JP2002350657A - Photonic crystal waveguide - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a slab type two-dimensional photonic crystal waveguide which enables single-mode propagation having a group velocity improved and propagation loss reduced. SOLUTION: The slab type two-dimensional photonic crystal waveguide, constituted in defective structure by removing some of gratings of slab type two-dimensional photonic crystal linearly in a waveguide direction, is characterized in that 1st width as the width between the gratings on both sides of the defective part of the defective structure is made different from 2nd width as the width between the gratings on both sides of the defective part of a normal defective structure wherein only one array of gratings of the slab type two-dimensional photonic crystal is removed. Further, the slab type two-dimensional photonic crystal waveguide may be constituted by moving a low-refractive-index column present at a part which should become an optical waveguide part, in the optical waveguide direction from the position of two-dimensional periodic arrangement of the normal slab type two-dimensional photonic crystal and arranging it.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a photonic crystal waveguide which can be used for basic structures and optical components constituting various optical devices such as lasers and optical integrated circuits used for optical information processing and optical transmission. About.

[0002]

2. Description of the Related Art In current optical devices, since light is confined by a difference in refractive index, the light confinement region cannot be made small, so that the element cannot be made small. Furthermore, if a steep bending waveguide is formed to increase the degree of integration of the element, scattering loss occurs. Therefore, the optical circuit cannot be miniaturized and integrated, and its size is much larger than that of an electronic device. Therefore, a photonic crystal that can confine light with a concept completely different from the conventional one is expected as a new light material that can solve the above-described problem.

A photonic crystal is different from a photonic crystal in that it has a different refractive index.
It is an artificial multi-dimensional periodic structure that has a periodicity comparable to the wavelength of light formed by more than one type of medium, and has a light band structure similar to the band structure of electrons. Therefore, a light forbidden band (photonic band gap) appears in a specific structure, and a photonic crystal having this band functions as a light insulator.

[0004] It is theoretically possible to realize an optical waveguide in which a waveguide mode is formed in a frequency region of a band gap and a light is completely confined by introducing a line defect that disturbs periodicity in a photonic crystal having a photonic band gap. (JD Joannopoulos, PRVilleneuv
e, and S. Fan, Photonic Crystal: putting a new twis
ton light, Nature 386,143 (1997)). JD Joannopo
ulos et al. describe a line defect in which a single column is not arranged in a two-dimensional photonic crystal in which a cylinder having a radius a / 5 having a refractive index as large as a semiconductor is arranged on a square lattice having a lattice constant a of about the wavelength of light. It was theoretically shown that it is possible to construct an optical waveguide in which scattering loss does not occur in principle even when bent at a sharp angle. Such a waveguide can be a very important waveguide for forming a micro optical integrated circuit.

In order to realize an optical waveguide for constructing such a microminiature optical integrated circuit, it is necessary to realize a single waveguide mode within a photonic band gap frequency. This is because, when a multimode waveguide having a plurality of modes having different properties is used, for example, when a bending waveguide is manufactured, a part of the mode propagating in the bending portion is converted into a different mode, so that an ultra-small light This is because there is an inconvenience that a highly efficient bending waveguide required for an integrated circuit cannot be realized. Also, the multimode waveguide is not suitable for high-speed communication.

At present, several types of waveguides are manufactured, but it is technically very difficult to form a waveguide in a three-dimensional photonic crystal having a full band gap. A method of forming a waveguide using a two-dimensional photonic crystal is promising.

When a two-dimensional photonic crystal is used as a waveguide, it is necessary to confine light in a direction perpendicular to a two-dimensional plane, and several methods have been proposed. Among them, a structure in which a thin film of a high-refractive-index semiconductor (refractive index of about 3 to 3.5) is attached on a low-refractive-index dielectric (often an oxide or a polymer, a refractive index of about 1.5). A structure in which a two-dimensional photonic crystal is formed (an oxide-clad two-dimensional slab type photonic crystal) can be easily manufactured in a large area, and various functional elements can be easily added to the same structure.

In recent years, Silicon-On-Insulator (SO
Silicon (S) on silicon dioxide (SiO ₂ ) called I)
i) A substrate having a thin film has been applied to an LSI, and a very high quality substrate has been obtained. By using this substrate, a high quality oxide clad type two-dimensional slab can be easily obtained. There is also an advantage that a photonic crystal can be manufactured. Such advantages cannot be obtained by other structures (for example, an air bridge type two-dimensional slab photonic crystal in which the upper and lower claddings of the photonic crystal are air).

As described above, in terms of fabrication, the oxide clad type 2
Although the two-dimensional slab photonic crystal is more advantageous than an air-bridge type two-dimensional slab photonic crystal or the like, this structure has the following problems. A waveguide structure that realizes a mode has not been realized.

In a waveguide mode caused by a defect in an optical waveguide using a two-dimensional slab photonic crystal, light is strongly confined in a two-dimensional plane due to the presence of a photonic band gap as described above.
Although there is no in-plane scattering loss, the mode is generally leaky in a higher frequency region than the light line of the clad, that is, light easily leaks to the clad layer. (The light line is a representation of the lowest frequency at which light can propagate in the medium with respect to the propagation constant, and w = ck / n (w: angular frequency, c: speed of light, n: refractive index, k: wave number) )). Therefore, it is customary to use a lower frequency region than the light line so that the guided light does not leak to the upper and lower cladding layers.

FIGS. 1A and 1B are schematic structural views of a typical air hole type single-row line defect photonic crystal waveguide in a conventional example. FIG. 1A is a top view, and FIG.
FIG. 1B is a sectional view taken along the line BB ′ in FIG. 1 (a) and 1 (b), 5 is an optical waveguide, 2 is Si
Layers 3 and 3 are SiO ₂ layers serving as cladding layers, and 4 is an air hole triangular lattice, and the lattice constant is represented by a. Fig. 1
It is a cylinder or a polygonal pillar penetrating the Si layer 2 shown in (b), and the hole diameter is 0.215 μm in this case. An air hole triangular lattice is a structure in which air holes are arranged at each lattice point of a triangular lattice, and a triangular lattice is a rule in which lattice points are arranged at vertices of an equilateral triangle arranged so as to fill a two-dimensional surface. It is a lattice.

