2D photonic crystal laser

Abstract

A two-dimensional photonic crystal laser comprising: a pair of electrodes (a first electrode 171, a second electrode 172); an active layer (11) provided between the pair of electrodes to produce a predetermined wavelength of light through injection of a current from the electrodes; and a two-dimensional photonic crystal layer (12) provided between one of the pair of electrodes and the active layer (11), and comprising a planar base material (121) and a plurality of different refractive index regions (122) disposed on the base material (121) and having refractive indexes different from that of the base material (121). The plurality of different refractive index regions (122) are displaced from the respective lattice points of a two-dimensional lattice periodically disposed on the base material at a period corresponding to the predetermined wavelength, each region having a different displacement amount, or / and are disposed on the respective lattice points with respectively different areas, wherein the displacement amount or / and area of each of the plurality of different refractive index regions (122) are modulated at a composite modulation period comprising a superposition of a plurality of mutually different periods, the different refractive index regions (122) being represented by (1) a vector r↑ indicating the position of each of the lattice points of the two-dimensional lattice, a vector kn↑ indicating a combination of an inclination angle and an orientation angle of each of n (n is an integer of 2 or more) laser beams having mutually different inclination angles and / or orientation angles, and a modulation phase Ψ (r↑) which is indicated using an amplitude An and a phase exp(iαn) determined for each n, wherein the amplitude An and / or the phase exp(iαn) for each n value are different from each other for at least two different n values.

Description

[Technical Field]

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

[0002] A two-dimensional photonic crystal laser comprises an active layer, a two-dimensional photonic crystal layer, and a pair of electrodes (electrode pair) positioned to sandwich them. The active layer generates light emission in a specific emission wavelength band when carriers (holes, electrons) are injected from the electrode pair. The two-dimensional photonic crystal layer has a structure in which regions with different refractive indices are periodically arranged in two dimensions on a plate-shaped base material. The regions with different refractive indices consist of voids (air) formed in the base material, or materials different from the base material.

[0003] In such a two-dimensional photonic crystal laser, only the light of a predetermined wavelength corresponding to the period length of the arrangement of different refractive index regions from the light generated in the active layer is amplified in the two-dimensional photonic crystal layer, causing laser oscillation, and the laser beam is emitted from the surface of the two-dimensional photonic crystal layer.

[0004] In two-dimensional photonic crystal lasers, regions with different refractive indices generally have the same planar shape and are arranged at the lattice points of a two-dimensional lattice, such as a square, rectangular, or triangular lattice. In such a typical two-dimensional photonic crystal laser, the laser beam is emitted perpendicular to the two-dimensional photonic crystal layer.

[0005] In contrast, in the two-dimensional photonic crystal lasers described in Patent Documents 1 and 2, each of the multiple different refractive index regions is positioned at each lattice point of the two-dimensional lattice, shifted by a different amount from the lattice point, and / or, each of the multiple different refractive index regions is positioned with a different area. Here, the amount of shift is a vector quantity (i.e., a quantity with magnitude and direction) in a plane parallel to the two-dimensional photonic crystal layer, and "different amounts of shift" includes cases where the magnitude of the shift is the same but only the direction of the shift is different. These amounts of shift and / or areas change along a predetermined direction parallel to the two-dimensional photonic crystal layer with a predetermined period (longer than the period of the lattice point arrangement). The period of change in this amount of shift and / or area is called the "modulation period," and the amount of shift and / or area in each different refractive index region modulated by this modulation period is called the "modulation phase." A two-dimensional photonic crystal in which different refractive index regions are positioned with such modulated amounts of shift and / or area. layer In a two-dimensional photonic crystal laser, two laser beams are emitted that have an angle (inclination angle) that is tilted from a direction perpendicular to the two-dimensional photonic crystal layer by an angle corresponding to the modulation period, and whose azimuth angles are in the predetermined direction and are 180° apart from each other. [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] International Publication No. WO2014 / 136607 [Patent Document 2] United States Patent Publication No. US2016 / 0248224 [Patent Document 3] Japanese Patent Publication No. 2020-148512 [Non-patent literature]

[0007] [Non-Patent Document 1] Susumu Noda et al., "Photonic-Crystal Surface-Emitting Lasers: Review and Introduction of Modulated-Photonic Crystal," (USA), published by the Institute of Electrical and Electronics Engineers, IEEE Journal of Selected Topics in Quantum Electronics, vol. 23 (2017) 4900107. [Overview of the project] [Problems that the invention aims to solve]

[0008] As described above, the two-dimensional photonic crystal lasers in Patent Documents 1 and 2 emit two laser beams that have the same tilt angle but differ in azimuth angle by 180° from each other. However, in fields such as LIDAR (Laser Imaging Detection And Ranging), which are sensors used in remote sensing, there is a need for laser light sources that emit more than two laser beams.

[0009] The problem that this invention aims to solve is to provide a two-dimensional photonic crystal laser that emits more than two laser beams. [Means for solving the problem]

[0010] The two-dimensional photonic crystal laser according to the present invention, which was developed to solve the above problems, a) A pair of electrodes, b) An active layer provided between the pair of electrodes, which generates light of a predetermined wavelength when current is injected from the electrodes, c) A two-dimensional photonic crystal layer provided between one of the pair of electrodes and the active layer, having a plate-shaped base material and a plurality of regions with different refractive indices that are arranged on the base material and have refractive indices different from those of the base material. Equipped with, The plurality of regions with different refractive indices are positioned at different amounts of displacement from each lattice point of a two-dimensional lattice periodically arranged in the base material with a period corresponding to the predetermined wavelength, and / or are positioned at each lattice point with different areas. The respective displacement amounts and / or areas of the multiple regions with different refractive indices are modulated by a composite modulation period formed by superimposing multiple periods with different values, and a vector r↑ indicating the position of each grid point in the two-dimensional grid, and a vector k indicating the combination of the tilt angle and / or azimuth angle of each of the n (n is an integer of 2 or more) laser beams with different tilt angles and / or azimuth angles. n ↑, and amplitude A determined for every n n and phase exp(iα n The modulation phase Ψ(r↑) is shown using ).

number

[0011] The "composite modulation period formed by superimposing multiple different periods" may be a combination of modulations formed with multiple different period lengths along one direction (the same direction) parallel to the two-dimensional photonic crystal layer, a combination of modulations formed with one period length each along multiple directions parallel to the two-dimensional photonic crystal layer but different from each other, and a combination of the above (a combination of modulations formed with multiple different period lengths along the aforementioned multiple directions).

[0012] Similarly, "amount of displacement" is a vector quantity (a quantity with magnitude and direction) in a plane parallel to the two-dimensional photonic crystal layer, and "different amounts of displacement" include cases where the magnitude of the displacement is the same but only the direction of the displacement differs.

[0013] In the two-dimensional photonic crystal laser according to the present invention, the wavelength of the output laser beam is determined by the lattice point period in the two-dimensional photonic crystal layer (on the premise that light of a predetermined wavelength corresponding to this lattice point period is generated in the active layer), whereas the tilt angle and azimuth angle of the laser beam are determined by the composite modulation period in the modulation phase Ψ(r↑) (displacement amount or / and area). The modulation phase Ψ(r↑) (r↑ is a vector indicating the position of the lattice point) modulated by the composite modulation period is expressed using the vectors k↑ and k described later. n ↑ and is [Number] represented by. Here, "arg" is the argument of a complex number. c n is [Number] represented by. A n and α n will be described later. Substituting equation (3) into equation (2) results in equation (1). δ is the δ function (in δ(x), it is 1 when x = 0 and 0 when x ≠ 0). k↑ is a vector represented using the tilt angle θ and azimuth angle φ of the laser beam to be emitted, and the effective refractive index (the refractive index felt by light in the two-dimensional photonic crystal layer) n eff of the two-dimensional photonic crystal layer. For example, when the two-dimensional lattice is a square lattice with a period length a, it is [Number] represented by (see Non-Patent Document 1. However, in Non-Patent Document 1, the angles θ x = sinθcosφ and θ y = sinθsinφ defined by sinθ x and θ y are used.). k n↑(n=1, 2, 3, …) represent vectors k↑ whose magnitude and / or direction differ depending on the difference in n, and each value of n corresponds to a different inclination angle θ and / or azimuth angle φ. From equations (2) to (4), ψ(r↑) is a term a that can be obtained for each value of n, that is, for each combination (θ, φ) of inclination angle θ and azimuth angle φ of the laser beam to be emitted. n

number

[0014] According to the two-dimensional photonic crystal laser of the present invention, because regions with different refractive indices are arranged with a modulation phase Ψ(r↑) modulated by such a composite modulation period, one k nIn accordance with the above, one laser beam having a corresponding set of tilt angle and azimuth angle is emitted, along with another laser beam whose azimuth angle differs from that of the first laser beam by 180°. However, if the tilt angle of the first laser beam is 0°, the other laser beam is not emitted. Therefore, the two-dimensional photonic crystal laser according to the present invention provides 2n or (2n-1) laser beams (including one laser beam with a tilt angle of 0°) with different tilt angles and / or azimuth angles.

[0015] And the amplitude A for each value of n n and / or phase exp(iα) n The values ​​of n are to be different from each other for at least two distinct values ​​of n. In other words, the intensity of each laser beam can be adjusted by assigning different weights to each tilt angle and azimuth angle of the emitted laser beam (at least between two sets of different combinations of tilt and azimuth angles).

[0016] In the present invention, the phase exp(iα n It is preferable that the value of n is set randomly (without any pattern) for each value of n. This suppresses interference between laser beams and makes the intensity of the laser beams nearly uniform.

[0017] Thus, the phase exp(iα n ) is set randomly for each value of n, and furthermore, the amplitude A n It is more preferable to set the value of to a different value for each term where the value of n is different. This allows for further adjustment of the intensity of the laser beams, bringing the intensity of the laser beams closer to uniform.

[0018] Amplitude A for each term with different values ​​of n n The value of can be determined, for example, by the following method. First, the phase exp(iα n ) is set randomly for each value of n, and the amplitude A nWhen n is set to a predetermined value independent of the value of n (for example, 1), the amount of shift and / or area of ​​each different refractive index region is determined from the modulation phase Ψ(r↑) obtained from equation (1). The state modulated by the amount of shift and / or area of ​​each different refractive index region obtained here is called the "basic modulation state". From the 2D photonic crystal layer in this basic modulation state, the distribution of electric fields emitted from each position within the 2D photonic crystal layer (called the "radiated electric field distribution") is determined by applying the methods used in the design of conventional 2D photonic crystal lasers. Furthermore, by performing a Fourier transform on this radiated electric field distribution, the distribution of electric fields at a position far from the 2D photonic crystal layer (for example, the position where the laser beam irradiates the object) (called the "far electric field distribution") is obtained as a function of vector k↑. Note that, conversely to determining the far electric field distribution, the radiated electric field distribution can be obtained by performing an inverse Fourier transform on the far electric field distribution, but the calculation in brackets [] in equation (1) is the far electric field distribution Σ (shown as a complex number). n a n exp(iα n )δ(k↑-k n This is equivalent to obtaining the radiated electric field distribution (expressed as a complex number) by performing an inverse Fourier transform on the above.

