JP3800088B2 - Photonic crystal waveguide - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a basic structure constituting various optical devices such as lasers and optical integrated circuits used for optical information processing, optical transmission, and the like, and a photonic crystal waveguide that can be used for optical components.
[0002]
[Prior art]
Since current optical devices perform light confinement with a difference in refractive index, the light confinement region cannot be reduced, and the element cannot be made small. Further, if a steep bent waveguide is formed in order to increase the degree of integration of elements, scattering loss occurs, so that the optical circuit cannot be miniaturized and integrated, and its size is much larger than that of an electronic device. Therefore, a photonic crystal capable of confining light with a completely different concept from the conventional one is expected as a new light material that can solve the above-mentioned problems.
[0003]
A photonic crystal is an artificial multidimensional periodic structure in which a periodicity equivalent to the wavelength of light is formed by two or more types of media having different refractive indexes, and is a light band structure similar to the electronic band structure. Have Therefore, a forbidden band of light (photonic band gap) appears in a specific structure, and a photonic crystal having the band functions as an insulator of light.
[0004]
It is theoretically pointed out that if a line defect that disturbs periodicity is introduced into a photonic crystal having a photonic band gap, a waveguide mode is formed in the frequency region of the band gap and an optical waveguide that completely confines light can be realized. (JD Joannopoulos, PRVilleneuve, and S. Fan, Photonic Crystal: putting a new twist on light, Nature 386, 143 (1997)). JD Joannopoulos et al. Show a line in which a column is not arranged in a two-dimensional photonic crystal in which a cylinder with a radius a / 5 having a refractive index as large as a semiconductor is arranged on a square lattice with a lattice constant a of the wavelength of light. Theoretically, it was shown that an optical waveguide can be constructed in which no scattering loss occurs in principle even when defects are introduced and bent at a steep angle. Such a waveguide can be a very important waveguide for constructing an ultra-small optical integrated circuit.
[0005]
In order to realize an optical waveguide for constructing such an ultra-small optical integrated circuit, it is necessary to realize a single waveguide mode within the photonic band gap frequency. This is because, when a multimode waveguide having a plurality of modes with 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, and the ultra-compact light This is because there is a disadvantage that a highly efficient bending waveguide required for an integrated circuit cannot be realized. In addition, the multimode waveguide is not suitable for high-speed communication.
[0006]
At present, several types of waveguides have been fabricated. However, it is technically very difficult to fabricate a waveguide in a three-dimensional photonic crystal having a full band gap. A method of making a waveguide using a photonic crystal is promising.
[0007]
When a two-dimensional photonic crystal is used as a waveguide, it is necessary to confine light in a direction perpendicular to the 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 polymer, a refractive index of about 1.5). A structure in which a two-dimensional photonic crystal is formed (oxide clad two-dimensional slab type photonic crystal) can be most easily manufactured in a large area, and various functional elements can be easily added to the same structure.
[0008]
In recent years, silicon dioxide (SiOI) called silicon-on-insulator (SOI) ₂ ) Substrate with a silicon (Si) thin film on it has been applied to LSI, so that a very high quality one can be obtained. By using this substrate, a high quality oxide can be easily obtained. There is also an advantage that a clad type two-dimensional slab photonic crystal can be produced. Such an advantage cannot be obtained with other structures (for example, an air bridge type two-dimensional slab photonic crystal in which the upper and lower clads of the photonic crystal are air).
[0009]
As described above, the oxide clad type two-dimensional slab photonic crystal is advantageous in comparison with the air bridge type two-dimensional slab photonic crystal, etc., but this structure has the following problems. A waveguide structure that realizes a single waveguide mode within the photonic bandgap frequency has not been realized.
[0010]
In the waveguide mode caused by defects in an optical waveguide using a two-dimensional slab photonic crystal, light is strongly confined in the two-dimensional plane due to the presence of the photonic band gap as described above, and therefore, in-plane scattering is performed. Although there is no loss, in general, the mode is leaky in a higher frequency region than the light line of the clad, that is, light is likely to leak into the clad layer. (The light line is the minimum frequency at which light can propagate in the medium with respect to the propagation constant, 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.
[0011]
FIGS. 1A and 1B are structural schematic diagrams of a typical air hole type single-line defect photonic crystal waveguide in a conventional example. 1A is a top view, and FIG. 1B is a cross-sectional view taken along the line BB ′ in FIG. In FIGS. 1A and 1B, 5 is an optical waveguide, 2 is a Si layer, and 3 is a cladding layer. ₂ Layers 4 and 4 are air hole triangular lattices, and the lattice constant is represented by a. The air hole is a cylinder or a polygonal column penetrating the Si layer 2 shown in FIG. 1B, and the hole diameter is 0.215 μm in this example. The air hole triangular lattice is a structure in which air holes are arranged at each lattice point of the triangular lattice, and the triangular lattice is a rule in which the lattice points are arranged at the vertices of an equilateral triangle arranged so as to fill the two-dimensional surface. It is a lattice.
