JP5273051B2 - Photonic crystal - Google Patents

Description

  The present invention relates to a photonic crystal in which a line defect waveguide is formed, and more particularly to a structure of a bent portion of a line defect waveguide.

  In recent years, a technique for realizing an optical integrated circuit in which optical components are integrated has been desired. An optical circuit in which optical components such as an optical switch, a wavelength filter, and a 3 dB coupler (optical coupler) are connected via an optical waveguide such as an optical fiber is known. However, if a plurality of optical components can be integrated in a small chip, the volume, power consumption, and manufacturing cost of the optical circuit can be drastically reduced.

  Many technologies have been developed to realize optical integrated circuits. One of the technologies aimed at realizing an optical integrated circuit is a photonic crystal technology. Photonic crystal or photonic crystal is a general term for structures whose refractive index changes periodically. In this specification, unless otherwise specified, “photonic crystal” and “photonic crystal” are used as synonyms.

  Photonic crystals exhibit various special optical characteristics due to the periodic structure of the refractive index distribution. The most typical feature is a photonic band gap (PBG). Light can be transmitted through the photonic crystal. However, if the periodic refractive index change in the photonic crystal is sufficiently large, light in a specific frequency band cannot propagate in the photonic crystal. The frequency band (or wavelength band) of light that can propagate through the photonic crystal is called a photonic band. On the other hand, the frequency band (or wavelength band) of light that cannot propagate through the photonic crystal is called a photonic band gap (PBG). The photonic band gap means a gap existing between photonic bands. There may be multiple PBGs in different frequency bands. The photonic bands divided by the PBG may be referred to as the first band, the second band, and the third band from the smaller frequency.

  If there is a minute defect in the photonic crystal that breaks the periodic structure of the refractive index distribution (periodicity of the refractive index distribution), the light in the PBG is confined in the minute defect. In that case, only light having a frequency corresponding to the size of the defect is confined, so that the photonic crystal functions as an optical resonator. Therefore, such a photonic crystal can be used as a frequency (wavelength) filter.

  In addition, when micro defects are continuously arranged in a row in the photonic crystal and a line defect is formed in the crystal, the light in the PBG is confined in the line defect and along the line defect. Propagate. Therefore, such a photonic crystal can be used as an optical waveguide. The above optical waveguide formed in the photonic crystal is called a line defect waveguide.

  If an optical filter or an optical waveguide is formed, an optical functional element such as an optical modulator or an optical switch can be configured by the optical filter or the optical waveguide. Furthermore, an optical circuit can be configured if main optical functional elements are formed in the photonic crystal and these optical functional elements are connected to each other. For these reasons, photonic crystals are expected as an optical integrated circuit platform.

  Here, in order to use the effect of PBG in three directions of x, y, and z perpendicular to each other, it is necessary that the refractive index distribution of the photonic crystal has a three-dimensional periodic structure. However, since the three-dimensional periodic structure is complicated, the manufacturing cost increases. Therefore, a photonic crystal whose refractive index distribution has a two-dimensional periodic structure (hereinafter sometimes referred to as “two-dimensional photonic crystal”) is often used. Specifically, a two-dimensional photonic crystal having a finite thickness is used in which the refractive index distribution in the in-plane direction of the substrate has periodicity, but the refractive index distribution in the thickness direction of the substrate does not have periodicity. In that case, confinement of light in the thickness direction of the substrate is realized not by the effect of PBG but by total reflection due to the difference in refractive index.

  However, the characteristics of the two-dimensional photonic crystal having a finite thickness do not completely match the characteristics of the two-dimensional photonic crystal having an infinite thickness. However, if the refractive index distribution in the thickness direction of a two-dimensional photonic crystal having a finite thickness is mirror-symmetric in the light propagation region, the optical characteristics of the two-dimensional photonic crystal are two-dimensional photonic crystals having an infinite thickness. It almost coincides with the optical properties of the crystal. The operation prediction of a device based on a two-dimensional photonic crystal having an infinite thickness is much easier than the operation prediction of a device based on a two-dimensional photonic crystal having a finite thickness. Therefore, if a two-dimensional photonic crystal whose refractive index distribution has mirror symmetry can be used, device design becomes easy.

  There are several specific structures of the two-dimensional photonic crystal of finite thickness realized so far. Among them, a pillar-type square lattice photonic crystal has a feature that light propagation speed in a line defect waveguide is slow in a wide band. That is, a low group velocity. In general, when a waveguide having a low propagation speed is used, an optical circuit having the same function can be realized by a short waveguide. Therefore, a line defect waveguide using a columnar square lattice photonic crystal is suitable for an optical integrated circuit.

  FIG. 1 is a schematic diagram showing the structure of a line defect waveguide of a columnar square lattice photonic crystal having a finite thickness. In the columnar square lattice photonic crystal shown in the figure, a low dielectric constant material 1 includes a cylinder 2a having a finite height made of a high dielectric constant material and a cylinder 2b having a smaller diameter than the cylinder 2a. Arranged in a square lattice. However, the low dielectric constant material and the cylindrical material do not need to be crystalline, and may be amorphous.

