In addition, a different refractive index region can also be composed of a combination of multiple holes or components different from the base material.

[0120] The position deviation Δd(r↑) shown in formula (12) is obtained by converting A in formula (8) to n The value of is set to 1, but it is also possible to set A for each n. n The same applies to the area deviation ΔS(r↑) shown in formula (14).

[0121] In the examples shown so far, the positional deviation amount is set to any of the two directions (x direction and y direction) in which the lattice points of the square lattice are arranged, but it is also possible to arrange it so as to deviate from the lattice points in directions other than these. In addition, in the examples shown so far, the distance from the lattice point is set as the positional deviation amount, but it is also possible to use the angle ξ (see ) formed by the direction of deviation from the lattice point with respect to a predetermined reference direction (for example, the x direction or the y direction) instead of or in addition to it. Figure 8 , with the x direction being the reference direction in the figure) is set as the positional deviation amount (ie, the angle ξ is different for each lattice point).

[0122] exist Figure 1 In the example shown in (b), the same vector k is used. n ↑ (n is any one of 1 to N) to determine the position deviation Δ(r↑) and area deviation ΔS(r↑), thereby emitting 2N laser beams, but the position deviation Δ(r↑) is calculated using the vector k n ↑ (n is any one of 1 to N) is determined, and the area deviation ΔS (r↑) can be used with k n ↑ Different vector k m ↑ (m is any one of 1 to M, and M may be the same as or different from N).

[0123] (2) Second embodiment

[0124] like Figure 9 As shown, the two-dimensional photonic crystal laser 20 of the second embodiment has the same structure as the two-dimensional photonic crystal laser 10 of the first embodiment, except that the structure of the two-dimensional photonic crystal layer 22 is different from the two-dimensional photonic crystal layer 12 of the two-dimensional photonic crystal laser 10 of the first embodiment. Therefore, only the structure of the two-dimensional photonic crystal layer 22 will be described below.

[0125] The two-dimensional photonic crystal layer 22 comprises a first different-refractive-index region 2221 and a second different-refractive-index region 2222, each having a refractive index different from that of the base material 221, periodically arranged on a plate-like base material 221. In this embodiment, both the first different-refractive-index region 2221 and the second different-refractive-index region 2222 are configured as holes (air), but regions formed from a member other than the base material 221 (other than air) may also be used. When such a member is used, the first different-refractive-index region 2221 and the second different-refractive-index region 2222 may be formed from the same material or from different materials.

[0126] The first different refractive index region 2221 is arranged so that the center of gravity of the planar shape coincides with the first lattice point 2241 which is a lattice point of the first square lattice 2231. Figure 9 The square lattice of period a is shown by the dashed line extending in the x direction and the dashed line extending in the y direction in (b). The second different refractive index region 2222 is arranged so that the center of gravity of the planar shape coincides with the second lattice point 2242 which is the lattice point of the second square lattice 2232. Figure 9 The dashed line extending in the x-direction and the dashed line extending in the y-direction (the latter being common to the first square lattice 2231) in (b) of FIG. A square lattice with a period a is shown. That is, the first modified refractive index region 2221 and the second modified refractive index region 2222 are arranged at lattice points of the square lattice that are offset from each other by a / 2 in the y-direction.

[0127] The planar shape of each first different refractive index region 2221 is an ellipse, and its area S1 (r↑) is determined by a first reference area S that is independent of the first different refractive index region 2221 (lattice point). 01 and the area deviation ΔS1(r↑) depending on the position vector r↑ of the first different refractive index region 2221 (lattice point)

[0128] S1(r↑)=S 01 +ΔS1(r↑)…(15)

[0129] ΔS1(r↑) is expressed by using σ shown in formula (11) and the first upper limit value ΔS1 which is the upper limit value of the area of ​​the first different refractive index region 2221.

[0130]

[0131] Therefore, the first lower limit value is -ΔS1.

[0132] In addition, the planar shape of each second different refractive index region 2222 is an ellipse, and its area S2 (r↑) is determined by the second reference area S that is independent of the second different refractive index region 2222 (lattice point). 02 and the area deviation ΔS2(r↑) depending on the position vector r↑ of the second different refractive index region 2222 (lattice point)

[0133] S2(r↑)=S 02 +ΔS2(r↑)…(17)

[0134] ΔS2(r↑) uses σ shown in formula (11) and the second upper limit value ΔS2 which is the upper limit value of the area of ​​the first different refractive index region 2221, and is expressed by

[0135]

[0136] Therefore, the second lower limit is -ΔS2. In addition, the first reference area S 01 and the second reference area S 02 They may be the same value or different values. In addition, the first upper limit value ΔS1 and the second upper limit value ΔS2 may be the same value or different values.