[0012]
Now, a typical two-dimensional photonic crystal having a photonic band gap has a structure in which columns with a high refractive index are arranged in the air, and air holes (low refractive index columns in the high refractive index plate as described above. Alternatively, it can be called a low refractive index cylinder). The former is a structure used by JD Joannopoulos et al., But this structure requires a cladding layer to support the column because the column cannot stand on its own. Since this layer has a higher refractive index than the air that forms the core of the line defect waveguide, it requires very long pillars to prevent light from leaking up and down the waveguide and is extremely difficult to fabricate. Become. On the other hand, since the latter air holes can be self-supporting, the selection of the cladding layer is free, and it is easy to make the refractive index of the core larger than that of the cladding layer, so there are less restrictions on fabrication, and light does not easily leak up and down Easy to select structural conditions.
[0013]
In addition, there are various patterns in the two-dimensional arrangement of photonic crystal holes using a high refractive index plate, but holes (cylinders or polygonal columns) are arranged in a triangular lattice pattern as shown in FIG. This structure is known as a pattern having a photonic band gap in a wide frequency band. This means that the frequency band in which this structure functions as an insulator with respect to light is wide, which is advantageous because a wide frequency selection range can be obtained when designing a waveguide.
[0014]
FIG. 2 is a diagram showing the waveguide mode dispersion of a typical single-line-drawn defect photonic crystal waveguide in the conventional example. When an oxide clad photonic crystal is used to form such a waveguide, the waveguide mode formed is as shown in FIG. Here, the angular frequency uses a dimensionless normalized frequency expressed by (lattice constant / wavelength), and the propagation constant uses a dimensionless normalized propagation constant expressed by (wave number / lattice constant / 2π). ing. FIG. 2 shows the clad (SiO 2 in this case. ₂ A light line with a refractive index of 1.46) is also shown.
[0015]
However, in the structure shown as the conventional example, the waveguide mode that satisfies the condition that light does not leak into the cladding layer is only the region surrounded by the ellipse below the light line in FIG. However, in this region, the gradient of the waveguide mode is very small, and the group velocity (energy propagation velocity) of the waveguide mode whose size is determined by this gradient is very small. In such an extremely small group velocity mode, the propagation time becomes long, so there are many problems when used as a waveguide and it is difficult to use. Furthermore, since there is some structural non-uniformity in a realistic structure, a mode with an extremely small group velocity is affected by slight non-uniformity and cannot propagate. In addition, the mode above the light line (on the high frequency region side) has too much diffraction loss due to the photonic crystal, and light cannot propagate. That is, light in the photonic crystal waveguide propagates while being perturbed by the periodic structure of the crystal, and light leaks to the cladding layer as a diffraction loss in the mode above the light line.
[0016]
When the inventor actually manufactured a single-row line defect waveguide, no propagation was observed in this waveguide. The cause of this problem is that there is no waveguide mode with a group velocity of a certain size that is practically easy to use below the light line determined by the cladding, and the diffraction loss is very large above the light line. There is.
[0017]
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 an oxide clad structure is employed, the position of the light line depends on the refractive index of the clad. Because it is limited by rate, it cannot be changed greatly.
[0018]
As for the guided mode, as long as the condition that a single guided mode is obtained within the band gap is imposed, it is difficult to give a certain large group velocity under the light line in the structure of FIG. Although the case of a triangular lattice has been described here, the situation becomes more difficult in the case of other crystal structures such as a tetragonal lattice, and there is no waveguide mode that meets the requirements. Thus, it is very difficult to use the mode below the light line.
[0019]
The above conventional technique will be described from another viewpoint.
[0020]
FIG. 3 is a diagram for explaining a conventional single-drawn line defect photonic crystal waveguide. (A) is a top view of an optical waveguide, (b) is an AA ′ sectional view, and (c) is a BB ′ sectional view.
[0021]
In FIG. 3, the optical waveguide 30 is composed of a dielectric thin film slab 31 (corresponding to the 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 that of the dielectric thin film slab 31 in a triangular lattice shape, and one row of the low refractive index cylinders 35 is guided to the light. In order to obtain the wave portion 32, the dielectric thin film slab 31 is replaced with a dielectric having the same refractive index. An arrow ← → in the optical waveguide portion 32 indicates an optical waveguide direction. In the waveguide shown in FIG. 1, in the structure shown in FIG. 3, the upper cladding layer 36 and the low refractive index cylinder 35 are air, and the lower cladding layer 37 is SiO. ₂ In this example, the dielectric thin film slab 31 is Si.
[0022]
Here, as an example, the refractive indexes of the dielectric thin film slab 31, the low refractive index cylinder 35, the upper cladding layer 36, and the lower cladding layer 37 are set to n. ₁ = 3.5, 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 0.50a. The low refractive index cylinder 35 having a refractive index of 1.0 is the same as the air hole. a is a lattice constant of the photonic crystal (here, a triangular lattice).
[0023]
Since the relative dielectric constant corresponds to the square of the refractive index, the relative dielectric constant or the dielectric constant may be used instead of the refractive index in the description in this specification.
[0024]
In addition, these refractive indexes are Si, air (vacuum), and SiO often used for forming this kind of waveguide for communication infrared rays having a wavelength of about 1.55 μm. ₂ Corresponds to the refractive index of.
[0025]
FIG. 4 is a diagram for explaining a waveguide mode in the optical waveguide. (A) is the result of calculating the dispersion relation of guided modes that can pass through the optical waveguide by the plane wave expansion method with periodic boundary conditions (RDMeade et al., Physical Review B 48, 8434 (1993)). FIG. 3 is a diagram similar to FIG. 2. (B) is a figure which shows a magnetic field component perpendicular | vertical to the dielectric thin film slab of mode 1, and (c) is a figure which shows a magnetic field component perpendicular | vertical to the dielectric thin film slab of mode 2.