  In the case of the photonic crystal shown in FIG. 1, the cylinder 2a is a complete photonic crystal cylinder, whereas the cylinder 2b is smaller in diameter than the cylinder 2a. Therefore, the cylinder 2b is regarded as a defect introduced into the complete crystal. In the following description, the former is referred to as a “non-defect line column” and the latter is referred to as a “defect column”, “defect column”, or “line defect column” in order to distinguish between a perfect crystal cylinder and a cylinder corresponding to a defect. There is a case. However, the line defect column itself is not defective. The line defect pillars 2b shown in FIG. 1 are arranged in a line on a certain straight line. A line defect waveguide is formed by the line of the line defect pillars 2b and the surrounding non-defect line pillars 2a.

  In the line defect waveguide of the cylindrical square lattice photonic crystal shown in FIG. 1, the line of the line defect column corresponds to the core in the total reflection type waveguide such as an optical fiber. Further, the lattice of non-defective line pillars on both sides of the line of line defect pillars and the surrounding dielectric material correspond to the cladding. In the case of a total reflection type waveguide, a core and a clad are indispensable for forming the waveguide. In the case of a line defect waveguide, in order to form a waveguide, a line defect and its surrounding non-defective line pillar or dielectric material are essential. In the following description, the line defect column may be referred to as a “line defect”.

  In order to increase the density of the optical wiring in the optical integrated circuit, a bent waveguide having a high light transmittance in a wide band is required.

  When the propagation direction of the guided light propagating through the line defect waveguide of the columnar square lattice photonic crystal is changed by 90 °, the direction of the line defect waveguide is changed by 90 ° in the middle. In the following description, a structure in which the direction of the line defect waveguide is changed by 90 ° in the middle may be referred to as a “90 ° bent structure”.

  Even if the line defect waveguide is simply bent by 90 ° in one place, the light transmission characteristics are not improved unless a specific condition is satisfied. Non-Patent Document 1 discloses an improved 90 ° bending structure that is different from a simple 90 ° bending structure. The bending structure disclosed in Non-Patent Document 1 is based on the premise that the cross-sectional area of the line defect column forming the line defect waveguide is zero. In the 90 ° bending structure disclosed in Non-Patent Document 1, linear waveguides having different 90 ° orientations are connected via oblique waveguides having an inclination of 45 ° with respect to these linear waveguides. The length of the oblique waveguide corresponds to one to several periods of the grating.

  However, the bending structure disclosed in Non-Patent Document 1 is a structure devised for a square lattice photonic crystal having an infinite thickness, and cannot be actually realized. This is because a line defect waveguide constituted by a line defect column having a zero cross-sectional area cannot confine light in the thickness direction. In order to confine light in the thickness direction, it is necessary to use a line defect waveguide including a line defect column having a finite diameter. However, when the cross-sectional area of the line defect column has a finite value, the light transmission characteristic is not good in a bending structure in which a waveguide having a short inclination angle of 45 ° is interposed.

  When the cross-sectional area of the line defect column has a finite value, if a specific condition is satisfied, even a simple 90 ° bent structure shows a high transmittance in a wide band. This is described in Non-Patent Document 2.

  According to Non-Patent Document 2, the electromagnetic field structure of guided light in the vicinity of a line defect column is approximately represented by the sum of two plane wave electromagnetic fields. The two plane wave electromagnetic fields travel while intersecting each other with the center line of the line defect column as the mirror symmetry axis. The specific condition for increasing the light transmittance of the line defect waveguide having a 90 ° bent structure is that the traveling directions of the two intersecting plane waves are orthogonal.

Therefore, if the line defect waveguide is designed so as to satisfy the above-mentioned specific condition, it is possible to realize a line defect waveguide having a 90 ° bent structure with high light transmittance in a wide band.
1996 Physical Review Letter, Vol. 77, pages 3787-3790 (A. Mekis, JC Chen, I. Kurland, S. Fan, PR Villeneuve, and JD Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides , ”Phys. Rev. Lett., Vol. 77, pp. 3787-3790, 1996.) 2005 Journal of Optical Society of America B, B22, 11, 11472 (M. Tokushima, J. Ushida, A. Gomyo, and H. Yamada, “Efficient Transmission Mechanisms for Waveguides with 90 ° Bends in Pillar Photonic Crystals ”, J. Opt. Soc. Am. B 22, 11, 2472 (2005).)

  However, in actual optical circuit design, it may not be possible to design a line defect waveguide in consideration of only the light transmission characteristics of a portion (bent portion) where the propagation direction of guided light is changed. For example, the line defect waveguide has a feature that the propagation speed of guided light, that is, the group velocity is low, so that the line defect waveguide can be used as an optical delay line. In that case, in order to design a line defect waveguide having a slower group velocity, the cross-sectional area of the line defect column must be made larger than the optimum value at which the light transmittance of the bent portion is maximized.

  Conversely, in order to increase the group velocity and increase the transmission speed of the optical signal, the cross-sectional area of the line defect column must be made smaller than the optimum value.

  The present invention has been made in view of the above situation. An object of the present invention is to achieve both a light transmission characteristic and other characteristics in a bent portion of a line defect waveguide formed in a photonic crystal body.

  The photonic crystal body of the present invention is a photonic crystal body in which a line defect waveguide including a line defect whose direction is changed by 90 ° is formed. The line defect has a first straight portion, a second straight portion, and a curved portion. The first straight line portion is formed along the straight line Y. The second straight line portion is formed along a straight line X orthogonal to the straight line Y. The curved portion connects the end portions of the first straight portion and the second straight portion that are close to each other.