Now, a typical two-dimensional photonic crystal having a photonic band gap has a structure in which columns having a high refractive index are arranged in air, and air holes (low holes) in a high refractive index plate as described above. (Also referred to as a refractive index column or a low refractive index cylinder). The former is JD Joannopoul
Although this is the structure used by os et al., this structure requires a cladding layer to support the pillar because the pillar cannot stand on its own.
Since this layer has a higher refractive index than air, which is the core of the line-defect waveguide, a very long column is required to prevent light from leaking above and below the waveguide, making fabrication extremely difficult. Become. On the other hand, since the latter air hole can be self-supporting, the cladding layer can be freely selected, and it is easy to make the refractive index of the core larger than that of the cladding layer. Easy to select structural conditions.

There are various patterns in the two-dimensional arrangement of the holes of the photonic crystal using the high refractive index plate.
A structure in which holes (cylindrical or polygonal columns) are arranged in a triangular lattice as shown in FIG. 1A is known as a pattern having a photonic band gap in a wide frequency band.
This means that this structure has a wide frequency band in which it functions as an insulator for light, and is advantageous because a wide frequency selection range can be obtained when designing a waveguide.

FIG. 2 is a diagram showing the waveguide mode dispersion of a typical single-row-outline defect photonic crystal waveguide in a conventional example. When an attempt is made to form such a waveguide with an oxide clad type photonic crystal, the formed waveguide mode is as shown in FIG. Here, an angular frequency uses a dimensionless normalized frequency expressed by (lattice constant / wavelength), and a propagation constant uses a dimensionless normalized propagation constant expressed by (wave number / lattice / 2/2). ing. FIG.
In this case, the cladding (SiO ₂ , refractive index 1.46)
Are also shown.

However, in the structure shown as a conventional example, the waveguide mode satisfying the condition that light does not leak to the cladding layer is only the region surrounded by the ellipse below the light line in FIG. However, in this region, the inclination of the guided mode is very small, and the group velocity (energy propagation velocity) of the guided mode whose size is determined by this inclination is very small. In such a mode having an extremely small group velocity, the propagation time is long, and when used as a waveguide, there are many problems and it is difficult to use. Furthermore, in a practical structure, since there is a slight structural non-uniformity, a mode having an extremely small group velocity is affected by a slight non-uniformity and does not propagate. In addition, above the light line (high-frequency range side)
In the mode (2), light cannot be propagated because the diffraction loss due to the photonic crystal is too large. That is, the light in the photonic crystal waveguide propagates while being perturbed by the periodic structure of the crystal, and in the mode above the light line, the light leaks to the cladding layer as diffraction loss.

[0016] When the present inventor actually produced a single-row line defect waveguide, no propagation was observed in this waveguide. The cause of this problem is that there is no guided mode with a certain large group velocity below the light line determined by the cladding, and the diffraction loss is very large above the light line It is in.

In order to use the mode below the light line, it is necessary to raise the light line or move the guided mode in the graph of FIG. 2, but as long as the oxide clad structure is adopted, the position of the light line is Because it is limited by the refractive index of the cladding, it cannot be changed significantly.

Regarding the guided mode, as long as the condition of obtaining a single guided mode within the band gap is imposed,
In the structure of FIG. 1, it is difficult to have a somewhat large group velocity below the light line. Here, the case of a triangular lattice has been described, but in the case of another crystal structure such as a square lattice, the situation becomes more difficult, and there is no waveguide mode that meets the demand. It is very difficult to use the mode below the light line in this way.

The above-mentioned conventional technique will be described from another viewpoint.

FIG. 3 is a view for explaining a conventional one-line-cut defect photonic crystal waveguide. (A) is a top view of the optical waveguide, (b) is an AA ′ sectional view, and (c) is a BB ′ sectional view.

In FIG. 3, the optical waveguide 30 is composed of a dielectric thin film slab 31 (corresponding to the above high refractive index plate) sandwiched between an upper clad layer 36 and a lower clad layer 37. The dielectric thin film slab 31 constitutes a photonic crystal by providing a low refractive index cylinder 35 having a lower refractive index than the dielectric thin film slab 31 in a triangular lattice shape. In order to make the wave portion 32, the dielectric thin film slab 31 is replaced with a dielectric having the same refractive index as the dielectric thin film slab 31 again. The arrow ← → in the optical waveguide 32 indicates the optical waveguide direction. In the waveguide shown in FIG. 1, in the structure shown in FIG. 3, the upper cladding layer and the low refractive index cylinder 35 are air, and the lower cladding layer 37 is S
This is an example in which iO ₂ is used and the dielectric thin film slab 31 is Si.

Here, as an example, the dielectric thin film slab 3
1. The refractive indices of the low refractive index cylinder 35, the upper cladding layer 36, and the lower cladding layer 37 are n ₁ = 3.5 and n ₂ = 1.
0, n ₃ = n ₄ = 1.46, the radius of the low refractive index cylinder 35 is 0.275a, and the thickness of the dielectric thin film slab 31 is 0.40.
The characteristics of the optical waveguide 30 will be described as 50a. The low refractive index cylinder 35 having a refractive index of 1.0 is the same as an air hole.
a is a lattice constant of the photonic crystal (here, a triangular lattice).

Since the relative dielectric constant is equivalent to the square of the refractive index, in the description in this specification, the relative dielectric constant or the dielectric constant may be used instead of the refractive index.

Further, their refractive indices are about 1.55 μm.
This type of waveguide is intended for communication infrared
Si, air (vacuum) and S commonly used in forming
iO ₂Corresponds to the refractive index of

FIG. 4 is a view for explaining a waveguide mode in the above-mentioned optical waveguide. (A) is a plane wave expansion method that imposes periodic boundary conditions on the dispersion relation of guided modes that can pass through the optical waveguide (RDMeade et al., Physical Review
B 48, 8434 (1993)), and is a diagram similar to FIG. 2. (B) is a diagram showing a magnetic field component perpendicular to the dielectric thin film slab in mode 1, and (c) is a diagram showing a magnetic field component perpendicular to the dielectric thin film slab in mode 2.

4A are lattice constants a and light velocities c.
It is standardized in. The shaded area indicates the photonic band gap (J D. Joanno Poulos, R D. Meade, J N. Winn,
“Photonic Crystals”, Princeton University Press,
Princeton (1995)), and as a result, an area where light is not confined to the optical waveguide 32 (A. Mekiset)
al., Physical Review B 58, 4809 (1998)).

The vertical hatched portion is the dielectric thin film slab 31
There is no light confining force due to the difference in refractive index between the upper cladding layer 36 and the lower cladding layer 37 sandwiching the dielectric thin film slab 31 above and below, and as a result, the region where light is not confined in the optical waveguide portion 32 ( S G. Johnson et a
l., Physical Review B 60,5751 (1999)). This region corresponds to the upper side of the above-mentioned write line. That is, in the drawing, the region to be considered as the waveguide is only the white region.