[0026]
Each quantity in FIG. 4A is normalized by the lattice constant a and the speed of light c. The shaded area corresponds to the outside of the photonic band gap (J D. JoannoPoulos, R D. Meade, J N. Winn, “Photonic Crystals”, Princeton University Press, Princeton (1995)), and as a result, light is transmitted. A region (A. Mekis et al., Physical Review B 58, 4809 (1998)) that is not confined in the wave portion 32 is shown.
[0027]
In the vertical hatched portion, there is no light confinement force due to the difference in refractive index between the dielectric thin film slab 31 and the upper cladding layer 36 and the lower cladding layer 37 sandwiching the dielectric thin film slab 31 from above and below. Is a region that is not confined in the optical waveguide 32 (S G. Johnson et al., Physical Review B 60,5751 (1999)). This region corresponds to the upper side of the above-described light line. That is, in the figure, the only area to be considered as a waveguide is the white area.
[0028]
As can be seen from the figure, the conventional optical waveguide 30 has two waveguide modes 1 and 2 in the region to be studied. If the band gap is wide, more guided modes may exist, but only these two modes 1 and 2 are considered here for simplicity. Note that mode 1 corresponds to the mode enclosed by an ellipse in FIG. 2, and mode 2 corresponds to the upper dotted mode.
[0029]
Of these two modes 1 and 2, mode 1 on the low frequency side generally has an electromagnetic field distribution as shown in (b). The mode 2 on the high frequency side generally has an electromagnetic field distribution as shown in (c).
[0030]
Of these guided modes 1 and 2, a practical guided mode is mode 1 having an electromagnetic field distribution substantially 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, and therefore it is difficult to introduce light from an external circuit. That is, mode 2 is not a practical guided mode. In addition, the higher frequency modes that appear when the band gap is wide are also significantly different from the electromagnetic field distribution in general single-mode waveguides. It is clear from
[0031]
Therefore, mode 1 is used in the conventional waveguide, but as can be seen from FIG. 4A, mode 1 can be used because the waveguide frequency hardly changes even if the propagation constant changes. There is a drawback that the frequency band is extremely narrow. The frequency band in this case is about 1%.
[0032]
In addition, the fact that the frequency hardly changes even if the propagation constant changes means that the group velocity of the electromagnetic field is physically very slow. Therefore, there is a drawback that the propagation time becomes very long and the propagation loss due to the dielectric loss of the constituent material of the waveguide becomes large.
[0033]
[Problems to be solved by the invention]
The present invention has been made in view of the above points, and is a slab that solves the problems of the photonic crystal waveguide described above, improves group velocity, and enables single mode propagation with reduced propagation loss. An object of the present invention is to provide a type two-dimensional photonic crystal waveguide.
[0034]
[Means for Solving the Problems]
In order to achieve the above object, the present invention can be configured as follows.
[0035]
The present invention relates to a slab type two-dimensional photonic crystal waveguide having a defect structure in which a part of a lattice of a slab type two-dimensional photonic crystal is removed in a straight line in the waveguide direction.
The first width, which is the width between the lattices on both sides of the defect portion in the defect structure, is defined as the space 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 second width is different from the second width.
[0036]
In the above structure, the first width of the defect portion is any value between 0.50 times and 0.85 times the second width.
[0037]
According to the present invention, an optical waveguide having a structure capable of forming a single waveguide mode having a large group velocity below the light line can be provided.
[0038]
The lattice may be an air hole type triangular lattice, and the slab type two-dimensional photonic crystal may have an oxide clad or a polymer clad. Furthermore, the slab type two-dimensional photonic crystal can be manufactured using a silicon-on-insulator (SOI) substrate.
[0039]
Further, in the above structure, the first width of the defect portion is wider than the second width, and the optical waveguide has a width having a single mode on a higher frequency side than the light line of the clad. be able to. Moreover, as such a width | variety, the 1st width | variety of the said defect part can be taken as the value in any one between 1.3 times and 1.6 times of the said 2nd width | variety.
[0040]
According to the present invention, it is possible to provide an optical waveguide having a structure capable of forming a low-loss single waveguide mode above a light line.
[0041]
The present invention can also be configured as follows.
[0042]
In the present invention, a dielectric thin film slab is provided with cylindrical or polygonal pillars having a lower refractive index than the dielectric thin film slab at appropriate two-dimensional periodic intervals, and the dielectric thin film slab is placed above and below the dielectric thin film slab. 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,
A dielectric column existing in a portion to be an optical waveguide is moved and arranged in the optical waveguide direction from a position of a two-dimensional periodic arrangement to be arranged in a normal slab type two-dimensional photonic crystal.
[0043]
The present invention can also provide an optical waveguide having a structure capable of forming a single waveguide mode having a large group velocity below the light line. The dielectric column is a low refractive index column having a refractive index lower than that of the dielectric thin film slab.
[0044]
In the above structure, the diameter of the dielectric column disposed in the optical waveguide unit is different from the diameter of the dielectric column other than the optical waveguide unit, and is in contact with other dielectric columns not disposed in the optical waveguide unit. It can be configured to be a value in the range without
[0045]
Further, the movement position of the dielectric pillar arranged in the optical waveguide portion is a position moved from the position of the two-dimensional periodic interval before shifting the position by a half distance of the two-dimensional periodic interval in the optical waveguide direction. You may comprise as follows.