[0019] As described above, the far-field electric field distribution obtained from a two-dimensional photonic crystal laser equipped with a two-dimensional photonic crystal layer in the fundamental modulation state, with multiple laser beams, typically involves a vector k for each laser beam (which is applied to the vector k↑, which is a variable of the far-field electric field distribution). n A difference in intensity occurs (corresponding to the above). Therefore, based on the obtained far-field electric field distribution, the laser beam that is judged to have a weaker intensity than the other laser beams corresponds to (the vector k of the laser beam in question). n Amplitude A (having the same value of n as "n" in the above) n The value of is increased above the predetermined value in the basic modulation state, and the amplitude A corresponds to a laser beam that is judged to have a stronger intensity than other laser beams. nA new modulation phase Ψ(r↑) is obtained from equation (1) by reducing the value of from the predetermined value. Then, the amount of shift and / or area of ​​each different refractive index region (new modulation state) is determined from this new modulation state, the radiated electric field distribution is determined from this new modulation state, and further the far electric field distribution is determined. The far electric field distribution obtained from the new modulation state in this way has an amplitude A from the fundamental modulation state. n As long as the increase / decrease is not excessive, the difference in intensity between laser beams will be smaller than in the basic modulation state (if this difference is actually larger, the amplitude A from the basic modulation state will be smaller). n By using a modulation phase Ψ(r↑) with a reduced degree of increase / decrease, and repeating the operation described here, the intensity can be made more uniform.

[0020] By repeating the above operation using the newly obtained modulation state as the basic modulation state, the intensity of the laser beams can be made even more uniform.

[0021] In the two-dimensional photonic crystal laser according to the present invention, The aforementioned two-dimensional lattice is a square lattice, Furthermore, a second region with a different refractive index from the base material is arranged at a second lattice point, which is a lattice point of a square lattice that has the same period length a as the two-dimensional lattice and is shifted from the two-dimensional lattice, or at a position shifted by a different amount from the second lattice point. This configuration can be adopted.

[0022] In a two-dimensional photonic crystal layer with such a second differential refractive index region added, there is a double lattice structure in which a first square lattice (the two-dimensional lattice) in which the differential refractive index region is located and a second square lattice having the same period length as the first square lattice and in which the second differential refractive index region is located at the lattice points (the second lattice points) are offset from each other. Within such a two-dimensional photonic crystal layer, photon propagation occurs in a direction tilted at 45° with respect to the two fundamental translation vectors of the square lattices, and the wavelength is 2 1 / 2The phase difference between a first beam of light, whose direction of propagation changes by 180° when reflected in a region of different refractive indices, and a second beam of light, whose direction of propagation changes by 180° when reflected in a second region of different refractive indices with the same wavelength and phase as the first beam, has different values ​​depending on the direction and magnitude of the shift described above. When this phase difference (defined in the range of 0 to 2π) is greater than (1 / 2)π and less than (3 / 2)π, the first and second beams are weakened by interference, and the intensity of the light whose direction of propagation changes in a direction other than 180° in the region of different refractive indices and the second region of different refractive indices becomes relatively larger, allowing for stable laser oscillation over a wider area within the two-dimensional photonic crystal layer than when there is no second region of different refractive indices. On the other hand, when the phase difference is less than (1 / 2)π or greater than (3 / 2)π, the first and second beams are strengthened by interference, allowing for laser oscillation over a narrower area within the two-dimensional photonic crystal layer than when there is no second region of different refractive indices.

[0023] For example, the second lattice point can be positioned at a distance greater than 0.25a and less than 0.75a from the lattice point of the two-dimensional lattice by the same direction as one of the fundamental translation vectors of the two-dimensional lattice. In this case, the displacement between the lattice point of the two-dimensional lattice and the second lattice point is preferably 0.4a or more and 0.6a or less, and most preferably 0.5a. With such a configuration, the first light and the second light are weakened by interference, and stable laser oscillation can be obtained over a wide area within the two-dimensional photonic crystal layer.

[0024] Up to this point, we have discussed photonic crystal lasers that emit two or more beams. However, by applying the methods described so far, it is possible to obtain a photonic crystal laser that emits a laser beam with a wide cross-sectional area (broad cross-sectional beam), as described below.

[0025] In other words, in the two-dimensional photonic crystal laser according to the present invention, the modulation phase Ψ(r↑) is modulated in a direction parallel to the two-dimensional photonic crystal layer so as to change periodically with a predetermined modulation period, and the modulation period is continuously increasing or decreasing.

[0026] This results in a laser that emits a wide cross-sectional beam. In this case, the modulation phase Ψ(r↑) expressed on the right-hand side of equation (1) has the above modulation period. Hereinafter, a two-dimensional photonic crystal laser having such a configuration will be referred to as "wide cross-sectional beam of the first embodiment". Load They call it "-za".

[0027] In the first embodiment of the wide-cross-section laser, the modulation phase Ψ(r↑) of each of the multiple different refractive index regions is modulated to change periodically in a direction parallel to the two-dimensional photonic crystal layer, and this modulation period is formed to continuously increase or decrease in that direction. By injecting current into the active layer from a single pair of electrodes provided so as to sandwich the two-dimensional photonic crystal layer in which such modulation is formed, light emission occurs in the active layer, and this light is introduced over a wide area of ​​the two-dimensional photonic crystal layer. As a result, laser beams of similar intensity with an inclination angle θ corresponding to the modulation period at that position are emitted from each position within the two-dimensional photonic crystal layer. Therefore, since laser beams with different inclination angles θ and similar intensities are emitted as a bundle from the entire photonic crystal region, laser light can be irradiated onto an object with a nearly uniform intensity over a wider area than the diameter of the laser beam generated by a normal photonic crystal laser.

[0028] In the two-dimensional photonic crystal laser according to the present invention, The aforementioned two-dimensional lattice is a square lattice, At each lattice point of the two-dimensional lattice, each of the plurality of different refractive index regions is positioned offset from the lattice point in a predetermined direction or in a direction 180° different from that direction, wherein the direction is parallel to the two-dimensional photonic crystal layer and is inclined from both of the two directions in which the lattice points are aligned in the lattice point period. This configuration can be adopted. The structure of the two-dimensional photonic crystal layer defined here can be suitably used in the wide-cross-sectional-area laser of the first embodiment, but it may also be applied to other two-dimensional photonic crystal lasers according to the present invention.

[0029] In this way, by making the structure asymmetrical by arranging regions with different refractive indices at each lattice point of a two-dimensional lattice in a direction tilted from the two directions in which the lattice points are aligned according to the lattice point period, or in a direction 180° different from one of those directions, laser oscillation can be made at only one band edge of the multiple photonic bands formed by the two-dimensional photonic crystal. By making laser oscillation occur at only one band edge in this way (laser oscillation does not occur at the other band edges), a laser beam having a single resonance mode and a single polarization can be emitted.

[0030] When the direction of the displacement of the different refractive index regions is specified as one direction or a direction 180° different therefrom, the modulation is formed such that the distance of the different refractive index regions from the grid points (corresponding to the amount of displacement) and / or the area of ​​the planar shape of the different refractive index regions changes periodically with the modulation period.

[0031] Furthermore, in the wide-cross-sectional-area laser of the first embodiment, A plurality of two-dimensional photonic crystal lasers according to the present invention, each with different modulations, A current supply unit that simultaneously supplies current to the electrodes provided on each of the plurality of two-dimensional photonic crystal lasers. A two-dimensional photonic crystal laser array (also called a "two-dimensional photonic crystal surface-emitting laser array") may be constructed. By simultaneously supplying current from a current supply unit to multiple two-dimensional photonic crystal lasers with different modulations, it is possible to irradiate a wider area with laser light than when using a single two-dimensional photonic crystal laser according to the present invention.

[0032] In the aforementioned two-dimensional photonic crystal laser array, The current supply unit includes a mesh electrode in which a plurality of holes are formed in a conductive plate material. Each of the plurality of holes is equipped with the two-dimensional photonic crystal laser, In each of the plurality of holes, the plate material surrounding the hole is the same as One of a pair of electrodes Connected or the above One of a pair of electrodes That is This configuration allows for the supply of current to each two-dimensional photonic crystal laser using mesh electrodes, and the laser light emitted from the two-dimensional photonic crystal lasers to be released from the holes to the outside of the two-dimensional photonic crystal laser array.

[0033] The multiple holes provided in the mesh electrode may be arranged in a two-dimensional manner or in a one-dimensional arrangement. When the holes are arranged in a one-dimensional manner, it is preferable that the shape of each hole be a long line in the direction perpendicular to the direction of hole arrangement. Furthermore, the two-dimensional photonic crystal laser may be provided as one per hole in the mesh electrode or as multiple lasers.

[0034] The wide-cross-section laser of the first embodiment can also be defined as follows: That is, the wide-cross-section laser of the first embodiment is a) With only one pair of electrodes, b) Provided between the pair of electrodes, and when current is injected from the electrodes, a predetermined wavelength λ L An active layer that generates light containing, c) A two-dimensional photonic crystal layer provided between one of the pair of electrodes and the active layer, having a plate-shaped base material and a plurality of regions with different refractive indices arranged within the base material, each having a refractive index different from that of the base material. Equipped with, The predetermined wavelength λ L In a two-dimensional grid where grid points are periodically arranged with a corresponding grid point period, each of the multiple regions with different refractive indices is positioned at a grid point with a different amount of displacement from that grid point, and / or, each of the multiple regions with different refractive indices is positioned with an area of ​​a different planar shape. The amount of displacement and / or the area of ​​the planar shape of each of the plurality of different refractive index regions is modulated in a direction parallel to the two-dimensional photonic crystal layer so as to change periodically with a predetermined modulation period, and the modulation period is continuously increasing or decreasing. It is characterized by the following:

[0035] In the first embodiment of the wide-cross-sectional laser, by limiting the direction of the shift in the different refractive index regions to the aforementioned one direction or a direction 180° different therefrom, a laser beam having a single resonant mode and a single polarization can be emitted not only when emitting a bundle of laser beams with different inclination angles θ and similar intensities, as described above, but also when emitting a single laser beam with different inclination angles θ by changing the current injection position, as described in Patent Document 1. Such a two-dimensional photonic crystal laser is, a) A pair of electrode groups, at least one of which consists of an electrode group having multiple partial electrodes, b) Provided between the pair of electrode groups, a predetermined wavelength λ is injected from a portion of the plurality of partial electrodes, to a position corresponding to the partial electrode into which the current is injected. L An active layer that generates light containing, c) A two-dimensional photonic crystal layer provided between one of the pair of electrodes and the active layer, the layer having a plate-shaped base material and a plurality of regions with different refractive indices that are arranged within the base material and have refractive indices different from those of the base material. Equipped with, The predetermined wavelength λ L In a square lattice where lattice points are periodically arranged with a corresponding lattice point period, each of the plurality of different refractive index regions is positioned offset from the lattice point in a predetermined direction or in a direction 180° different from that direction, wherein the direction is parallel to the two-dimensional photonic crystal layer and is inclined from both of the two directions in which the lattice points are aligned with the lattice point period. The distance from the lattice point and / or the area of ​​the planar shape of each of the plurality of different refractive index regions is modulated in a direction parallel to the two-dimensional photonic crystal layer so as to change periodically with a predetermined modulation period, and the modulation period differs depending on the position within the two-dimensional photonic crystal layer. This is the structure it takes.

