JP2008040230A - Photonic crystal waveguide - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a photonic crystal waveguide in which terminal end reflection of a waveguide can be sharply reduced using comparatively simple structure. <P>SOLUTION: The photonic crystal waveguide is constituted of a photonic crystal PC of which the grid B is periodically arranged, the waveguide 10 constituted by introducing a line defect into the photonic crystal PC, a radioactive guide 21 projecting along the optical axis direction of the waveguide 10 from an interface 11 of the photonic crystal PC, and the like, the number of grids arranged in the direction perpendicular to the optical axis direction is designed so as to be less in the radioactive guide 21 than in the waveguide 10. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a photonic crystal waveguide applicable to an optical integrated circuit or the like.

  A photonic crystal is a functional material having a periodic refractive index distribution, and the Bragg reflection condition is established when the grating is aligned with a period of the wavelength order of light and electromagnetic waves, so-called photonic band gap (forbidden band). Form.

  When a line defect is introduced into such a photonic crystal, light is strongly confined in that region, and a minute waveguide for the light can be formed. Further, when a point defect is introduced into the photonic crystal, a minute resonator for light can be formed.

  FIG. 14 is a plan view showing an example of a conventional photonic crystal waveguide. The photonic crystal PC is a two-dimensional photonic crystal in which a large number of lattices B are arranged in a triangular lattice pattern in the xy plane.

  A waveguide 10 is formed by introducing a line defect into the photonic crystal PC. The photonic crystal PC is bonded to an external medium 20 such as the atmosphere at the interface 11. The output end of the waveguide 10 is connected to the external medium 20 at the interface 11, and the input end of the waveguide 10 is connected to an optical circuit (not shown) formed inside the crystal.

  When the light L1 travels in the x direction and reaches the interface 11 along the waveguide 10, most of the light enters the external medium 20 as light L2, but a part of the light L1 enters the inside of the crystal as light L3. reflect. Such terminal reflection is caused by an abrupt structural change at the interface 11, and the reflected light L3 becomes noise light, which may deteriorate the function of the internal optical circuit or adversely affect it.

JP 2004-109269 A John D. Joannopoulos, Robert D. Meade, and Joshun N. Winn, "Photonic Crystals", Princeton University Press, 1995 Yasuaki Hirose and Toshio Kamibayashi, “Analysis of Input / Output Characteristics of Triangular PBG Waveguide”, IEICE Electronics Society Conference, C-3-92, 2004 Masatoshi Tokushima, Atsushi Ushida, Akiko Gomei, “Group Delay Measurement of Pillar-type Square Lattice Photonic Crystal Defect Waveguide”, IEICE General Conference, C-3-80, 2006 Satoshi Uno, "Electromagnetic field and antenna analysis by FDTD method", Corona, 1998

  Non-Patent Document 2 proposes an attempt to reduce reflection by providing a non-reflective (AR) coating at the input / output portion of the photonic slab waveguide or by forming the output end shape into a lens shape.

  An object of the present invention is to provide a photonic crystal waveguide that can significantly reduce the terminal reflection of the waveguide by using a relatively simple structure.

In order to achieve the above object, a photonic crystal waveguide according to the present invention includes a photonic crystal in which lattices are periodically arranged,
A waveguide configured by introducing a line defect into the photonic crystal;
A radioactive guide protruding from the interface of the photonic crystal along the optical axis direction of the waveguide,
The number of gratings arranged in the direction perpendicular to the optical axis direction is smaller in the radioactive guide than in the inside of the waveguide.

  In the present invention, it is preferable that the radioactive guide is composed of a grid row on both sides.

  In the present invention, the radioactive guide is preferably composed of a plurality of grid rows on both sides.

  In the present invention, in the radioactive guide constituted by a plurality of grating arrays on both sides, the number of gratings along the optical axis direction of the waveguide is preferably smaller in the outer grating array than in the inner grating array.

  In the present invention, the radioactive guide preferably has a smaller number of lattice rows on one side than the number of lattice rows on the other side.