[0046]
The photonic crystal has a structure having dielectric pillars arranged in a triangular lattice shape having a lattice constant a, the radius or half width of which is 0.2a to 0.45a, and the optical waveguide section The dielectric pillars arranged in the above can be configured to have a diameter that does not contact each other.
[0047]
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. Construct material.
[0048]
Further, in the above structure, the photonic crystal is a dielectric column arranged in a square lattice shape having a lattice constant a, a radius or a half width thereof is 0.35a to 0.45a, and the light guide A structure in which the dielectric pillars arranged in the wave portion have a diameter in a range not in contact with each other may be employed.
[0049]
Furthermore, silicon, germanium, a gallium / arsenic compound, an indium / phosphorus compound, or an indium / antimony compound is used for the dielectric thin film slab material, and silicon dioxide, A polyimide organic compound, an epoxy organic compound, an acrylic organic compound, air, or vacuum can be used.
[0050]
DETAILED DESCRIPTION OF THE INVENTION
The optical waveguide according to the first and second embodiments of the present invention is an optical waveguide having a defect structure in which a part of the lattice of the slab type two-dimensional photonic crystal is removed in a straight line. The grid arrangement on both sides sandwiching the defect is shifted so that the width is narrower than the width of one row of the grid arrangement (first embodiment) or wider (second embodiment). It is structured. With such a structure, a structure having a single mode with a low loss and a large group velocity can be realized while using the optical confinement method based on the photonic band gap and the refractive index difference as described in the prior art.
[0051]
Further, the same effect can be obtained by shifting the position of one column of low refractive index columns (air holes, etc.) in the slab type two-dimensional photonic crystal in the optical waveguide direction or changing the hole diameter. (Third Embodiment)
[0052]
The slab type two-dimensional photonic crystal is a dielectric thin film slab provided with a low refractive index column having a lower refractive index than that of the dielectric thin film slab at an appropriate two-dimensional periodic interval. It is a photonic crystal in which the upper and lower sides of a thin film slab are sandwiched between an upper cladding layer and a lower cladding layer having a refractive index lower than that of a dielectric thin film slab.
[0053]
In addition, the width of one row of the above-described lattice arrangement is a width between lattices on both sides of a defect portion in a normal defect structure except for one row of lattices of the slab type two-dimensional photonic crystal.
[0054]
Each embodiment will be described below.
<First Embodiment>
First, a first embodiment of the present invention will be described.
[0055]
5A and 5B are schematic views of an optical waveguide 1 composed of a single-line-drawn defect photonic crystal waveguide according to the first embodiment of the present invention. FIG. 5A is a top view thereof, and FIG. FIG. In the present invention, when a single-line defect is formed in an oxide-clad type two-dimensional slab photonic crystal, the defect width is adjusted so that the entire crystal lattice on both sides of the line defect is shifted, so A single waveguide mode having a large group velocity is formed below the line.
[0056]
That is, 0.2 μm thick Si layer 2, 3 μm thick SiO layer ₂ An air hole triangular lattice photonic crystal having a lattice constant a = 0.39 μm was fabricated on the SOI substrate 3 by electron beam exposure and dry etching, and a single-line defect having various widths was introduced. The width adjustment method of the defect waveguide is performed by shifting the crystal lattices on both sides sandwiching this row in a direction perpendicular to the fixed length row in the structure after the holes for one row are removed.
[0057]
The width of the defect in a normal single-line defect photonic crystal waveguide is simply defined as the distance between the centers of the nearest lattices 4 on both sides across the defect when a single line of lattice is extracted. The defect width is expressed by a constant multiple, where W is the defect width in the normal case. The photonic crystal itself has a photonic band gap between wavelengths of 1.35 μm and 1.57 μm, and no light transmission was observed in the defect-free crystal within this wavelength range. Next, the light transmission spectrum of each defect waveguide was measured. With one simple grating (with a width of 1.0 W), no light transmission was observed in the band gap wavelength region. 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.
[0058]
FIG. 6 shows waveguide mode dispersion of an optical waveguide composed of a single-line-drawn 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 same as FIG. ₂ ) Are overlaid with light lines. In the prior art shown in FIG. 7, the slope of the propagation mode below the light line (propagation mode corresponding to mode 1 in FIG. 4) is small, whereas in the present invention shown in FIG. There is a waveguide mode with a large inclination, that is, a large group velocity. It is also clear from the figure that the single mode condition is satisfied in that region.
[0059]
The wavelength region where light transmission was observed in the experiment coincided with the region where this guided mode exists, and by reducing the width, a single mode with a large group velocity was formed below the light line. Therefore, the light transmission is realized. As a result of calculating waveguide mode dispersion for various structural parameters by the time-domain finite difference method and the plane wave expansion method, a large group below the light line when the waveguide width is set between 0.50 W and 0.85 W. It was found that a guided mode with velocity was formed. Also in the experiment, light propagation was observed in this waveguide width range.
[0060]
8A and 8B show the theoretical calculation results of the waveguide mode dispersion when the waveguide widths are 0.85 W and 0.50 W. FIG. FIG. 8A shows the case of 0.85 W, and FIG. 8B shows the case of 0.50 W. When the waveguide width is between 0.85 W and 0.50 W, for example, as shown in FIG. 6 (in the case of 0.7 W), the transmission bandwidth of the waveguide is larger than the results of FIGS. 8A and 8B. Since it becomes wide, it turns out that it functions as a practical waveguide in this range.