[0036] In this case, the modulation period does not need to continuously increase or decrease in the direction parallel to the two-dimensional photonic crystal layer; for example, it may change randomly. Even if the modulation period does not continuously increase or decrease, the tilt angle θ of the laser beam can be changed by moving the current injection point (changing the partial electrode to which the current is injected).

[0037] In the first embodiment of the wide-cross-section laser, interference of light can occur, potentially causing unevenness in intensity within the cross-section. Therefore, we will further consider a configuration to suppress the occurrence of such unevenness. First, as in the first embodiment, the "basic modulation state" in this example is defined as a state in which the modulation phase Ψ(r↑) of each of the multiple different refractive index regions changes periodically with a predetermined modulation period in a direction parallel to the two-dimensional photonic crystal layer, and this modulation period is continuously increasing or decreasing. For example, if the two-dimensional lattice is a square lattice, the tilt angle of the laser light emitted from each position (x, y) of the lattice point is defined as θ(x, y) and the azimuth angle as φ(x, y), and then sinθ x (x)=sinθ(x, y)cosφ(x, y), and sinθ y The angle θ is defined by (y) = sinθ(x, y)sinφ(x, y). x (x), θ y Define (y). In this case, the modulation phase Ψ(x, y) for each position (x, y) is given by equation (1).

number

[0038] For the modulation phase Ψ(x, y) expressed in this way, the above c n =A n exp(iα n The adjustment using ) is applied as follows. First, c n =A n exp(iα n Without considering the term ), the modulation phase Ψ(r↑) for each position r↑=(x, y) was determined as in equation (6) (i.e., the fundamental modulation state was determined), and then the radiated electric field distribution E, which shows the distribution of the electric field emitted from each position (at each of those positions) within the two-dimensional photonic crystal layer, was obtained. rad (r↑) is calculated. Such calculations of electric field distributions can be performed using methods used in the design of conventional two-dimensional photonic crystal lasers. This radiant electric field E rad By performing a Fourier transform on (r↑), we obtain the far-field electric field distribution E, which shows the distribution of the electric field at a distance from the 2D photonic crystal layer (for example, the position where the laser beam irradiates the object). far (K↑) can be found using equation (7) below.

number

[0039] On the other hand, the electric field distribution to be formed at a distance from the two-dimensional photonic crystal layer (called the "target far-field electric field distribution") can be arbitrarily defined as E far_iFFT Defined as (K↑). Target far-field electric field distribution E far_iFFT (K↑) is, for example, the far-field electric field distribution obtained in equation (7). E far (K↑)In this case, the phase distribution of the electric field remains unchanged, and the intensity distribution is updated to a uniform distribution. Such a target distant electric field distribution E far_iFFT The target radiated field distribution E is the distribution of the electric field that should be emitted from the two-dimensional photonic crystal layer in order to obtain (K↑). rad_iFFT (r↑) is the target far-field electric field distribution E far_iFFT By performing an inverse Fourier transform on (K↑), it can be obtained using equation (8) below.

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[0040] Therefore, the radiated electric field distribution E can be determined from the modulation phase Ψ(r↑) for each position r↑=(x, y). rad (r↑) is the target radiated electric field distribution E obtained by equation (8). rad_iFFT Adjust the modulation phase Ψ(r↑) for each position r↑=(x, y) so that it approaches (r↑). For example, equation (8) is replaced with the following equation (9).

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[0041] Target radiated electric field distribution E rad_iFFT By discretizing (r↑) for each wavenumber, each point can be expressed as a delta function. Therefore, the modulation phase Ψ(r↑) after such adjustment is equivalent to the original modulation phase Ψ(r↑) shown in equation (1) plus a correction coefficient (constant). In other words, the above adjustment is equivalent to adding an appropriate correction coefficient to the original modulation phase Ψ(r↑). The adjusted modulation phase Ψ(r↑) is obtained using the correction coefficient ΔΨ.

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[0042] The distant electric field distribution E obtained in this second step far By using (K↑), for example, as in the example above, the phase distribution remains the same while updating the intensity distribution to a uniform distribution, a new target far-field electric field distribution E can be obtained. far_iFFT (K↑) is determined. Next, the far electric field distribution E is determined for the second time. far The following far-field electric field distribution E is obtained by the same operation as the operation to obtain (K↑). far The operation of obtaining (K↑) is repeated. After repeating this operation any number of times, the final target far-field electric field distribution E far_iFFT By determining (K↑) and the modulation phase Ψ(r↑) for each position r↑=(x, y) adjusted immediately after it (for example using equation (9)), as a parameter that determines the amount of shift and / or area of ​​each of the final multiple different refractive index regions, the final target far-field electric field distribution E is determined. far_iFFT A wide cross-sectional beam with high uniformity of intensity within the cross-section, close to (K↑), can be obtained.

[0043] In summary, the wide cross-sectional area laser of the second embodiment is a two-dimensional photonic crystal laser according to the present invention, characterized in that the modulation phase Ψ(r↑) of each of the plurality of different refractive index regions changes periodically with a predetermined modulation period in a direction parallel to the two-dimensional photonic crystal layer, and the modulation phase Ψ(r↑) is adjusted from the basic modulation state to be closer to the target radiated electric field distribution obtained by inverse Fourier transforming a predetermined target far-field electric field distribution to be formed at a position away from the two-dimensional photonic crystal layer than to the radiated electric field distribution showing the distribution of the electric field emitted from the two-dimensional photonic crystal layer in the basic modulation state in which the modulation period is continuously increasing or decreasing.

[0044] The wide-cross-section laser of the second embodiment can also be defined as follows: That is, the wide-cross-section laser of the second embodiment is a) A pair of electrodes, b) An active layer provided between the pair of electrodes, which generates light of a predetermined wavelength when current is injected from the electrodes, c) A two-dimensional photonic crystal layer provided between one of the pair of electrodes and the active layer, having a plate-shaped base material and a plurality of regions with different refractive indices that are arranged on the base material and have refractive indices different from those of the base material. Equipped with, The plurality of regions with different refractive indices are positioned at different amounts of displacement from each lattice point of a two-dimensional lattice periodically arranged in the base material with a period corresponding to the predetermined wavelength, and / or are positioned at each lattice point with different areas. The amount of displacement and / or area of ​​each of the multiple different refractive index regions is modulated in a direction parallel to the two-dimensional photonic crystal layer so as to change periodically with a predetermined modulation period, and the amount of displacement and / or area is adjusted from the basic modulation state so as to be closer to the target radiated electric field distribution obtained by inverse Fourier transforming a predetermined target far-field electric field distribution to be formed at a position away from the two-dimensional photonic crystal layer than to the radiated electric field distribution showing the distribution of the electric field emitted from the two-dimensional photonic crystal layer in the basic modulation state in which the modulation period is continuously increasing or decreasing. It is characterized by the following: [Effects of the Invention]

[0045] The present invention makes it possible to obtain a two-dimensional photonic crystal laser that emits more than two laser beams.

[0046] Furthermore, according to the first embodiment of the present invention, a wide-cross-section laser can irradiate an object with laser light over a wide area. Moreover, according to the second embodiment of the present invention, a wide-cross-section laser can irradiate an object with laser light at a nearly uniform intensity over a wide area. [Brief explanation of the drawing]