  Moreover, in this invention, it is preferable to provide the directional coupler comprised by arrange | positioning the 1st line defect and the 2nd line defect adjacently in a photonic crystal.

  In the present invention, it is preferable that the photonic crystal is a three-dimensional photonic crystal, and the radioactive guide has a region where the number of lattices arranged in a predetermined circumferential direction is reduced with respect to the optical axis direction.

  According to the present invention, the radioactive guide is provided so as to protrude from the interface of the photonic crystal along the optical axis direction of the waveguide, and the number of gratings arranged in the direction perpendicular to the optical axis direction is larger than that in the waveguide. The design is such that there are fewer radioactive guides. This alleviates sudden structural changes at the output end of the waveguide, and light gradually leaks out from the periphery of the radioactive guide as evanescent waves, greatly reducing reflected light traveling toward the inside of the crystal. it can.

  FIG. 1 is a perspective view showing various photonic crystals. FIG. 1A shows a one-dimensional photonic crystal having a periodic refractive index distribution in the x direction. FIG. 1B shows a two-dimensional photonic crystal having a periodic refractive index distribution in the x and z directions. FIG. 1C shows a three-dimensional photonic crystal having a periodic refractive index distribution in the x, y, and z directions.

  Such photonic crystals are classified into a type in which a large number of real lattices are arranged in a space and a type in which a large number of vacancies are arranged in a base material. The Bragg reflection condition for the two-dimensional direction or the three-dimensional direction is satisfied.

  FIG. 2 is a perspective view showing how a waveguide is formed by a line defect. One lattice B has a cylindrical shape parallel to the y direction, and a large number of lattices B are arranged in a triangular lattice shape in the xz plane to constitute a two-dimensional photonic crystal PC.

  In such a photonic crystal PC, by removing the lattice B for one column along the x direction and providing a line defect D for one column, the light L passes as shown in FIG. A waveguide 10 can be formed.

  For example, when the cylinder constituting the lattice B is formed of GaAs crystal (relative permittivity ε = 11.4), the cylinder radius is 0.113 μm, and the distance between the centers of the cylinders is 0.563 μm, the wavelength is 1.5 μm. The Bragg reflection condition is established for the light of, and the waveguide 10 for the light having a wavelength of 1.5 μm is formed by providing the line defect D for one row.

  FIG. 3 is a plan view showing the first embodiment of the present invention. The photonic crystal PC is a two-dimensional photonic crystal in which a large number of lattices B are arranged in a triangular lattice pattern in the xy plane. By introducing a line defect into the photonic crystal PC, a waveguide 10 having an optical axis along the x direction is formed. The photonic crystal PC is bonded to an external medium 20 such as the atmosphere at the interface 11.

  The radioactive guide 21 protrudes from the interface 11 along the optical axis direction of the waveguide 10. The number of gratings arranged in the y direction perpendicular to the optical axis direction is designed so that the radioactive guide 21 is smaller than the inside of the waveguide 10.

  The output end of the waveguide 10 is connected to the radioactive guide 21, and the input end of the waveguide 10 is connected to an optical circuit (not shown) formed inside the crystal.

  When the light L1 travels in the x direction and enters the radioactive guide 21 along the waveguide 10, the light L4 gradually emanates from the periphery of the radioactive guide 21 to the external medium 20 as an evanescent wave. . Further, the light L2 that has entered the radioactive guide 21 is gradually attenuated, and the light intensity becomes zero before reaching the end of the radioactive guide 21. Therefore, the reflected light traveling toward the inside of the crystal can be greatly reduced.

  In the present embodiment, since the radioactive guide 21 is composed of one row of grids on both sides, the light L4 is quickly leaked to the outside. As a result, the light L2 is also attenuated quickly, so that the length of the radioactive guide 21 in the x direction can be shortened.

