JP2007047604A - Optical resonator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an optical resonator capable of realizing a large Q value.
In an optical resonator composed of a two-dimensional photonic crystal, a line defect in which one row of vacancies in the crystal coordination direction is removed is basically used, and the distance between the centers of vacancies on both sides facing the defect is set. A line defect waveguide having a basic width is formed, and at least the holes on both sides facing the line defect in the longitudinal center of the line defect waveguide are separated from the lattice point of the crystal lattice from the center of the line defect. A mode gap barrier is introduced into the line defect waveguide with a gap between the centers of the holes on both sides larger than the basic width, and a direction along the longitudinal direction of the line defect by the mode gap barrier. Do light confinement.
[Selection] Figure 7

Description

  The present invention relates to an optical resonator, and more particularly to an optical resonator configured in a two-dimensional photonic crystal.

  The Q value (Quality factor) is widely accepted as an index representing the degree of light confinement in an optical resonator that confines light, and is expressed by the following equation.

Q = −ωU / du
Here, ω is the frequency of the resonance mode, U is the total energy of the photons stored in the optical resonator, and du is the attenuation due to leakage of the photons to the outside per unit time. That is, in order to increase the Q value, it is fundamental to reduce light leakage from the optical resonator.

Here, an optical resonator is a cladding layer made of a low refractive index material such as air or SiO ₂ having a lower refractive index above and below a thin film (hereinafter referred to as slab) having a high refractive index in an optical wavelength region such as Si (silicon). In a two-dimensional photonic crystal structure (hereinafter referred to as a photonic crystal slab) in which vertical holes (hereinafter referred to as vacancies) made of a low refractive material are arranged in a triangular lattice or a square lattice in a sandwiched structure, Only so-called point-defect optical resonators and linear-defect optical resonator structures with a finite length, in which vacancies forming a linear lattice are removed, will be considered.

  As a factor of the reduction in the Q value of this type of optical resonator, the fact that the disturbance of the shape introduced during processing is actually large, the reduction in the Q value occurs regardless of whether the present invention is applied or not. Therefore, in the following, we will consider the case where the ideal shape as designed is obtained, ignoring the shape disturbance.

  In an ideal photonic crystal slab, the light trapped in the resonance order of the isolated optical resonator formed in the photonic band gap is photonic in the direction parallel to the slab (hereinafter referred to as the in-plane direction). In principle, there is no leakage due to the band gap. Light confinement in directions other than the in-plane direction (out-of-plane direction) is provided by total reflection due to the refractive index difference between the slab and the upper and lower clads. The total reflection condition is not satisfied under any circumstances. When the critical angle determined by Snell's law is exceeded, total reflection does not occur and a part of the light is radiated out of the plane by refraction.

  Further, when a periodic structure such as a hole grating or a diffraction grating is provided in the slab or clad, out-of-plane radiation due to diffraction is also generated. The function of the frequency and wave number at the critical point where out-of-plane radiation due to refraction and diffraction begins to occur is called a light line.

  FIG. 1 shows a relationship between a band structure and a light line in a typical photonic crystal slab. In the figure, PRG indicates a photonic band gap, and a broken line indicates a light line. Light leakage due to out-of-plane radiation occurs on the upper side of the light line (Γ point side), and no leakage occurs on the lower side (M point or K point side). The light trapped in the optical resonator is localized in the real space due to the uncertainty principle, but spreads over the whole area in the wave number space (momentum space), so the electromagnetic field distribution in the real space is Fourier transformed. The distribution in the wave number space is obtained and examined.

  FIG. 1 shows a band structure of a bulk slab structure. FIG. 2 specifically shows the case of an optical resonator. In the case of a point defect optical resonator as shown in FIG. 2 (B), as shown in FIG. 2 (A), in the real space distribution, the electromagnetic field has a maximum near the center of the optical resonator and then attenuates rapidly from there. It shows a distribution that spreads out. The region where the electromagnetic field is strong is limited to a very small range near the center of the optical resonator, and the light is strongly localized.