[0061]
The reason why the above effect can be obtained by narrowing the width is as follows.
[0062]
As described in the prior art, in the typical single-line defect state shown in FIG. 2, the photonic band gap and a lower frequency region than the light line (hereinafter, this region is referred to as an α region). This mode (circled in the figure) has a very small group velocity and is not practical. Therefore, pay attention to the mode with the largest group velocity outside the band gap.
[0063]
When the waveguide width is narrowed, the refractive index is equivalently lowered, and this bottom mode can be shifted to the high frequency side. Thus, this mode can be used in the α region. Therefore, a mode with a large group velocity can be realized within the band gap and under the light line.
[0064]
As a method for lowering the refractive index of the waveguide portion, there are a method of using a medium having a small refractive index in the waveguide portion and a method of lowering the refractive index equivalently by making a hole in the waveguide portion. Note that a method corresponding to making a hole in the waveguide portion will be described in the third embodiment.
[0065]
<Second Embodiment>
Next, a second embodiment of the present invention will be described.
[0066]
FIG. 9 is a schematic diagram of an optical waveguide 1A made up of a single-line-drawn 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 widen the defect width. A single waveguide mode having a small propagation loss is formed above the light line.
[0067]
That is, 0.2 μm thick Si layer 2, 3 μm thick SiO layer ₂ An air hole triangular lattice photonic crystal having a lattice constant a = 0.39 μm was fabricated on the SOI substrate 3 by electron beam exposure and dry etching, and a single-line defect having various widths was introduced. The width of the defect waveguide is adjusted by adopting a structure in which the crystal lattices on both sides sandwiching this row are shifted in the direction of separating in the structure after removing the holes for one row.
[0068]
The defect width of the second embodiment is 1.5 times that of one row of lattices. Also in this case, the definition of the width is expressed by a constant multiple, where W is the distance between the centers of the nearest lattices 4 on both sides of the defect when a single row of lattices is removed as shown in the figure. The photonic crystal itself has a photonic band gap between wavelengths of 1.35 μm and 1.57 μm, and no light transmission was observed in the defect-free crystal within this wavelength range.
[0069]
Next, the light transmission spectrum of each defect waveguide was measured. With one simple grating (with a width of 1.0 W), no light transmission was observed in the band gap wavelength region. 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 region within the band gap.
[0070]
FIG. 10 shows the waveguide mode dispersion of the optical waveguide 1A composed of the one-line-drawn defect photonic crystal waveguide according to the second embodiment of the present invention. As in FIG. 2, cladding (in this case SiO ₂ ) Light lines are shown superimposed. The wavelength region in which 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 diffraction loss is reduced and the leakage problem is solved by increasing the width. That is, a low-loss waveguide mode is formed despite being above the light line.
[0071]
FIG. 11 shows the single-mode bandwidth (indicated by the dotted line) above the light line of the single-line defect photonic crystal waveguide according to the second embodiment of the present invention and the waveguide width dependence of propagation loss ( FIG. 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. When the waveguide width exceeds 1.6 W, the single mode bandwidth cannot be obtained. This occurs because the mode within the photonic band gap in FIG. 10 shifts to the low frequency side by increasing the width. Propagation loss is reduced by increasing the width.
[0072]
As a result of calculating waveguide mode dispersion and propagation loss for various structural parameters by the time domain finite difference method, the propagation mode satisfying the single mode condition on the light line when the waveguide width is set to 1.6 W or less. It was found that the propagation loss becomes a practical loss value of 20 dB / mm or less at 1.3 W or more. 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 satisfies the single mode condition can be obtained.
[0073]
That is, it is difficult to realize a structure having a mode with a large group velocity on the lower frequency side than the light line of the clad in the wide waveguide, but the perturbation received from the crystal becomes small by widening the waveguide. As a result, the effect of increasing the group velocity and making it difficult to be diffracted appears. As a result, the propagation loss is effectively reduced despite the fact that it is in a higher frequency region than the light line of the cladding as shown in FIG. Will be able to. However, since the effective refractive index of the waveguide increases as the width increases, the single mode band shown in FIG. 10 shifts to the low frequency side as described above, and the single mode band gradually narrows. Therefore, to realize a single mode, the waveguide width needs to be 1.6 W or less.
[0074]
Now, a method for calculating a waveguide mode dispersion curve (FIGS. 6, 7, 10 and the like) used for explaining the present invention will be described here.
[0075]
This dispersion curve is obtained by analyzing the Maxwell equation by a calculation method called the FDTD method (Finite Difference Time Domain method), and the analysis method will be described below.
[0076]
First, the crystal band analysis performed in crystal engineering or the like will be briefly described. A periodic structure such as a crystal can be expressed by repeating a unit cell. It is a well-known fact that a field in such a structure is a Bloch wave. The band analysis is an operation of applying a periodic boundary condition that satisfies the Bloch condition to the boundary where the unit cells touch and extracting a field satisfying this condition as an eigenmode. At this time, the subject of analysis is the Schrödinger equation, and since the spatial potential distribution included in the equation varies depending on the material, various band structures exist. This concept is applied to a photonic crystal that is a periodic structure. However, since the object is light, not electrons, the equation handled is the Maxwell equation, and the refractive index (dielectric constant) distribution is used for calculation instead of the potential distribution.