  In the present embodiment, the example in which the radioactive guide 21 configured by one side of the lattice array is provided on the two-dimensional photonic crystal has been described. However, in the case of the three-dimensional photonic crystal, the lattice array for one column is provided. A similar effect can be obtained by providing a radioactive guide arranged in a cylindrical shape.

  Next, the results of numerical analysis of the operation of the radioactive guide 21 using the FDTD (Finite Difference Time Domain) method (time domain difference method) will be described.

  FIG. 4 is an explanatory diagram showing an example of an analysis result by the FDTD method. In addition, FIG. 4 itself has calculated | required the photonic band gap by the plane wave expansion method. As a photonic crystal, a GaAs crystal (ε = 11.4) in a vacuum (ε = 1) background and dielectric cylinders with a radius r = 0.1126 μm arranged in a triangular lattice with a lattice spacing a = 0.563 μm As shown in FIG. 3, the properties of the waveguide were imparted by removing one row of lattice rows along the x direction.

The polarization mode of light in the two-dimensional photonic crystal includes a TE (Transverse Electric) mode having a magnetic field component in the y direction along the cylinder, an electric field component in the x direction and the z direction, an electric field component in the y direction, and the x direction. There is also a TM (Transverse Magnetic) mode having a magnetic field component in the z direction. Here, the polarization mode of light was set to TM mode, and the wavelength characteristics were analyzed for wavelengths of 1.45 to 1.7 μm. The spatial cell size of the FDTD method was 38.5 nm, and the time step was 9.1 × 10 ⁻¹⁷ seconds. As the absorbing boundary condition, a perfectly matched layer (PML) was used, the number of PML layers was 24, and the conductivity order was 2.

  As a result, as indicated by white lines in FIG. 4, when the radius (r / a) normalized by the lattice spacing a is 0.2, the normalized frequency (ωa / 2πc) is about 0.3 to about 0.00. It has been found that light having a wavelength corresponding to 45 is guided in the line defect waveguide in the TM mode.

  FIG. 5 shows the result of analysis of a waveguide without a radioactive guide as a comparative example. FIG. 5A is a plan view of the waveguide without a radioactive guide, and FIG. 5B is a schematic diagram of the waveguide. FIGS. 5C to 5E are images depicting temporal changes in pulsed light.

  The photonic crystal is obtained by arranging dielectric cylinders in a triangular lattice shape under the same conditions as in FIG. 4, and a waveguide is formed by removing one lattice row along the x direction. The analysis conditions of the FDTD method were also the same as those in FIG. 4, and the light wavelength was 1.45 μm.

  First, when the pulsed light travels in the x direction along the waveguide according to the initial conditions, after elapse of 109 fs (femtosecond), as shown in FIG. A light intensity distribution that oozes out. Further, after the elapse of 218 fs, the pulsed light is radiated toward the external medium 20 through the output end of the waveguide 10 as shown in FIG. Further, after 309 fs has elapsed, light due to terminal reflection proceeds in the waveguide 10 in the −x direction.

  Therefore, it can be seen that in a waveguide without a radioactive guide, reflected light traveling toward the inside of the crystal is generated at the output end of the waveguide.

  FIG. 6 shows the result of analysis of a waveguide with a radioactive guide according to the first embodiment of the present invention. FIG. 6 (a) is a plan view of the waveguide with a radioactive guide, and FIG. Schematic diagrams of the waveguide, FIGS. 6C to 6E are images depicting temporal changes in pulsed light. The analysis conditions of the FDTD method are the same as those in FIG.

  First, when the pulsed light travels in the x direction along the waveguide in accordance with the initial conditions, after elapse of 109 fs (femtosecond), as shown in FIG. A light intensity distribution that oozes out. Further, after the elapse of 218 fs, as shown in FIG. 6D, the pulsed light passes through the output end of the waveguide 10 and leaks to the external medium 20 while passing through the radioactive guide 21. Further, after 309 fs has elapsed, most of the light has disappeared, and almost no reflected light is generated due to terminal reflection.