[0137] Next, the results of calculating the intensity of the laser beam emitted by the two-dimensional photonic crystal laser 20 according to the second embodiment are shown. In this calculation example, the vector k n ↑ is set to θ in formula (2) n and combination of There are 12 types (N=12) of vectors, namely (11°, 0°), (11°, 90°), (23°, 0°), (23°, 90°), (36°, 0°), (36°, 90°), (11×21 / 2°, 45°), (11×21 / 2°, 135°), (23×21 / 2°, 45°), (23×21 / 2°, 135°), (36×21 / 2°, 45°), and (36×21 / 2°, 135°). These vectors k n ↑ works as follows: the tilt angle θ n =11°, 23° and 36° laser beams are emitted at azimuth angles And these 4 lines of 270°, and the inclination angle θ n =11×2 1 / 2 °, 23×2 1 / 2 ° and 36×2 1 / 2 ° laser beams are emitted at azimuth angles And 4 lines of 305°, a total of 24 (2N) lines. Regarding the parameters in equations (16) and (18), the first reference area S01 Set to 0.075a 2 , the second reference area S 02 Set to 0.055a 2 , the first upper limit value ΔS1 is set to 0.03a 2 The second upper limit value ΔS2 is set to 0.025a 2 .

[0138] The calculation results are as follows Figure 10 As shown in the figure, 24 laser beam spots are obtained, and no other spots are observed. However, in fact, Figure 10 Since a negligibly weak unnecessary laser beam was emitted, the ratio of the total intensities of the unnecessary laser beams to the total intensities of all the laser beams was calculated to be 22%.

[0139] As a comparative example, the first different-refractive-index region 2221 is modulated based on the formula (4) without setting the upper limit and the lower limit, and the second different-refractive-index region 2222 is not modulated in terms of position and area and has a second reference area S 02 =0.055a 2 Here, in the first different refractive index region 2221, in order to correspond to the example of the second embodiment, all n in the formula (4) are set to A n =1, and the constant ΔS is set to the first upper limit value ΔS1=0.03a 2 In this comparative example, the ratio of the total intensities of the unnecessary laser beams to the total intensities of all the laser beams was calculated to be 4.7%. Thus, it was confirmed that the second embodiment suppressed the emission of unnecessary laser beams compared to the comparative example.

[0140] Figure 11 The figure shows the results of calculating the electric field distribution within the two-dimensional photonic crystal layer for an example (a) of a two-dimensional photonic crystal laser according to the second embodiment and an example (b) of a two-dimensional photonic crystal laser according to the first embodiment in which only the area is modulated. (b) is equivalent to a configuration in which only the first different-refractive-index region 2221 is provided (the second different-refractive-index region 2222 is removed) in the two-dimensional photonic crystal layer 22 of the two-dimensional photonic crystal laser according to (a). The direction and length of the multiple arrows shown in these figures represent the direction and magnitude of the electric field at that position. It can be seen that the electric field in both (a) and (b) becomes smaller near the first different-refractive-index region 2221. On the other hand, as shown in (a), the electric field near the second different-refractive-index region 2222 is larger than that near the first different-refractive-index region 2221. Therefore, compared with the example (b), the example (a) is more likely to emit a laser beam to the outside of the two-dimensional photonic crystal layer.

[0141] Various modifications are also possible in the second embodiment. For example, the shapes of the first and second different refractive index regions 2221 and 2222 are not limited to ellipses and can be various shapes, as in the examples given in the first embodiment. Furthermore, the direction and magnitude of the deviation between the first and second square lattices are not limited to the above example (1 / 2a in the y direction) and can be various directions and magnitudes.

[0142] In addition, if Figure 12 As shown, the first different-refractive-index region 2221A may be arranged at each first lattice point of the first square lattice (the square lattice shown by the vertical and horizontal single-dot dash lines in the figure) in a manner that respectively becomes a specified position deviation and area deviation, and the second different-refractive-index region 2222A may be arranged at each second lattice point of the second square lattice (the square lattice shown by the horizontal double-dot dash line and the vertical single-dot dash line in the figure) in a manner that respectively has no position deviation and area deviation. Thus, even if the area of ​​the region where the laser oscillates is increased, oscillation in a high-order mode can be prevented, and the quality of the laser beam can be maintained. In addition, in Figure 12 , an example is shown in which the second square lattice is arranged so as to be offset from the first square lattice by 1 / 2 period in the vertical direction of the figure, but the size and direction of the offset are arbitrary.