  The first straight line portion is composed of a plurality of line defect columns in which the center of gravity of the cross section in the xy plane including the straight line X and the straight line Y is arranged on the straight line Y. The second straight line portion includes a plurality of line defect columns in which the center of gravity of the cross section in the xy plane is arranged on the straight line X. The curved line portion has the center of gravity of the cross section of the line defect column closest to the intersection point P between the straight line X and the straight line Y among the plurality of line defect columns constituting the first straight line portion. And a plurality of line defect columns arranged on a curve connecting the center of gravity of the cross section of the line defect column closest to the intersection P among the plurality of line defect columns constituting the second straight line portion. .

  According to the present invention, the above object can be achieved.

  The above and other objects, features, and advantages of the present invention will become apparent from the following description and reference to the accompanying drawings illustrating an example of the present invention.

It is a schematic diagram showing a typical structure of a columnar square lattice photonic crystal of finite thickness. FIG. 3 is a schematic cross-sectional view showing the arrangement of cylinders forming the photonic crystal optical waveguide according to the first embodiment. It is typical sectional drawing which shows arrangement | positioning of the cylinder which forms the conventional photonic crystal optical waveguide. It is a figure which shows the electromagnetic field distribution of the light which propagates the line defect optical waveguide shown in FIG. It is a figure which shows the electromagnetic field distribution of the light which propagates the line defect optical waveguide shown in FIG. FIG. 6 is a schematic cross-sectional view showing the arrangement of cylinders forming a photonic crystal optical waveguide according to Embodiment 2. 6 is a schematic cross-sectional view showing an example of an arrangement of cylinders forming a photonic crystal optical waveguide according to Embodiment 3. FIG. FIG. 10 is a schematic cross-sectional view showing another example of the arrangement of the columns forming the photonic crystal optical waveguide according to the third embodiment.

  The waveguide mode of the line defect waveguide formed in the photonic crystal body has an inherent electromagnetic field distribution that propagates along the center line of the line defect. The light transmittance of the waveguide mode of the line defect waveguide is strictly 100% according to the definition of the waveguide mode. When a bent portion (90 ° bend) in which the propagation direction of the guided light is changed by 90 ° exists in the middle of the line defect waveguide, the electromagnetic field distribution of the guided light may deviate from the center line of the line defect in the bent portion. is there. The light transmittance is reduced by an amount corresponding to the position of the electromagnetic field distribution being shifted from the center line of the line defect, and at the same time, reflection occurs. Here, the fact that the electromagnetic field distribution deviates from the center line of the line defect means that the center of the electromagnetic field distribution (the position where the electromagnetic field intensity is greatest) deviates from the center line of the line defect.

In the present invention, when the electromagnetic field distribution shifts, attention is paid to the fact that the electromagnetic field distribution shifts to the inner side (inner angle side) or the outer side (outer angle side) of the 90 ° bend. The present invention is characterized in that the line defect of the line defect waveguide is composed of two straight portions and a curved portion that smoothly connects the ends of the straight portions. For example, when the electromagnetic field distribution is shifted to the outer angle side, the curve portion is formed along a curve inscribed in the inner angle of 90 ° bending, thereby avoiding the shift of the electromagnetic field distribution to the outer angle side. In other words, the line defect columns constituting the curved portion are arranged on the curve inscribed in the inner angle of the 90 ° bend or in the vicinity thereof, thereby avoiding the shift of the electromagnetic field distribution to the outer angle side.
(Embodiment 1)
Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings.

  FIG. 2 is a schematic cross-sectional view showing the arrangement of cylinders constituting the photonic crystal body according to the present embodiment. On the other hand, FIG. 3 is a schematic cross-sectional view showing the arrangement of cylinders constituting a conventional photonic crystal.

  In the photonic crystal body shown in FIG. 2, a large number of cylinders 10a are arranged in a square lattice shape, and a line defect column 10b is arranged in the many cylinders 10a. In the photonic crystal body shown in FIG. 3, a large number of cylinders 20a are arranged, and a line defect column 20b is arranged in the many cylinders 20a. In other words, the line defect 10 is formed in the photonic crystal shown in FIG. 2, and the line defect 20 is formed in the photonic crystal shown in FIG.

  Further, the line defect 10 shown in FIG. 2 and the line defect 20 shown in FIG. 3 are common in that they are line defects constituting a line defect optical waveguide having a bent portion whose propagation direction of guided light is changed by 90 °. To do.

  Next, differences will be described. The line defect 20 shown in FIG. 3 includes a first straight line portion 3 and a second straight line portion 4. The first straight line portion 3 is composed of a plurality of line defect pillars 20b arranged on the straight line Y. On the other hand, the second straight line portion 4 is constituted by a plurality of line defect columns 20b arranged on a straight line X orthogonal to the straight line Y. As a result, the line defect 20 shown in FIG. 3 is steeply bent by 90 ° at the position of the line defect column 20b disposed at the intersection P between the straight line X and the straight line Y. In other words, the bent portion of the line defect 20 shown in FIG. 3 is configured by one line defect column 20b.

  On the other hand, the line defect 10 formed in the photonic crystal body shown in FIG. 2 includes a first straight portion 3, a second straight portion 4, and a curved portion that gently connects the straight portions 3 and 4. And 5. The curved portion 5 connects the end point (end point) of the first straight line portion 3 and the start point (start point) of the second straight line portion 4 along a gentle curve.