  On the other hand, the distribution in the wave number space is significantly different from that in the real space. In the wave number space, attention must be paid to the existence of a region (also called a light cone) above the light line shown in gray in FIGS. 2 (C) and 2 (D). 2 (C) and 2 (D), the origin is the Γ point in FIG. 1, and the upper area of the light line extends from the origin. In the case of the simple point defect shown in FIG. 2B, a considerable electromagnetic field component exists also in the region above the light line as shown in FIG. In other words, it means that the optical loss due to out-of-plane radiation and the resulting decrease in the Q value are large.

  In order to improve the Q value, it is essential to reduce the intensity of the electromagnetic field distributed above the light line. In a single-point defect optical resonator, all in-plane directions are photonic bandgap confinement, and a large electromagnetic field component is distributed above the light line due to the strong periodicity of the photonic crystal, so the Q value is Limited to a few thousand at most. By arranging a plurality of point defects in series to form a multi-point defect, the resonance mode changes like a line defect waveguide, and the influence of a light line oriented perpendicular to the line defect can be almost ignored.

  As a result, the Q value becomes higher than that of a single point defect, but the Q value is limited to about several tens of thousands due to the influence of the write line remaining in the line defect direction. As a further improvement, by shifting the holes on both ends of the multipoint defect and its extension line (see Non-Patent Document 1), shifting while changing the size of the holes (see Non-Patent Document 2), etc. An attempt was made to reduce the electromagnetic field intensity on the upper side of the light line by making the electromagnetic field distribution close to a Gaussian distribution, and the Q value was improved to about 300,000 in the theoretical value and about 100,000 in the experimental value. However, since point defects and several point-defect optical resonators connected with several of them are basically affected by the periodicity of the photonic crystal, it is considered difficult to further improve the Q value in the optical resonators. Yes.

  In order to further reduce the electromagnetic field intensity on the upper side of the light line and further improve the Q value, it is necessary to confine the light in the direction of the line defect by a new method that is less affected by the periodicity of the photonic crystal. As a new method, a method of confining light by a mode gap barrier generated at the interface (heterointerface) when connecting photonic crystal waveguides having different waveguide modes is first proposed. The concept will be described with reference to FIG.

  FIG. 3 shows a basic propagation mode of a typical single-line defect waveguide in a photonic crystal slab. The vertical axis represents the normalized frequency ω, which corresponds to the light wavelength λ according to ω = a / λ (where a is a lattice constant). In the figure, there is no propagation mode below the frequency ωmg (mode gap region). In the mode gap region, light can only exist as an evanescent wave.

  Next, a mode gap barrier generated at the heterointerface will be described. By changing the width of the line defect waveguide and the lattice constant of the crystal, ωmg changes. When two line defect waveguides having different waveguide widths and lattice constants are joined (heterojunction), a difference (mode gap barrier) occurs in ωmg (ωmgl, ωmgr) on both sides of the junction. In the figure, light of ωmgl <ω ≦ ωmgr can propagate in the waveguide on the left side of the junction (the side where ωmg is low). However, such light can only penetrate from the left side of the interface to the right side as an evanescent wave and cannot enter.

  Note that the solution of the Maxwell equation becomes a pure imaginary number on the mode gap (photonic band gap) side from the barrier boundary, and light attenuates from the barrier boundary and enters a short distance as a standing wave. However, it does not progress. This is an evanescent wave, and when the mode gap barrier is sufficiently thin, light can pass through the mode gap barrier by the tunnel effect.

  Next, a double heterojunction in a line defect waveguide will be described with reference to FIG. In a structure in which both sides of a waveguide having a mode gap frequency ωw are sandwiched between waveguides having the same mode gap frequency ωb (ωw <ωb), light having a frequency satisfying ωw ≦ ω <ωb is in a region sandwiched between two heterojunctions. Be trapped. Based on this principle, an optical resonator using a double heterojunction can be realized.

  The light confinement by the mode gap barrier is physically equal to the light confinement by the photonic band gap. However, since the latter introduces a barrier with a photonic crystal, the effect of refractive index change and crystal periodicity at the end of the optical resonator cannot be reduced, whereas the former has a difference in waveguide width and lattice constant particularly in a heterojunction. By making it small, the refractive index change in the mode gap barrier and heterojunction can be made extremely small, and the influence of the periodicity of the crystal can be reduced, so the intensity of the electromagnetic field component above the light line is better than the best point defect type optical resonator It can be reduced by an order of magnitude or more, and a Q value exceeding 1 million can be realized theoretically. Further, as shown in Non-Patent Document 3, even when the resonance level exists outside the photonic bandgap in the optical resonator portion, the optical resonator is formed by forming a double heterojunction by a mode gap barrier. It becomes feasible. There are the following three methods for realizing a double heterojunction in a line defect waveguide.