[0143] (3) Third embodiment

[0144] Thus far, an embodiment of a two-dimensional photonic crystal laser that suppresses the emission of unnecessary laser beams and emits multiple laser beams has been described. However, as described in Patent Document 3, if the number of laser beams is sufficiently large, it is possible to form a distribution of laser spots representing various patterns, such as patterns that uniformly illuminate a wide angle range, patterns representing text and / or images, etc. In such a case, a method of setting upper and lower limits for the position deviation and / or area deviation of the different refractive index regions can also be used.

[0145] The electric field distribution in the wave number space corresponding to the distribution of the laser spot to be formed at a position far from the two-dimensional photonic crystal laser (far-field image) is defined as the target far-field electric field distribution E far_iFFT (K↑), in order to form such a target remote electric field distribution E far_iFFT (K↑) The electric field distribution (near-field image) of the laser beam emitted from the two-dimensional photonic crystal layer of the two-dimensional photonic crystal laser in the real space in the cross section parallel to the layer within the two-dimensional photonic crystal layer is set as the target radiation electric field distribution E rad_iFFT (r↑). Target radiation electric field distribution E rad_iFFT (r↑) is calculated by using the complex correction coefficient A(K↑) to calculate the target remote electric field distribution E far_iFFT (K↑) performs inverse Fourier transform, and the following formula (21)

[0146] E rad_iFFT (r↑)=C∫∫A(K↑)E far_iFFT (K↑)exp(iK↑·r↑)dK↑…(21)Calculate.

[0147] Therefore, the radiation electric field distribution E is obtained based on the modulation phase Ψ(r↑) of the different refractive index region at each position r↑=(x, y). rad (r↑) is close to the target radiation electric field distribution E obtained by equation (21) rad_iFFT The modulation phase Ψ(r↑) is adjusted at the position r↑=(x, y) of each lattice point where the different refractive index region is arranged.

[0148] For example, by applying the following formula (22) using formula (21)

[0149]

[0150] The adjusted modulation phase Ψ(r↑) can be determined (see Patent Document 3).

[0151] The position deviation amount Δd(r↑) without considering the upper and lower limits is expressed by the following equation (23):

[0152] Δd(r↑)=B·Δd·sin(Ψ(r↑))…(23).

[0153] Here, B·Δd is a positive constant, and is represented by the product of a constant B greater than 1 and a value Δd set as an upper limit value and a lower limit value in the following formula (24).

[0154] If the upper limit Δd and the lower limit -Δd are applied to equation (23), the position deviation Δd(r↑) is expressed by equation (24):

[0155] Δd(r↑)=B·Δd·sin(Ψ(r↑))(|B·sin(Ψ(r↑))|≤1)

[0156] Δd(B·sin(Ψ(r↑)>1)

[0157] -Δd(B·sin(Ψ(r↑)<-1)…(24).

[0158] Similarly, the area deviation ΔS(r↑) is expressed by the following formula (25) using a constant C greater than 1, an upper limit ΔS, and a lower limit -ΔS:

[0159] ΔS(r↑)=C·ΔS·sin(Ψ(r↑))(|C·sin(Ψ(r↑))|≤1)

[0160] ΔS(C·sin(Ψ(r↑)>1)

[0161] -ΔS(C·sin(Ψ(r↑)<-1)…(25).

[0162] The area S(r↑) of the different refractive index region is expressed as S(r↑)=S0+ΔS(r↑) using the reference area S0 as in the first embodiment.

[0163] Next, an example of a two-dimensional photonic crystal laser according to the third embodiment, which was produced by forming characters as far-field images, is described together with a comparative example. In both these examples and the comparative example, E is determined by forming a far-field image of the character string "Kyoto" written horizontally and the character string "Univ." written vertically. far_iFFT (K↑). In both the embodiment and the comparative example, the different refractive index regions are arranged in a manner such that the positions in the absence of positional deviation form a square lattice with a period length a (=195 nm), and the positional deviation amount and area deviation amount described later are added (both of which are different in the embodiment and the comparative example). In the embodiment, B in formula (24) is set to 2.5, Δd is set to 0.08a, C in formula (25) is set to 2.5, and ΔS is set to 0.03a. 2 , set S0 to 0.10a 2 In the comparative example, no upper limit or lower limit is set, and the position deviation Δd(r↑) is set to B·Δd·sin(Ψ(r↑)) and the area deviation ΔS(r↑) is set to C·ΔS·sin(Ψ(r↑)) in all the different refractive index regions, and the same values ​​as those in the embodiment are used for B, Δd, C, ΔS, and S0.

