JP2007011219A - Photonic crystal - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a photonic crystal with long-distance transmission loss being reduced or prevented over the whole region of a photonic crystal structure, inside the structure of which an optical waveguide is provided. <P>SOLUTION: In the photonic crystal, a large number of dots, having a second refractive index constitute an ordered lattice in a continuous body that has a first refractive index. The photonic crystal is characterized in that the fluctuations within a range where regularity is kept for generating photonic band gap as a photonic crystal is given at least to one of dot diameter or dot pitch over the whole region, where at least defects as an optical waveguide is provided. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a photonic crystal.

  A photonic crystal is a man-made material in which a regular lattice is composed of a large number of dots having a second refractive index in a continuous body having a first refractive index, and a region in which light cannot exist (photonic band gap). : PBG), it is expected to be used as a device for controlling the traveling direction and intensity of light. Here, since the refractive index has a direct relationship of [dielectric constant = the square of the refractive index] with respect to the dielectric constant, “refractive index” may be replaced with “dielectric constant”.

  One of the forms of the photonic crystal is a two-dimensional photonic crystal, which can be produced, for example, by forming through holes (dots) having a diameter of about 100 nm at a lattice position of a diamond crystal lattice at a pitch of 250 nm on an SOI silicon wafer. The incident infrared light can be controlled by the band gap.

  In the photonic crystal structure, the dot pitch that defines the spacing of the regular lattice is constant, and a light (or electromagnetic wave) waveguide called a line defect is provided in the structure, and the light (or electromagnetic wave) is directed to a predetermined path. Can lead.

  However, there is a problem that transmission loss increases at a constant distance (for example, several tens of centimeters), and a long-distance optical wiring cannot be realized using a line defect as an optical waveguide. This is thought to be because resonance occurs due to the relationship between the wavelength and the grating pitch.

  In relation to this, Patent Document 1 proposes changing the dot interval of the line defect portion or changing the size of the dot adjacent to the defect. However, the proposed method suppresses the deterioration of switching characteristics due to a sudden change in reflectance at the resonator part due to the fluctuation of the wavelength when the resonator is configured by defects, and the entire photonic crystal structure. The long-distance transmission loss of the optical waveguide cannot be reduced or prevented.

  Further, Patent Document 2 discloses a hole constituting a lattice in a PBG lattice constituted by an array of holes arranged in a triangular manner in relation to the principle of generating a desired frequency characteristic by introducing a defect into the lattice structure. It is shown that some of them are eliminated to form a gap, or a large-sized hole is arranged instead of this gap (page 50, line 17 to line 21, FIG. 37). In addition, holes of the same size are arranged at equal intervals to form the main photonic band gap region PBG, and at the boundary of this region, the size of the holes is gradually increased to the lattice positions corresponding to the main band gap structure. It has also been shown that the packing density is reduced as the distance from the band gap region decreases (see page 52, line 3 to line 10, figure). 43).

  While this may be effective in reducing transmission loss at each location addressed as described above, it is not possible to reduce or prevent long distance transmission loss of the optical waveguide for the entire photonic crystal structure.

JP 2004-334190 A (paragraphs 0137 to 0138, FIG. 11) JP-T-2002-51952 (50 pages, 17 lines to 21 lines, Fig. 37, 52 pages, 3 lines to 10 lines, Fig. 43)

  In view of the above-described conventional problems, an object of the present invention is to provide a photonic crystal in which long-distance transmission loss is reduced or prevented in at least the entire area where the optical waveguide is provided.

In order to achieve the above object, the photonic crystal of the present invention is a photonic crystal in which a large number of dots having a second refractive index constitute a regular lattice in a continuum having a first refractive index. ,
Fluctuation within a range that can maintain regularity for generating a photonic band gap as a photonic crystal is imparted to at least one of the dot diameter and the dot pitch over at least the entire area where the defect as the optical waveguide is provided. It is characterized by.

  In the photonic crystal of the present invention, the fluctuation of the lattice regularity of the photonic crystal that causes the resonance occurs over the entire area where the optical waveguide exists, and the degree of this fluctuation functions as a photonic crystal. Therefore, the long-distance optical transmission in which the occurrence of resonance is effectively suppressed and the transmission loss caused by the resonance is effectively reduced can be realized.

  FIG. 1 shows a three-dimensional structure of a photonic crystal to which the present invention is applied. The illustrated photonic crystal 100 is fabricated on an SOI (Silicon On Insulator) wafer as a whole. That is, the SOI wafer includes a Si oxide film 12 formed on a Si substrate 10 and a single crystal Si thin film 14 formed thereon by a SIMOX (Separation by Implantation of Oxygen) method. A part of the Si oxide film 12 between the substrate Si10 and the single crystal Si 14 is removed to make a cavity 16, and both surfaces of the single crystal Si 14 are free surfaces, reflection due to a difference in refractive index at the interface with the Si oxide film 12, etc. This prevents unnecessary phenomena from occurring. A large number of through holes 18 are formed in the single crystal Si layer 14 in this state to form a regular lattice 20.

