JP3999152B2 - Two-dimensional photonic crystal slab and optical device using the same - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a two-dimensional photonic crystal slab used for a micro optical circuit element or the like, and includes a two-dimensional photonic crystal waveguide having a light extraction / introduction port formed by introducing linear defects and point defects, and the same. Related to optical devices.
[0002]
[Prior art]
A material having a refractive index change periodic structure of the order of the wavelength of light is known as a photonic crystal, in which a so-called photonic band gap for light in which light having a wavelength corresponding to that period is prohibited is prohibited. Appears, and the existence and propagation of light in a specific wavelength range becomes impossible. For this reason, photonic crystals are attracting attention as next-generation electronics and optoelectronic materials because of the possibility of freely controlling light.
[0003]
As a type of a conventional two-dimensional photonic crystal waveguide, one shown in FIG. 25 is known (for example, see Patent Document 1).
This two-dimensional photonic crystal waveguide has a two-dimensional photonic crystal in which cylindrical holes 86 are arranged in a triangular lattice shape in a slab material 81 made of a material having a refractive index higher than that of air. As shown in FIG. By extracting a part of the cylindrical holes 86 arranged in a lattice shape into a linear shape, a linear defect 92 is introduced into the photonic crystal, and this linear defect 92 becomes a waveguide. A point defect 94 that disturbs the periodic arrangement of the cylindrical holes 86 is formed, and the point defect 94 functions as a light extraction / introduction port.
[0004]
In this two-dimensional photonic crystal waveguide, when light 103 having a wavelength corresponding to the photonic bandgap frequency is incident on the two-dimensional photonic crystal from the outside, the point defect 94 or the line defect 92 is not formed. By the way, since there is a photonic band gap in the in-plane direction, light is prohibited from propagating, and in the direction perpendicular to the plane, it is confined by total reflection due to refractive index difference confinement, but the linear defect 92 is guided. Since light is propagated because it is regarded as a waveguide, light having a wavelength resonating with the point defect 94 is captured by the point defect 94 when propagating to the vicinity of the point defect 94 and is resonating inside the defect. The light is emitted in the vertical direction.
Since the spot-like defect 94 is a through hole, the light captured by the spot-like defect is emitted from above and below, but the only available light is that emitted from either the top or bottom of the spot-like defect 94. Since it cannot be used, in order to improve efficiency, the diameter of the hole is inclined to form an asymmetrical structure so that a large amount of light 103a is emitted from one direction.
[0005]
[Patent Document 1]
JP 2001-272555 A
[0006]
[Problems to be solved by the invention]
However, in the conventional two-dimensional photonic crystal waveguide, the two-dimensional photonic crystal is arranged only in one of the TE-like mode and the TM-like mode of the polarization mode of light (for example, arranged in the above triangular lattice shape). Since the cylindrical hole has a photonic band gap (only for the TE-like mode), for example, the TE-like mode light 103 is introduced into the point-like defect 94 of the vertically asymmetrical structure and emitted from one direction. Attempting to do so results in a mode conversion from the TE-like mode to the TM-like mode. Since this conventional photonic crystal has a structure that does not have a photonic band gap with respect to the TM-like mode, light in the TM-like mode leaks in the in-plane direction of the photonic crystal, and is extracted. Efficiency will be reduced.
There is a need for a two-dimensional photonic crystal slab having a structure having a common photonic band gap for both the TE-like mode and the TM-like mode, but there has never been such a two-dimensional photonic crystal. .
[0007]
The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a two-dimensional photonic crystal slab having a common photonic band gap with respect to light in both the TE-like mode and the TM-like mode. I will.
Another object of the present invention is to provide a two-dimensional photonic crystal waveguide provided with the two-dimensional photonic crystal slab.
Another object of the present invention is to provide a two-dimensional photonic crystal waveguide that includes the two-dimensional photonic crystal slab and can improve the light extraction efficiency of a specific wavelength.
Another object of the present invention is to provide an optical device provided with the two-dimensional photonic crystal waveguide.
[0008]
[Means for Solving the Problems]
  The two-dimensional photonic crystal slab of the present invention has a common photonic band gap for light in both the TE-like mode and the TM-like mode,A slab material made of a high refractive index material is formed by periodically arranging a low refractive index material region than the slab material to form a refractive index distribution, and Δ = (n _H ² -N _L ² ) / 2n _H ² (Where n _H Is the refractive index of the high refractive index material, n _L Indicates the refractive index of the low refractive index material. ) Is greater than 0.35, and 0.35 <(t / a) <2.0 (where t is the thickness of the slab material, and a is a low refractive index material). The minimum refractive index material region of the two-dimensional photonic crystal is formed to be more than 25%, and the low refractive index material region is formed in a triangular lattice on the slab material. The low refractive index material region is formed in a triangular prism shape.It is characterized by that.