[0047] [Figure 1] A perspective view (a) showing a first embodiment of a two-dimensional photonic crystal laser according to the present invention, and a partial plan view (b) of the two-dimensional photonic crystal layer provided by the two-dimensional photonic crystal laser. [Figure 2] A perspective view showing examples of two-dimensional photonic crystal lasers with different electrode shapes. [Figure 3] A partial plan view showing an example of setting the position of the centroid of the different refractive index regions in the two-dimensional photonic crystal laser of the first embodiment. [Figure 4] A partial plan view showing another example of setting the position of the centroid of the different refractive index regions in the two-dimensional photonic crystal laser of the first embodiment. [Figure 5]A partial plan view showing an example of setting the area of ​​the different refractive index regions in the two-dimensional photonic crystal layer of the two-dimensional photonic crystal laser of the first embodiment. [Figure 6] This figure shows the calculated far-field image of laser beams emitted from a two-dimensional photonic crystal laser designed to emit 100 laser beams by forming a composite modulation period by superimposing 50 modulation periods that differ in terms of displacement and area. [Figure 7] This figure shows the results of a calculation to obtain a far-field image of the laser beam emitted from the two-dimensional photonic crystal laser of the first embodiment. [Figure 8] This figure shows the results of calculating the far-field image of the laser beam emitted from an improved 2D photonic crystal laser, which was modified from the 2D photonic crystal laser used in the calculations shown in Figure 7. [Figure 9] A partial plan view of the two-dimensional photonic crystal layer of the two-dimensional photonic crystal laser of the second embodiment. [Figure 10] This figure schematically shows an example of the optical path difference between light traveling in a direction tilted 45° with respect to the fundamental translation vector of a square lattice in a two-dimensional photonic crystal laser of the second embodiment, where the light is reflected from a region of different refractive indices at a first lattice point and the light is reflected from a second region of different refractive indices at a second lattice point. [Figure 11] A graph showing the results of calculating the one-dimensional coupling coefficient (a) and the two-dimensional coupling coefficient (b) in the two-dimensional photonic crystal laser of the second embodiment. [Figure 12] A graph showing the results of calculating the emission coefficient in the two-dimensional photonic crystal laser of the second embodiment. [Figure 13] This figure shows the results of calculating the electric field distribution within the two-dimensional photonic crystal layer in the two-dimensional photonic crystal laser (a) of the second embodiment and the two-dimensional photonic crystal laser (b) obtained by removing the second different refractive index region from the same embodiment. [Figure 14] A partial plan view of the two-dimensional photonic crystal layer of the two-dimensional photonic crystal laser of the third embodiment. [Figure 15]A partial plan view showing the position of the centroid of the different refractive index regions in the two-dimensional photonic crystal layer of the two-dimensional photonic crystal laser of the third embodiment. [Figure 16] A partial plan view showing a modified example of the position of the centroid of the different refractive index regions in the third embodiment. [Figure 17] A partial plan view showing a modified example of the planar shape of the different refractive index regions of the two-dimensional photonic crystal layer in the third embodiment. [Figure 18] Photographs (a) and (b) showing a cross-section of the laser beam emitted from the two-dimensional photonic crystal laser of the third embodiment, and a figure (c) obtained by calculation. [Figure 19] A photograph showing a cross-section of the laser beam emitted from a two-dimensional photonic crystal laser in a comparative example. [Figure 20] A graph showing the results of calculating the difference in the emission coefficient with respect to angle ξ for each band in a modified example of the third embodiment. [Figure 21] Plan views of the fourth embodiment, a two-dimensional photonic crystal laser array, as seen from the first electrode array side (a) and the second electrode array side (b), respectively. [Figure 22] A photograph showing a cross-section of a laser beam emitted from a two-dimensional photonic crystal laser array of the fourth embodiment. [Figure 23] A figure showing two modified examples of the second electrode assembly in the two-dimensional photonic crystal laser array of the fourth embodiment. [Figure 24] A schematic perspective view (a), a partially enlarged cross-sectional view (b), and a circuit diagram (c) illustrating other modifications of the two-dimensional photonic crystal laser array of the fourth embodiment. [Figure 25] This figure shows the experimental results of obtaining a far-field image of a laser beam emitted from a modified two-dimensional photonic crystal laser array, as shown in Figure 24. [Figure 26] Figure 24 shows a graph illustrating the current-power characteristics of a laser beam emitted from a modified two-dimensional photonic crystal laser array. [Figure 27]Figure 24 shows a graph illustrating the oscillation spectrum of a laser beam emitted from a modified two-dimensional photonic crystal laser array. [Figure 28] This figure shows the results of a calculation of the far-field image of the laser beam emitted from the 2D photonic crystal laser of the 5th embodiment, which is an improved version of the 2D photonic crystal laser of the 3rd embodiment. [Figure 29] A magnified view of a portion of the far-field image of the laser beam shown in Figure 28. [Figure 30] This figure shows the results of calculating the far-field image of the laser beam emitted from an improved 2D photonic crystal laser, which was modified from the 2D photonic crystal laser used in the calculations shown in Figure 28. [Figure 31] A photograph showing an example of displaying characters and figures using a two-dimensional photonic crystal laser fabricated by applying the first embodiment. [Modes for carrying out the invention]

[0048] An embodiment of the two-dimensional photonic crystal laser according to the present invention will be described using Figures 1 to 31.

[0049] (1) First Embodiment The two-dimensional photonic crystal laser 10 of the first embodiment has a configuration in which the first electrode 171, first cladding layer 141, two-dimensional photonic crystal layer 12, spacer layer 13, active layer 11, second cladding layer 142, substrate 16, and second electrode 172 are stacked in this order, as shown in Figure 1(a). However, the order of the active layer 11 and the two-dimensional photonic crystal layer 12 may be reversed from the above. In Figure 1(a), for convenience, the first electrode 171 is shown on the bottom and the second electrode 172 on the top, but the orientation of the two-dimensional photonic crystal laser 10 during use is not limited to what is shown in this figure. The configuration of each layer and electrode will be described below.

[0050] The active layer 11 emits light having a predetermined wavelength band when charges are injected from the first electrode 171 and the second electrode 172. For the material of the active layer 11, for example, InGaAs / AlGaAs multiple quantum wells (emission wavelength band: 935 - 945 nm) can be used.

[0051] As shown in Fig. 1(b), the two-dimensional photonic crystal layer 12 is formed by arranging, at each lattice point of a two-dimensional lattice, a refractive-index-different region 122 having a refractive index different from that of the plate-shaped base material 121 one by one. In Fig. 1(b), only a part of the two-dimensional photonic crystal layer 12 is enlarged and shown. In the actual two-dimensional photonic crystal layer 12, a large number of Different refractive index region 122 are arranged within a range approximately the same as the outer edge of the planar shape (described later) of the second electrode 172. In the first embodiment, the two-dimensional lattice is a square lattice, but other two-dimensional lattices such as a rectangular lattice or a triangular lattice may also be used. The lattice point period (length) a of the square lattice is appropriately determined according to the material of the base material 121 and the emission wavelength band in the active layer 11. For the material of the base material 121, for example, p-type GaAs (p-type semiconductor) can be used. Typically, holes are used for the refractive-index-different region 122, but instead of holes, a member having a refractive index different from that of the base material 121 may be used. The position and planar shape where the refractive-index-different region 122 is arranged will be described in detail later.

[0052] The first cladding layer 141 and the second cladding layer 142 have the role of injecting charges from the first electrode 171 and the second electrode 172, and also have the role of suppressing the leakage of in-plane guided light guided parallel to the layer from the layer within the two-dimensional photonic crystal layer 12. To fulfill the former role, p-type semiconductor (for example, p-type Al 0.37 Ga 0.63 As) is used for the first cladding layer 141, and n-type semiconductor (for example, n-type Al 0.37 Ga 0.63 As) is used for the second cladding layer 142, respectively (the reason for using p-type semiconductor for the material of the base material 121 of the two-dimensional photonic crystal layer 12 is the same as this).

[0053] 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 (therefore, they would combine with holes on the first electrode 171 side of the active layer 11). The material of the spacer layer 13 is, for example, p-type Al. 0.45 Ga 0.55 You can use As.

[0054] The substrate 16 is made sufficiently thicker than the other layers in order to maintain the overall mechanical strength of the two-dimensional photonic crystal laser 10. For the same reasons as the second cladding layer 142, an n-type semiconductor is used for the material of the substrate 16.

[0055] In the first embodiment, the first electrode 171 is square. The second electrode 172 has a configuration in which a square metal plate-like member, whose side lengths are sufficiently longer than those of the first electrode 171, has a square cutout in the center. The cutout portion of the plate-like member is called the window portion 1722, and the remaining portion of the plate-like member is called the frame portion 1721. The window portion 1722 is provided to allow the laser beam emitted from the two-dimensional photonic crystal layer 12 to pass through, as will be described later. In Figure 1(a), the first electrode 171 and the first cladding layer 141 are shown separated to show the shape of the first electrode 171, but in reality, the first electrode 171 and the first cladding layer 141 are in contact.

[0056] The materials for each layer described so far are merely examples, and other materials may be used. Furthermore, the shapes of the first electrode 171 and the second electrode 172 are not limited to those described above, and other shapes may be used. For example, as shown in Figure 2, a circular first electrode 171A and a second electrode 172A having a circular frame portion 1721A and a window portion 1722A can be used.

[0057] The following describes in detail the position and planar shape of the different refractive index regions 122 in the two-dimensional photonic crystal layer 12.

[0058] In the example shown in FIG. 1(b), anisotropic refractive index regions 122 having the same planar shape (including their areas) are used. The planar shape is an equilateral triangle in the example of FIG. 1(b), but it may be an isosceles triangle, other triangles, polygons other than triangles, a circle, an ellipse, or the like. Also, one anisotropic refractive index region may be formed by combining two or more anisotropic refractive index regions (partial anisotropic refractive index regions). Each anisotropic refractive index region 122 is arranged such that the center of gravity of its planar shape is displaced from the lattice points of a square lattice having a period length a (the point where the vertical and horizontal dashed-dotted lines intersect in the figure). Examples of this displacement amount are shown in FIGS. 3 and 4. In each figure, together with the square lattice (dashed-dotted line), the position of the center of gravity G in the planar shape of the anisotropic refractive index region 122 is shown by a black circle. In the example of FIG. 3, each center of gravity G is displaced from the lattice point in the same direction (a direction displaced by an angle ξ (a constant in this example) from the x direction), and the magnitude d of the displacement is set for each lattice point. Here, the magnitude of the displacement is defined including positive and negative values (when the magnitude of the displacement is defined only by positive values, the directions of the displacements are two directions different from each other by 180°). On the other hand, in the example of FIG. 4, in addition to the magnitude of the displacement, the direction of the displacement (the angle ξ (a variable in this example) whose direction is displaced from the x direction) is also set for each lattice point. That is, the vector amount of the displacement is set for each lattice point.

[0059] In the first embodiment, the vector amount of the displacement at each lattice point is modulated so as to have a composite modulation period in which a plurality of different periods are superimposed.

[0060] Here, the magnitude d(x, y) of the displacement at each lattice point represented by coordinates (x, y) is d(x, y)=C1·sin(k1x)+C2·sin(k2x)+C3·sin(k3x)+…+C n ·sin(k n x)+B·y …(11) (C1, C2, C3, …C n 、k1, k2, k3, …k n 、B are constants, respectively). Here, the amplitude An and the phase αn in the formula (1) are not considered. When the displacement is set as in the formula (11), k1, k2, k3, …kn Depending on the value of , n laser beams are emitted in directions with different inclination angles θ / azimuth angles φ, and these are combined with n laser beams whose azimuth angles differ by 180° from each of the n laser beams, resulting in 2n laser beams (or (2n-1) beams including one with an inclination angle θ of 0°).

[0061] In the example defined by equation (11), the compound modulation period is applied only in the x direction, but it may also be applied only in the y direction, or in both the x and y directions. As an example of the latter, d(x, y) d(x, y)=C1·sin(k1x)+C2·sin(k2x)+C3·sin(k3x)+…+C n ·sin(k n x) +C n+1 ·sin(k n+1 y)+C n+2 ·sin(k n+2 y)+C n+3 ·sin(k n+3 y) + ... + C n+m ·sin(k n+m y) …(12) (C1, C2, C3, …C n , C n+1 , C n+2 , C n+3 , …C n+m k1, k2, k3, …k n , k n+1 , k n+2 , k n+3 ...k n+m (These are constants.) By doing so, two (n+m) laser beams are obtained, each emitting in a direction with a different inclination angle θ / azimuth angle φ.