As can be seen from the figure, the conventional optical waveguide 30 has two waveguide modes 1 and 1 in a region to be studied.
There are two. If the band gap is wide, more waveguide modes may exist, but only two modes 1 and 2 will be considered here for simplicity. Mode 1 corresponds to the mode of the portion enclosed by the ellipse in FIG. 2, and mode 2 corresponds to the upper dotted mode.

Of these two modes 1 and 2, mode 1 on the low frequency side generally has an electromagnetic field distribution as shown in FIG. Mode 2 on the high frequency side generally has an electromagnetic field distribution as shown in FIG.

The practical waveguide mode among these waveguide modes 1 and 2 is mode 1 having an electromagnetic field distribution almost similar to the electromagnetic field in a general single mode waveguide. In mode 2, the electromagnetic field distribution is significantly different from the electromagnetic field in a general single-mode waveguide, so that it is difficult to introduce light from an external circuit. That is, mode 2 is not a practical waveguide mode. Also, the higher-frequency mode that appears when the band gap is wide has a significantly different electromagnetic field distribution from the electromagnetic field in a general single-mode waveguide, and is not practical. It is clear from

Therefore, mode 1 is used in a conventional waveguide. As can be seen from FIG. 4A, mode 1 has almost no change in the waveguide frequency even when the propagation constant changes. However, there is a disadvantage that the usable frequency band is extremely narrow. The frequency band in this case is about 1%.

Further, the fact that the frequency hardly changes even if the propagation constant changes means that the group velocity of the electromagnetic field is extremely low physically. Therefore, there is a disadvantage that the propagation time becomes very long, and the propagation loss due to the dielectric loss of the constituent material of the waveguide increases.

[0033]

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and has solved the above-mentioned problems of the photonic crystal waveguide, improved the group velocity, and reduced the propagation loss. Slab type 2 that enables single mode propagation
It is an object to provide a two-dimensional photonic crystal waveguide.

[0034]

In order to achieve the above object, the present invention can be configured as follows.

According to the present invention, there is provided a slab type two-dimensional photonic crystal waveguide in which a part of the lattice of the slab type two-dimensional photonic crystal is linearly removed in the waveguide direction and has a defect structure. The first width, which is the width between the lattices on both sides, is the second width, which is the width between the lattices on both sides of the defect portion in the normal defect structure, except for one row of the lattice of the slab type two-dimensional photonic crystal. The structure is different from the width.

In the above structure, the first of the defective portions is
Is a value between 0.50 and 0.85 times the second width.

According to the present invention, it is possible to provide an optical waveguide having a structure capable of forming a single guided mode having a large group velocity below the light line.

Further, the lattice may be an air hole type triangular lattice, and the slab type two-dimensional photonic crystal may be:
It can be configured to have an oxide cladding or a polymer cladding. Further, the slab type two-dimensional photonic crystal can be manufactured using a silicon-on-insulator (SOI) substrate.

In the above structure, the first width of the defective portion is wider than the second width, and the optical waveguide has a single mode at a higher frequency side than the light line of the clad. It can be structured. Further, as such a width, the first width of the defective portion is the second width.
May be any value between 1.3 times and 1.6 times the width of.

According to the present invention, it is possible to provide an optical waveguide having a structure capable of forming a single waveguide mode with low loss above a light line.

The present invention can also be configured as follows.

According to the present invention, a cylindrical or polygonal dielectric column having a lower refractive index than the dielectric thin film slab is provided on the dielectric thin film slab at an appropriate two-dimensional periodic interval. Slab type 2 sandwiched between an upper cladding layer and a lower cladding layer having a lower refractive index than the body thin film slab
In a two-dimensional photonic crystal waveguide, a dielectric pillar existing in a portion to be an optical waveguide is moved in a light guiding direction from a position of a two-dimensional periodic arrangement to be arranged in a normal slab type two-dimensional photonic crystal. To place.

According to the present invention, it is also possible to provide an optical waveguide having a structure capable of forming a single guided mode having a larger group velocity below the light line. The dielectric pillar is a low refractive index pillar having a lower refractive index than the dielectric thin film slab.

In the above structure, the diameter of the dielectric pillar disposed in the optical waveguide is different from the diameter of the dielectric pillar other than the optical waveguide, and the diameter of the dielectric pillar is different from that of the other dielectric pillar not disposed in the optical waveguide. The values can be configured to be in a range that does not touch each other.

In addition, the moving position of the dielectric pillar disposed in the optical waveguide portion is shifted from the position of the two-dimensional periodic interval before shifting the position by half the distance of the two-dimensional periodic interval in the optical waveguide direction. It may be configured to be a position.

The photonic crystal has a structure having dielectric pillars arranged in a triangular lattice with a lattice constant a, the radius or half width of which is 0.2a to 0.45a. The diameter of the dielectric pillars arranged in the optical waveguide portion can be set so that the diameters of the dielectric pillars do not touch each other.

The refractive index of the dielectric thin film slab material is between 3.0 and 4.5, and the refractive index of the material other than the dielectric thin film slab is between 1.0 and 1.7. Configure the material as you would.

Further, in the above-mentioned structure, the photonic crystal is a dielectric pillar arranged in a square lattice with a lattice constant a, and has a radius or a half width of 0.35a to 0.45a, and Alternatively, a structure may be employed in which the dielectric pillars arranged in the optical waveguide have a diameter in a range where they do not touch each other.

Further, silicon is used for the dielectric thin film slab material.
Germanium, gallium / arsenic compounds, indium /
Using a phosphorus-based compound or an indium-antimony-based compound, and using silicon dioxide, a polyimide-based organic compound, an epoxy-based organic compound, an acrylic-based organic compound, air, or vacuum for the material other than the dielectric thin film slab Can be used.

[0050]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An optical waveguide according to the first and second embodiments of the present invention has a defect structure in which a part of a lattice of a slab type two-dimensional photonic crystal is removed linearly and has a defect structure. In the waveguide, the width of the defect structure is made narrower than the width of one row of the lattice arrangement (first embodiment) or widened (second embodiment) so that both sides of the defect are sandwiched. Are shifted from each other. With such a structure, a structure having a single mode with low loss and large group velocity can be realized while using the light confinement method based on the photonic band gap and the refractive index difference as described in the related art.