[0077]
Next, an operation for extracting the eigenmode using the FDTD method will be described. The FDTD method is a method in which the Maxwell equation is differentiated between time and space, and an electromagnetic field of light propagating in a given structure (a spatial distribution of refractive index (dielectric constant)) is obtained by sequential calculation with respect to time. This is not a calculation method for directly obtaining eigenvalues. However, it is possible to obtain a mode suitable for a given structure by the following method.
[0078]
First, an appropriate initial field is given within a given structure. When performing sequential calculations, fields that fit the given structure survive and others are deceived. 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, the Bloch condition used for the calculation is a function of the wave number, so the frequency at which the peak appears is a function of the wave number. This is a band diagram of a photonic crystal.
[0079]
Next, mode calculation of a 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, line defects are introduced inside the crystal, and the periodicity is broken in the direction perpendicular to the line defects. Therefore, the structure shown in FIGS. 12A to 12C is a unit cell. In other words, a periodic boundary condition that satisfies the Bloch condition is applied in the light propagation direction, and a periodic structure in which the waveguides are arranged at a distance that does not significantly interfere with each other in the orthogonal direction is realized at the mirror surface boundary. Set an area to absorb light leaking without being in mode.
[0080]
FIG. 12A shows the waveguide structure shown in FIG. 12B is a structure in which the dotted line portion shown in FIG. 12A is extracted, and FIG. 12C is a three-dimensional view of FIG. 12B, which is a unit cell of a photonic crystal waveguide. The wavenumber-frequency graph described above can be drawn by solving the Maxwell equation for this unit cell by the FDTD method. This is the dispersion curve shown in the description of the present invention.
[0081]
In this calculation, if the mode stays in the waveguide for a long time, modes other than the eigenmode can be picked up as a spectrum peak. Therefore, it is possible to analyze the leaky mode on the 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 also utilized in the present invention. In addition, since this calculation method can calculate the confinement time of light in the waveguide, it has a feature that a theoretical propagation loss can be shown using a group velocity (energy propagation velocity) obtained from a dispersion curve.
[0082]
In the waveguide whose width is narrowed, it has been confirmed that there is a single mode region including not only the low frequency side of the light line of the cladding layer but also the high frequency side of the line.
[0083]
In the first and second embodiments, Si and SiO are used as the medium. ₂ For example, silicon-on-insulator (SOI) can be used for manufacturing, but it is clear that the effects of the present invention are not limited to this material. When constructing a defect waveguide using a slab-type photonic crystal in which a low-refractive-index dielectric is generally disposed under a thin film of a high-refractive-index medium, the waveguide width is the same as in the above embodiment. It is generally possible to form a waveguide mode that satisfies the single mode condition below or above the light line by adjusting the.
[0084]
For example, a structure using a semiconductor such as gallium arsenide compound (GaAs, InGaAs, InGaAsP, etc.), indium / phosphorus compound (InP, etc.) instead of Si, or SiO ₂ It is clear that the same effect can be expected even in a structure using a material such as polymer or alumina instead of. In addition, here, the lower cladding is made of SiO. ₂ Although only the case where the upper part is air is described, the upper and lower sides are both SiO. ₂ It is clear that the same effect can be expected even in a structure in which a dielectric cladding such as is arranged.
[0085]
<Third Embodiment>
Next, a third embodiment of the present invention will be described as Example 3-1 to Example 3-2.
[0086]
In this embodiment, a low-refractive index cylinder or a low-refractive index polygonal column having a refractive index lower than that of the dielectric thin film slab is optically guided to the optical waveguide portion of the conventional optical waveguide described with reference to FIGS. By providing it parallel to the direction, the frequency of the waveguide mode, the group velocity, etc. are improved.
(Example 3-1)
FIG. 13 is a diagram illustrating a slab type two-dimensional photonic crystal waveguide in Example 3-1. (A) is a top view of the optical waveguide, and (b) is a cross-sectional view taken along line AA ′. It is a figure explaining a wave structure.
[0087]
That is, cylinders made of a dielectric material having a refractive index lower than that of the dielectric thin film slab are arranged in a triangular lattice shape, and one column of these cylinders existing in the optical waveguide portion is arranged in the optical waveguide direction in the period of the triangular lattice (lattice It is a structure that is moved by a half distance of (constant). Further, if necessary, the diameter of the column arranged at this moving position is changed according to the optical waveguide characteristics.
[0088]
Here, as an example, the refractive index of the dielectric thin film slab 11, the low refractive index column 15, the upper cladding layer 16, the lower cladding layer 17, and the low refractive index column A13 is set to n. ₁ = 3.5, n ₂ = 1.0, n ₃ = N ₄ = 1.46, n ₅ = 1.0, the radius of the low refractive index column 15 other than the optical waveguide 12 is 0.275a, the thickness of the dielectric thin film slab 11 is 0.50a, and the low refractive index column A13 installed in the optical waveguide 12 is The characteristics of the waveguide structure will be described with a radius of 0.225a.