[0164] Figure 13 A photograph of the far-field image obtained in the example is shown. A far-field image consisting of a designed character string was obtained. This demonstrates that even in the two-dimensional photonic crystal laser of the third embodiment, adverse effects such as laser light extinction caused by high-order diffraction can be suppressed, allowing for the formation of clear patterns such as characters.

[0165] exist Figure 14 In the embodiment and the comparative example, the results of experimentally determining the relationship between the optical output power of the laser beam during the injection of a pulsed current into a two-dimensional photonic crystal laser, i.e., the peak optical output power, and the magnitude of the current are shown. Here, the pulse width of the pulsed current is set to 100 nanoseconds. If the same current value is used for comparison, the peak optical output power of the embodiment is greater than that of the comparative example. The slope efficiency value obtained based on the experimental results is 0.70W / A in the embodiment and 0.31W / A in the comparative example. In this way, the two-dimensional photonic crystal laser of the third embodiment can suppress high-order diffraction as described above and achieve high slope efficiency.

[0166] (4) Fourth embodiment

[0167] In the fourth embodiment, the position deviation and / or area deviation of each of the plurality of different refractive index regions are defined by a function that uses the position of the lattice point as a variable and is saturated at an upper limit and a lower limit. An example of such a function is a sigmoid function. There are several forms of sigmoid functions. For example, the error function generally uses the variable x as the variable and uses

[0168]

[0169] Here, after replacing the variable x with the variable σ containing the position vector r↑ represented by equation (11), setting the maximum value of the position deviation amount to Δd and the maximum value of the area deviation amount to ΔS, the position deviation amount and the area deviation amount are defined as functions of the variable σ, Δd(σ) and ΔS(σ), as shown in the following equation (27).

[0170]

[0171] Here, t is an arbitrary constant. It should be noted that since the variable σ includes the position vector r↑, Δd(σ) and ΔS(σ) are also functions using position as a variable.

[0172] The function ΔS(σ) in equation (27) (hereinafter, the same applies to Δd(σ) in this paragraph) saturates at the lower limit -ΔS as σ approaches negative infinity, and saturates at the upper limit ΔS as σ approaches positive infinity. Near σ = 0, it increases monotonically as σ increases, and when σ = 0, the slope becomes approximately (0.8 / t). For example, when t = 0.09 in equation (27), ΔS(σ) is as follows Figure 15 As shown in the graph of , the lower limit value -ΔS and the upper limit value ΔS are saturated, and the slope becomes about 8.9 when σ = 0. Thus, the function ΔS(σ) of formula (27) is the change of σ when t = 0.09, which is the same as the calculation example ( Figure 6 ) using 50 (N=50) vectors k n ↑The determined area deviation is expressed as σ Figure 16 The graph is close to the changes.

[0173] Thus, when t=0.09 in formula (27), Figure 6 Similarly, in the calculation example of Δd=0.008a、S0=0.095a 2 ,ΔS=0.03a 2 The intensity of the laser beam spot is calculated under the condition of Figure 17 As shown, almost no Figure 7 The unwanted laser beam spot shown in the comparative example is close to Figure 6 The light spot of the calculation example.

[0174] The above shows an example of using an error function, which is one of the sigmoid functions, to determine the position deviation and area deviation of the different refractive index region, but as long as the function uses the position of the lattice point as a variable and is saturated at the upper and lower limits respectively, a sigmoid function or other functions other than the error function can also be used.

[0175] The method of determining the positional deviation and area deviation of the different refractive index region using the Sigmoid function can also be applied to the case of forming the distribution of the laser spot representing the various patterns described in the third embodiment. Specifically, using the modulation phase Ψ(r↑) shown in formula (22) obtained from formula (21), the function of r↑ represented by formula (23), that is, Δd(r↑)=B·Δd·sin(Ψ(r↑)), is used as the function Δd(σd) of the variable σd, and the area deviation is used as the function ΔS(r↑)=C·ΔS·sin(Ψ(r↑)) as the variable σ S Function ΔS(σ S ) are set as the position deviation and area deviation. These functions Δd(σd) and ΔS(σ S ) is expressed as follows.

[0176]

[0177] [Way]

[0178] It will be apparent to those skilled in the art that the above-described exemplary embodiments are specific examples of the following aspects.