  In this two-dimensional photonic crystal slab, it is possible to inhibit propagation by the photonic band gap even if light incident on the crystal slab from the outside is in either the TE-like mode or the TM-like mode.
[0009]
  Further, the two-dimensional photonic crystal slab of the present invention has a refractive index distribution in which a region made of a low refractive index material is periodically arranged on a slab material made of a high refractive index material. Is,
  Δ = (n_H ²-N_L ²) / 2n_H ²(Where n_HIs the refractive index of the high refractive index material, n_LIndicates the refractive index of the low refractive index material. ) Is greater than 0.35, and 0.35 <(t / a) <2.0, where t is the thickness of the slab material, and a is a low refractive index material. Satisfying the relationship of the minimum center distance or the lattice constant in the periodic structure portion, and the region of the two-dimensional photonic crystal made of the low refractive index material (sometimes referred to as a low refractive index material region) is formed to be more than 25% IsTheThe ratio of the low refractive index material region here is the volume% of the low refractive index material region.
[0010]
A relative refractive index difference Δ of 0.35 or less is not preferable because the photonic band gap in both the TE-like mode and the TM-like mode cannot be opened.
Further, if the t / a is outside the above range, a photonic common to the light in both the TE-like mode and the TM-like mode regardless of the proportion of the low refractive index material region. It cannot have a band gap.
Further, when the proportion of the low refractive index material region is 25% or less, even if t / a is within the above range, it is common to light in both the TE-like mode and the TM-like mode. It cannot have a photonic band gap.
[0011]
  In the two-dimensional photonic crystal slab of the present invention, the low refractive index material region is arranged in a triangular lattice pattern on the slab material.TheAccording to such a two-dimensional photonic crystal slab, a 60-degree bent waveguide can be easily formed. Further, the low refractive index material region has a triangular prism shape.It is.
[0012]
Further, in the two-dimensional photonic crystal slab in the case where the shape of the low refractive index material region is a regular triangular prism shape, a plurality of low refractive index material regions are arranged in the slab material. Are preferably arranged at a constant inclination angle in a range excluding an odd multiple of ± 30 ° with respect to the direction of a group of parallel lines.
When the plurality of low refractive index material regions are an odd multiple of ± 30 ° with respect to the direction of a group of parallel lines, a photonic band gap does not appear.
[0013]
  The two-dimensional photonic crystal slab of the present invention isThe (t / a) is 0.65 ≦ (t / a) ≦ 1.50.
  The two-dimensional photonic crystal slab of the present invention is configured such that the low refractive index material region is filled with air in a regular triangular hole formed in the slab material, and the low refractive index material region is two-dimensional. It is characterized by being formed in a range of more than 25% and less than 50% of the volume of the photonic crystal slab.
  In the two-dimensional photonic crystal slab of the present invention, the low refractive index material region has a regular triangular prism shape, and one side of a regular triangle forming the low refractive index material region has a range of 0.3 μm to 0.4 μm. The pitch of adjacent low refractive index material regions is in the range of 0.35 μm to 0.55 μm.
  In the two-dimensional photonic crystal slab of the present invention, the regular triangular prism-shaped low refractive index material region is arranged at an inclination angle of 0 degree with respect to a group of parallel lines formed in the surface direction of the slab material. It is characterized by.
  In the two-dimensional photonic crystal slab of the present invention, the value of (t / a) is 0.65 ≦ (t / a) ≦ 1.50, and the low refractive index material region is used as the slab material. The formed planar triangular hole is filled with air, and the low refractive index material region is formed in a range of more than 25% and less than 50% of the volume of the two-dimensional photonic crystal slab. It is characterized by that.
  The two-dimensional photonic crystal slab of the present invention is a TE-like introduced into the slab material. Mode light or TM-like The mode light is prohibited from propagating by the photonic band gap in the in-plane direction of the slab material, and confined by total reflection by the upper and lower low-refractive index material regions in the plane direction.
[0014]
Moreover, the two-dimensional photonic crystal slab of the present invention may be one in which regions of the low refractive index material are arranged in a square lattice pattern on the slab material.
According to such a two-dimensional photonic crystal slab, a right-angle bending waveguide can be easily formed.
[0016]
In the two-dimensional photonic crystal waveguide of the present invention, linear defects that disturb the periodic arrangement of the photonic crystals are formed on the two-dimensional photonic crystal slab of the present invention having any one of the above-described configurations. This linear defect is a waveguide through which light passes, and at least one point-like defect that disturbs the periodic arrangement of the photonic crystal is formed in the vicinity of the waveguide. The TE-like mode and TM-like mode light propagating in the waveguide can be captured and emitted, or the TE-like mode and TM-like mode light from the outside can be captured and guided. It is characterized in that it functions as a light extraction / introduction port that can be introduced into the waveguide.