[0062] In the example in Figure 4, in addition to the magnitude of the displacement defined by equations (11), (12), etc., periodicity can be added to the direction of the displacement. For example, the angle ξ(x, y) indicating the direction of the displacement at each grid point (x, y) can be... ξ(x, y)=C n+m+1 ·sin(k n+m+1 x)+C n+m+2·sin(k n+m+2 x) …(13) By setting m=0 (when combined with equation (11)), 2(n+m+2) laser beams can be obtained. Periodicity is imparted to the direction of the shift in only one of the x or y directions (using equation (13) C n+m+1 or +C n+m+2 If (n=0, m=0), then 2(n+m+1) laser beams are obtained. Alternatively, if we apply different modulations to the x and y directions with respect to the direction of the shift, without modulating the magnitude of the shift (n=0, m=0), then 2×2=4 laser beams are obtained.

[0063] Up to this point, we have explained how to modulate the amount of deviation, but it is also possible to modulate the area of ​​the different refractive index region 122 instead of the amount of deviation (Figure 5). Similar to equations (11) and (12), the area S(x, y) of the different refractive index region 122 at each grid point represented by coordinate (x, y) is S(x, y)=S1·sin(k1x)+S2·sin(k2x)+S3·sin(k3x)+…+S n ·sin(k n x) + D·y …(14) or S(x, y)=S1·sin(k1x)+S2·sin(k2x)+S3·sin(k3x)+…+S n ·sin(k n x) +S n+1 ·sin(k n+1 y)+S n+2 ·sin(k n+2 y)+S n+3 ·sin(k n+3 y) + ... + S n+m ·sin(k n+m y) …(15) (S1, S2, S3, …S n , S n+1 , S n+2 , S n+3 , … S n+m k1, k2, k3, …k n , k n+1 , k n+2 , kn+3 ...k n+m By setting D to constants, 2n or (2n-1) laser beams (in the case of equation (14)) or 2(n+m) or (2(n+m)-1) laser beams (in the case of equation (15)) are obtained, each emitting in a direction with a different inclination angle θ / azimuth angle φ.

[0064] Furthermore, by combining the amount of displacement (magnitude and direction) with the area, it is possible to obtain even more laser beams.

[0065] Figure 6 shows an example of the calculation results of the far-field image of the laser beams emitted from a two-dimensional photonic crystal laser 10, which is designed to emit 2 × 50 = 100 laser beams by forming a composite modulation period by superimposing 50 modulation periods that differ in terms of displacement and area. The emission range is set such that the tilt angle θ in the x and y directions is within ±25°, corresponding to each modulation period. n The above setting was applied. Figure 6 shows 100 spots arranged in 10 rows and 10 columns, confirming that 100 laser beams were emitted as designed.

[0066] However, the two rows of spots (20 spots) indicated by the two thick arrows in Figure 6, which are five rows apart from each other, have a weaker intensity than the other spots. Also, the 16 spots in the two rows indicated by the two thin arrows, which are five columns apart from each other and not included in the aforementioned two rows, have a stronger intensity than the spots in those two rows, but are slightly weaker than the other spots. This is thought to be due to light interference that occurred when the laser beam was emitted from the two-dimensional photonic crystal layer.

[0067] Therefore, in the first embodiment, in equation (1) described above, k n Phase exp(iα) n ) randomly (one k n Each of the above points is given a phase, and different k nFor a two-dimensional photonic crystal laser 10 having a two-dimensional photonic crystal layer 12 (with the phase randomized when compared to other layers), a far-field image of the laser beam was calculated. The results are shown in Figure 7. The position of the laser beam spots is the same as in Figure 6. The intensity of each spot does not show any weakening in specific rows or columns as in Figure 6, and is closer to uniform than in Figure 6. However, some spots appear to have a weaker intensity than others.

[0068] Therefore, in equation (1) mentioned above, k n Amplitude A for each upward movement n The size of the spot was repeatedly adjusted until the intensity of all spots was as uniform as possible. An example of a far-field image of the laser beam adjusted in this way is shown in Figure 8. From Figure 8, it can be seen that 100 laser beams with nearly uniform intensity have been obtained.

[0069] (2) Second embodiment (Example using a two-dimensional photonic crystal having a double lattice structure) The two-dimensional photonic crystal laser of the second embodiment is 、2 Except for the configuration of the 2D photonic crystal layer, it has the same configuration as the 2D photonic crystal laser 10 of the first embodiment. Below, the configuration of the 2D photonic crystal layer 12A in the 2D photonic crystal laser of the second embodiment will be described.

[0070] As shown in Figure 9, the two-dimensional photonic crystal layer 12A is formed by arranging a region with a different refractive index 122A, which has a refractive index different from that of the base material 121A, and a second region with a different refractive index 123, which also has a different refractive index from that of the base material 121A. In this embodiment, both the region with a different refractive index 122A and the second region with a different refractive index 123 are voids. Either one or both of the region with a different refractive index 122A and the second region with a different refractive index 123 may be made of a material with a refractive index different from that of the base material 121A (a material other than air). In that case, the material of the region with a different refractive index 122A and the material of the second region with a different refractive index 123 may be made of the same material, or they may be made of different materials.

[0071] The differential refractive index region 122A has a period length a and is positioned offset by a predetermined amount (vector value) from the first lattice point 1251 of the first square lattice, which is indicated by a black circle in Figure 9. Its area also differs for each first lattice point 1251. The amount of offset and area of ​​these differential refractive index regions 122A can be set in the same way as in the first embodiment. In this embodiment, the shape of the differential refractive index region 122A is elliptical, but it may be other shapes such as the equilateral triangle exemplified in the first embodiment.

[0072] The second differential refractive index region 123 has a period length a and is located on the second lattice point 1252 of a second square lattice having the second lattice point 1252 indicated by a white circle in Figure 9. The second lattice point 1252 is located at a position shifted by 0.5a from the first lattice point 1251 in a direction parallel to the a2↑ of the fundamental translation vectors a1↑ and a2↑ of the first and second square lattices. In this embodiment, the shape of the second differential refractive index region 123 is elliptical and all have the same area. However, the shape of the second differential refractive index region 123 may be other shapes such as an equilateral triangle.

[0073] Thus, because the different refractive index region 122A is located at the first lattice point 1251 and the second different refractive index region 123 is located at the second lattice point 1252, among the light that propagates in a direction 45° with respect to the fundamental translation vectors a1↑ and a2↑, the wavelength λ is 2 0.5 What is a is amplified. In this case, the difference in optical path length between the first light (thick solid arrow in Figure 10) which is reflected by 180° from a first lattice point 1251 or a region with a different refractive index 122A located at a predetermined distance from there, and the second light (thick dashed arrow in Figure 10) which is reflected by 180° from a second lattice point 1252 located at a position 0.5a shifted from the first lattice point 1251 in the direction of the fundamental translation vector a2↑, and the second light (thick dashed arrow in Figure 10) which is reflected by 180° from there. -0.5This is a. Note that along the dashed line shown in Figure 10, the light traveling at a 45° angle to a1↑ and a2↑ is in phase, so here the optical path length is determined based on the position of this dashed line. The difference in optical path length between these first and second rays is 2. -0.5 As a result of this, the light is weakened by interference (in this example, it disappears). Therefore, the intensity of light whose propagation direction changes in a direction other than 180° in the different refractive index region and the second different refractive index region becomes relatively large, and stable laser oscillation can be obtained over a wide area within the two-dimensional photonic crystal layer 12A.

[0074] Next, for the two-dimensional photonic crystal laser of the second embodiment, the one-dimensional coupling coefficient κ 1D and the two-dimensional coupling coefficient κ 2D The one-dimensional coupling coefficient κ was calculated. 1D While κ is a coefficient that indicates the magnitude of the interaction between light traveling in a specific direction within the two-dimensional photonic crystal layer 12A, the two-dimensional coupling coefficient κ 2D This coefficient represents the magnitude of the interaction between light rays traveling in different directions within the two-dimensional photonic crystal layer 12A. The one-dimensional coupling coefficient κ 1D The smaller the value, the more important the two-dimensional coupling coefficient κ is. 2D The larger the value of κ, the easier it is for light to spread in two dimensions within the two-dimensional photonic crystal layer, meaning that stable laser oscillation can be obtained over a wide area. Here, calculations were performed for numerous examples with different areas of the second heterorefractive index region 123. The larger the area of ​​the second heterorefractive index region 123, the larger the one-dimensional coupling coefficient κ of the second heterorefractive index region 123. 1D and the two-dimensional coupling coefficient κ 2D This means that the impact will become significantly apparent.

[0075] One-dimensional coupling coefficient κ 1D The calculation results are shown in the graph in Figure 11(a), where the two-dimensional coupling coefficient κ 2DThe calculation results are shown in the graphs in Figure 11(b). In these graphs, the horizontal axis represents the value obtained by dividing the area of ​​the second heterorefractive index region 123 by the square of the period length a of the square lattice. From these calculation results, the larger the area of ​​the second heterorefractive index region 123, the greater the one-dimensional coupling coefficient κ. 1D While the two-dimensional coupling coefficient κ decreases significantly, 2D Although the one-dimensional coupling coefficient κ gradually decreases, 1D It can be seen that the decrease is more gradual. This result indicates that stable laser oscillation can be easily obtained over a wide area within the two-dimensional photonic crystal layer. Furthermore, this result indicates that the wavelength λ propagating at a 45° angle to the fundamental translation vectors a1↑ and a2↑ is 2 0.5 This is thought to reflect the fact that light from region a is attenuated by interference due to 180° reflection in the different refractive index region 122A and the second different refractive index region 123.

[0076] Next, the emissivity coefficient of the two-dimensional photonic crystal laser of the second embodiment was calculated. The emissivity coefficient is the ratio of light present as a waveguide mode in the two-dimensional photonic crystal layer that is emitted perpendicular to or tilted from perpendicular to the two-dimensional photonic crystal layer due to diffraction while guiding along length L, expressed as {exp(α v The coefficient α when expressed as L)-1 v The emission coefficient is α. v The smaller α is, the easier it is to confine light within the two-dimensional photonic crystal layer 12A, thereby making laser oscillation more likely. The calculation results are shown in Figure 12. Within the two-dimensional photonic crystal layer 12A, four oscillation modes, modes A to D, can occur near the band edge of the photonic band. Regardless of the area of ​​the second differential refractive index region 123, the emissivity coefficients α of modes A and B are... v The emission coefficient α of modes C and D is greater than that of modes C and D. v This is significantly larger. As a result, laser oscillation due to modes C and D is less likely to occur, and unwanted laser oscillation due to higher-order modes can be suppressed.

[0077] Next, for the two-dimensional photonic crystal laser of the second embodiment, the electric field distribution within the two-dimensional photonic crystal layer 12A was calculated. In this calculation, the area of ​​the second differential refractive index region 123 was set to 0.03a. 2 The same calculation was performed for the case where a two-dimensional photonic crystal layer is provided, having a configuration in which the second differential refractive index region 123 is removed from the two-dimensional photonic crystal layer 12A. The calculation results for the former are shown in Figure 13(a), and the calculation results for the latter are shown in Figure 13(b). In Figure 13, the direction of the electric field is shown by the direction of the arrow, and the magnitude of the electric field is shown by the length of the arrow. From Figure 13, no significant difference is observed between (a) and (b), and it can be seen that the presence or absence of the second differential refractive index region 123 does not have much effect on the electric field.