  As a wafer for forming the photonic crystal 100, for example, an SOI wafer having a diameter of 6 inches (150 mm) can be used. An example of a typical size of each part is as follows.

<Examples of photonic crystal dimensions>
Si single crystal layer 14: thickness 300 nm (refractive index: 3.9)
Si insulating film 12: thickness 200 nm (dielectric constant: 3.9)
Si substrate 10: thickness 675 μm
Dot arrangement: Staggered or latticed (in the example shown, latticed)
Dot diameter: 50 nm
Dot pitch: 250 nm
Dot formation region: 10 mm × 10 mm range of 6-inch wafer FIG. 2A shows a conventional diamond dot arrangement constituting the regular lattice 20 and a line defect 22 as a waveguide. The Si single crystal 14 as a continuous body in which the dots 18 are arranged is not particularly shown, but the space between the dots 18 is continuously filled with the Si single crystal 14.

  That is, a large number of dots (through holes or air) having the second refractive index 1 form a regular lattice in the single crystal Si continuum having the first refractive index 3.9.

  The dots 18 are all circular with the same diameter, and are arranged at a constant dot pitch to constitute a regular lattice 20. For example, the light L travels from right to left in a line defect 22 provided as an optical waveguide in the illustrated region. At that time, transmission loss occurs due to resonance with the regular lattice 20.

  In order to prevent this, the present invention provides a regularity for generating a photonic band gap as a photonic crystal in at least one of the dot diameter and the dot pitch over the entire area where the defect as the optical waveguide is provided. Fluctuation within the range that can be maintained was added.

  2 (2) and 2 (3) show an embodiment of a dot array to which fluctuation is applied according to the present invention.

  In the embodiment shown in FIG. 2 (2), the pitch is fluctuated while the diameter of the dots 18 constituting the diamond-type lattice 30 is fixed. However, the fluctuation range is limited to a range from the lower limit of the pitch to the upper limit of the pitch necessary for generating the photonic band gap.

  The dots 18 are all circular with an equal diameter, and are arranged at a dot pitch having fluctuations within the above range to form a regular lattice 30. The light L travels from right to left in a line defect 32 provided as an optical waveguide in the illustrated region, for example. At this time, the regular lattice 30 has fluctuations in regularity, so that the occurrence of resonance is suppressed and transmission loss is reduced.

  In contrast, in the embodiment shown in FIG. 2 (3), the pitch diameter is fluctuated while the pitch of the dots constituting the diamond-type lattice is fixed. However, the fluctuation range is limited to a range from a dot diameter lower limit to a dot diameter upper limit necessary for generating a photonic band gap.

  The dots 18 are the same constant dots as in FIG. 2 (1), with the shape being circular and the diameter varied variously, and the shape of the dot being elliptical and varying the major axis and minor axis. The regular lattice 40 is configured by being arranged at a pitch. The light L travels from right to left in a line defect 42 provided as an optical waveguide in the illustrated region, for example. At this time, the regular lattice 40 has fluctuations in regularity, thereby suppressing the occurrence of resonance and reducing transmission loss.

  Thus, in the present invention, the fluctuation of the dot diameter includes not only changing the diameter of the circle while maintaining the dot shape in a circle but also changing the dot shape from a circle to an ellipse. However, the range of the major axis and the minor axis of the ellipse is limited to the range from the lower limit of the dot diameter necessary for generating the photonic band gap to the upper limit of the dot diameter. The embodiment shown in FIG. 2 (3) includes both circular and elliptical dots of various sizes.

  In the embodiments shown in FIG. 2 (2) and FIG. 2 (3), the fluctuation is applied only to the dot pitch and the fluctuation is applied only to the dot diameter, but the fluctuation is simultaneously applied to both the dot pitch and the dot diameter. May be.

  As described above, in the present invention, transmission loss due to resonance is provided by providing fluctuations within a range in which generation of a photonic band gap can be ensured to the regularity of the dot grating over at least the entire area where defects as an optical waveguide are provided. The long-distance optical wiring having high transmission performance can be realized by effectively suppressing the occurrence of the above.

  An example of a specific procedure for imparting fluctuation to the dot arrangement according to the present invention will be described.

  Basically, with respect to a regular dot array such as a lattice or staggered pattern, the coordinates of each dot are converted with a random number (pseudorandom number) within a certain range, and fluctuations are imparted to the dot array. The certain range of random numbers is a range in which a photonic band gap for functioning as a photonic crystal is generated by the dot arrangement after conversion. For example, if the coordinate conversion amount of each dot and the conversion amount of the dot diameter are suppressed to within 5%, a random number is set so that the conversion amount is within 5% when functioning as a photonic crystal depending on the dot arrangement after conversion. Set the range.