[0089]
FIG. 14 is a diagram illustrating a waveguide mode in the photonic crystal waveguide according to Example 3-1 of the present invention. (A) is a figure which shows the dispersion | distribution relationship of a waveguide electromagnetic field mode, (b) is a figure which shows a magnetic field component perpendicular | vertical to the dielectric thin film slab of modes 1 and 2, (c) is a dielectric of mode 3 It is a figure which shows a magnetic field component perpendicular | vertical to a body thin film slab.
[0090]
In this case, the dispersion relation of the waveguide electromagnetic field mode 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. It 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 throughout the effective propagation constant region. As a result, the effective frequency band is expanded to about 4.7%, and the group velocity is also improved.
[0091]
Further, when this example is applied to a communication infrared light having a wavelength of about 1.55 μm, Si is applied to the dielectric thin film slab 11, air (or vacuum) is applied to the low refractive index column 15 and the low refractive index column A13, Other parts are SiO ₂ , The period of the triangular lattice is about 0.42 μm, the radius of the low refractive index column 15 other than the optical waveguide unit 12 is about 0.115 μm, and the radius of the low refractive index column A13 installed in the optical waveguide unit 12 is 0. 094 μm, which is a value that can be manufactured using conventional semiconductor processing technology.
[0092]
In this example, the description is given assuming that the radius of the low refractive index column A13 disposed at the moving position of the optical waveguide unit 12 is 0.225a. By changing this radius, the frequency or group of the waveguide mode is changed. It is clear that the speed can be changed. Considering the structure of the waveguide, that is, considering the range where the other low refractive index columns not arranged in the optical waveguide portion do not contact each other, the radius of the low refractive index column A13 is the minimum width of the optical waveguide portion 12. About 0.1 to 0.4 times is realistic.
[0093]
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 unit 12, but these may be a polygonal column such as a rectangle or a hexagon. Similar effects can be expected. In addition, as the range of the diameters of these cylinders and polygonal columns, the same effect as the above-described example can be expected within the range that allows the existence of the photonic band gap. 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 portion is about 1 to 1.7, according to the theoretical calculation by the plane wave expansion method described above, These diameters are in the range of approximately 0.2a to 0.45a, preferably 0.275a to 0.375a, which is realistic and highly effective.
[0094]
Further, in the above example, a cylinder is used for the low refractive index column A13 disposed at the movement position of the optical waveguide unit 12, but the same effect can be expected even if it is an elliptical column or a polygonal column.
[0095]
In addition, the refractive index of a cylinder or the like for providing a photonic crystal, the refractive index of a cladding sandwiching the dielectric thin film slab up and down, and the refractive index of a cylinder or the like provided in the waveguide section are the refractive If it is lower than the rate, the same effect can be expected even if the value is the same or different.
[0096]
In addition, regarding the material, when the guided light is in the infrared region for communication near the wavelength of 1.55 μm, the dielectric thin film slab has a high refractive index and can transmit infrared rays, and has few problems in workability and stability. As materials, silicon, germanium, gallium / arsenic compounds, indium / phosphorus compounds, indium / antimony compounds, and the like can be used. The refractive index of these materials is approximately between 3.0 and 4.5. In addition to the dielectric thin film slab in this case, silicon dioxide, polyimide organic compounds, epoxy organic compounds, materials with low refractive index, which can transmit infrared rays, and have few problems in workability and stability, Acrylic organic compounds, air, vacuum, etc. can be used as the material. The refractive index of these materials is approximately between 1.0 and 1.7.
[0097]
These materials can be used similarly in the first embodiment and the second embodiment. Also in the third embodiment, a slab type two-dimensional photonic crystal waveguide can be manufactured using a silicon-on-insulator (SOI) substrate.
[0098]
(Example 3-2)
FIG. 15 is a diagram illustrating a slab type two-dimensional photonic crystal waveguide according to Example 3-2 of the present invention. (A) is a top view of an optical waveguide, (b) is AA 'sectional drawing.
[0099]
In the previous Example 3-1, in order to provide a photonic crystal outside the optical waveguide section 12, a low refractive index region having a cylindrical shape or a polygonal column is provided with a triangular lattice period. A similar effect can be expected even when a square lattice is used. That is, low refractive index columns 25 having a refractive index lower than that of the dielectric thin film slab 21 are provided in a square lattice shape, and the upper cladding layer 26 having a lower refractive index than that of the dielectric thin film slab 21 is provided above and below the dielectric thin film slab 21. In the structure sandwiched between the lower clad layers 27, one row of the low refractive index columns 25 arranged in the optical waveguide direction existing in the portion to be the optical waveguide portion 22 is arranged in the optical waveguide direction in the lattice constant of the square lattice. The diameter of the low refractive index column 25 arranged at this moving position is changed according to the optical waveguide characteristics if necessary.
[0100]
In this case, the range of the diameter of the low refractive index column that gives the photonic crystal can be a range that allows the existence of the photonic band gap. According to the theoretical calculation by the plane wave expansion method, specifically, the refractive index of the dielectric thin film slab 21 is about 3 to 4.5, and the refractive index of the other low refractive index portions is about 1 to 1.7. In this case, the diameters of these low refractive index columns 25 are approximately in the range of 0.35a to 0.45a.
In addition, the operating principle is the same as that of Example 3-1 for the supplemental matters regarding 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 Example 3-1. This is also true in the present embodiment.
[0101]
The present invention is not limited to the above-described embodiments, and various modifications and applications can be made within the scope of the claims.