[0078] In the second embodiment described so far, the distance between the first lattice point 1251 and the nearest second lattice point 1252 was set to 0.5a, but this distance can be greater than 0.25a and less than 0.75a. By setting the distance between the first lattice point 1251 and the second lattice point 1252 in this way, the wavelength λ is 2 0.5 Light traveling at a 45° angle to the fundamental translation vectors a1↑ and a2↑, the light reflected at 180° from the first lattice point 1251 or a region with a different refractive index 122A located at a predetermined distance therefrom, and the light reflected at 180° from the second region with a different refractive index 123 located at the second lattice point 1252, can be weakened by interference (even if not completely annihilated).

[0079] Furthermore, in the second embodiment described so far, the second differential refractive index region 123 is placed at the second lattice point 1252. However, the second differential refractive index region 123 may be positioned offset from the second lattice point 1252 by a different amount of offset (vector value) for each second lattice point 1252, and its area may also differ for each second lattice point 1252.

[0080] (3) Third embodiment (broad cross-sectional area laser of the first embodiment) The two-dimensional photonic crystal laser of the third embodiment has the same configuration as the two-dimensional photonic crystal laser 10 of the first embodiment, except for the configuration of the two-dimensional photonic crystal layer. The configuration of the two-dimensional photonic crystal layer 12B in the two-dimensional photonic crystal laser of the third embodiment will be described below.

[0081] As shown in Figure 14, the two-dimensional photonic crystal layer 12B consists of numerous regions 122B with different refractive indices, each having an equal planar shape (including its area), positioned at locations offset from the lattice points of a square lattice with lattice period a (the points where the vertical and horizontal dashed lines intersect in the same figure). To illustrate this offset, Figure 15 shows the positions of the centroids G in the planar shape of the regions with different refractive indices 122B, along with the square lattice (dashed lines), indicated by black circles. Each centroid G is offset by an equal distance d from the lattice points of the square lattice. On the other hand, the line segments connecting the centroids G to the lattice points (thick solid lines in Figure 15) point in different directions for each lattice point. This direction is defined by the angle Ψ with respect to a reference line, with the reference line being a straight line extending in one of the two directions in which the lattice points are aligned with lattice period a (let's call this the x-direction shown in Figure 15). In this example, only the angle Ψ is modulated (the distance d and the area of ​​the different refractive index region 122B are not modulated), so the angle Ψ corresponds to the modulation phase. Observing the difference in angle Ψ for each grid point, the angle Ψ changes periodically in the x-direction with a predetermined modulation period, while the modulation period gradually shortens. As a result, the phase difference (difference in angle Ψ) between adjacent grid points increases in the x-direction as Ψ0+δ, Ψ0+2δ, Ψ0+3δ, and so on. Similarly, in the y-direction (the direction different from the x-direction mentioned above), the angle Ψ changes periodically in the y-direction with a predetermined modulation period, while the modulation period gradually shortens.

[0082] Note that in Figure 14, the differential refractive index region 122 has a planar shape that is an equilateral triangle. B This shows the different refractive index region 122 B The planar shape is not limited to this.

[0083] Figure 16 shows an example where the displacement of the centroid G in the differential refractive index region 122B from the grid points of the square grid differs from that in Figure 15. The planar shape of the differential refractive index region 122B in this example is the same as that shown in Figure 14. In this example, the direction in which the centroid G is displaced from the grid points is the same angle ξ (0° < ξ < 90°) from the x direction at every grid point (and (ξ - 90)° from the y direction), and the distance d that the centroid G is displaced from the grid points changes periodically in the x direction with a predetermined modulation period, while the modulation period gradually shortens. In the example in Figure 16, the distance d at each grid point is d in the x direction max sinΨ0, d max sin(2Ψ0+δ), d max sin(3Ψ0+3δ), d max The expression changes as sin(4Ψ0+6δ)..., and the phase difference in the change of distance between adjacent lattice points increases as Ψ0+δ, Ψ0+2δ, Ψ0+3δ.... The change in distance d for each lattice point is similar in the y direction.

[0084] Note that the angle ξ may be within the range of -90° < ξ < 0°. In the cases of -90° < ξ < 0° and 0° < ξ < 90°, the direction in which the centroid G deviates from the grid point will be different from the x and y directions, thereby producing the additional effects described later. If these additional effects are not considered, the direction in which the centroid G deviates from the grid point may be the x or y direction.

[0085] Figure 17 shows yet another example of the two-dimensional photonic crystal layer 12B. In this two-dimensional photonic crystal layer 12B, the centroids of the different refractive index regions 122B are grid points It is positioned above. Each different refractive index region 122 B The planar shapes are similar but have different areas S. This area S changes periodically in the x-direction with a predetermined modulation period, while the modulation period gradually shortens. 17 In this example, each different refractive index region 122 at each lattice point B The area S of the planar shape is given by S = S0 + S'sinΨ, where Ψ changes in the x direction as Ψ0, 2Ψ0 + δ, 3Ψ0 + 3δ, 4Ψ0 + 6δ, between adjacent lattice points. areaThe phase difference of the change increases as follows: Ψ0+δ, Ψ0+2δ, Ψ0+3δ, and so on. The same applies to the y-direction.

[0086] In the three examples shown so far, the modulation period is shortened in the x and y directions by changing either the direction of the displacement of the centroid of the different refractive index region 122B from the grid points of the square grid, the distance of the displacement, or the area of ​​the different refractive index region 122B, respectively. However, similar changes may be formed by combining two or three of these three methods.

[0087] The areas of the first electrode 171 and the second electrode 172 are set so that current is injected over a range in the two-dimensional photonic crystal layer 12B where there are many regions 122B with different refractive indices, differing orientations, distances, or areas from one another.

[0088] Next, the operation of the two-dimensional photonic crystal laser of the third embodiment will be described. By applying a predetermined voltage between the first electrode 171 and the second electrode 172, current is injected from both electrodes into the active layer 11. As a result, light emission having a wavelength within a predetermined wavelength band according to the material of the active layer 11 is generated from the active layer 11. The light emission thus generated is introduced over a range in the two-dimensional photonic crystal layer 12B where there are many different refractive index regions 122B with different orientations of misalignment, distances of misalignment, or areas, corresponding to the size of the area in which the current is injected. B Within the lattice, light with a resonant wavelength corresponding to the lattice point period a of the square lattice resonates, is selectively amplified, and generates laser oscillation.

[0089] The oscillating laser light is emitted from both surfaces of the two-dimensional photonic crystal layer 12B, respectively, to the outside of the two-dimensional photonic crystal layer 12B. Of these, the laser light emitted towards the first electrode 171 is reflected by the first electrode 171 and emitted out of the two-dimensional photonic crystal laser 10 through the window portion 1722 of the second electrode 172. The laser light emitted towards the second electrode 172 is emitted directly out of the two-dimensional photonic crystal laser through the window portion 1722 of the second electrode 172.

[0090] The emission angle θ(x, y), which is the angle between the laser beam emitted from each point (x, y) on the two-dimensional photonic crystal layer 12B and the normal to the two-dimensional photonic crystal layer 12B, and the azimuth angle φ(x, y), which is the angle between the projection of the laser beam onto the surface of the two-dimensional photonic crystal layer 12B and a reference line parallel to the surface, depend on the modulation at the position on the two-dimensional photonic crystal layer 12B from which the laser beam is emitted. These emission angle θ and azimuth angle φ can be determined as follows (see Patent Document 1).

[0091] First, we determine the modulation phase Ψ at each grid point. The modulation phase Ψ is obtained by modulating the distance d from the grid point, where d = d max sinΨ(d max The value of Ψ that satisfies the relationship (maximum value of the outlier) corresponds to S = S0 + S'sinΨ (where S0 is the average value of the area) when modulating the area S of the different refractive index region. 、 The Ψ that satisfies the relationship S' (where S' is the amplitude of the area modulation) corresponds to this. When the modulation phase Ψ described in Patent Document 1 is applied, the wavelength λ in the two-dimensional photonic crystal layer L The wave vector of light k↑ = (k x , k y ), the effective refractive index n of the two-dimensional photonic crystal layer eff , and the reciprocal lattice vector G'↑=(g') expressed using the azimuthal angle φ from a predetermined reference line of the 2D lattice. x , g' y )=(k x ±|k↑|(sinθcosφ) / n eff , k y ±|k↑|(sinθsinφ) / n eff Using ) and the position vector r↑ of each lattice point, Ψ=r↑·G'↑ It is represented as follows.

[0092] In the two-dimensional photonic crystal layer 12B of the two-dimensional photonic crystal laser of the third embodiment, different refractive index regions 122 B These are arranged in a square grid. In the case of a square grid, the position vector r↑ is an integer m. x , m y Using r↑=(m xa, m y a) The wave vector k↑ is k↑=(π / a, π / a), and the reciprocal lattice vector G'=(g' x , g' y )teeth

number

number

[0093] From equation (17), two adjacent lattice points in the x direction (na, m y a) and ((n+1)a, m y a)(m y The difference in modulation phase Ψ between two lattice points (where the values ​​are the same for any two lattice points) depends on sinθ. The same applies to the difference in modulation phase Ψ between two adjacent lattice points in the y direction. Therefore, if the modulation phase Ψ is set such that the value of θ increases within the range of 0 to 90° as the x-direction and y-direction move in either the positive or negative direction within the two-dimensional photonic crystal layer 12B, the difference in modulation phase Ψ between adjacent lattice points will increase. This corresponds to a shortening of the modulation period. As a result, the emission angle θ of the laser beam is set such that the position from which it is emitted from the two-dimensional photonic crystal layer 12B increases as it moves in the aforementioned direction. Since laser beams with different emission angles θ are bundled together and emitted outside the two-dimensional photonic crystal laser, the laser light can be irradiated onto the target object over a wide area.

[0094] Although we used the case of a square lattice as an example here, the same principles apply to rectangular and triangular lattices.