[0017]
According to the two-dimensional photonic crystal waveguide having such a configuration, the periodic arrangement of the photonic crystals is performed regardless of whether the light incident on the two-dimensional photonic crystal slab from the outside is in the TE-like mode or the TM-like mode. Propagation is prohibited by the photonic band gap in the portion where the light is present, but this incident light can propagate in the waveguide (linear defect). In addition, regardless of whether the light propagating in the waveguide is in the TE-like mode or the TM-like mode, at least a part of the propagating light can be captured by the point-like defects and emitted to the outside.
In addition, by designing the point-like defect to capture only the wavelength of a specific channel in the wavelength band, it can function as a duplexer, a multiplexer, or a filter that extracts light or electromagnetic waves having a specific wavelength.
[0018]
In the two-dimensional photonic crystal waveguide of the present invention, the point-like defect may have a shape that is asymmetrical with respect to the slab surface.
In the two-dimensional photonic crystal waveguide having such a configuration, light propagating in the waveguide is captured by the point-like defect, and a lot of light is emitted from one direction above and below the point-like defect. In addition, regardless of whether the light propagating in the waveguide is in the TE-like mode or the TM-like mode, the light emitted from the dot-like defect is emitted after mode conversion. Since the two-dimensional photonic crystal slab has a common photonic band gap for both TE-like mode and TM-like mode light, the mode-converted light leaks into the two-dimensional photonic crystal slab. Since it can prevent, the extraction efficiency of the light of a specific wavelength can be improved.
[0019]
The optical device of the present invention includes a two-dimensional photonic crystal waveguide. The optical device of the present invention can be suitably used for an add / drop element such as an optical add / drop photonic device (optical add / drop multiplexer).
[0020]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described in detail with reference to the drawings.
In the embodiment described below, a case where the optical device of the present invention is applied to a wavelength demultiplexer will be described. The present invention is of course not limited to the embodiments described below, and in the following drawings, the constituent parts are shown so that the scale of each constituent part can be easily shown in the drawings. The scale is changed every time.
(First embodiment)
FIG. 1 is a perspective view illustrating a schematic configuration of the wavelength demultiplexer according to the first embodiment, and FIG. 2 is a schematic plan view illustrating a two-dimensional photonic crystal waveguide provided in the wavelength demultiplexer of FIG. FIG. 3 is an enlarged plan view showing a plurality of low-refractive index material regions formed in the two-dimensional photonic crystal slab provided in the two-dimensional photonic crystal waveguide of FIG.
The wavelength demultiplexer of this embodiment is mainly provided with the two-dimensional photonic crystal waveguide 10 of the embodiment of the present invention.
In the two-dimensional photonic crystal waveguide 10, linear defects (linear defects) 22 disturbing the periodic arrangement of the photonic crystals are formed in the two-dimensional photonic crystal slab 10a of the embodiment of the present invention. This linear defect 22 is a waveguide through which light passes, and a point-like defect (point defect) 24 that disturbs the periodic arrangement of the photonic crystal is formed in the vicinity of the waveguide 22.
[0021]
The two-dimensional photonic crystal slab 10a has a common photonic band gap for light in both the TE-like mode and the TM-like mode.
As a specific structure of the two-dimensional photonic crystal slab 10a, a region (low refractive index material region) 15 made of a material having a lower refractive index than that of the slab material 11 is triangular. By arranging in a lattice pattern, the low refractive index material regions 15 are periodically arranged in the slab material 11 to form a refractive index distribution.
[0022]
The material used as the slab material 11 is a high refractive index material, for example, one type selected from InGaAsP, GaAs, In, Ga, Al, Sb, As, Ge, Si, P, N, and O. Alternatively, a material including two or more kinds, an inorganic material such as Si, an inorganic semiconductor material, and an organic material are appropriately selected and used.
The material used for the low refractive index material region 15 is a low refractive index material having a refractive index lower than that of the high refractive index material constituting the slab material 11, and air is used in this embodiment.
[0023]
In the present embodiment, a plurality of triangular holes 14 are formed in the slab material 11. The triangular holes 14 are formed at positions corresponding to the lattice points of the triangular lattice. Each of the plurality of triangular holes 14 is filled with air as a low refractive index material to form a plurality of triangular columnar low refractive index material regions 15, thereby forming a periodic array of photonic crystals. .