[0102]
【The invention's effect】
As described above, the optical waveguide of the present invention is an optical waveguide having a defect structure in which a part of the lattice of the slab type two-dimensional photonic crystal is removed in a straight line, and the width of the defect structure is one row of the lattice arrangement. Because the structure of the lattices on both sides of the defect is shifted so that it is narrower than the width of the minute, the light of the structure that can form a single guided mode with a large group velocity below the light line A waveguide can be provided.
[0103]
Further, in the optical waveguide having a defect structure in which a part of the lattice of the slab type two-dimensional photonic crystal is removed in a straight line, the defect is formed so that the width of the defect structure is wider than the width of one column of the lattice arrangement. Since the arrangement of the grids on both sides of the sandwiched structure is shifted, it is possible to provide an optical waveguide having a structure capable of forming a single waveguide mode with a low loss above the light line.
[0104]
Furthermore, the position of the low-refractive-index column part constituting one row of the lattice of the slab type two-dimensional photonic crystal is made to be phased in the waveguide direction, and further, the lattice hole diameter is changed to be larger below the light line. An optical waveguide having a structure capable of forming a single waveguide mode having a group velocity can be provided.
[0105]
Therefore, according to the present invention, it is possible to provide an ultra-compact optical waveguide structure with improved group velocity and low loss.
[Brief description of the drawings]
FIGS. 1A and 1B are structural schematic views of a typical single-line defect photonic crystal waveguide in a conventional row, in which FIG. 1A is a top view and FIG. 1B is a cross-sectional view along BB ′;
FIG. 2 is a diagram for explaining waveguide mode dispersion of a typical single-line-drawn defect photonic crystal waveguide in a conventional example.
FIGS. 3A and 3B are structural schematic diagrams of a typical single-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 for explaining a waveguide mode in a typical single-line-drawn defect photonic crystal waveguide in a conventional row, and FIG. 4A is a diagram showing a dispersion relation of a waveguide electromagnetic field mode; (b) is a figure which shows a magnetic field component perpendicular | vertical to the dielectric thin film slab of mode 1, (c) is a figure which shows a magnetic field component perpendicular to the dielectric thin film slab of mode 2.
FIGS. 5A and 5B are schematic views of an optical waveguide composed of a single-line-drawn defect photonic crystal waveguide according to the first embodiment of the present invention, where FIG. 5A is a top view thereof, and FIG. 5B is a cross-sectional view along BB ′. is there.
FIG. 6 is a diagram for explaining waveguide mode dispersion of an optical waveguide composed of a single-line-drawn defect photonic crystal waveguide according to the first embodiment of the present invention.
FIG. 7 is a diagram for explaining waveguide mode dispersion of a typical single-line-drawn defect photonic crystal waveguide in a conventional example.
FIG. 8 is a diagram showing a theoretical calculation result of waveguide mode dispersion when the waveguide width is 0.85 W (a) and 0.50 W (b).
FIGS. 9A and 9B are schematic views of an optical waveguide composed of a single-line-drawn defect photonic crystal waveguide according to a second embodiment of the present invention, where FIG. 9A is a top view and FIG. 9B is a cross-sectional view along BB ′; is there.
FIG. 10 is a diagram for explaining waveguide mode dispersion of an optical waveguide composed of a single-line-drawn defect photonic crystal waveguide according to the second embodiment of the present invention.
FIG. 11 illustrates propagation loss above the cladding light line of an optical waveguide composed of a single-line defect photonic crystal waveguide according to the second embodiment of the present invention and the dependence of the single mode bandwidth on the waveguide width. It is a figure to do.
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 an optical waveguide, (b) is AA 'sectional drawing.
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 figure which shows the dispersion | distribution relationship of a waveguide electromagnetic field mode, (b) is a figure which shows a magnetic field component perpendicular | vertical to the dielectric thin film slab of modes 1 and 2, (c) is a dielectric of mode 3 It is a figure which shows a magnetic field component perpendicular | vertical 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 an optical waveguide, (b) is AA 'sectional drawing.
[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 section
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

Claims (6)

In 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 to form a defect structure,
The first width, which is the width between the lattices on both sides of the defect portion in the defect structure, is defined as the space 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 structure that is narrower than the second width,
When the first width is lower than the light line of the cladding and within the photonic band gap with respect to the light transmitted through the slab type two-dimensional photonic crystal waveguide, the first width and the second width A slab type two-dimensional photonic crystal waveguide characterized by having a width that forms a single mode having a group velocity larger than the group velocity of light passing through a waveguide having the same width.   2. The slab type two-dimensional photonic according to claim 1, wherein the first width of the defect portion is any value between 0.50 times and 0.85 times the second width. Crystal waveguide. The slab type two-dimensional photonic crystal waveguide according to claim 1 or 2 , wherein the lattice is an air hole type triangular lattice. The slab type two-dimensional photonic crystal waveguide according to any one of claims 1 to 3, wherein the slab type two-dimensional photonic crystal has an oxide cladding or a polymer cladding.   The slab type two-dimensional photonic crystal waveguide according to claim 4, wherein the slab type two-dimensional photonic crystal is manufactured using a Si1icon-On-Insulator (SOI) substrate.   The slab type two-dimensional photonic crystal waveguide according to any one of claims 1 to 5, wherein a slab thickness of the slab type two-dimensional photonic crystal waveguide is about half of a lattice constant.

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