[0179] (Item 1) A two-dimensional photonic crystal laser according to one embodiment of the present invention is characterized by comprising:

[0180] a) a pair of electrodes;

[0181] b) an active layer provided between the pair of electrodes and generating light of a predetermined wavelength by injection of current from the electrodes; and

[0182] c) a two-dimensional photonic crystal layer disposed between one of the pair of electrodes and the active layer, comprising a plate-shaped base material and a plurality of different refractive index regions disposed on the base material and having a refractive index different from that of the base material;

[0183] The plurality of different refractive index regions are arranged at different positional deviations from each lattice point of the two-dimensional lattice periodically arranged at an in-plane period corresponding to the predetermined wavelength, or / and are arranged at each lattice point or at a position deviated from the lattice point by the positional deviation with an area different from a predetermined reference area, i.e., an area deviation amount.

[0184] For the position deviation and / or area deviation of each of the aforementioned multiple different refractive index regions, the modulation value determined by the composite period formed by overlapping multiple different in-plane periods is a value between a specified upper limit value and a specified lower limit value at the lattice point where the different refractive index region is configured is the modulation value, the upper limit value is the different refractive index region where the modulation value exceeds the upper limit value, and the lower limit value is the different refractive index region where the modulation value is less than the lower limit value.

[0185] (Second Item) The two-dimensional photonic crystal laser of the second item is characterized in that, in the two-dimensional photonic crystal laser of the first item,

[0186] The vector r↑ representing the position of each lattice point of the two-dimensional lattice and the vector k representing the combination of the tilt angle and the azimuth angle of each of n laser beams having different tilt angles and / or azimuth angles are used. n ↑、Amplitude A determined for each n n and phase exp(iα n ) and a constant Δd, the modulation value Δ'd (r↑) of the position deviation at each lattice point is given by

[0187]

[0188] Represents, wherein n is an integer greater than 2.

[0189] (Item 3) The two-dimensional photonic crystal laser of Item 3 is characterized in that, in the two-dimensional photonic crystal laser of Item 1,

[0190] The vector r↑ representing the position of each lattice point of the two-dimensional lattice and the vector k representing the combination of the tilt angle and the azimuth angle of each of n laser beams having different tilt angles and / or azimuth angles are used. n ↑、Amplitude A determined for each n n and phase exp(iα n ) and constant ΔS, the modulation value Δ'S (r↑) of the aforementioned area deviation at each lattice point is given by

[0191]

[0192] Represents, wherein n is an integer greater than 2.

[0193] (Item 4) The two-dimensional photonic crystal laser of Item 4 is characterized in that, in the two-dimensional photonic crystal laser of Item 1 or Item 3,

[0194] The aforementioned two-dimensional lattice is a first square lattice belonging to the square lattice,

[0195] The plurality of different refractive index regions are arranged so as not to deviate from a first lattice point, which is a lattice point of the first square lattice, and each has an area determined by the area deviation amount.

[0196] Furthermore, the two-dimensional photonic crystal laser comprises a plurality of second different-refractive-index regions having a refractive index different from that of the base material.

[0197] The plurality of second different refractive index regions are arranged so as not to deviate from second lattice points that are lattice points of a second square lattice having the same period length as the first square lattice and arranged at positions different from those of the first square lattice.

[0198] The area of ​​the aforementioned second refractive index region at each second lattice point is a value that deviates from the specified second reference area by a second area deviation amount, and the second area deviation amount is the modulation value in the refractive index region where the aforementioned modulation value at the second lattice point is between the specified second upper limit value and the specified second lower limit value, the second upper limit value in the refractive index region where the modulation value exceeds the second upper limit value, and the second lower limit value in the refractive index region where the modulation value is less than the second lower limit value.

[0199] (Item 5) The two-dimensional photonic crystal laser of Item 5 is the two-dimensional photonic crystal laser of any one of Items 1 to 3,

[0200] The aforementioned two-dimensional lattice is a first square lattice belonging to the square lattice,

[0201] The plurality of different refractive index regions are arranged so as to be deviated from the first lattice point, which is the lattice point of the first square lattice, by the positional deviation amount, and each has an area determined by the area deviation amount.

[0202] Furthermore, the two-dimensional photonic crystal laser comprises a plurality of second different-refractive-index regions having a refractive index different from that of the base material.

[0203] The multiple second different refractive index regions are arranged in a manner that does not deviate from the second lattice points that are lattice points of the second square lattice, and each has the same area. The second square lattice is a square lattice having the same period length as the aforementioned first square lattice and arranged at a position different from the first square lattice.

[0204] (Item 6) The two-dimensional photonic crystal laser of Item 6 is characterized in that, in the two-dimensional photonic crystal laser of Item 4 or Item 5, the second square lattice is configured in a manner that deviates from a period within a range of 0.4 to 0.6 periods (more preferably 0.5 periods) in the same direction as one of the two basic translation vectors of the first square lattice.