The length L of one side of the low refractive index material region 15 is about 0.3 μm to 0.4 μm when the center wavelength is 1.55. The pitch a between the adjacent low refractive index material regions 15 and 15 is set to about 0.35 μm to 0.55 μm.
In the present embodiment, since the low refractive index material region 15 has a regular triangular prism shape, the pitch a between the adjacent low refractive index material regions 15 and 15 is a low refractive index material in which the low refractive index material regions 15 are periodically arranged. It is the same size as the minimum center distance a in the periodic structure portion.
[0024]
In this two-dimensional photonic crystal slab 10a, Δ = (n_H ²-N_L ²) / 2n_H ²(Where n_HIs the refractive index of the high refractive index material, n_LIndicates the refractive index of the low refractive index material. It is preferable for the reason described above to select the material used for the slab material 11 and the material used for the low refractive index material region 15 so that the relative refractive index difference Δ defined by It is preferable to use a material such that Δ is 0.45 or more.
[0025]
Further, the thickness t of the slab material 11 is preferably set to satisfy the relationship of 0.35 <(t / a) <2.0, and 0.80 <(t / a). It is more preferable to satisfy the relationship <0.90.
Further, the proportion of the low refractive index material region (the aperture ratio when the low refractive index material region is made of air) is 100% of the volume of the two-dimensional photonic crystal slab (here, the linear defect 22 and the point defect 24 are It is preferable that it is more than 25% with respect to the above reason, and more preferably more than 35%.
[0026]
The plurality of low-refractive index material regions 15 are arranged at a constant inclination angle in a range excluding an odd multiple of ± 30 ° with respect to the direction of a group of parallel lines M as shown in FIGS. It is preferable for the reason described above. 2 and 3 show a case where a plurality of triangular prism-shaped low refractive index material regions 15 are arranged at an inclination angle of 0 degree with respect to the direction of a group of parallel lines M. FIG.
[0027]
TE-like mode or TM-like mode light R is externally applied to the two-dimensional photonic crystal slab 10a.₁In the photonic crystal, propagation is prohibited by the photonic band gap in the in-plane direction, and confined by total reflection by the upper and lower low refractive index materials in the in-plane direction.
[0028]
Further, in the present embodiment, a part of the plurality of low refractive index material regions 15 arranged in a triangular lattice pattern on the two-dimensional photonic crystal slab 10a is extracted in a linear shape, thereby causing a linear defect in the photonic crystal slab. 22 is introduced, and a waveguide mode exists in the linear defect 22, which is a waveguide 22. This waveguide 22 is a light R incident on the two-dimensional photonic crystal slab 10a.₁Can propagate in either the TE-like mode or the TM-like mode. Note that the waveguide 22 has a relatively large wavelength range in which light can be propagated with low loss. Therefore, the waveguide 22 can propagate light in a wavelength band including wavelengths of several channels.
[0029]
In the present embodiment, a part of the low refractive index material region 15 in the vicinity of the waveguide 22 formed in the two-dimensional photonic crystal slab 10a is extracted in a dot shape, thereby forming a point defect 24. Yes. This point-like defect 24 is generated regardless of whether the light R propagating in the waveguide 22 is in the TE-like mode or the TM-like mode.₁Can capture and radiate at least a part of the light, or function as a light extraction / introduction port that can capture and introduce the light into the waveguide 22 regardless of whether the light introduced from the outside is in the TE-like mode or the TM-like mode. It is supposed to be configured.
[0030]
As shown in FIG. 4, the above-mentioned dot-like defect 24 has a conical shape so that its inner diameter is changed above and below the slab material 11. It has an asymmetric shape.
Light R captured by the point defect 24₁Is radiated in the vertical direction with a small Q factor due to the slab shape while resonating inside the point defect 24, and a lot of light is emitted from the direction in which the diameter of the point defect 24 is large. The
[0031]
The light radiated to the outside from the point defect 24 is the light R that has undergone mode conversion regardless of whether the light propagating in the waveguide 22 is in the TE-like mode or the TM-like mode.₂However, as described above, the two-dimensional photonic crystal slab 10a has a common photonic band gap for light in both the TE-like mode and the TM-like mode. Light R₂Can be prevented from leaking into the two-dimensional photonic crystal slab, so that the light extraction efficiency of a specific wavelength such as the TE-like mode or the TM-like mode can be improved.
In addition, by appropriately setting the interval between the waveguide 22 and the point defect 24, the ratio of light having a specific wavelength to be captured and emitted can be controlled. For this reason, light of a specific wavelength can be extracted at a predetermined ratio.
[0032]
In the above embodiment, the case where the shape of the low refractive index material region 15 is a triangular prism shape has been described, but the low refractive index material region 15 may be any one of a triangular prism shape, a quadrangular prism shape, a pentagonal prism shape, and an elliptical prism shape. It may be any shape.