  Therefore, it can be seen that in the waveguide provided with the radioactive guide according to the present invention, almost no reflected light traveling toward the inside of the crystal is generated. As a result, it is possible to reliably prevent the function deterioration of the internal optical circuit due to the reflected noise light.

  Next, the quantitative evaluation of the reflectance by the terminal reflection will be described.

  Fig.7 (a) is a top view which shows the power evaluation area | region of reflected light, FIG.7 (b) is a graph which shows the wavelength dependence of terminal reflectance. The time width of the pulsed light is set to 90 fs, and the evaluation formula calculates the sum of the square values of the electric fields of all the cells in the power evaluation region at each time step as shown in the following formula (1). By adding the values for each step, the energy of light passing through the region is obtained. The reflectance is obtained by dividing the energy of the reflected light by the energy of the incident pulsed light. And the termination | terminus reflectance was calculated about wavelength 1.45-1.7micrometer.

  As a result, as shown in FIG. 7B, the waveguide without the radioactive guide (FIG. 5) exhibited a reflectivity of about 0.17 to about 0.26. On the other hand, the waveguide (FIG. 6) provided with the radioactive guide 21 according to the present invention exhibits a reflectance of about 0.01 to about 0.03, and it can be seen that the terminal reflection of the waveguide can be greatly reduced.

  FIG. 8A is a plan view showing a second embodiment of the present invention, and FIG. 8B is a schematic diagram thereof. FIG. 8C is a graph showing the wavelength dependence of the terminal reflectance.

  As described above, the photonic crystal PC is a two-dimensional photonic crystal in which a large number of lattices are arranged in a triangular lattice pattern in the xy plane. By introducing a line defect into the photonic crystal PC, a waveguide 10 having an optical axis along the x direction is formed. The photonic crystal PC is bonded to an external medium 20 such as the atmosphere at the interface 11.

  The radioactive guide 22 protrudes from the interface 11 along the optical axis direction of the waveguide 10. The number of gratings arranged in the y direction perpendicular to the optical axis direction is designed so that the radioactive guide 22 is smaller than the inside of the waveguide 10.

  The output end of the waveguide 10 is connected to the radioactive guide 22, and the input end of the waveguide 10 is connected to an optical circuit (not shown) formed inside the crystal.

  In the present embodiment, the radioactive guide 22 is configured by a plurality of grid rows on both sides (here, two rows). For this reason, the structural change at the interface 11 becomes more gradual than in the case of the lattice array of one side on both sides shown in FIG. 6, and the reflected light can be further reduced.

  In the radioactive guide 22, the number of lattices along the x direction is designed to be smaller in the outer lattice row than in the inner lattice row. Therefore, the number of lattices along the y direction of the radioactive guide 22 gradually decreases, and the generation of reflected light at the step portion can be suppressed.

  As shown in FIG. 8C, compared with the waveguide having the radioactive guide 21 shown in FIG. 6, the waveguide having the radioactive guide 22 according to this embodiment has a wavelength of 1.6 to 1.7 μm. It can be seen that the reflectance is further reduced.

  In this embodiment, the example in which the radioactive guide 21 configured by a plurality of lattice arrays on both sides is provided on the two-dimensional photonic crystal has been described. However, in the case of a three-dimensional photonic crystal, the plurality of lattice arrays are cylindrical. A similar effect can be obtained by providing radioactive guides arranged in a shape.

  Fig.9 (a) is a top view which shows 3rd Embodiment of this invention, FIG.9 (b) is the schematic diagram. FIG. 9C is a graph showing the wavelength dependence of the terminal reflectance.

  As described above, the photonic crystal PC is a two-dimensional photonic crystal in which a large number of lattices are arranged in a triangular lattice pattern in the xy plane. By introducing a line defect into the photonic crystal PC, a waveguide 10 having an optical axis along the x direction is formed. The photonic crystal PC is bonded to an external medium 20 such as the atmosphere at the interface 11.

  The radioactive guide 23 protrudes from the interface 11 along the optical axis direction of the waveguide 10. The number of gratings arranged in the y direction perpendicular to the optical axis direction is designed so that the radioactive guide 23 is smaller than the inside of the waveguide 10.