  The first straight line portion 3 shown in FIG. 2 is constituted by a plurality of line defect pillars 10b arranged on the straight line Y. On the other hand, the second straight line portion 4 is constituted by a plurality of line defect pillars 10b arranged on a straight line X orthogonal to the straight line Y. The curved line part 5 is composed of a plurality of line defect columns 11b and 11b'11b 'arranged on a curved line 6 connecting the end point of the first straight line part 3 and the start point of the second straight line part 4. Here, the end point of the first straight line portion 3 is the point where the line defect column 10b closest to the intersection P among the line defect columns 10b constituting the first straight line portion 3 is arranged. Say. The starting point of the second straight line portion 4 is the point where the line defect column 10b closest to the intersection P among the line defect columns 10b constituting the second straight line portion 4 is arranged. Say. The curved line 6 is inscribed at an angle where the straight line X and the straight line Y are orthogonal to each other, and is bent in one direction.

  The line defect column 10b and the line defect columns 11b and 11b'11b 'have the same shape and size. The reason why the different signs are used here is to distinguish the line defect columns constituting the straight portions 3 and 4 from the line defect columns constituting the curved portion 5.

  In short, the bent portion of the line defect 10 shown in FIG. 2 is constituted by a plurality of line defect columns 11b and 11b′11b ′, and the line defect columns 11b and 11b′11b ′ are arranged to form a curve. Yes.

  Here, the center of gravity of the cross section of each line defect column 10b constituting the first straight line portion 3 is on the straight line Y. The center of gravity of the cross section of each line defect column 10b constituting the second straight line portion 4 is on the straight line X. Further, the center of gravity of the cross section of each of the line defect columns 11 b, 11 b ′, 11 b ′ constituting the curved portion 5 is on the curved line 6. In other words, the center of gravity of the cross section of each line defect column 11b, 11b ', 11b' is shifted from the straight lines X, Y. In other words, the line defect pillars 11b, 11b 'and 11b' constituting the curved portion 5 are deviated from the periodic arrangement of the square lattice.

  In order to explain the positions of the three line defect columns 11b and 11b′11b ′ constituting the curved portion 5 more clearly, an X and Y coordinate system having an origin at an intersection P between the straight line X and the straight line Y is defined. . In such a coordinate system, the right direction in FIG. 2 from the origin is the + X direction, and the left direction is the -X direction. Further, the upper direction in FIG. 2 from the origin is defined as + Y direction, and the lower direction is defined as −Y direction.

  The line defect column 11b located at the apex (center) of the curved portion 5 is shifted from the origin in the + X direction and the −Y direction by a distance (ax1, ay1) corresponding to 12.5% of the lattice constant. One of the two line defect columns adjacent to the line defect column 11b (the line defect column 11b ′ close to the X axis) is a distance (ay2) corresponding to 5% of the lattice constant in the −Y direction from the X axis. ) Is just off. The other of the two line defect columns adjacent to the line defect column 11b (the line defect column 11b ′ adjacent to the Y axis) is a distance corresponding to 3.75% of the lattice constant in the + X direction from the Y axis. It is shifted by (ax2). The distance (ax2) corresponding to 3.75% of the lattice constant is a distance corresponding to 30% of the distance (ax1).

  According to the numerical calculation, when the deviation amount (distance ax1, ay1) with respect to the origin of the line defect column 11b is 12.5% of the lattice constant, the transmission characteristic of the bent portion of the waveguide is maximized. However, if the distance (ax1, ay1) is within the range of 5% to 20% of the lattice constant, substantially the same improvement in transmission characteristics can be obtained.

  Further, according to the numerical calculation, when the deviation amount (distance ax2, ay2) of the line defect column 11b ′ is 30% of the deviation amount (distance ax1, ay1) of the line defect column 11b, the transmission through the bent portion of the waveguide is performed. Maximum characteristics. However, if the distance (ax2, ay2) is within the range of 20% to 60% of the distance (ax1, ay1), substantially the same improvement in transmission characteristics can be obtained.

  The characteristics of the curved portion 5 constituting the bent portion of the line defect waveguide shown in FIG. 2 will be described in comparison with the bent portion of the conventional line defect waveguide shown in FIG.

  The line defect column 11b located at the center of the bent portion of the line defect waveguide shown in FIG. 2 corresponds to the line defect column 20b located at the intersection P shown in FIG. Moreover, two line defect pillars 11b 'and 11b' adjacent to the line defect pillar 11b shown in FIG. 2 are two lines adjacent to the line defect pillar 20b located at the intersection P shown in FIG. It corresponds to the defect pillars 20b and 20b. That is, the three line defect pillars 11b, 11b ′, 11b ′ constituting the curved line part 5 shown in FIG. 2 are inside the bent portion of the bending part with respect to the three line defect pillars 20b shown in FIG. It is displaced. The line defect column is made of a high dielectric constant material. Since the light tends to be distributed in the high dielectric constant medium, the electromagnetic field distribution of the guided light is shifted in the direction in which the line defect pillars 11b, 11b 'and 11b' are shifted. As a result, the electromagnetic field distribution is returned to the center line of the line defect. If the electromagnetic field distribution is returned to the center line of the line defect, whether the line defect waveguide is observed from the light incident side to the bent portion or the line defect waveguide is observed from the light exit side, The wave light always propagates on the center line of the line defect, so that the distortion of the guided light is eliminated. As a result, the reduction and reflection of the light transmittance of the guided light are eliminated.