Moreover, although the case where the shape of the point defect 24 was made conical as a method for introducing vertical asymmetry into the point defect 24 has been described, the diameter of the point defect 24 is changed stepwise as shown in FIG. Thus, vertical asymmetry may be introduced.
Moreover, although the case where the low refractive index material region 15 is arranged in a triangular lattice shape on the slab material 11 has been described, the low refractive index material region may be arranged in a square lattice shape, and the low refractive index in that case The material region may be any one of a cylindrical shape, an elliptical column shape, a triangular column shape, a quadrangular column shape, a pentagonal column shape, and a hexagonal column shape.
[0033]
(Second Embodiment)
FIG. 6 is a perspective view showing a schematic configuration of the wavelength demultiplexer according to the second embodiment, and FIG. 7 is a schematic plan view showing a two-dimensional photonic crystal waveguide provided in the wavelength demultiplexer of FIG. FIG. 8 is an enlarged plan view showing a plurality of low-refractive index material regions formed in the two-dimensional photonic crystal slab provided in the two-dimensional photonic crystal waveguide of FIG.
The difference between the wavelength demultiplexer of the second embodiment and the wavelength demultiplexer of the first embodiment is that a two-dimensional photonic crystal waveguide 50 as shown in FIG. 6 is provided. Is that the arrangement state of the low refractive index material regions 65 formed in the slab material 11 constituting the two-dimensional photonic crystal slab 50a provided in the two-dimensional photonic crystal waveguide 50 is different.
[0034]
As a specific structure of the two-dimensional photonic crystal slab 50a, a low refractive index material region 65 is arranged in a slab material 11 in a honeycomb lattice shape, and the low refractive index material region 65 is arranged at the center of each honeycomb lattice described above. Also arranged.
As a material used for the low refractive index material region 65, a low refractive index material having a refractive index lower than that of the high refractive index material constituting the slab material 11 is used, and air is used in this embodiment.
The low refractive index material region 65 (also referred to as the first low refractive index material region 65a) arranged in the honeycomb lattice shape and the low refractive index material region 65 (the second low refractive index material region 65 arranged in the center of the honeycomb lattice). The low refractive index material region 65b) is different in size.
[0035]
In the present embodiment, a plurality of circular holes 64 a and 64 b are formed in the slab material 11. The circular holes (sometimes referred to as first circular holes) 64a are formed at positions corresponding to the lattice points of the honeycomb lattice, and the circular holes (sometimes referred to as second circular holes) 64b are each honeycomb. It is formed at a position corresponding to the center of the lattice. Each of the plurality of first circular holes 64a is filled with air as a low refractive index material to form a plurality of columnar first low refractive index material regions 65a, and a plurality of second circular holes 64b. A plurality of cylindrical second low-refractive-index material regions 65b are formed by filling each of these with air as a low-refractive-index material, thereby forming a periodic array of photonic crystals.
[0036]
The pitch a between the adjacent first low refractive index material regions 65a and 65a is set to about 0.35 μm to 0.55 μm. The pitch a can also be referred to as the minimum center distance a in the low refractive index material periodic structure portion.
The radius r of the first low refractive index material region 65a is about 0.30 to 0.45 times the pitch a.
The radius R of the second low refractive index material region 65b is about 0 to 1.5 times the radius r of the first low refractive index material region 65a.
Also in the two-dimensional photonic crystal slab 50a of this embodiment, the material used for the slab material 11 and the material used for the low refractive index material region 15 are selected and used so that the relative refractive index difference Δ is larger than 0.35. ing.
Further, the relationship between the thickness t of the slab material 11 and the minimum center distance a in the low refractive index material periodic structure portion satisfies the condition of 0.35 <(t / a) <2.0.
[0037]
The proportion of the low refractive index material region 65 is 25% with respect to the volume of the two-dimensional photonic crystal slab 100% (excluding the portion where the linear defect 22 and the point defect 24 are formed here). There have been many.
Furthermore, in the present embodiment, the relationship between the radius R of the second low refractive index material region 65b and the radius r of the adjacent first low refractive index material region 65a is 0 ≦ R / r ≦ 1.25 ( However, it is preferable to satisfy the condition (except for the case of R / r = 1), and more preferably 0 ≦ R / r ≦ 0.75 and 1.1 ≦ R / r ≦ 1.25.
[0038]
In the above embodiment, the case where the second low refractive index material region 65b is disposed at the center of each honeycomb lattice has been described. However, the second low refractive index material region 65b is not necessarily provided in each honeycomb lattice. It does not need to be arranged at the center, and may be arranged inside (inside) each honeycomb lattice.