[0095] Up to this point, the explanation has been based on the modulation phase Ψ described in Patent Document 1, but by using the method described in Patent Document 2, a more precise modulation phase Ψ can be obtained. According to this method, when the two-dimensional lattice is a square lattice, each component of the reciprocal lattice vector G'(x, y)↑ is

number

[0096] Figures 18(a) and (b) illustrate cross-sections of laser beams emitted from a two-dimensional photonic crystal laser of the third embodiment. In (a) and (b), a two-dimensional photonic crystal laser was fabricated with modulation set so that the emission angle θ changes within the range of 10° to ±2° (4° overall, in the case of (a)) or ±4° (8° overall, in the case of (b)) within the two-dimensional photonic crystal layer 12B, and a cross-section of the emitted laser beam was photographed. In (c), the cross-section of the laser beam was calculated for a two-dimensional photonic crystal laser with modulation set so that the emission angle θ changes within the range of 25° to ±15° (30° overall) within the two-dimensional photonic crystal layer 12B. For comparison, Figure 19 shows a photograph of a cross-section of a laser beam emitted from the entire two-dimensional photonic crystal layer 12 at an emission angle θ of 10°, similar to that described in Patent Document 2. In both cases, two laser beams with azimuth angles differing by 180° are emitted. It can be seen that the beam emission range is wider in the third embodiment shown in Figures 18(a) to (c) than in the comparative example shown in Figure 19.

[0097] Up to this point, we have described an example of expanding the diameter of a laser beam by changing the modulation period depending on its position within the two-dimensional photonic crystal layer 12B. However, if the direction in which the position of the centroid of the region with different refractive indices is shifted from the lattice point is tilted from the direction in which the lattice points are aligned at a predetermined lattice point period, a laser beam having a single resonant mode and a single polarization can be emitted regardless of whether the modulation period is changed or not (in the example shown in Figure 16, the modulation period is changed).

[0098] Figure 20 shows the results of calculating the emission coefficients for each of the multiple photonic bands possessed by a two-dimensional photonic crystal for several examples where the angle ξ of the slope of the line connecting the lattice point and the centroid differs for one of the directions in which the lattice points are aligned with lattice point period a, by modulating the distance between the lattice point of a square lattice and the centroid of the region with different refractive indexes, and the area of ​​the region with different refractive indexes (without introducing a change in the modulation period). Here, the emission coefficient refers to the proportion of light that is emitted by diffraction during guidance of a unit length, out of the light that exists as a guided mode in the two-dimensional photonic crystal layer. The smaller the emission coefficient, the easier it is to confine light within the two-dimensional photonic crystal layer, and therefore laser oscillation is more likely to occur.

[0099] As can be seen from Figure 20, when the angle ξ is not 0°, the emission coefficient of band edge A is the smallest among the multiple photonic bands. Furthermore, as the angle ξ increases from 0°, the difference in emission coefficient between band edge A and band edge B, which has the next smallest emission coefficient, increases. From these results, it can be seen that as the angle ξ increases, laser oscillation at band edge A alone becomes more likely. This makes it possible to emit a laser beam with a single resonant mode and a single polarization.

[0100] (4) Fourth embodiment (2D photonic crystal laser array) Next, as a fourth embodiment, an embodiment of a two-dimensional photonic crystal laser array will be described. This two-dimensional photonic crystal laser array 20 has a plurality of two-dimensional photonic crystal lasers of the third embodiment. However, as will be described later, the shapes of the first electrode 171 and the second electrode 172 are different from those of the third embodiment. In the plan views of Figures 21(a) and (b), each two-dimensional photonic crystal laser (labeled "10B" in the figure) is shown by a dashed line. The modulation in the two-dimensional photonic crystal layer 12B is different for each two-dimensional photonic crystal laser 10B, and as a result, the range of emission angles of the laser beam emitted from each two-dimensional photonic crystal laser 10B is also different.

[0101] The two-dimensional photonic crystal laser array 20 further includes a first aggregate electrode 21 consisting of a square conductive plate and a second aggregate electrode 22 which is a mesh electrode having multiple holes 222 formed in a square conductive plate 221. The current supply unit is composed of these first aggregate electrode 21 and second aggregate electrode 22 and a power supply (not shown). Each of the two-dimensional photonic crystal lasers 10B is positioned to block one of the holes 222 in the second aggregate electrode 22, and the substrate 16 is in contact with the portion of the plate 221 surrounding the hole 222. In addition, the first cladding layer 141 of each two-dimensional photonic crystal laser 10B is in contact with the first aggregate electrode 21. Therefore, in each two-dimensional photonic crystal laser 10B, the first aggregate electrode 21 and the second aggregate electrode 22 serve as the first and second electrodes. Alternatively, a first electrode and a second electrode may be separately provided for each two-dimensional photonic crystal laser 10B, and each first electrode may be connected to the first electrode assembly 21, and each second electrode may be connected to the second electrode assembly 22.

[0102] In the four-dimensional photonic crystal laser array 20, when current is passed between the first aggregate electrode 21 and the second aggregate electrode 22 from a power supply (not shown), current is supplied to each two-dimensional photonic crystal laser 10B, thereby generating a laser beam with a different emission angle and spread for each two-dimensional photonic crystal laser 10B. 2 collective electrode 22 The light is emitted to the outside through the hole 222. This allows the laser light to be irradiated over a wider area with a nearly uniform intensity than when using a single two-dimensional photonic crystal laser 10B.

[0103] Figure 22 shows a photograph of a cross-section of the laser beam emitted from the two-dimensional photonic crystal laser array 20 of this embodiment. A laser beam with an emission angle θ of ±15° (30° in total) is obtained. This is wider than the laser beam emitted from a single two-dimensional photonic crystal laser 10B.

[0104] The shapes of the first electrode assembly 21 and the second electrode assembly 22 are not limited to those described above. For example, the first electrode assembly 21 may be a circular flat plate, and the second electrode assembly 22 may be a circular flat plate with many holes. Also, in the example shown in Figure 21(b), one two-dimensional photonic crystal laser 10B is placed for each hole 222 of the second electrode assembly 22, but multiple two-dimensional photonic crystal lasers 10B (four in the example shown in Figure 23(a)) may be placed for each hole 222A. Furthermore, in the example shown in Figure 21(b), the holes 222 of the second electrode assembly 22 are arranged in a two-dimensional manner, but the holes 222B may be arranged in a one-dimensional manner, as in the second electrode assembly 22B shown in Figure 23(b). In this case, the holes 222 B The shape is hole 222 B It is preferable to have a long line-shaped (slit-shaped) configuration perpendicular to the direction of arrangement.

[0105] Figure 24 shows a modified example of a two-dimensional photonic crystal laser array 20A. In this two-dimensional photonic crystal laser array 20A, 100 two-dimensional photonic crystal lasers 10B are arranged in a 10x10 grid, and the two-dimensional photonic crystal lasers 10B are insulated from each other by an insulating layer 24 made of i-type GaAs, which is an intrinsic semiconductor. A cover layer 23 made of n-type GaAs, which is an n-type semiconductor, is provided on the outside of the second electrode 172B of each two-dimensional photonic crystal laser 10B, and the insulating layer 24 is formed on the outside of the cover layer 23 as an integral part of the portion between the two-dimensional photonic crystal lasers 10B. n-type GaAs and i-type GaAs are materials that can transmit laser light generated by the two-dimensional photonic crystal lasers 10B.

[0106] In the two-dimensional photonic crystal laser 10B, the ten two-dimensional photonic crystal lasers 10B arranged in the row direction are electrically connected by a conductive connecting member 173. The first electrode 171 of each laser is electrically connected to the second electrode 172B of the adjacent two-dimensional photonic crystal laser 10B on one side, and the second electrode 172B is connected to the first electrode 171 of the adjacent two-dimensional photonic crystal laser 10B on the other side. As a result, as shown in Figure 24(c), the ten two-dimensional photonic crystal lasers 10B arranged in the row direction are connected in series. On the other hand, in the column direction, each two-dimensional photonic crystal laser 10B is electrically insulated from the adjacent two-dimensional photonic crystal laser 10B. Note that the connecting member 173 is not shown in Figure 24(a). Furthermore, the second electrode 172B is formed to extend outward from the two-dimensional plane than the second electrode 172 shown in Figure 1 in order to secure the connection portion with the connecting member 173.

[0107] Figure 25 shows a photograph of a cross-section of the laser beam emitted from the modified two-dimensional photonic crystal laser array 20A. Note that the two-dimensional photonic crystal laser array 20A emits two laser beams with azimuth angles differing by 180°, but Figure 25 shows only one of them. From this figure, it can be said that the intensity is greater and the uniformity of intensity at each position is higher than that of the laser beam emitted from the aforementioned two-dimensional photonic crystal laser array 20 (Figure 22). Figures 26 and 27 show the current-output characteristics and oscillation spectrum of the laser beam emitted from the modified two-dimensional photonic crystal laser array 20A, respectively. In both cases, sufficient laser characteristics are obtained.

[0108] (5) Fifth embodiment (broad cross-sectional area laser of the second embodiment) Next, an embodiment of a two-dimensional photonic crystal laser according to a second embodiment will be described. As a prerequisite, the third embodiment has a two-dimensional photonic crystal layer 12B having the structure shown in Figure 16, in which the two-dimensional photonic crystal layer has a fundamental modulation state (no adjustment of the deviation amount and / or area according to the present invention has been made from the fundamental modulation state). formLet's consider an example of a two-dimensional photonic crystal laser. In this example, the distance d at which the centroid G is shifted from the lattice point changes periodically in the x-direction with a predetermined modulation period, while the modulation period gradually shortens. Specifically, the distance d at each lattice point changes in the x-direction and y-direction, respectively, in the positive direction. max sinΨ0, d max sin(2Ψ0+δ), d max sin(3Ψ0+3δ), d max The modulation changes as follows: sin(4Ψ0+6δ)..., and the phase difference of the change in distance between adjacent grid points increases as Ψ0+δ, Ψ0+2δ, Ψ0+3δ.... This modulation phase is in a fundamental modulation state where it is continuously increasing in the positive x and positive y directions.

[0109] A two-dimensional photonic crystal laser having a two-dimensional photonic crystal layer in this basic modulation state emits two wide-section laser beams with azimuth angles differing by 180° from each other, as shown in the calculation results of the far-field image in Figure 18. In the example shown in Figure 18(c), the wide-section laser beams are spread out within a tilt angle range of 30° (±15°). The cross-section of the obtained wide-section laser beam is circular, and the intensity decreases as you move away from the center of this circle.