  The random number (pseudorandom number) may be generated by any method. As an example, a case will be described in which pseudorandom numbers are generated as described below and the coordinates of each dot are converted.

(1) Generation of virtual lattice A virtual lattice is generated in accordance with the dot arrangement to which fluctuation is applied. For example, when a fluctuation is given to a dot arrangement of 5 dots × 5 dots, a grid of 5 squares × 5 squares is generated.

  If the dot array is huge, a virtual grid is generated according to a part of the entire dot array, a fluctuation applied to a part of the array is generated, and the fluctuation is applied to the remaining part. This also applies to dot arrays. For example, when the dot arrangement to which fluctuation is applied is 1,000,000 dots × 1,000,000 dots, fluctuation is generated for a part of the dot arrangement of 1,000 dots × 1,000 dots, and this fluctuation is This also applies to the remaining dot array.

  FIG. 3 shows a virtual grid of 5 squares × 5 squares, which corresponds to a dot arrangement of 5 dots × 5 dots that gives fluctuations. The size of the square A may be set arbitrarily. Here, the side a of the square A is 20.

  Note that the lattice shown in FIG. 3 is only for generating pseudo-random numbers, and is not related to the actual lattice of photonic crystals.

(2) Randomly disposing points on each square A point P is provided on each square A in a random arrangement. At this time, an average of N points P is provided in each cell A. That is, N × 5 × 5 points P are randomly provided on a 5 × 5 grid. N is set according to a certain range of random numbers for giving fluctuation to the dot array. In this embodiment, N = 30. That is, an average of 30 points P per square A are randomly provided for the entire grid of 5 squares × 5 squares. This state is shown in FIG.

(3) Calculation of dot conversion amount for each square [Number of points P in square A] / N is calculated for each square. This value is used as a conversion amount when converting the coordinates of each dot 18 of the photonic crystal. Here, the conversion amount is the movement amount of the dot coordinates, the change amount of the dot diameter, and the deformation amount of the dot shape.

  If the difference in the amount of conversion between adjacent cells is too large and moire occurs in the converted photonic crystal, the difference in the amount of conversion between adjacent cells is gently reduced by means using a spline function or the like. Can be adjusted.

(4) Conversion of dot arrangement The actual dot arrangement of the photonic crystal is converted according to the conversion amount calculated above. That is, the conversion amount obtained for the 5 squares × 5 squares is applied to the dot arrangement of 5 dots × 5 dots of the photonic crystal. Specifically, the coordinate conversion of each dot 18 is performed by multiplying the conversion value of each square A by the coordinate value of the corresponding dot 18. Note that the amount of conversion of each square A may be applied to the diameter of the corresponding dot 18 (including deformation that makes a circle oval).

  FIG. 5 shows an example in which both dot coordinates and dot diameter are converted. FIG. 5 (1) is a rule array without fluctuation before conversion, and FIG. 5 (2) is a rule array with fluctuation after conversion. 5 (1), the dots 18 are all circular with the same diameter and the dot pitch is constant, whereas in the array with fluctuations in FIG. 5 (2), the dots 18 are individually elliptical. The fluctuation of the diameter including the change and the fluctuation of the pitch between the dots are given.

  According to the present invention, a photonic crystal is provided in which long-distance transmission loss is reduced or prevented for the entire area where the optical waveguide is provided in the photonic crystal structure.

FIG. 1 is a perspective view showing the basic structure of a two-dimensional photonic crystal. FIG. 2 is a plan view showing (1) a conventional regular lattice without fluctuation, (2) a regular grid in which fluctuation is applied to the dot pitch according to the present invention, and (3) a regular grid in which fluctuation is applied to the dot diameter according to the present invention. It is. FIG. 3 is a plan view showing a virtual lattice for calculating a conversion amount for giving fluctuation to the dot arrangement. FIG. 4 is a plan view showing a state in which dots are randomly arranged on the virtual grid of FIG. 3 in order to calculate a conversion amount for giving fluctuation to the dot arrangement. FIG. 5 is a plan view showing (1) a conventional dot arrangement based on a regular arrangement and (2) a fluctuation dot arrangement obtained by converting the dot arrangement (1) based on the calculated conversion amount.

Explanation of symbols

100 Photonic crystal 10 Si substrate 12 Si oxide film 14 Single crystal Si thin film 16 Cavity 18 Through hole (dot)
20, 30, 40 Regular lattice 22, 32, 42 Optical waveguide (line defect)

Claims (1)

In a photonic crystal in which a large number of dots having a second refractive index form a regular lattice in a continuous body having a first refractive index,
Fluctuation within a range that can maintain regularity for generating a photonic band gap as a photonic crystal is imparted to at least one of the dot diameter and the dot pitch over at least the entire area where the defect as the optical waveguide is provided. Photonic crystal featuring

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