[0205] (Item 7) The two-dimensional photonic crystal laser of Item 7 is a two-dimensional photonic crystal laser of Item 1, wherein the modulation phase Ψ(r↑) is used as follows. The positional deviation of each of the plurality of different refractive index regions, i.e., Δd(↑), and / or the area deviation of each of the plurality of different refractive index regions, i.e., ΔS(r↑), are expressed by the following equation using the upper limit of the positional deviation, i.e., Δd, and / or the upper limit of the area deviation, i.e., ΔS:

[0206] When |B·sin(Ψ(r↑))|≤1, Δd(r↑)=B·Δd·sin(Ψ(r↑)), where B is a constant;

[0207] When B·sin(Ψ(r↑)>1, Δd(r↑)=Δd;

[0208] When B·sin(Ψ(r↑)<-1, Δd(r↑)=-Δd;

[0209] or / and,

[0210] When |C·sin(Ψ(r↑))|≤1, ΔS(r↑)=C·ΔS·sin(Ψ(r↑));

[0211] When C·sin(Ψ(r↑)>1, ΔS(r↑)=ΔS;

[0212] When C·sin(Ψ(r↑)<-1, ΔS(r↑)=-ΔS,

[0213] The modulation phase Ψ(r↑) uses the target radiation electric field distribution E rad_iFFT (r↑), by

[0214]

[0215] express,

[0216] The target radiation electric field distribution E rad_iFFT (r↑) is the electric field distribution E in the wave number space corresponding to the far-field image formed by the laser beam emitted by the two-dimensional photonic crystal laser. far_iFFT The electric field distribution in real space in the cross section of the two-dimensional photonic crystal layer parallel to the layer is obtained by inverse Fourier transform of (K↑), which uses the position vector r↑ and wave number vector K↑ of each lattice point, and is given by

[0217] E rad_iFFT (r↑)=C∫∫A(K↑)E far_iFFT (K↑)exp(iK↑·r↑)dK↑ represents.

[0218] (Item 8) In the two-dimensional photonic crystal laser of Item 8, in the two-dimensional photonic crystal laser of Item 1, the position deviation and / or area deviation of each of the aforementioned multiple different refractive index regions are represented by a function that takes the position of the aforementioned lattice point as a variable and saturates at the aforementioned upper limit value and the aforementioned lower limit value, respectively.

[0219] (Item 9) The two-dimensional photonic crystal laser of Item 9 is a two-dimensional photonic crystal laser of Item 8, wherein the position vector r↑ of each lattice point and the vector k representing the combination of the tilt angle and the azimuth angle of each of n laser beams having different tilt angles and / or azimuth angles are used. n ↑ and the phase exp(iα determined for each n n ) represents σ, where n is an integer greater than 2,

[0220]

[0221] As a function of σ as a variable, the positional deviation of each of the plurality of different refractive index regions, i.e., Δd(σ), or / and the area deviation of each of the plurality of different refractive index regions, i.e., ΔS(σ), are calculated using the upper limit of the positional deviation, i.e., Δd, or / and the upper limit of the area deviation, i.e., ΔS, and a constant t.

[0222]

[0223] express.

[0224] (Item 10) The two-dimensional photonic crystal laser of Item 10 is characterized in that, in the two-dimensional photonic crystal laser of Item 8, as the following variable σd or σ S function, the position deviation of each of the plurality of different refractive index regions, namely Δd (σd) or / and the area deviation of each of the plurality of different refractive index regions, namely ΔS (σ S ) using the aforementioned upper limit value of the position deviation, Δd, or / and the aforementioned upper limit value of the area deviation, ΔS,

[0225]

[0226] express,

[0227] The variable σd or σ S It is represented by the following modulation phase Ψ(r↑) and constant B or C,

[0228] σd=B·Δd·sin(Ψ(r↑))

[0229] σ S =C·ΔS·sin(Ψ(r↑)),

[0230] The modulation phase Ψ(r↑) uses the target radiation electric field distribution E rad_iFFT (r↑), by

[0231]

[0232] express,

[0233] The target radiation electric field distribution E rad_iFFT (r↑) is the electric field distribution E in the wave number space corresponding to the far-field image formed by the laser beam emitted by the two-dimensional photonic crystal laser. far_iFFT The electric field distribution in real space of the cross section of the two-dimensional photonic crystal layer parallel to the layer obtained by inverse Fourier transform of (K↑) is obtained by using the position vector r↑ and wave number vector K↑ of each lattice point.

[0234] E rad_iFFT (r↑)=C∫∫A(K↑)E far_iFFT (K↑)exp(iK↑·r↑)dK↑ represents.