  The output end of the waveguide 10 is connected to the radioactive guide 23, and the input end of the waveguide 10 is connected to an optical circuit (not shown) formed inside the crystal.

  In the present embodiment, the radioactive guide 23 is designed so that the number of lattice rows on the lower side with respect to the waveguide 10 is smaller than the number of lattice rows on the upper side. Typically, it is configured as a one-side radioactive guide 23 in which the upper half lattice line is continuous with the photonic crystal PC and the lower half lattice line number is only one. For this reason, the structural change at the interface 11 becomes more gradual than in the case of the lattice array of one side on both sides shown in FIG. 6, and the reflected light can be further reduced.

  As shown in FIG. 9C, compared with the waveguide having the radioactive guide 21 shown in FIG. 6, the waveguide having the radioactive guide 23 according to the present embodiment has a wavelength of 1.55 to 1.7 μm. It can be seen that the reflectance is further reduced.

  FIG. 10 is a plan view showing a fourth embodiment of the present invention. As described above, the photonic crystal PC is a two-dimensional photonic crystal in which a large number of lattices are arranged in a triangular lattice pattern in the xy plane. The photonic crystal PC is bonded to an external medium 20 such as the atmosphere at the interface 11. By introducing a line defect into the photonic crystal PC, a waveguide 10 having an optical axis along the x direction is formed.

  In the present embodiment, the second waveguide 12 made of a line defect is formed so as to be close to the waveguide 10, for example, so that one row of lattices is interposed, and the directional coupler 15 is configured. ing.

  The radioactive guide 21 protrudes from the interface 11 along the optical axis direction of the waveguide 12. The number of gratings arranged in the y direction perpendicular to the optical axis direction is designed so that the radioactive guide 21 is smaller than the inside of the waveguide 12.

  The output end of the waveguide 12 is connected to the radioactive guide 21, and the input end of the waveguide 10 is connected to an optical circuit (not shown) formed inside the crystal.

  When the light L1a travels along the waveguide 10 and enters the directional coupler 15, it shifts to the waveguide 12 via the evanescent wave and travels in the x direction as light L1b. When the light L 1 b enters the radioactive guide 21, the light L 4 becomes an evanescent wave from the periphery of the radioactive guide 21 and gradually leaks toward the external medium 20. Further, the light L2 that has entered the radioactive guide 21 is gradually attenuated, and the light intensity becomes zero before reaching the end of the radioactive guide 21. Therefore, the reflected light traveling toward the inside of the crystal can be greatly reduced.

  By combining the directional coupler 15 and the radioactive guide 21 in this way, various termination circuits can be configured. Although the combination with the radioactive guide 21 shown in FIG. 3 has been described here, the combination with the radioactive guide 22 shown in FIG. 8 or the radioactive guide 23 shown in FIG. 9 can also be easily realized.

  FIG. 11 is a perspective view showing a fifth embodiment of the present invention, and FIG. 12 is a cross-sectional view along the yz plane near the end of the waveguide. The photonic crystal PC is a three-dimensional photonic crystal in which a large number of lattices are arranged in unit cells of Brave lattice, for example, cubic crystals. The photonic crystal PC is bonded to an external medium 20 such as the atmosphere at the interface 11. By introducing a line defect into the photonic crystal PC, a waveguide 16 having an optical axis along the x direction is formed.

  In the vicinity of the end of the waveguide 16, as shown in FIG. 12, there is provided a region where the number of lattices arranged in a predetermined circumferential direction with respect to the optical axis direction of the waveguide 16 is reduced. Function as. Here, an example is shown in which one grid row arranged in a specific circumferential direction is removed.

  FIG. 13 is a cross-sectional view along the yz plane showing another example of the radioactive guide 24. The radioactive guide 24 is configured by removing the lattice rows over a specific circumferential angular range with respect to the optical axis direction of the waveguide 16.