  The first method changes the waveguide width (see Non-Patent Documents 3 and 4).

  The second technique changes the diameter of the holes.

  The third method changes the lattice constant.

  Although it is reported in Non-Patent Document 5 that an optical resonator is constituted by mode gap barriers generated at the bending, branching, and termination of a line defect, these are double-intentionally introduced into the line defect. It is hard to say that it is a heterojunction.

FIG. 5 shows the structure of a line defect double heterojunction optical resonator using a mode gap barrier using the first technique (see Non-Patent Documents 3 and 4). Here, in the middle of the waveguide extending in the Z-axis direction with a line defect width of 0.6 Wo (Wo = a × √3), the diameter of the nearest hole is increased to reduce the width of the line defect. A portion with 0.4 W 2 _O is formed. The control of the waveguide width can be realized with high reproducibility and high accuracy in the lithography technique, which is an advantageous method for realizing the device.

  The second method for changing the size of the holes has an advantage that the waveguide mode can be modulated without changing the lattice arrangement of the photonic crystal. However, in the existing lithography technology, there is a problem that the size control is disadvantageous in terms of accuracy compared to the control of the waveguide width and the lattice constant.

The third method for changing the lattice constant is a method in which controllability and reproducibility are easy to ensure in the lithography technique as in the first method. A heterojunction based on a difference in lattice constant was first proposed as a high-pass filter for the purpose of demultiplexing light of a single wavelength from among wavelength-multiplexed light (see Non-Patent Document 6). Later, it was applied to an optical resonator using a double heterojunction (see Non-Patent Document 7). Recently, a Q value of 20 million was reported as a theoretical value and approximately 600,000 as an experimental value (see Non-Patent Document 8). As described above, this Q value is a value that cannot be realized by a conventional point defect type optical resonator, and can be said to be an epoch-making report clearly showing the superiority of optical confinement by a mode gap barrier.
Y. Akahane, T .; Asano, and B.M. S. Song, and S.M. Noda, Nature 425, 944 (2003) Satoshi Mitsugi, Akihiko Shinya, Eiichi Kuramochi, Masaya Notomi, Tai Tshchizawa and Toshifumi Watanabe, "Resonant tunneling wavelength filters with high Q and high transmittance based on photonic crystal slabs", IEEE Lasers and Electro-Optics Society 2003 (LEOS2003), Tuscon, America, Oct. TuE3 2003 (p214-215, Vol. 1) Tatsuro Kawabata, Research on wavelength selective filter using photonic crystal waveguide, 2002 Tokai University Master thesis Tatsuro Kawabata, Masaya Notomi, Akihiko Shinya, Satoshi Futaki, Eiichi Kuramochi, Yasushi Tsuchisawa, Toshifumi Watanabe, Photonic Crystal Resonant Tunneling Filter with Spot Size Conversion Mechanism Using Mode Gap, The 64th JSAP Scientific Lecture, 1P-ZM-5 (2003) and M.P. Notomi, A .; Shinya, S .; Mitsugi, E .; Kuramochi, and HY Ryu, Optics Express 12, 1551 (2004) K. Inoshita and T.A. Baba, Electron. Lett. 39,844 (2003) B. S. Song, T .; Asano, and S.M. Noda, Science 300, 1537 (2003) Taku Asano, Fumiaki Tsuji, Yoshihiro Akabane, Susumu Noda, High Q Defect Optical Resonator Using Small Double Heterojunction of Two-dimensional Photonic Crystal Slab, The 64th Japan Society of Applied Physics, 1P-ZM-11 (2003 ) B. S. Song, S.M. Noda, T .; Asano, and Y.M. Akahane, Nature Materials, 4, 207 (2005)

  The waveguide width variable double heterojunction optical resonator described in Non-Patent Documents 3 and 4 aims to solve the situation where the photonic band gap confinement becomes invalid because the waveguide mode goes out of the photonic band gap. Therefore, the theoretical value of the Q value in the document is about several thousand at the maximum, and the feasibility of a high Q value exceeding 100,000 and the technology necessary for this are not examined or mentioned.