Further, the case where the radius R of the second low refractive index material region 65b is 0, that is, the case where the second low refractive index material region 65b is not provided is also within the scope of the present invention.
In the above embodiment, the low refractive index material region 65 has a triangular prism shape. However, the low refractive index material region 65 has a cylindrical shape, an elliptical column shape, a triangular prism shape, a quadrangular prism shape, a pentagonal prism shape, Any shape of hexagonal columns may be used.
In the first to second embodiments, the two-dimensional photonic crystal waveguide in which the linear defects and the point defects are formed one by one has been described. One or more may be provided.
[0039]
【Example】
(Experimental example 1)
1 to 3 except that the inclination angle θ with respect to a group of parallel lines M formed on the slab material 11 is changed within a range of −30 degrees to +30 degrees. Various similar two-dimensional photonic crystal slabs were produced. The two-dimensional photonic crystal slab produced here was under the conditions of Δ = 0.46, L / a = 0.85, and t / a = 0.80.
Light of λ = 1.55 μm was incident from the outside to the various two-dimensional photonic crystal slabs produced, and the dependence of the band gap on the tilt angle of the low refractive index material region was examined. The result is shown in FIG. 10 shows an arrangement state of the triangular prismatic low refractive index material regions when the inclination angle θ is 30 degrees, and FIG. 11 shows an arrangement of the triangular prismatic low refractive index material regions when the inclination angle θ is 15 degrees. FIG. 12 shows an arrangement state of the triangular columnar low refractive index material regions when the inclination angle θ is 0 degree.
[0040]
In the graph of FIG. 9, the horizontal axis represents the tilt angle θ, and the vertical axis represents the ratio of the band gap frequency width Δωg to the center value ωg of the band gap frequency.
From the results shown in FIG. 9, in the plurality of triangular prism-shaped low refractive index material regions, Δωg / ωg is 0 when the inclination angle θ with respect to a group of parallel lines M is −30 degrees and +30 degrees, and a photonic band gap appears. Absent. A photonic band gap exists in the range of −30 degrees <θ <+30 degrees. In particular, when the inclination angle θ is 0 degree, Δωg / ωg shows the maximum value, and the photonic band gap is It can be seen that the frequency range shown is very wide.
[0041]
(Experimental example 2)
Various two-dimensional photonic crystal slabs similar to those shown in FIGS. 1 to 3 were manufactured except that the thickness t of the slab material 11 and the ratio (opening ratio) of the triangular columnar low refractive index material region 15 were changed. Note that the two-dimensional photonic crystal slab produced here was in a condition of Δ = 0.46.
Slab material thickness dependence of two-dimensional complete photonic band gap (two-dimensional complete PBG) when TE-like mode and TM-like mode light is incident on each of various fabricated two-dimensional photonic crystal slabs from the outside. Then I investigated. The results are shown in FIGS.
[0042]
In the graphs of FIGS. 13 to 18, the horizontal axis represents the aperture ratio of the triangular prism-shaped low refractive index material region made of air, and the vertical axis represents the normalized frequency. In the graphs of FIGS. 13 to 18, a region surrounded by a dotted line indicates a relationship between an aperture ratio and a band gap in the TM-like mode, and a region surrounded by a solid line indicates an opening in the TE-like mode. The relationship between rate and band gap is shown. Further, in the graphs of FIGS. 13 to 18, a portion where a region surrounded by a dotted line and a region surrounded by a solid line overlap (region indicated by diagonal lines) is both TM-like mode and TE-like mode. The photonic band gap common to all the lights is shown.
[0043]
In the case of t / a = 0.60 shown in FIG. 13 and the case of t / a = ∞ in FIG. It can be seen that there is no common photonic band gap for both modes of light.
On the other hand, in the case of t / a = 0.65 to 1.50 in FIGS. 14 to 17, the photonic band gap is common to the light in both the TM-like mode and the TE-like mode. It can be seen that a two-dimensional complete photonic band gap exists. The two-dimensional complete photonic band gap means having a common photonic band gap for light in both the TE-like mode and the TM-like mode.
In the case of t / a = 0.80 in FIG. 15, it can be seen that the frequency width indicating the two-dimensional complete photonic band gap is wide.
[0044]
(Experimental example 3)
6 to 8 except that the thickness t of the slab material 11 and R / a (R is the radius of the second low-refractive index material region, a is the pitch of the adjacent first low-refractive index material region) are changed. Various two-dimensional photonic crystal slabs similar to those shown were prepared. The two-dimensional photonic crystal slab produced here was under the conditions of Δ = 0.46 and r = 0.4a.