  In the simulation performed by the present inventors, the best results were obtained when the positions of the line defect pillars 11b, 11b 'and 11b' shown in FIG. 2 were as described above. Specifically, it is as follows.

  FIG. 4 is a map showing the electromagnetic field distribution of guided light propagating through the line defect optical waveguide shown in FIG. On the other hand, FIG. 5 is a map showing the electromagnetic field distribution of the guided light propagating through the line defect optical waveguide shown in FIG. In any of the maps, light enters the waveguide from the lower side of the paper and is emitted toward the right side. In addition, the illustrated map shows the electromagnetic field distribution obtained by simulation.

  As can be seen from FIG. 4, the electromagnetic field of the guided light propagating through the line defect waveguide shown in FIG. 3 deviates from the periodic arrangement of the grating to the outside of the bend at the bending point where the direction of the waveguide changes. This deviation of the electromagnetic field causes a decrease in light transmittance. In addition, as shown in FIG. 4, the magnitude (strength) of the electromagnetic field in the vicinity of the bending point is larger than the surroundings, and a local mode having resonator characteristics is generated. This is a factor that increases the wavelength dependency of the light transmittance in the vicinity.

  On the other hand, FIG. 5 shows that the electromagnetic field of the guided light propagating through the line defect waveguide according to the present embodiment does not deviate from the periodic arrangement of the grating even at the bending point where the direction of the waveguide changes. This is because as a result of arranging the three line defect columns 11b, 11b ′, 11b ′ constituting the bent portion (curved portion 5) as described above, the electromagnetic field is pulled back to the inside of the bent portion. is there. Therefore, the light transmittance at the bent portion of the line defect waveguide according to the present embodiment is higher than the light transmittance at the bent portion of the conventional line defect waveguide. Furthermore, in the line defect waveguide according to the present embodiment, an increase in the electromagnetic field in the vicinity of the inflection point is not observed, and a local mode that causes a reflection does not appear.

  In order to prevent the electromagnetic field of guided light from deviating from the periodic arrangement of the grating at the bending point where the direction of the waveguide changes, as another means, a non-linear defect column arranged inside the bending of the bending part The area may be reduced.

  Light has the property of bending toward a higher refractive index. If a column having a large cross-sectional area and a high refractive index is arranged inside the bent portion, the average refractive index in the vicinity of the column increases. Therefore, the guided light passing through the bent portion is attracted to the inside.

  This will be described more specifically. The cross-sectional area of the non-linear defect column 10c shown in FIG. 2 in the xy plane is the xy plane of the non-linear defect column 10a ′ adjacent to the line defect constituting the first linear portion 3. 100 to the arithmetic average value (area S2) of the cross-sectional area in the xy plane and the cross-sectional area in the xy plane of the non-linear defect 10a ″ adjacent to the line defect constituting the second straight line portion The area corresponds to 120%. Here, the non-linear defect column 10 c is a non-linear defect column that is closest to each of the three line defect columns 11 b, 11 b ′, and 11 b ′ constituting the bent portion. Furthermore, as described above, the line defect column 11b is the line defect column 11b closest to the intersection point P. The two line defect columns 11b 'and 11b' are line defect columns adjacent to the line defect column 11b.

  According to the simulation, the effect of correcting the position of the electromagnetic field in the bent portion can be obtained when the cross-sectional area of the non-linear defect column 10c is within the above range. In particular, when the cross-sectional area of the non-linear defect column 10c is an area corresponding to 110% of the arithmetic mean value (area S2), the effect of correcting the position of the electromagnetic field in the bent portion is great.

  So far, a phenomenon has been described in which guided light passing through the bent portion deviates from the periodic arrangement of the grating. This phenomenon is a phenomenon in which the orbit of guided light deviates from the orbit of the bent portion. However, the transmittance also decreases when the distribution of the light energy in the traveling direction of the guided light becomes non-uniform. This is because the refractive index distribution in the vicinity of the line defect column row loses periodicity and becomes non-uniform.

  That is, the transmission speed of guided light is high in a portion where the refractive index is low, and is low in a portion where the refractive index is large. If the distribution of the portion with a small refractive index and the portion with a large refractive index, including their sizes, maintain perfect periodicity, the guided light travels regularly with a constant rhythm as a whole. However, if the periodicity of the refractive index distribution is disrupted due to the presence of the bent portion, the regularity of the local transmission speed of the guided light is disrupted, and the overall transmittance of the guided light is reduced.

  When the average refractive index in the vicinity of the bent portion of the line defect waveguide decreases, the decrease in the refractive index may be compensated for by increasing the cross-sectional area of the line defect column constituting the bent portion. This will be described more specifically. The cross-sectional area of the line defect column 11b shown in FIG. 2 in the xy plane is an arithmetic average of the cross-sectional areas of the line defect columns 10b at the ends of the first straight line portion 3 and the second straight line portion 4 The value (area S1), the cross-sectional area in the xy plane of the non-linear defect column 10a adjacent to the first straight line portion 3, and the xy plane of the non-linear defect column 10a adjacent to the second straight line portion 4 The area corresponding to 100% to 140% of the area (S12) corresponding to the arithmetic average value with the cross-sectional area (area S2). The line defect pillars 10b at the ends of the first straight part 3 and the second straight part 4 are two line defect pillars adjacent to each other. Further, as described above, the line defect pillar 11b is the line defect pillar closest to the intersection P.