[0235] Description of Reference Numerals

[0236] 10, 20…Two-dimensional photonic crystal lasers

[0237] 11…Active layer

[0238] 12, 22…Two-dimensional photonic crystal layer

[0239] 121, 221…base material

[0240] 122…different refractive index region

[0241] 1221…different refractive index region located at the lattice point

[0242] 1222 ... a region of different refractive index arranged to be offset in the positive direction in the y direction relative to the lattice point

[0243] 1223 ... a region of different refractive index arranged to be offset in the negative direction in the y direction relative to the lattice point

[0244] 13…Spacer layer

[0245] 141…first coating layer

[0246] 142…Second coating layer

[0247] 16...Substrate

[0248] 171…first electrode

[0249] 172…Second electrode

[0250] 1721…Frame

[0251] 1722…Window

[0252] 2221, 2221A…first different refractive index region

[0253] 2222, 2222A…second different refractive index region

[0254] 2231…the first square lattice

[0255] 2232…Second square lattice

[0256] 2241…first lattice point

[0257] 2242…the second lattice point

Claims

1. A two-dimensional photonic crystal laser, characterized in that have: a) a pair of electrodes; b) an active layer provided between the pair of electrodes and generating light of a predetermined wavelength by injection of current from the electrodes; as well as c) a two-dimensional photonic crystal layer provided between one of the pair of electrodes and the active layer, comprising a plate-shaped base material and a plurality of different refractive index regions arranged on the base material and having a refractive index different from that of the base material, The plurality of different refractive index regions are arranged at different positional deviations from each lattice point of the two-dimensional lattice periodically arranged at an in-plane period corresponding to the predetermined wavelength, or / and are arranged at each lattice point with an area that is different from a predetermined reference area, i.e., an area deviation amount, or at a position deviated from the lattice point by the positional deviation amount. For the position deviation and / or area deviation of each of the multiple different refractive index regions, the modulation value determined by the composite period formed by overlapping multiple different in-plane periods is a value between a specified upper limit value and a specified lower limit value at the lattice point where the different refractive index region is configured is the modulation value, the upper limit value is the different refractive index region where the modulation value exceeds the upper limit value, and the lower limit value is the different refractive index region where the modulation value is less than the lower limit value.

2. The two-dimensional photonic crystal laser according to claim 1, characterized in that A vector r↑ representing the position of each lattice point of the two-dimensional lattice and a vector k representing a combination of the tilt angle and the azimuth angle of each of n laser beams having different tilt angles and / or azimuth angles are used. n ↑、Amplitude A determined for each n n and phase exp(iα n ) and a constant Δd, the modulation value Δ'd (r↑) of the position deviation at each lattice point is given by Represents, wherein n is an integer greater than 2.

3. The two-dimensional photonic crystal laser according to claim 1, characterized in that A vector r↑ representing the position of each lattice point of the two-dimensional lattice and a vector k representing a combination of the tilt angle and the azimuth angle of each of n laser beams having different tilt angles and / or azimuth angles are used. n ↑、Amplitude A determined for each n n and phase exp(iα n ) and constant ΔS, the modulation value Δ'S (r↑) of the area deviation at each lattice point is given by Represents, wherein n is an integer greater than 2.

4. The two-dimensional photonic crystal laser according to claim 1, characterized in that The two-dimensional lattice is a first square lattice belonging to the square lattice, The plurality of different refractive index regions are arranged so as not to deviate from a first lattice point, which is a lattice point of the first square lattice, and each has an area determined by the area deviation amount. Furthermore, the two-dimensional photonic crystal laser comprises a plurality of second different-refractive-index regions having a refractive index different from that of the base material. The plurality of second different refractive index regions are arranged so as not to deviate from second lattice points that are lattice points of a second square lattice having the same period length as the first square lattice and arranged at positions different from those of the first square lattice. The area of ​​the second refractive index region at each second lattice point is a value that deviates from the specified second reference area by a second area deviation amount, and the second area deviation amount is the modulation value in the refractive index region where the modulation value at the second lattice point is between the specified second upper limit value and the specified second lower limit value, the second upper limit value in the refractive index region where the modulation value exceeds the second upper limit value, and the second lower limit value in the refractive index region where the modulation value is less than the second lower limit value.