Next, the dependence of the two-dimensional complete band gap on the thickness of the slab material when TE-like mode and TM-like mode mode light was incident on each of the prepared two-dimensional photonic crystal slabs from the outside was investigated. The results are shown in FIGS.
[0045]
In the graphs of FIGS. 19 to 24, the horizontal axis represents R / a and the vertical axis represents the normalized frequency. In the graphs of FIGS. 19 to 24, a region surrounded by a dotted line indicates a relationship between an aperture ratio and a band gap in the TM-like mode, and a region surrounded by a solid line indicates an opening in the TE-like mode. The relationship between rate and band gap is shown. Further, in the graphs of FIGS. 19 to 24, a portion where a region surrounded by a dotted line and a region surrounded by a solid line overlap (region indicated by hatching) is in both TM-like mode and TE-like mode. A common photonic band gap for light is shown.
[0046]
In the case of t / a = 0.50 shown in FIG. 19 and the case of t / a = ∞ in FIG. 24, either R / a has almost no two-dimensional complete band gap, or not at all. I don't have it.
On the other hand, in the case of t / a = 0.60 to 1.50 in FIGS. 20 to 23, it can be seen that a two-dimensional complete photonic band gap exists.
When t / a = 0.80 in FIG. 21 and t / a = 0.90 in FIG. 22, the frequency width indicating the two-dimensional complete photonic band gap is wide, and the R / a dependency is small. I understand that.
[0047]
【The invention's effect】
As described above, according to the two-dimensional photonic crystal slab of the present invention, a two-dimensional photonic crystal slab having a common photonic band gap with respect to light in both the TE-like mode and the TM-like mode is obtained. realizable.
Moreover, according to the two-dimensional photonic crystal waveguide of the present invention, the light extraction efficiency of a specific wavelength can be improved.
[Brief description of the drawings]
FIG. 1 is a perspective view showing a schematic configuration of a wavelength demultiplexer according to a first embodiment.
2 is a schematic plan view showing a two-dimensional photonic crystal waveguide provided in the wavelength demultiplexer of FIG. 1. FIG.
3 is an enlarged plan view showing a plurality of low-refractive index material regions formed in a two-dimensional photonic crystal slab provided in the two-dimensional photonic crystal waveguide of FIG. 2. FIG.
4 is an enlarged cross-sectional view showing a point defect formed in the two-dimensional photonic crystal waveguide of FIG. 2. FIG.
FIG. 5 is an enlarged cross-sectional view showing another form of the point defect formed in the two-dimensional photonic crystal waveguide of FIG. 2;
FIG. 6 is a perspective view illustrating a schematic configuration of a wavelength demultiplexer according to a second embodiment.
7 is a schematic plan view showing a two-dimensional photonic crystal waveguide provided in the wavelength demultiplexer of FIG. 6. FIG.
8 is an enlarged plan view showing a plurality of low-refractive index material regions formed in a two-dimensional photonic crystal slab provided in the two-dimensional photonic crystal waveguide of FIG.
FIG. 9 is a graph showing the dependence of the band gap on the tilt angle of the low refractive index material region.
FIG. 10 is a diagram showing an arrangement state of low refractive index material regions when θ = 30 degrees.
FIG. 11 is a diagram showing an arrangement state of low refractive index material regions when θ = 15 degrees.
FIG. 12 is a diagram showing an arrangement state of low refractive index material regions in the case of θ = 0 degree.
FIG. 13 is a diagram showing a relationship between a two-dimensional complete PBG width and an aperture ratio when t / a = 0.60.
FIG. 14 is a diagram showing a relationship between a two-dimensional complete PBG width and an aperture ratio when t / a = 0.65.
FIG. 15 is a diagram showing a relationship between a two-dimensional complete PBG width and an aperture ratio when t / a = 0.80.
FIG. 16 is a diagram showing a relationship between a two-dimensional complete PBG width and an aperture ratio when t / a = 0.90.
FIG. 17 is a diagram showing the relationship between the two-dimensional complete PBG width and the aperture ratio when t / a = 1.50.
FIG. 18 is a diagram showing a relationship between a two-dimensional complete PBG width and an aperture ratio when t / a = ∞.
FIG. 19 is a diagram showing the relationship between the two-dimensional complete PBG width and R / a when t / a = 0.50.
FIG. 20 is a diagram showing a relationship between a two-dimensional complete PBG width and R / a when t / a = 0.60.
FIG. 21 is a diagram showing a relationship between a two-dimensional complete PBG width and R / a when t / a = 0.80.
FIG. 22 is a diagram showing a relationship between a two-dimensional complete PBG width and R / a when t / a = 0.90.