The same applies to the case where the position of one row of low refractive index columns (air holes or the like) in the slab type two-dimensional photonic crystal is shifted in the optical waveguide direction or the hole diameter is further changed. An effect can be obtained (third embodiment).

The slab-type two-dimensional photonic crystal is a dielectric thin film slab in which cylindrical or polygonal low refractive index columns having a lower refractive index than the dielectric thin film slab are provided at appropriate two-dimensional periodic intervals. Further, it refers to a photonic crystal in which the upper and lower portions of a dielectric thin film slab are sandwiched between an upper cladding layer and a lower cladding layer having a lower refractive index than the dielectric thin film slab.

The width of one row of the lattice arrangement is the width between the lattices on both sides of the defect portion in the normal defect structure except for one row of the lattice of the slab type two-dimensional photonic crystal. is there.

Hereinafter, each embodiment will be described. <First Embodiment> First, a first embodiment of the present invention will be described.

FIG. 5 shows an optical waveguide 1 composed of a single-row out-of-line defect photonic crystal waveguide according to the first embodiment of the present invention.
(A) is a top view thereof, (b) is B-
It is B 'sectional drawing. The present invention relates to an oxide clad type 2
When a single line defect is formed in a two-dimensional slab photonic crystal, by adjusting the defect width by displacing the entire crystal lattice on both sides of the line defect, it has a large group velocity below the clad light line. And a single guided mode is formed.

That is, a 0.2 μm thick Si layer 2 or 3 μm
An air hole triangular lattice photonic crystal having a lattice constant a = 0.39 μm is fabricated on an m-thick SiO ₂ SOI substrate by electron beam exposure and dry etching, and a single-row defect having various widths is introduced. did. The method of adjusting the width of the defective waveguide is
In the structure after one row of holes is punched out, the crystal lattices on both sides sandwiching this row are vertically shifted from the row of a certain length.

The width of a defect in a normal one-line-outline defect photonic crystal waveguide is simply defined as the distance between the centers of the closest lattices 4 on both sides of the defect when one line of the lattice is removed. The width of the defect in the form (1) is expressed by a constant multiple of W, where W is the width of the defect in a normal case. This photonic crystal itself has a wavelength of 1.35 μm to 1.5 μm.
There was a photonic band gap between 7 μm, and no light transmission was observed in the defect-free crystal within this wavelength range. Next, the light transmission spectrum of each defective waveguide was measured. No light transmission was observed within the bandgap wavelength region when one line of the grating was simply removed (with a width of 1.0 W). On the other hand, when the width was 0.7 W, clear light transmission was observed in a certain wavelength region within the band gap.

FIG. 6 shows the waveguide mode dispersion of an optical waveguide composed of a single-row line defect photonic crystal waveguide according to the first embodiment of the present invention. FIG. 2 is shown in FIG. 7 corresponding to FIG. FIG. 7 shows the light lines of the cladding (in this case, SiO ₂ ) superimposed as in FIG. In the conventional device shown in FIG. 7, the inclination of the propagation mode below the light line (the propagation mode corresponding to mode 1 in FIG. 4) is small, whereas in the present invention shown in FIG. There is a waveguide mode having a large inclination, that is, a large group velocity. It is also clear from the figure that the region satisfies the single mode condition.

The wavelength region where the light transmission was observed in the experiment coincides with the region where the waveguide mode exists, and the reduced width has a single group with a large group velocity below the light line. This indicates that light transmission has been realized due to the mode being formed. As a result of calculating the waveguide mode dispersion by the time domain finite difference method and the plane wave expansion method for various structural parameters, the waveguide width was changed from 0.50 W to 0.8 W.
It was found that a waveguide mode having a large group velocity was formed below the light line when set between 5 W. Also, in the experiment, light propagation was observed in this waveguide width range.

FIGS. 8A and 8B show that the waveguide width is 0.85.
The theoretical calculation results of the waveguide mode dispersion for W and 0.50 W are shown. FIG. 8A shows the case of 0.85 W, and FIG.
The case where (b) is 0.50 W is shown. Waveguide width is 0.85
Between W and 0.50 W, for example, as shown in FIG. 6 (for 0.7 W), the transmission bandwidth of the waveguide is as shown in FIG.
Since the result is wider than the result of (b), it can be seen that it functions as a practical waveguide in this range.

The reason why the above effects can be obtained by reducing the width is as follows.

As described with reference to the prior art, in the state of the typical single-line line defect shown in FIG. 2, a region within the photonic band gap and lower in frequency than the write line (hereinafter, this region is referred to as the α region) ) Mode (circled in the figure) has a very low group velocity, and is not practical. Therefore, focus on the mode with the largest group velocity at the bottom outside the band gap.

When the width of the waveguide is reduced, the refractive index is reduced equivalently, and the lowest mode can be shifted to the higher frequency side. As a result, this mode can be used in the α region. Therefore, a mode having a large group velocity can be realized within the band gap and below the write line.

As a method of lowering the refractive index of the waveguide portion, a method of using a medium having a small refractive index in the waveguide portion,
There is also a method in which a hole is made in the waveguide portion to lower the refractive index equivalently. A method corresponding to making a hole in the waveguide portion will be described in a third embodiment.

<Second Embodiment> Next, a second embodiment of the present invention will be described.
An embodiment will be described.

FIG. 9 is a schematic view of an optical waveguide 1A comprising a single-row line defect photonic crystal waveguide according to the second embodiment of the present invention. In the second embodiment, when a single line defect is formed in an oxide clad type two-dimensional slab photonic crystal, the entire crystal lattice on both sides of the line defect is shifted to increase the defect width. A single waveguide mode with small propagation loss is formed above the light line.

That is, an Si layer having a thickness of 0.2 μm
An air hole triangular lattice photonic crystal having a lattice constant a = 0.39 μm is fabricated on an m-thick SiO ₂ SOI substrate by electron beam exposure and dry etching, and a single-row defect having various widths is introduced. did. The width adjustment of the defective waveguide is 1
In the structure after the holes for the rows are formed, the crystal lattices on both sides of the rows are shifted in a direction to separate them.

The defect width of the second embodiment is 1.5 times as large as one grid line. In this case as well, the width is defined as a constant multiple of W, which is the distance between the centers of the closest grids 4 on both sides of the defect when a single grid is simply removed as shown in the figure. This photonic crystal itself had a photonic band gap between wavelengths of 1.35 μm and 1.57 μm, and no light transmission was observed in the defect-free portion of the crystal within this wavelength range.