  According to the simulation, the effect of correcting the position of the electromagnetic field in the bent portion is obtained when the cross-sectional area of the line defect column 11b in the xy plane is within the above range. In particular, when the cross-sectional area of the line defect column 11b in the xy plane is 120% of the area (S12), the effect of correcting the position of the electromagnetic field in the bent portion is great.

As described above, according to the present invention, the light transmittance at the bent portion of the line defect waveguide is improved as compared with the conventional case. Therefore, even if the line defect waveguide is designed by giving priority to characteristics other than the light transmittance at the bent portion, the light transmittance at the bent portion is maintained equal to or higher than the conventional one. Therefore, it is possible to achieve both the light transmittance at the bent portion and other characteristics, and to improve the characteristics of the entire optical integrated circuit using the photonic crystal. As a result, high integration and productivity improvement of the optical integrated circuit are realized.
(Embodiment 2)
Next, another example of the embodiment of the photonic crystal optical waveguide of the present invention will be described. In the first embodiment, the case where the bent portion of the line defect waveguide is configured by three line defect pillars has been described. However, simply shifting the three-line defect column from the periodic arrangement may not sufficiently improve the light transmittance at the bent portion of the line-defect waveguide. For example, when the crossing angle of the plane wave electromagnetic fields constituting the waveguide mode is greatly deviated from 90 °, the light transmittance is not sufficiently improved. In such a case, the light transmittance can be increased by increasing the number of line defect columns constituting the bent portion.

  FIG. 6 shows the arrangement of cylinders (crystals) constituting the photonic crystal body according to the present embodiment. However, the basic structures of the photonic crystal body according to the present embodiment and the photonic crystal body according to the first embodiment are the same. Therefore, the same components are replaced with descriptions using the same reference numerals.

The difference between the photonic crystal body of this example and the photonic crystal body of the first embodiment is the number of line defect columns constituting the curved portion of the line defect waveguide.
The curved portion 5 shown in FIG. 6 is composed of a total of five line defect columns obtained by adding the line defect columns 12b ′ and 12b ′ adjacent to the two line defect columns 11b ′ and 11b ′ shown in FIG. All of these five line defect columns constituting the curved portion 5 are shifted to the inside of the bent portion with respect to the straight line X and the straight line Y. The distance (ax1, ay1) corresponding to 12.5% of the lattice constant from the intersection point P to the + X direction and the −Y direction from the intersection P is the largest, with the amount of deviation of the line defect column 11b located at the center (vertex) of the curved portion 5 being maximized. It is only shifted. Further, the line defect columns 11b ′ and 11b ′ adjacent to the line defect column 11b are shifted by a distance (ax2, ay2) corresponding to 40% of the shift amount of the line defect column 11b. Specifically, the line defect column 11b ′ adjacent to the straight line Y is shifted from the straight line Y in the + X direction by a distance (ax2). On the other hand, the line defect column 11b ′ adjacent to the straight line X is shifted from the straight line X in the −Y direction by a distance (ay2). Further, the shift amount of the line defect columns 12b ′ and 12b ′ is the smallest, and is shifted by a distance (ax3, ay3) corresponding to 50% of the shift amount of the line defect columns 11b ′ and 11b ′. Specifically, the line defect column 12b ′ adjacent to the straight line Y is shifted from the straight line Y in the + X direction by a distance (ax3). On the other hand, the line defect column 12b ′ adjacent to the straight line X is shifted from the straight line X in the −Y direction by a distance (ay3). The reason why the shift amount of each line defect column constituting the curved portion 5 is set as described above is to distribute each line defect column on a smooth curve.

  When the curved portion is constituted by three line defect columns, the amount of deviation in the X and Y directions of the line defect column (for example, the line defect column 11b shown in FIG. 2) located at the apex (center) of the curve portion is It is desirable that the range be 5% to 20% of the lattice constant. The deviation amount of the line defect column closest to the central line defect column is desirably 20% to 60% of the deviation amount of the central line defect column. Furthermore, it is desirable that the shift amount of the line defect column that is second adjacent to the center line defect column is 30% to 70% of the shift amount of the line defect column that is closest to the center line defect column.

Including the case where the curved portion has an untargeted structure, the number of line defect columns constituting the curved portion is not limited. At least the line defect column at the apex of the 90 ° bend, that is, the line defect column closest to the intersection P between the straight line X and the straight line Y only needs to deviate from the periodic arrangement. However, if the curved portion is composed of five line defect pillars, a sufficient effect of improving transmission characteristics can be obtained. When the curved portion is constituted by a smaller number of line defect pillars, the method of determining the position of each line defect pillar becomes simple and productivity is improved.
(Embodiment 3)
So far, in the conventional line defect waveguide, some of the embodiments of the present invention have been described on the assumption that the electromagnetic field distribution of the guided light is shifted outside the center line of the line defect in the bent portion.
However, in some cases, the electromagnetic field distribution of the guided light is shifted inward from the center line of the line defect at the bent portion of the line defect waveguide. In such a case, as shown in FIG. 7, the line defect pillars 11b, 11b ′ and 11b ′ constituting the curved portion 5 are shifted to the outside of the bent portion. As a result, the electromagnetic field is pulled back to the outside of the bent portion of the waveguide. In the example shown in FIG. 7, the line defect column 11 is shifted from the intersection (origin) P in the −X direction and the + Y direction. One of the two line defect columns 11b ′ is shifted from the straight line Y in the −X direction, and the other of the two line defect columns 11b ′ is shifted from the straight line X in the + Y direction.