FIG. 23 is a diagram showing a relationship between a two-dimensional complete PBG width and R / a when t / a = 0.15.
FIG. 24 is a diagram showing a relationship between a two-dimensional complete PBG width and R / a when t / a = ∞.
FIG. 25 is a schematic perspective view showing a conventional two-dimensional photonic crystal waveguide.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 10,50 ... Photonic crystal waveguide, 10a, 50a ... Two-dimensional photonic crystal slab, 11 ... Slab material, 14 ... Triangular hole, 15, 65 ... Air (low refractive index) Material region), 22 ... linear defect (waveguide), 24 ... point defect, 64a ... first circular hole, 64b ... second circular hole, 65a ... first low refractive index Material region, 65b ... second low refractive index material region, a ... pitch, L ... length, M ... parallel line, r ... radius of first low refractive index material region, R ... radius of second low refractive index material region, t ... thickness of slab material.

Claims (12)

A two-dimensional photonic crystal slab having a common photonic band gap for light in both TE-like mode and TM-like mode ,
In the slab material made of a high refractive index material, the refractive index distribution is formed by periodically arranging the low refractive index material regions than the slab material,
Δ = (n _H ² −n _L ² ) / 2n _H ²
(In the formula, n _H represents the refractive index of the high refractive index material, and n _L represents the refractive index of the low refractive index material.)
The relative refractive index difference Δ defined by is greater than 0.35, and
0.35 <(t / a) <2.0
(Where, t is the thickness of the slab material, a is the minimum center distance or lattice constant in the periodic structure portion of the low refractive index material), and the low refractive index material region has a volume of the two-dimensional photonic crystal slab. More than 25% formed,
The two-dimensional photonic crystal slab characterized in that the low refractive index material regions are arranged in a triangular lattice pattern on the slab material, and the low refractive index material regions are triangular prisms . 2. The two-dimensional photo according to claim 1, wherein the low-refractive-index material regions are arranged at a constant inclination angle in a range excluding an odd multiple of ± 30 ° with respect to the direction of a group of parallel lines. Nick crystal slab. 3. The two-dimensional photonic crystal slab according to claim 1, wherein the low refractive index material regions are arranged in a square lattice pattern on the slab material. 4. 4. The two-dimensional photonic crystal slab according to claim 1, wherein the value of (t / a) is 0.65 ≦ (t / a) ≦ 1.50. 5. The low refractive index material region is configured by filling a plane-view regular triangular hole formed in the slab material with air, and the low refractive index material region is more than 25% of the volume of the two-dimensional photonic crystal slab. The two-dimensional photonic crystal slab according to claim 1, wherein the two-dimensional photonic crystal slab is formed in a range of less than 50%. The low refractive index material region has a regular triangular prism shape, and one side of a regular triangle forming the low refractive index material region is in a range of 0.3 μm to 0.4 μm, and the pitch of adjacent low refractive index material regions is The two-dimensional photonic crystal slab according to any one of claims 1 to 5, wherein is a range of 0.35 µm to 0.55 µm. 7. The regular triangular prism-shaped low refractive index material region is arranged at an inclination angle of 0 degree with respect to a group of parallel lines formed in the surface direction of the slab material. The two-dimensional photonic crystal slab according to crab. The value of (t / a) is 0.65 ≦ (t / a) ≦ 1.50, and the low refractive index material region is formed in a regular triangular hole formed in the slab material. 1 to 3, wherein the low refractive index material region is formed in a range of more than 25% and less than 50% of the volume of the two-dimensional photonic crystal slab. The two-dimensional photonic crystal slab according to any one of 6 and 7. TE-like introduced into the slab material Mode light or TM-like The mode light is prohibited from propagating by a photonic band gap in the in-plane direction of the slab material, and confined by total reflection by the upper and lower low-refractive index material regions in the plane direction. The two-dimensional photonic crystal slab according to any one of the above. A linear defect that disturbs a periodic arrangement of the photonic crystal is formed in the two-dimensional photonic crystal slab according to any one of claims 1 to 9, and the linear defect guides light through. At least one point-like defect that disturbs the periodic arrangement of the photonic crystal is formed in the vicinity of the waveguide, and the point-like defect is a TE-like mode that propagates in the waveguide and TM. As a light extraction / introduction port that can capture and emit light in both modes of -like mode, or can capture light in both TE-like mode and TM-like mode from the outside and introduce it into the waveguide. A two-dimensional photonic crystal waveguide characterized by being configured to function. The two-dimensional photonic crystal waveguide according to claim 10 , wherein the point-like defect has an asymmetric shape with respect to the slab surface. Optical device, characterized in that provided that the two-dimensional photonic crystal waveguide of claim 10 or 11.

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