Next, the light transmission spectrum of each defective waveguide was measured. No light transmission was observed within the bandgap wavelength region when one line of the grating was simply removed (with a width of 1.0 W). On the other hand, in the optical waveguide 1A of the present embodiment having a width of 1.5 W, clear transmitted light was observed in a certain wavelength range within the band gap.

FIG. 10 shows a second embodiment of the present invention.
This is the waveguide mode dispersion of the optical waveguide 1A formed of the line defect photonic crystal waveguide. As in FIG. 2, the light lines of the cladding (in this case, SiO ₂ ) are shown overlapping. The wavelength region where light transmission was observed in the experiment coincides with the region where the even mode exists in the single mode region in the figure.
In this case, a single mode region exists in the photonic band gap above the light line, but the widening reduces the diffraction loss and solves the problem of leakage. That is, a low-loss waveguide mode is formed despite the position above the light line.

FIG. 11 shows a single-mode bandwidth (shown by a dotted line) above a light line of a one-row open-line defect photonic crystal waveguide according to the second embodiment of the present invention.
FIG. 3 is a diagram illustrating the dependence of propagation loss on the waveguide width (indicated by a solid line). The bandwidth is standardized at the center frequency of the single mode band. As shown in FIG. 11, when the waveguide width is increased from 1 W, the single mode bandwidth increases and then decreases.
If it exceeds 6 W, a single mode band cannot be obtained. This occurs because the mode in the photonic band gap in FIG. 10 shifts to the lower frequency side by increasing the width. Also, the propagation loss is reduced by increasing the width.

As a result of calculating the waveguide mode dispersion and the propagation loss by the time domain finite difference method for various structural parameters, when the waveguide width is set to 1.6 W or less, the single mode condition is set on the light line. A propagation mode that satisfies the condition is formed.
It was found to be less than dB / mm. Also, in the experiment, light propagation was observed in this waveguide width range. That is, by setting the waveguide width to 1.6 W or less and 1.3 W or more, a propagation mode in which the propagation loss is less than the practical loss value and which satisfies the single mode condition can be obtained.

That is, while it is difficult to realize a structure having a mode having a large group velocity on the lower frequency side than the light line of the clad with the widened waveguide, the perturbation received from the crystal by widening the width of the waveguide is difficult. Has the effect of increasing the group velocity and making it difficult to diffract. As a result, as shown in FIG. 10, even though the frequency is higher than the light line of the cladding, the propagation loss is reduced. Can be reduced. However, since the effective refractive index of the waveguide increases as the width increases, the single mode band shown in FIG. 10 shifts to a lower frequency side as described above, and the single mode band gradually narrows. Therefore, in order to realize a single mode, the waveguide width needs to be 1.6 W or less.

Now, a method of calculating a waveguide mode dispersion curve (FIGS. 6, 7, 10 and the like) used in the description of the present invention will be described here.

This dispersion curve is calculated by the FDTD method (Finite
Difference TimeDomain me
(Time, finite difference method) is obtained by analyzing Maxwell's equations by a calculation method called "time domain finite difference method". The analysis method will be described below.

First, the band analysis of a crystal performed by crystal engineering or the like will be briefly described. A periodic structure such as a crystal can be represented by repeating a certain unit cell. It is a well-known fact that fields in such structures are Bloch waves. The band analysis is a work of applying a periodic boundary condition that satisfies the Bloch condition to a boundary where unit cells come into contact, and extracting a field that satisfies this condition as an eigenmode. At this time, the object to be analyzed is the Schrodinger equation, and the distribution of the spatial potential contained therein differs depending on the substance, so that various band structures exist.
This concept is applied to a photonic crystal that is a periodic structure. However, since the target is light rather than electrons, the equation handled is Maxwell's equation, and the refractive index (dielectric constant) distribution is used for calculation instead of the potential distribution.

Next, an operation of extracting an eigenmode using the FDTD method will be described. The FDTD method is a method in which the Maxwell equation is differentiated in time and space, and an electromagnetic field of light propagating in a given structure (spatial distribution of refractive index (dielectric constant)) is obtained by sequential calculation with respect to time. It is not a calculation method for directly obtaining an eigenvalue. However, it is possible to determine a mode that conforms to a given structure by the following method.

First, an appropriate initial field is provided in a given structure. When iterative calculations are performed, the fields that match the given structure survive, and the others are eliminated. A frequency spectrum can be obtained by Fourier-transforming the time change of this field. If a field suitable for a given structure exists, a peak appears in the frequency spectrum. At this time, since the Bloch condition used for the calculation is a function of the wave number, the frequency at which the peak appears is a function of the wave number. This is a band diagram of the photonic crystal.

Next, the mode calculation of the two-dimensional photonic crystal waveguide will be described. Basically, the same calculation method as described above is performed. However, in the photonic crystal used in the present invention, a line defect is introduced inside the crystal, and the periodicity is broken in a direction orthogonal to the line defect. Therefore, the structure shown in FIGS. 12A to 12C is referred to as a unit cell. In other words, a periodic boundary condition that satisfies the Bloch condition is applied to the light propagation direction, a periodic structure in which waveguides are arranged at a distance that does not significantly interfere with each other in the orthogonal direction is realized at the mirror boundary, and in the thickness direction, Set the area to absorb the light that leaks out of the mode.

FIG. 12A shows the waveguide structure shown in FIG. FIG. 12B is a structure extracted from a dotted line portion shown in FIG. 12A, and FIG. 12C is a three-dimensional view of FIG. 12B, which is a unit cell of a photonic crystal waveguide. Maxwell equation for this unit cell is FDT
By solving by the D method, the above-mentioned graph of wave number-frequency can be drawn. This is the dispersion curve shown in the description of the present invention.

In this calculation, if the mode stays in the waveguide for a long time, a mode other than the eigenmode can be picked up as a spectrum peak. Therefore, it is also possible to analyze a leaky mode on a higher frequency side than the light line of the cladding layer, and this feature is an advantage that cannot be obtained by other eigenvalue analysis methods. This advantage is utilized in the present invention. In addition, since this calculation method can calculate the confinement time of light in the waveguide, there is a feature that a theoretical propagation loss can be shown by using a group velocity (energy propagation velocity) obtained from a dispersion curve.

It has been confirmed that a single mode region exists not only in the lower frequency side of the light line of the cladding layer but also in the higher frequency side of the line in the waveguide whose width is reduced.