  Further, in Non-Patent Documents 3 and 4, only the second method for enlarging the size of a row of holes on both sides sandwiching the line defect of the waveguide in the mode gap barrier portion is described as a method for changing the waveguide width. Met. Further, the document discloses a structure in which a short finite length barrier portion is inserted, and does not describe whether a high Q value can be obtained by a short finite length barrier.

  In double-heterojunction optical resonators by changing the lattice constant, regions with different lattice constants and their heterointerfaces are installed across the entire crystal or a wide area from the line defect waveguide forming the optical resonator in the lateral direction. There must be.

  For example, in Non-Patent Document 6, regions having different lattice constants exist over the entire lateral width of the photonic crystal. In such a structure, when other devices and waveguides are integrated in parallel in the same photonic crystal, there is a problem that the lattice constant is restricted and the performance is restricted due to the presence of a hetero interface. .

  In order to introduce heterointerfaces having different lattice constants without restricting the photonic crystal devices arranged in parallel, for example, as shown in FIG. 6, the heterointerface is introduced in parallel with the line defects constituting the optical resonator. Therefore, it is necessary to limit regions having different lattice constants.

  In this case, in order to prevent the heterointerface parallel to the waveguide from affecting the optical resonator, the distance between the waveguide and the heterointerface parallel to the waveguide is increased as the Q value of the optical resonator is increased. Need to be separated. For this reason, in an optical resonator using a double heterojunction due to a difference in lattice constant, it is impossible to limit a region having a different lattice constant to the vicinity of the optical resonator in the lateral direction.

  In addition, there is a problem that a region where devices cannot be arranged over a wide area around the parallel heterointerface is widened, and the degree of integration is lowered. Furthermore, if an optical wiring crossing the parallel heterointerface is provided, the performance of the waveguide is restricted. In particular, when changing the lattice constant in the longitudinal direction along the waveguide, if the regions having different lattice constants are limited by introducing parallel heterointerfaces, mismatch due to the phase shift of the lattice as shown in FIG. 6 occurs. There was a problem that it was difficult to solve.

  The present invention has been made in view of the above points, and an object thereof is to provide an optical resonator capable of realizing a large Q value.

The optical resonator of the present invention is an optical resonator configured in a two-dimensional photonic crystal.
Forming a line defect waveguide based on a line defect in which one row of vacancies in the crystal coordination direction is removed, and having a basic width as the distance between the centers of vacancies on both sides facing the defect
At least the vacancies on both sides facing the line defect in the central portion in the longitudinal direction of the line defect waveguide are shifted from the lattice point of the crystal lattice in a direction away from the center of the line defect, Introducing a mode gap barrier into the line defect waveguide with a center spacing larger than the basic width;
A large Q value can be realized by performing light confinement in the direction along the longitudinal direction of the line defect by the mode gap barrier.

  In the optical resonator, the holes that are shifted to introduce the mode gap barrier are arranged so that the shift amount becomes larger toward the center of the optical resonator in the longitudinal direction of the line defect, and the light It arrange | positions so that it may become plane symmetry with respect to the plane orthogonal to the said line defect passing through the center of a resonator.

  In the optical resonator, the basic width of the line defect waveguide is 0.5 times or more and 1.2 times or less of √3 × a when the lattice constant a is used.

  In the optical resonator, the length of the line defect in the basic width portion of the line defect waveguide is not less than five times the lattice constant a.

  In the optical resonator, holes that shift to introduce a mode gap barrier in the line defect waveguide are up to the third row counting from holes on both sides facing the line defect waveguide.

  In the optical resonator, the holes that are shifted to introduce a mode gap barrier into the line defect waveguide are the holes in the first row counted from the holes on both sides facing the line defect waveguide. The shift amount is equal to or greater than the shift amount of the holes in the second row, and the shift amount of the holes in the second row is larger than the shift amount of the holes in the third row.

  According to the present invention, a large Q value can be realized.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

<Embodiment>
FIG. 7 shows a photonic crystal structure of one embodiment of the optical resonator of the present invention. In the figure, the basic structure is that a cylindrical hole 2 is provided in a Si substrate 1 in a regular triangular lattice arrangement with a lattice constant a, and the top and bottom of the Si substrate 1 and the hole are, for example, an air photonic crystal slab. It is.