5. The two-dimensional photonic crystal laser according to claim 1, characterized in that: The two-dimensional lattice is a first square lattice belonging to the square lattice, The plurality of different refractive index regions are arranged so as to be deviated from a first lattice point, which is a lattice point of the first square lattice, by the positional deviation amount, and each has an area determined by the area deviation amount. Furthermore, the two-dimensional photonic crystal laser comprises a plurality of second different-refractive-index regions having a refractive index different from that of the base material. The plurality of second different-refractive-index regions are arranged in a manner not to deviate from second lattice points which are lattice points of a second square lattice and each have the same area, wherein the second square lattice is a square lattice having the same period length as the first square lattice and arranged at a position different from the first square lattice.

6. The two-dimensional photonic crystal laser according to claim 4 or 5, characterized in that: The second square lattice is arranged so as to be deviated from the first square lattice in the same direction as one of the two fundamental translation vectors by a period within a range of 0.4 to 0.6 periods.

7. The two-dimensional photonic crystal laser according to claim 1, characterized in that: Using the modulation phase Ψ(r↑) as follows, the positional deviation of each of the plurality of different refractive index regions, i.e., Δd(↑), or / and the area deviation of each of the plurality of different refractive index regions, i.e., ΔS(r↑), are expressed by the following formula using the upper limit value of the positional deviation, i.e., Δd, or / and the upper limit value of the area deviation, i.e., ΔS: When |B·sin(Ψ(r↑))|≤1, Δd(r↑)=B·Δd·sin(Ψ(r↑)), where B is a constant; When B·sin(Ψ(r↑)>1, Δd(r↑)=Δd; When B·sin(Ψ(r↑)<-1, Δd(r↑)=-Δd; or / and, When |C·sin(Ψ(r↑))|≤1, ΔS(r↑)=C·ΔS·sin(Ψ(r↑)); When C·sin(Ψ(r↑)>1, ΔS(r↑)=ΔS; When C·sin(Ψ(r↑)<-1, ΔS(r↑)=-ΔS, The modulation phase Ψ(r↑) uses the target radiation electric field distribution E rad_iFFT (r↑), by express, The target radiation electric field distribution E rad_iFFT (r↑) is the electric field distribution E in the wave number space corresponding to the far-field image formed by the laser beam to be emitted by the two-dimensional photonic crystal laser. far_iFFT The electric field distribution in real space in the cross section of the two-dimensional photonic crystal layer parallel to the layer is obtained by inverse Fourier transform of (K↑), which uses the position vector r↑ and wave number vector K↑ of each lattice point and is expressed by E rad_iFFT (r↑)=C∫∫A(K↑)E far_iFFT (K↑)exp(iK↑·r↑)dK↑ represents.

8. The two-dimensional photonic crystal laser according to claim 1, characterized in that: The positional deviation amount and / or area deviation amount of each of the plurality of different refractive index regions is represented by a function that uses the position of the lattice point as a variable and is saturated at the upper limit value and the lower limit value, respectively.

9. The two-dimensional photonic crystal laser according to claim 8, characterized in that: The position vector r↑ of each lattice point and the vector k representing the combination of the tilt angle and the azimuth angle of each of the n laser beams having different tilt angles and / or azimuth angles are used. n ↑ and the phase exp(iα determined for each n n ) represents σ, where n is an integer greater than 2, As a function of σ as a variable, the position deviation of each of the plurality of different refractive index regions, i.e., Δd(σ), or / and the area deviation of each of the plurality of different refractive index regions, i.e., ΔS(σ), are calculated using the upper limit value of the position deviation, i.e., Δd, or / and the upper limit value of the area deviation, i.e., ΔS, and a constant t. express.

10. The two-dimensional photonic crystal laser according to claim 8, characterized in that: As the variable σd or σ S The function of the position deviation of each of the plurality of different refractive index regions is Δd (σd) or / and the area deviation of each of the plurality of different refractive index regions is ΔS (σ S ) using the upper limit value of the position deviation, Δd, or / and the upper limit value of the area deviation, ΔS, express, The variable σd or σ S It is represented by the following modulation phase Ψ(r↑) and constant B or C, σd=B·Δd·sin(Ψ(r↑)) s S =C·ΔS·sin(Ψ(r↑)), The modulation phase Ψ(r↑) uses the target radiation electric field distribution E rad_iFFT (r↑), by express, The target radiation electric field distribution E rad_iFFT (r↑) is the electric field distribution E in the wave number space corresponding to the far-field image formed by the laser beam to be emitted by the two-dimensional photonic crystal laser. far_iFFT The electric field distribution in real space in the cross section of the two-dimensional photonic crystal layer parallel to the layer obtained by inverse Fourier transform of (K↑) is obtained by using the position vector r↑ and wave number vector K↑ of each lattice point, and E rad_iFFT (r↑)=C∫∫A(K↑)E far_iFFT (K↑)exp(iK↑·r1)dK↑ represents.

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