In the first and second embodiments, Si and SiO ₂ are used as the medium, and for example, Silicon-On-Ins
ulator (SOI) can be used,
It is clear that the effect of the present invention is not limited to this material. In general, when constructing a defect waveguide using a slab-type photonic crystal in which a low-refractive-index dielectric is arranged under a thin film of a high-refractive-index medium, the width of the waveguide is the same as in the above embodiment. It is generally possible to form a guided mode that satisfies the single mode condition below or above the light line by adjusting.

For example, a structure using a semiconductor such as a gallium arsenide-based compound (GaAs, InGaAs, InGaAsP, etc.) or an indium-phosphorus-based compound (InP, etc.) instead of Si, or a polymer, alumina, etc., instead of SiO ₂ It is clear that the same effect can be expected even with a structure using a substance. Also, here, the lower cladding is made of SiO
₂ has been described only when air is used for the upper part, but it is clear that a similar effect can be expected even in a structure in which a dielectric clad such as SiO ₂ is disposed on both the upper and lower sides.

<Third Embodiment> Next, a third embodiment of the present invention will be described.
Will be described as Examples 3-1 to 3-2.

In this embodiment, a low-refractive-index column or a low-refractive-index polygonal column having a lower refractive index than the dielectric thin film slab is provided in the optical waveguide portion of the conventional optical waveguide described with reference to FIGS. Is provided in parallel with the optical waveguide direction, thereby improving the frequency and group velocity of the waveguide mode. (Embodiment 3-1) FIG. 13 is a view for explaining the slab type two-dimensional photonic crystal waveguide in the embodiment 3-1. (A) is a top view of the optical waveguide, and (b) is a cross-sectional view taken along the line AA '. FIG. It is a figure explaining a wave structure.

That is, cylinders made of a dielectric material having a lower refractive index than the dielectric thin film slab are arranged in a triangular lattice, and a row of these cylinders existing in the optical waveguide section is aligned with the triangular lattice in the optical waveguide direction. This is a structure that is arranged by being moved by a distance of half the period (lattice constant). Further, if necessary, the diameter of the column disposed at the moving position is changed according to the optical waveguide characteristics.

Here, as an example, the dielectric thin film slab 1
1, low refractive index column 15, upper cladding layer 16, lower cladding layer
The refractive index of the doped layer 17 and the low refractive index column A13 is n₁= 3.
5, n ₂= 1.0, n₃= N₄= 1.46, n₅= 1.
0 and the radius of the low refractive index columns 15 other than the optical waveguide 12
0.275a, the thickness of the dielectric thin film slab 11 is 0.50
a, the radius of the low refractive index column A13 installed in the optical waveguide 12 is
The characteristics of the present waveguide structure will be described as 0.225a.

FIG. 14 is a diagram for explaining the waveguide mode in the photonic crystal waveguide according to the embodiment 3-1 of the present invention. (A) is a diagram showing a dispersion relationship of a guided electromagnetic field mode, (b) is a diagram showing a magnetic field component perpendicular to a dielectric thin film slab in modes 1 and 2, and (c) is a diagram showing a dielectric property in mode 3. It is a figure which shows the magnetic field component perpendicular to a body thin film slab.

In this case, the dispersion relation of the guided electromagnetic field modes that can pass through the waveguide is as shown in FIG. In this case, there are three waveguide modes, and the electromagnetic field distribution of the first and second modes 1 and 2 from the low frequency side is a general single mode waveguide as shown in FIG. Is close to the electromagnetic field distribution at. In particular, in the second mode from the low frequency side (mode 2), the frequency change with respect to the propagation constant becomes large in the entire effective propagation constant region. As a result, the effective frequency band is about 4.7
% And the group speed also increases.

Further, in this example, the guided light was changed to a wavelength of 1.55 μm.
When applied to the nearby communication infrared rays, when the dielectric thin film slab 11 is made of Si, the low-refractive-index columns 15 and the low-refractive-index columns A13 are made of air (or vacuum), and other portions are made of SiO ₂ , the triangular shape is obtained. The period of the grating is about 0.42 μm,
The radius of the low-refractive-index columns 15 other than the above is about 0.115 μm, and the radius of the low-refractive-index columns A13 installed in the optical waveguide 12 is 0.02 μm.
It is 94 μm, which is a value that can be manufactured using a conventional semiconductor processing technique or the like.

In this example, the radius of the low-refractive index column A13 disposed at the position where the optical waveguide section 12 is moved is described as 0.225a, but by changing this radius, the waveguide mode can be changed. Obviously, the frequency and group velocity can be changed. Considering the structure of the waveguide, that is, considering the low refractive index column A13 which is not disposed in the optical waveguide portion and does not come into contact with each other, the low refractive index column A13
Is practically about 0.1 to 0.4 times the minimum width of the optical waveguide 12.

Further, in the above example, a cylindrical low refractive index region is provided with a triangular lattice period in order to provide a photonic crystal outside the optical waveguide portion 12. Similar effects can be expected when used. As for the diameter range of these cylinders and polygonal columns, the same effects as in the above-described example can be expected within a range in which the existence of a photonic band gap is allowed. When the refractive index of the dielectric thin film slab is about 3.0 to 4.5 and the refractive index of the other low refractive index parts is about 1 to 1.7, according to the theoretical calculation by the plane wave expansion method described above, These diameters are approximately 0.2
a to 0.45a, preferably 0.2
75a to 0.375a are realistic and highly effective.

In the above example, a circular cylinder is used for the low-refractive-index column A13 disposed at the position where the optical waveguide section 12 is moved. However, the same effect can be expected by using an elliptical column or polygonal column. .

The refractive index of a cylinder or the like for providing a photonic crystal, the refractive index of the cladding sandwiching the dielectric thin film slab above and below, and the refractive index of the cylinder or the like provided in the waveguide portion are determined by the dielectric thin film. If the refractive index is lower than the refractive index of the slab, the same effect can be expected even if the value is the same or different.

Further, regarding the material, the guided light is transmitted at a wavelength of 1.
In the case of a communication infrared region near 55 μm, silicon, germanium, gallium / arsenic compounds, which have a high refractive index, transmit infrared light, and have few problems in workability and stability, are used for the dielectric thin film slab. Indium-phosphorus compounds, indium-antimony compounds, and the like can be used as materials. The refractive index of these materials is approximately 3.
It is between 0 and 4.5. In addition, in this case, the portion other than the dielectric thin film slab has a low refractive index and can transmit infrared rays,
Silicon dioxide, a polyimide-based organic compound, an epoxy-based organic compound, an acrylic-based organic compound, air, vacuum, and the like can be used as a material having few problems in workability and stability. The refractive index of these materials is approximately 1.
It is between 0 and 1.7.