  Here, a line defect waveguide 3 having a basic width W (the basic width W is the distance between the centers of the innermost holes sandwiching the line defect) extending in the Z-axis direction overlapping the crystal coordination direction is provided. For example, four first holes A facing the both sides of the line defect waveguide 3 at the center in the Z-axis direction of the line defect waveguide 3 are X outward from the line defect waveguide 3 as indicated by arrows. For example, ten second holes B adjacent to the hole A are shifted several nanometers in the X-axis direction from the line defect waveguide 12 toward the outside as indicated by arrows. Yes. Due to the shift of the holes A and B, a double heterojunction optical resonator 4 is formed in which the line defect waveguide 3 having a basic width without shift is used as a mode gap barrier.

  In the present embodiment, the Si substrate 1 as the light confinement layer and the air as the upper and lower light guide layers having a lower refractive index, and at least the hole 2 having a circular cross section penetrating the light confinement layer vertically is triangular, for example. By utilizing a photonic crystal slab arranged in a lattice or square lattice, light is confined in the light confinement layer using total reflection at the interface between the light confinement layer and the light guide layer, and in the in-plane direction. Has emerged a photonic band gap.

  FIG. 8 shows how the waveguide mode changes when the basic width W of the line defect waveguide 3 is changed. The calculation is made for the case where the upper and lower sides and the holes of the Si substrate 1 are filled with air, the hole radius is 0.5 times the lattice constant a, and the slab thickness is 0.485 times the lattice constant a. This is a typical value for the Si photonic crystal slab, and even if the lattice constant, hole diameter, etc. slightly change, no significant qualitative difference occurs from FIG.

  The solution of the Maxwell equation for such a slab structure is either the TE mode (the mode having only the electric field component in the horizontal direction is the TE mode) or the TM mode, and is used as the confinement mode of the optical resonator. Is an even mode of the TE mode within the photonic band gap (mode in which the vertical magnetic field amplitude becomes an even function with respect to the center of the waveguide: transverse mode). In the slab structure, the TM mode has no photonic band gap and does not confine light. Even in the TE mode, the odd mode (mode in which the vertical magnetic field amplitude is an odd function with respect to the center of the waveguide: transverse odd mode) cannot be used because the loss is large and the Q value of the optical resonator is low. The waveguide mode shifts to the high frequency side (long wavelength side) when the basic width W is narrowed.

  In FIG. 8, the hatched portion indicates the outside of the photonic band gap. The solid line indicates the lower limit of the even-even mode, and the upper side of the solid line is an effective waveguide region. On the other hand, light cannot be confined on the upper side of the light line indicated by the broken line because of out-of-plane radiation. For this reason, the region that can be used as an optical resonator is the region between the solid line and the broken line in the figure.

  In the left side even mode (effective when the basic width is 0.8 times less than √3a), when less than 0.5 times √3a, the optical resonator cannot be realized due to the restriction of the light line (broken line). Furthermore, this even-even mode is characterized by a decrease toward the Γ point on the upper side of the light line and a minimum value indicated by the alternate long and short dash line, and a lower Q value due to in-band scattering and out-of-plane radiation above the alternate long and short dash line. Resulting in. When the normalized frequency is 0.258 or less, the light confinement becomes invalid because it is outside the photonic band gap. For this reason, in the left side even mode, a resonator cannot be configured in a region where the basic width exceeds 0.75 times √3a.

  On the other hand, the right side even mode is effective when the basic width is larger than 0.7 times √3a due to the restriction of the write line. This is a monotonous increase without wrapping even above the light line, so there is no restriction on the alternate long and short dash line. However, there is a laterally odd mode indicated by a two-point difference line nearby, and the Q value decreases due to interband scattering above the two-point difference line.

  Therefore, it can be seen from FIG. 8 that the range of the basic width W of the line defect waveguide 3 that can obtain a high Q value with the optical resonator of the present invention is 0.5 to 1.2 times √3a. .