  In any of the radioactive guides 24, when the light L1 travels in the x direction along the waveguide 16 and enters the radioactive guide 24, the light L4 becomes an evanescent wave from the lattice missing portion around the radioactive guide 24. It gradually begins to leak. In addition, by sufficiently securing the length in the x direction of the lattice missing portion, the light intensity that has entered the radioactive guide 24 becomes zero before reaching the end of the radioactive guide 24. Therefore, the reflected light traveling toward the inside of the crystal can be greatly reduced.

  The present invention is extremely useful industrially in that the end reflection of the waveguide can be greatly reduced.

It is a perspective view which shows various photonic crystals. It is a perspective view which shows the mode of the waveguide formation by a line defect. It is a top view which shows 1st Embodiment of this invention. It is explanatory drawing which shows an example of the analysis result by FDTD method. FIG. 5A shows a result of analysis of a waveguide without a radioactive guide as a comparative example. FIG. 5A is a plan view of the waveguide without a radioactive guide, FIG. 5B is a schematic diagram of the waveguide, and FIG. ) To (e) are images depicting temporal changes in pulsed light. FIGS. 6A and 6B show analysis results of the waveguide with a radioactive guide according to the first embodiment of the present invention, FIG. 6A is a plan view of the waveguide with a radioactive guide, and FIG. 6B is a schematic diagram of the waveguide. FIGS. 6 (c) to 6 (e) are images depicting temporal changes in pulsed light. FIG. 7A is a plan view showing a power evaluation region of reflected light, and FIG. 7B is a graph showing the wavelength dependence of the terminal reflectance. FIG. 8A is a plan view showing a second embodiment of the present invention, FIG. 8B is a schematic diagram thereof, and FIG. 8C is a graph showing the wavelength dependence of the terminal reflectance. is there. FIG. 9A is a plan view showing a third embodiment of the present invention, FIG. 9B is a schematic view thereof, and FIG. 9C is a graph showing the wavelength dependence of the terminal reflectance. is there. It is a top view which shows 4th Embodiment of this invention. It is a perspective view which shows 5th Embodiment of this invention. It is sectional drawing along yz plane in the vicinity of the termination | terminus of a waveguide. FIG. 6 is a cross-sectional view along the yz plane showing another example of the radioactive guide 24. It is a top view which shows an example of the conventional photonic crystal waveguide.

Explanation of symbols

10, 12, 16 Waveguide 11 Interface 15 Directional coupler 20 External medium 21, 22, 23, 24 Radiation guide B Lattice D Line defect PC Photonic crystal

Claims (7)

A photonic crystal with periodically arranged lattices;
A waveguide configured by introducing a line defect into the photonic crystal;
A radioactive guide protruding from the interface of the photonic crystal along the optical axis direction of the waveguide,
A photonic crystal waveguide characterized in that the number of gratings arranged in a direction perpendicular to the optical axis direction is smaller in the number of radioactive guides than in the inside of the waveguide.   2. The photonic crystal waveguide according to claim 1, wherein the radioactive guide is composed of a lattice array on one side.   2. The photonic crystal waveguide according to claim 1, wherein the radioactive guide is composed of a plurality of lattice arrays on both sides.   4. The photo according to claim 3, wherein the number of gratings along the optical axis direction of the waveguide is smaller in the outer grating array than in the inner grating array in the radioactive guide composed of a plurality of grating arrays on both sides. Nick crystal waveguide.   The photonic crystal waveguide according to claim 1, wherein the radioactive guide has a smaller number of lattice rows on one side than the number of lattice rows on the other side.   2. The photonic crystal waveguide according to claim 1, further comprising: a directional coupler in which the first line defect and the second line defect are arranged close to each other in the photonic crystal. 2. The photonic crystal according to claim 1, wherein the photonic crystal is a three-dimensional photonic crystal, and the radioactive guide has a region where the number of lattices arranged in a predetermined circumferential direction with respect to the optical axis direction is reduced. Crystal waveguide.

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