These materials can be used in the first and second embodiments as well. Also in the third embodiment, a slab type two-dimensional photonic crystal waveguide is formed by using a silicon-on-insulator (SOI).
It can be manufactured using a substrate.

(Embodiment 3-2) FIG. 15 is a diagram illustrating a slab type two-dimensional photonic crystal waveguide according to Embodiment 3-2 of the present invention. (A) is a top view of the optical waveguide,
(B) is an AA ′ sectional view.

In Embodiment 3-1 described above, a photonic crystal is provided outside the optical waveguide section 12 so as to provide a low refractive index region of a cylindrical or polygonal column with a triangular lattice period. Similar effects can be expected by using a square lattice as shown. That is, low refractive index columns 25 having a lower refractive index than the dielectric thin film slab 21 are provided in a square lattice shape, and an upper cladding layer 26 having a lower refractive index than the dielectric thin film slab 21 is provided above and below the dielectric thin film slab 21. In the structure sandwiched between the lower cladding layers 27, one of the low-refractive index columns 25 arranged in the optical waveguide direction and existing in a portion to be the optical waveguide 22.
The column is moved in the optical waveguide direction by a distance of half the lattice constant of the square lattice, and if necessary, the diameter of the low refractive index column 25 arranged at this position is changed according to the optical waveguide characteristics. are doing.

In this case, the range of the diameter of the low refractive index column providing the photonic crystal may be a range in which the existence of the photonic band gap is allowed. According to the theoretical calculation by the plane wave expansion method, specifically, the dielectric thin film slab 2
When the refractive index of the low refractive index column 1 is about 3 to 4.5 and the refractive indexes of the other low refractive index portions are about 1 to 1.7, the diameter of these low refractive index columns 25 is about 0.35a to 0.3. 45a. The supplementary items concerning the improvement of the optical waveguide characteristics, the shape of the low refractive index column A, the refractive index of each part, and the material of each part described in the embodiment 3-1 are the same as those in the embodiment 3-1. This is also true in this embodiment.

The present invention is not limited to the above embodiments, but can be variously modified and applied within the scope of the claims.

[0102]

As described above, the optical waveguide of the present invention has a defect structure in which a part of the lattice of the slab type two-dimensional photonic crystal is linearly removed and the width of the defect structure is the lattice. The structure of the grating on both sides sandwiching the defect is shifted so that it is narrower than the width of one row of the array, so that a single guided mode with a large group velocity below the light line is formed An optical waveguide having a possible structure can be provided.

In an optical waveguide having a defect structure by removing a part of the lattice of the slab type two-dimensional photonic crystal in a straight line, the width of the defect structure is set to be wider than one column width of the lattice arrangement. Since the structure of the lattices on both sides of the defect is shifted, it is possible to provide an optical waveguide having a structure capable of forming a single waveguide mode with low loss above the light line.

Further, the positions of the low refractive index columns constituting one row of the lattice of the slab type two-dimensional photonic crystal are phased in the waveguide direction, and the lattice hole diameter is further changed to be smaller than that of the light line. An optical waveguide having a structure capable of forming a single guided mode having a large group velocity below can be provided.

Therefore, according to the present invention, it is possible to provide an ultra-small optical waveguide structure with improved group velocity and low loss.

[Brief description of the drawings]

FIGS. 1A and 1B are schematic structural views of a typical single-row line defect photonic crystal waveguide in a conventional row, in which FIG. 1A is a top view and FIG. 1B is a BB ′ cross-sectional view.

FIG. 2 is a view for explaining the waveguide mode dispersion of a typical single-row line defect photonic crystal waveguide in a conventional example.

3A and 3B are schematic diagrams of a typical single-row line defect photonic crystal waveguide in a conventional row, where FIG. 3A is a top view of an optical waveguide, FIG. 3B is a cross-sectional view along AA ′, and FIG. It is BB 'sectional drawing.

4A and 4B are diagrams illustrating a waveguide mode in a typical single-row line defect photonic crystal waveguide in a conventional column, and FIG. 4A is a diagram illustrating a dispersion relation of a guided electromagnetic field mode; (b) is a diagram showing a magnetic field component perpendicular to the dielectric thin film slab in mode 1, and (c) is a diagram showing a magnetic field component perpendicular to the dielectric thin film slab in mode 2.

FIGS. 5A and 5B are schematic views of an optical waveguide including a single-row line defect photonic crystal waveguide according to the first embodiment of the present invention, wherein FIG. 5A is a top view thereof, and FIG. is there.

FIG. 6 is a diagram for explaining the waveguide mode dispersion of the optical waveguide including the single-row line defect photonic crystal waveguide according to the first embodiment of the present invention.

FIG. 7 is a view for explaining the waveguide mode dispersion of a typical single-row line defect photonic crystal waveguide in a conventional example.

FIG. 8 shows waveguide widths of 0.85 W (a) and 0.50 W
It is a figure which shows the theoretical calculation result of the waveguide mode dispersion in the case of (b).

FIGS. 9A and 9B are schematic views of an optical waveguide including a single-row line defect photonic crystal waveguide according to a second embodiment of the present invention, wherein FIG. 9A is a top view thereof, and FIG. is there.

FIG. 10 is a diagram for explaining the waveguide mode dispersion of an optical waveguide including a single-row line defect photonic crystal waveguide according to the second embodiment of the present invention.

FIG. 11 illustrates the propagation loss above the cladding light line of an optical waveguide composed of a single-row line defect photonic crystal waveguide and the dependence of the single mode band on the waveguide width in the second embodiment of the present invention. FIG.

FIG. 12 is a diagram for explaining mode calculation of a two-dimensional photonic crystal waveguide.

FIG. 13 is a diagram illustrating a photonic crystal waveguide according to a third embodiment of the present invention. (A) is a top view of the optical waveguide, and (b) is an AA ′ cross-sectional view.

FIG. 14 is a diagram illustrating a waveguide mode in a photonic crystal waveguide according to a third embodiment of the present invention. (A) is a diagram showing a dispersion relationship of a guided electromagnetic field mode, (b) is a diagram showing a magnetic field component perpendicular to a dielectric thin film slab in modes 1 and 2, and (c) is a diagram showing a dielectric property in mode 3. It is a figure which shows the magnetic field component perpendicular to a body thin film slab.

FIG. 15 is a diagram illustrating another example of the photonic crystal waveguide according to the third embodiment of the present invention. (A) is a top view of the optical waveguide, and (b) is an AA ′ cross-sectional view.