  Further, as shown in FIG. 8, the line defect columns 12b 'and 12b' adjacent to the two line defect columns 11b 'and 11b' shown in FIG. 7 may also be shifted to the outside of the bend. In any case, the other line defect columns 11b 'and 12b' are arranged so as to draw a smooth curve toward the bending point (line defect column 11b).

  In order to prevent the electromagnetic field of guided light from deviating from the periodic arrangement of the grating at the bending point where the direction of the waveguide changes, as another means, a non-linear defect column arranged inside the bending of the bending part The area may be reduced.

  Light has the property of bending toward a higher refractive index. If a column having a small cross-sectional area and a high refractive index is arranged inside the bent portion, the average refractive index in the vicinity of the column is lowered. Therefore, the guided light passing through the bent portion is pushed outward.

  Make it more specific. The cross-sectional area of the non-linear defect column 10c shown in FIG. 2 in the xy plane is the xy plane of the non-linear defect column 10a ′ adjacent to the line defect constituting the first linear portion 3. 80 to the arithmetic mean value (area S2) of the cross-sectional area in the xy plane and the cross-sectional area in the xy plane of the non-linear defect 10a ″ adjacent to the line defect constituting the second straight line portion The area corresponds to 100%. Here, the non-linear defect column 10 c is a non-linear defect column that is closest to each of the three line defect columns 11 b, 11 b ′, and 11 b ′ constituting the bent portion. Furthermore, as described above, the line defect column 11b is the line defect column 11b closest to the intersection point P. The two line defect columns 11b 'and 11b' are line defect columns adjacent to the line defect column 11b. According to the simulation, the effect of correcting the position of the electromagnetic field in the bent portion can be obtained when the cross-sectional area of the non-linear defect column 10c is within the above range. In particular, when the cross-sectional area of the non-linear defect column 10c is an area corresponding to 90% of the arithmetic mean value (area S2), the effect of correcting the position of the electromagnetic field in the bent portion is great.

  So far, a phenomenon has been described in which guided light passing through the bent portion deviates from the periodic arrangement of the grating. This phenomenon is a phenomenon in which the orbit of guided light deviates from the orbit of the bent portion. However, the transmittance also decreases when the distribution of the light energy in the traveling direction of the guided light becomes non-uniform. This is because the refractive index distribution in the vicinity of the line defect column row loses periodicity and becomes non-uniform.

  When the average refractive index in the vicinity of the bent portion of the line defect waveguide increases, the increase in the refractive index may be compensated by reducing the cross-sectional area of the line defect column constituting the bent portion. This will be described more specifically. The cross-sectional area of the line defect column 11b shown in FIG. 2 in the xy plane is the arithmetic average of the cross-sectional areas in the xy plane of the line defect columns 10b at the ends of the first straight line portion 3 and the second straight line portion 4. The value (area S1), the cross-sectional area in the xy plane of the non-linear defect column 10a adjacent to the first straight line portion 3, and the xy plane of the non-linear defect column 10a adjacent to the second straight line portion 4 The area corresponding to 60% to 100% of the area (S12) corresponding to the arithmetic average value with respect to the cross-sectional area (area S2). The line defect pillars 10b at the ends of the first straight part 3 and the second straight part 4 are two line defect pillars adjacent to each other. Further, as described above, the line defect pillar 11b is the line defect pillar closest to the intersection P.

  According to the simulation, the effect of correcting the position of the electromagnetic field in the bent portion is obtained when the cross-sectional area of the line defect column 11b in the xy plane is within the above range. In particular, when the cross-sectional area of the line defect column 11b in the xy plane is 80% of the area (S12), the effect of correcting the position of the electromagnetic field in the bent portion is great.

  Although some of the embodiments of the photonic crystal optical waveguide of the present invention have been described above, the present invention is not limited to the above embodiments. For example, the numerical value described above as an amount of deviation with respect to the periodic arrangement of the line defect columns constituting the curved portion is an example, and can be appropriately changed as necessary. In this case, it is desirable to optimize the number of line defect columns and the amount of deviation constituting the curved portion by FDTD simulation (finite difference time domain simulation). Specifically, it is confirmed that the deviation of the electromagnetic field distribution with respect to the center line of the line defect is corrected while changing the number of line defect columns and the amount of deviation.

  In addition, it is possible to displace a cylinder other than the line defect column constituting the curved portion, and to increase or decrease the cross-sectional area thereof. Furthermore, the column does not necessarily have to be a cylinder, and may have another shape such as a quadrangular column or an octagonal column.

  Next, the method for producing the photonic crystal of the present invention will be outlined. The photonic crystal of the present invention can be produced using an SOI wafer (Silicon On Insulator Wafer). For example, an SOI wafer in which a buried oxide film having a thickness of 2.0 μm and a silicon active layer having a thickness of 1.0 μm are formed can be used.

First, the pattern shown in FIG. 2, FIG. 7, etc. is drawn using an electron beam exposure technique. When the wavelength of the guided light is 1.55 μm, the lattice constant is 0.4 μm, the diameter of the cylinder is 0.24 μm, and the diameter of the line defect column is 0.16 μm.
Next, the silicon active layer is vertically processed according to the drawn resist pattern by anisotropic dry etching.