[0110] Therefore, as a wide-cross-sectional-area laser beam having a more uniform intensity distribution, we consider a hypothetical wide-cross-sectional-area laser beam having a phase distribution at a distance obtained from the two-dimensional photonic crystal layer of the third embodiment, which has a square cross-section with inclination angles of 30° in the x-direction and 30° in the y-direction, and within that cross-section, the intensity is uniformly distributed and is in the basic modulation state. Then, we consider the target distant electric field distribution E, which is the electric field distribution at a position sufficiently far from the two-dimensional photonic crystal layer 12B in this hypothetical wide-cross-sectional-area laser beam. far_iFFT (K↑) is used as the model. Using equation (8) above, this target far-field electric field distribution E far_iFFT By performing an inverse Fourier transform on (K↑), the two-dimensional photonic crystal layer 12 B The target radiated electric field distribution E is the electric field distribution radiated from each position within (at each of those positions). rad_iFFT(r↑) was calculated. Then, the 2D photonic crystal layer 12 B Radiated electric field distribution E rad (r↑) is the target radiated electric field distribution E rad_iFFT The modulation phase Ψ(r↑) at each grid point is adjusted to approach (r↑). In this embodiment, the modulation phase Ψ(r↑) at each grid point r↑=(x, y) was determined using equation (9) above.

[0111] Then, the adjusted two-dimensional photonic crystal layer 12 B Radiated electric field distribution E from each position within rad After determining (r↑), this radiated electric field distribution E rad Using (r↑), the far-field electric field distribution E can be obtained from equation (7) above. far (r↑) is calculated, and the obtained far-field electric field distribution E far By applying the phase distribution of the electric field at (r↑), the target distant electric field distribution E far_iFFT The phase distribution of the electric field at (K↑) is updated, and the radiated electric field distribution E rad (r↑) is the target radiated electric field distribution E rad_iFFT The operation of adjusting the modulation phase Ψ(r↑) to approach (r↑) was repeatedly performed.

[0112] Figure 28 shows the 2D photonic crystal layer 12 after one adjustment of the modulation phase Ψ(r↑) (the operation up to the end of the previous paragraph). B Figure 29 shows the calculation results of the far-field image of a wide-section beam emitted from the device. Figure 29 also shows an enlarged view of the lower right portion of the lower of the two wide-section beams shown in Figure 28. From Figure 28, it can be seen that the cross-sectional shape of the wide-section beam is a square, similar to the hypothetical wide-section beam mentioned earlier. However, as can be seen from the enlarged view in Figure 29, a periodic pattern, thought to be due to interference, is observed in the intensity distribution. Figure 30 shows the calculation results of the far-field image of the wide-section beam after performing the above-described repetition 20 times. Figure 30 shows an improvement compared to Figures 28 and 29, indicating that the laser light intensity is almost uniform within the square cross-section.

[0113] The present invention is not limited to the embodiments described above, and various modifications are possible.

[0114] For example, in the examples shown in Figures 6 to 8, spots formed by 100 laser beams are arranged at approximately equal intervals vertically and horizontally. However, by appropriately changing the number of overlapping modulation periods and the magnitude of each modulation period, the number of laser beams and the arrangement of spots can be changed as needed. Also, in the examples shown in Figures 29 and 30, a uniform, square-shaped, wide-cross-section beam is formed with an angle of inclination of 30° in the x-direction and 30° in the y-direction. However, by appropriately changing the modulation phase of the two-dimensional photonic crystal, the shape and number of wide-cross-section beams can be changed as needed. By applying these techniques and changing the arrangement of spots, it is possible to display characters, marks, etc. Figures 31(a) to (c) show examples of such displaying characters, marks, etc.

[0115] In the fourth embodiment of the two-dimensional photonic crystal laser array, multiple two-dimensional photonic crystal lasers of the third embodiment were used, but instead, multiple two-dimensional photonic crystal lasers of the first, second, or fifth embodiment may be used. Alternatively, a two-dimensional photonic crystal laser array may be constructed by combining multiple two-dimensional photonic crystal lasers of several embodiments from the first to third and fifth embodiments. [Explanation of symbols]

[0116] 10, 10B...2D photonic crystal lasers 11...Active layer 12, 12A, 12B...2D photonic crystal layers 121, 121A…Base material 122, 122A, 122B...different refractive index region 123...Second different refractive index region 1251...1st grid point 1252…Second grid point 13…Spacer layer 141...First cladding layer 142...Second cladding layer 16… Circuit board 171, 171A...1st electrode 172, 172A, 172B…Second electrode 1721, 1721A... Frame portion of the second electrode 1722, 1722A... Window portion of the second electrode 173...Connecting member 20, 20A…2D photonic crystal laser array 21...First collective electrode 22, 22A, 22B…Second collective electrode 221...Flat plate of the second electrode assembly 222, 222A, 222B... Holes in the second electrode assembly 23…Cover layer 24…Insulating layer

Claims

1. a) A pair of electrodes, b) An active layer provided between the pair of electrodes, which generates light of a predetermined wavelength when current is injected from the electrodes, c) A two-dimensional photonic crystal layer provided between one of the pair of electrodes and the active layer, having a plate-shaped base material and a plurality of regions with different refractive indices that are arranged on the base material and have refractive indices different from those of the base material. Equipped with, The plurality of regions with different refractive indices are arranged with different amounts of displacement from each lattice point of a two-dimensional lattice periodically arranged in the base material with a period corresponding to the predetermined wavelength, or they are arranged with different areas at each lattice point, or they are arranged with different areas and different amounts of displacement from each lattice point. The amount of displacement and / or area of ​​each of the aforementioned multiple regions with different refractive indices is modulated by a composite modulation period formed by superimposing multiple periods that are different from each other, and a vector r↑ indicating the position of each grid point of the two-dimensional grid, and a vector k indicating the combination of the tilt angle and / or azimuth angle of each of the n (n is an integer of 2 or more) laser beams that have different tilt angles and / or azimuth angles from each other. n ↑, and amplitude A determined for every n n and phase exp(iα n The electric field distribution shown in complex numbers using Σ n A n exp(iα n )δ(k↑-k n The modulation phase Ψ(r↑) is expressed as the argument of the radiated electric field distribution, which is shown as a complex number, obtained by performing an inverse Fourier transform on the above. The aforementioned phase exp(iα) n ) is set randomly for each value of n. A two-dimensional photonic crystal laser characterized by the following features.

2. The two-dimensional photonic crystal laser according to claim 1, characterized in that a correction coefficient is added to the modulation phase Ψ(r↑).

3. The amplitude A n The two-dimensional photonic crystal laser according to claim 1, characterized in that the amplitude A has different values for each term with different values of n.

4. The aforementioned two-dimensional lattice is a square lattice, Furthermore, a second region with a different refractive index from the base material is arranged at a second lattice point, which is a lattice point of a square lattice that has the same period length a as the two-dimensional lattice and is shifted from the two-dimensional lattice, or at a position shifted by a different amount from the second lattice point. A two-dimensional photonic crystal laser according to any one of claims 1 to 3.

5. The two-dimensional photonic crystal laser according to claim 4, characterized in that the second lattice point is located at a position shifted from the lattice point of the two-dimensional lattice by a distance greater than 0.25a and less than 0.75a in the same direction as one of the fundamental translation vectors of the two-dimensional lattice.

6. The aforementioned two-dimensional lattice is a square lattice, At each lattice point of the two-dimensional lattice, each of the plurality of different refractive index regions is positioned offset from the lattice point in a predetermined direction or in a direction 180° different from that direction, wherein the direction is parallel to the two-dimensional photonic crystal layer and is inclined from both of the two directions in which the lattice points are aligned by the period length. A two-dimensional photonic crystal laser according to any one of claims 1 to 5.

7. The two-dimensional photonic crystal laser according to any one of claims 1 to 6, characterized in that the modulation phase Ψ(r↑) of each of the plurality of different refractive index regions is modulated in a direction parallel to the two-dimensional photonic crystal layer such that it changes periodically with a predetermined modulation period, and the modulation period is continuously increasing or decreasing.

8. A two-dimensional photonic crystal laser according to any one of claims 1 to 4, characterized in that the modulation phase Ψ(r↑) of each of the plurality of different refractive index regions changes periodically with a predetermined modulation period in a direction parallel to the two-dimensional photonic crystal layer, and the modulation phase Ψ(r↑) is adjusted from the basic modulation state to be closer to the target radiation field distribution obtained by inverse Fourier transforming a predetermined target far-field field distribution to be formed at a position away from the two-dimensional photonic crystal layer than to the radiation field distribution showing the distribution of the electric field emitted from the two-dimensional photonic crystal layer in the basic modulation state in which the modulation period is continuously increasing or decreasing.

9. A plurality of two-dimensional photonic crystal lasers according to any one of claims 1 to 8, each having a different modulation scheme, A current supply unit that simultaneously supplies current to the pair of electrodes provided on each of the plurality of two-dimensional photonic crystal lasers. A two-dimensional photonic crystal laser array characterized by having the following features.

10. The current supply unit includes a mesh electrode in which a plurality of holes are formed in a conductive plate material. Each of the plurality of holes is equipped with the two-dimensional photonic crystal laser, In each of the plurality of holes, the plate material surrounding the hole is connected to the first electrode or the second electrode, or is the first electrode or the second electrode. The two-dimensional photonic crystal laser array according to feature 9.

11. a) A pair of electrode groups, at least one of which consists of an electrode group having multiple partial electrodes, b) Provided between the pair of electrode groups, a predetermined wavelength λ is injected from a portion of the plurality of partial electrodes, and the current is injected at a position corresponding to the partial electrode to which the current is injected. L An active layer that generates light containing, c) A two-dimensional photonic crystal layer provided between one of the pair of electrodes and the active layer, the layer having a plate-shaped base material and a plurality of regions with different refractive indices that are arranged within the base material and have refractive indices different from those of the base material. Equipped with, The predetermined wavelength λ L Each of the plurality of different refractive index regions is positioned at each lattice point of a square lattice in which lattice points are periodically arranged with a lattice point period corresponding to the lattice point period, and each of the plurality of different refractive index regions is positioned offset from the lattice point in a predetermined direction or in a direction 180° different from that direction, wherein the direction is parallel to the two-dimensional photonic crystal layer and is inclined from both of the two directions in which the lattice points are aligned with the lattice point period, The laser beams are modulated in a direction parallel to the two-dimensional photonic crystal layer using a composite modulation period, which is a superposition of multiple periods in which the distance from the lattice point and / or the area of ​​the planar shape of each of the multiple different refractive index regions differs from one another. The vector r↑ indicates the position of each lattice point of the square lattice, and the vector k indicates the combination of the tilt angle and azimuth angle of each of the n (n is an integer of 2 or more) laser beams, each with a different tilt angle and / or azimuth angle. n ↑, and amplitude A determined for every n n and phase exp(iα n The electric field distribution shown in complex numbers using Σ n A n exp(iα n )δ(k↑-k n The modulation phase Ψ(r↑) is expressed as the argument of the radiated electric field distribution, which is shown as a complex number, obtained by performing an inverse Fourier transform on the above. The aforementioned phase exp(iα) n ) is set randomly for each value of n. A two-dimensional photonic crystal laser array characterized by the following features.

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