[Explanation of symbols]

1, 1A, 5 Optical waveguide 4 Lattice 2 Si layer 3 SiO ₂ layer 10, 20, 30 Optical waveguide 12, 22, 32 Optical waveguide 11, 21, 31 Dielectric thin film slab 15, 25 Low refractive index column 35 Low refractive index Cylinder 16, 26, 36 Upper cladding layer 17, 27, 37 Lower cladding layer

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Akihiko Shinya 2-3-1 Otemachi, Chiyoda-ku, Tokyo Inside Nippon Telegraph and Telephone Corporation (72) Inventor Junichi Takahashi 2-3-3, Otemachi, Chiyoda-ku, Tokyo No. 1 Within Nippon Telegraph and Telephone Corporation (72) Inventor Chiharu Takahashi 2-3-1 Otemachi, Chiyoda-ku, Tokyo Nippon Telegraph and Telephone Corporation (72) Inventor Yokohama to 2-Otemachi, Chiyoda-ku, Tokyo No.3-1 Nippon Telegraph and Telephone Corporation F term (reference) 2H047 KA02 PA21 PA24 QA02 QA04 QA05 TA36

Claims (19)

[Claims] 1. A slab-type two-dimensional photonic crystal waveguide in which a part of a lattice of a slab-type two-dimensional photonic crystal is linearly removed in a waveguide direction and has a defect structure. The first width, which is the width between the lattices, is the second width, which is the width between the lattices on both sides of the defect portion in the normal defect structure, except for one row of the lattice of the slab type two-dimensional photonic crystal. A slab-type two-dimensional photonic crystal waveguide having a different structure. 2. The slab according to claim 1, wherein the first width of the defective portion is any value between 0.50 and 0.85 times the second width. Type two-dimensional photonic crystal waveguide. 3. The slab-type two-dimensional photonic crystal waveguide according to claim 1, wherein the lattice is an air hole type triangular lattice. 4. The slab-type two-dimensional photonic crystal waveguide according to claim 2, wherein the slab-type two-dimensional photonic crystal has an oxide cladding or a polymer cladding. 5. The slab-type two-dimensional photonic crystal waveguide according to claim 4, wherein the slab-type two-dimensional photonic crystal is manufactured using a silicon-on-insulator (SOI) substrate. . 6. A method according to claim 1, wherein the first width of the defective portion is wider than the second width, and the optical waveguide has a single mode at a higher frequency side than a light line of the clad. 2. The slab type two-dimensional photonic crystal waveguide according to 1. 7. The slab according to claim 6, wherein the first width of the defective portion is any value between 1.3 times and 1.6 times the second width. Type two-dimensional photonic crystal waveguide. 8. The slab-type two-dimensional photonic crystal waveguide according to claim 7, wherein the lattice is an air hole type triangular lattice. 9. The slab-type two-dimensional photonic crystal waveguide according to claim 7, wherein the slab-type two-dimensional photonic crystal has an oxide cladding or a polymer cladding. 10. The slab-type two-dimensional photonic crystal waveguide according to claim 9, wherein the slab-type two-dimensional photonic crystal is manufactured using a silicon-on-insulator (SOI) substrate. . 11. A dielectric thin-film slab having cylindrical or polygonal dielectric pillars having a lower refractive index than the dielectric thin-film slab at an appropriate two-dimensional periodic interval. In a slab type two-dimensional photonic crystal waveguide sandwiched between an upper cladding layer and a lower cladding layer having a lower refractive index than a slab, a dielectric pillar existing in a portion to be an optical waveguide is replaced with a normal slab type 2 A slab-type two-dimensional photonic crystal waveguide characterized in that the slab type two-dimensional photonic crystal waveguide is moved in the optical waveguide direction from the position of the two-dimensional periodic arrangement to be arranged in the two-dimensional photonic crystal. 12. The diameter of a dielectric pillar disposed in the optical waveguide is different from the diameter of a dielectric pillar other than the optical waveguide, and the dielectric pillar is in contact with another dielectric pillar not disposed in the optical waveguide. 12. The slab-type two-dimensional photonic crystal waveguide according to claim 11, wherein the slab type two-dimensional photonic crystal waveguide has a value in a range where there is no difference. 13. The position of the dielectric pillar disposed in the optical waveguide portion is a position shifted from the position of the two-dimensional periodic arrangement before shifting the position by half a distance of the two-dimensional periodic arrangement interval in the optical waveguide direction. The slab-type two-dimensional photonic crystal waveguide according to claim 11, wherein: 14. The photonic crystal has a lattice constant a
Having a radius or a half width of 0.2a to 0.45a, and being in contact with the dielectric pillars arranged in the optical waveguide section. 12. The slab-type two-dimensional photonic crystal waveguide according to claim 11, wherein the diameter of the slab type two-dimensional photonic crystal waveguide is within a range where there is no gap. 15. The dielectric thin film slab material having a refractive index of 3.
The slab type two-dimensional structure according to claim 14, wherein the refractive index of the material other than the dielectric thin film slab is between 0 and 4.5 and the refractive index of the material of the portion other than the dielectric thin film slab is between 1.0 and 1.7. Photonic crystal waveguide. 16. The photonic crystal has a lattice constant a
Are arranged in a square lattice, and have a radius or a half width of 0.35a to 0.45a, and
The slab-type two-dimensional photonic crystal waveguide according to claim 11, wherein the diameter of the slab-type two-dimensional photonic crystal waveguide is within a range that does not make contact with the dielectric pillar disposed in the optical waveguide. 17. The dielectric thin film slab material having a refractive index of 3.
17. The slab-type two-dimensional structure according to claim 16, wherein the refractive index of the material other than the dielectric thin film slab is between 0 and 4.5 and the refractive index of the material other than the dielectric thin film slab is between 1.0 and 1.7. Photonic crystal waveguide. 18. The dielectric thin film slab material is made of silicon, germanium, gallium / arsenic compound, indium / phosphorous compound or indium / antimony compound, and the material other than the dielectric thin film slab is: The slab-type two-dimensional photonic crystal waveguide according to claim 11, wherein silicon dioxide, a polyimide-based organic compound, an epoxy-based organic compound, an acrylic-based organic compound, air, or vacuum is used. 19. The slab-type two-dimensional photonic crystal according to claim 18, wherein the slab-type two-dimensional photonic crystal waveguide is manufactured using a silicon-on-insulator (SOI) substrate. Waveguide.