  Thereafter, the remaining resist pattern is removed with acetone, and finally an ultraviolet curable resin having the same refractive index of 1.45 as that of the buried oxide film is applied and cured.

  This application claims the priority on the basis of Japanese application Japanese Patent Application No. 2007-257617 for which it applied on October 1, 2007, and takes in those the indications of all here.

Claims (15)

A photonic crystal formed with a line defect waveguide in which the direction of the line defect is changed by 90 °,
The line defect includes a first straight line portion formed along a straight line Y, a second straight line portion formed along a straight line X orthogonal to the straight line Y, the first straight line portion, and the first straight line portion. A curved portion connecting the adjacent ends of the two straight portions,
The first straight line portion is composed of a plurality of line defect columns in which the center of gravity of a cross section in an xy plane including the straight line X and the straight line Y is arranged on the straight line Y,
The second straight portion is composed of a plurality of line defect columns in which the center of gravity of the cross section in the xy plane is arranged on the straight line X,
The curved line is a line whose center of gravity of the cross section in the xy plane is closest to the intersection P between the straight line X and the straight line Y among the plurality of line defect columns constituting the first straight line part. Arranged on a curve connecting the center of gravity of the cross section of the defective column and the center of gravity of the cross section of the line defect column closest to the intersection point P among the plurality of line defect columns constituting the second straight line portion. A photonic crystal composed of a plurality of line defect pillars.   The photonic crystal body according to claim 1, which has a square lattice structure.   Of the line defect columns constituting the curved portion, the line defect column closest to the intersection point P is a distance corresponding to 5% to 20% of the lattice constant (a) along the straight line X from the intersection point P. (Ax1) is shifted to the inside or outside of the curve, and is shifted to the inside or outside of the curve by a distance (ay1) corresponding to 5% to 20% of the lattice constant (a) along the straight line Y. The photonic crystal body according to claim 2, which is disposed at a position.   The photonic crystal body according to claim 3, wherein the distance (ax1) and the distance (ay1) are equal.   The photonic crystal body according to claim 4, wherein the distance (ax1) and the distance (ay1) are distances corresponding to 12.5% of the lattice constant (a). Of the two line defect pillars adjacent to the line defect pillar closest to the intersection P,
The line defect pillars close to the straight line Y are arranged at positions shifted from the straight line Y along the straight line X by a distance (ax2) corresponding to 20% to 60% of the distance (ax1).
The line defect pillars close to the straight line X are arranged along the straight line Y by a distance (ay2) corresponding to 20% to 60% of the distance (ay1). The photonic crystal body according to any one of claims 3 to 5, wherein   The photonic crystal body according to claim 6, wherein the distance (ax2) and the distance (ay2) are equal.   The photonic crystal body according to claim 7, wherein the distance (ax2) and the distance (ay2) are equivalent to 40% of the distance (ax1) and the distance (ay1). Of the two line defect columns that are second adjacent to the line defect column closest to the intersection P,
The line defect column adjacent to the straight line Y is arranged at a position displaced from the straight line Y along the straight line X by a distance (ax3) corresponding to 30% to 70% of the distance (ax2).
The line defect pillar closer to the straight line X is arranged at a position shifted from the straight line X along the straight line Y by a distance (ay3) corresponding to 30% to 70% of the distance (ay2). The photonic crystal body according to any one of claims 6 to 8, wherein   The photonic crystal body according to claim 9, wherein the distance (ax3) and the distance (ay3) are equal.   The photonic crystal body according to claim 10, wherein the distance (ax3) and the distance (ay3) are 50% of the distance (ax2) and the distance (ay2). The cross-sectional area in the xy plane of the non-linear defect column that is closest to each line defect column that constitutes the curved portion is:
The cross-sectional area in the xy plane of the non-linear defect column adjacent to the line defect constituting the first linear portion and the non-linear defect column adjacent to the line defect constituting the second linear portion The area corresponding to 80% to 100% of the area (S2) corresponding to the arithmetic average value with the cross-sectional area in the xy plane, or the area corresponding to 100 to 120% of the area (S2). The photonic crystal body according to any one of claims 1 to 11.   The cross-sectional area in the xy plane of the non-linear defect column that is closest to each line defect column that constitutes the curved portion is an area corresponding to 90% of the area (S2) or the area (S2). The photonic crystal body according to claim 12, which has an area corresponding to 110%. The cross-sectional area of the line defect column closest to the intersection P in the xy plane is
An area (S1) corresponding to the arithmetic average value of the cross-sectional areas in the xy plane of the line defect pillars arranged at the ends adjacent to each other of the first straight part and the second straight part;
The cross-sectional area in the xy plane of the non-linear defect column adjacent to the line defect column constituting the first straight portion and the non-line adjacent to the line defect column constituting the second straight portion. An area corresponding to 60% to 100% of an area (S2) corresponding to an arithmetic average value of the cross-sectional area in the xy plane of the defective column (S2), or The photonic crystal body according to any one of claims 1 to 13, which is an area corresponding to 100% to 140% of the area (S12).   The cross-sectional area in the xy plane of the line defect column closest to the intersection P is an area corresponding to 80% of the area (S12) or an area corresponding to 120% of the area (S12). The photonic crystal body according to claim 14.

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