  Thus, in the linear line defect waveguide 3, the basic width W, which is the distance between the centers of the vacancies on both sides facing the defect, is not less than 0.5 times 1.2 times the lattice constant a and not more than 1.2 times. By arranging the optical resonator 4 on the line defect waveguide 3, the waveguide mode formed in the photonic band gap by the line defect waveguide 3 is used as the resonance level of the optical resonator 4. Further, by setting the basic width W of the line defect waveguide 3 to 0.5 times or more and 1.2 times or less of √3 times the lattice constant a, the band of the waveguide mode is set within the photonic band gap. In addition, a band in which the guided mode becomes a single mode is secured. When the resonance mode exists outside the photonic band gap, or when another waveguide mode exists at that position, light leakage occurs and the Q value of the optical resonator decreases.

  In the present embodiment, a mode gap barrier is introduced into the line defect waveguide 3 by shifting holes around the line defect waveguide 3 in a direction away from the center of the line defect waveguide 3 (in the direction of the arrow). Light confinement in the direction along the longitudinal direction of the waveguide 3 is performed by this mode gap barrier.

  In the present embodiment, the gap between the centers of the vacancies on both sides facing the defect at least in the center of the optical resonator 4 is made larger than the basic width W of the line defect waveguide, thereby introducing the line defect in the vicinity of the optical resonator 4. The change in the refractive index in the direction along the longitudinal direction (Z-axis direction) of the waveguide 3 is reduced, and the mode gap barrier is reduced. As a result, the resonance mode penetrates deeply into the barrier and gradually attenuates, so that the electromagnetic field component in the upper region of the light line is brought close to 0 to prevent light leakage, resulting in a high value exceeding 1 million. The Q value can be realized.

  Further, in the present embodiment, the length L of the line defect waveguide 3 acting as a mode gap barrier is set to be five times or more of the lattice constant, so that light in a resonance mode such as a waveguide can propagate outside the barrier portion. Even in the case of a structure and a small barrier, light leakage due to tunneling is sufficiently suppressed, and a high Q value is realized.

  The first hole A on both sides facing the line defect at the center in the longitudinal direction of the line defect waveguide 3 and the second hole B adjacent thereto are shifted in a direction away from the center of the line defect, By making the shift amount of the air holes A larger than the shift amount of the second air holes B, the change in the refractive index in the direction along the longitudinal direction of the line defect waveguide 3 in the vicinity of the optical resonator 4 is moderated, and By reducing the mode gap barrier, the resonance mode penetrates deeply into the barrier region and gradually attenuates, thereby bringing the electromagnetic field component in the upper region of the light line close to 0 and preventing light leakage. As a result, it is possible to realize an extremely high Q value. When holes A and B in FIG. 7 and another hole group are further added and a difference in shift amount is provided between them, the holes A and B and another hole group are optically resonated. Unless the optical resonator 4 is made symmetrical with respect to a plane passing through the center of the resonator 4 and perpendicular to the line defect waveguide 3, the electromagnetic field distribution is disturbed and the Q value is lowered.

  In addition, this embodiment greatly reduces the restrictions on other devices integrated in the periphery by limiting the structure constituting the optical resonator to the very vicinity of the optical resonator, and the layout of the device integrated structure is reduced. Increase the degree of freedom. That is, the holes to be shifted to give a change in the waveguide width for generating the mode gap barrier are limited to the holes located up to the third row from the line defect waveguide (in FIG. 7, two rows). To the eyes).

  In the line defect waveguide 3 of the photonic crystal slab, the guided mode light is strongly localized in the line defect portion due to the photonic band gap. For this reason, a small mode gap barrier that can be realized with a small change in waveguide width that can ignore a change in refractive index in a heterojunction can limit the vacancies to be shifted to the third column from the line defect waveguide 3. It can be generated without problems. However, in this case, there is a possibility that the lattice mismatch at the boundary between the shifted hole and the outer non-shifted hole or a change in the refractive index becomes large, leading to a decrease in the Q value. It is effective to employ an inclined shift structure in which the shift amount of the holes decreases as the distance from the line defect waveguide 3 increases from the first row, the second row, and the third row. In the structure of FIG. 7, the arrangement of the holes A and B is realized not only in the longitudinal direction of the line defect waveguide 3 but also in the lateral direction.

  Thereby, the structure of the optical resonator can be limited to the very vicinity of the optical resonator. Further, the mode volume of the electromagnetic field of light trapped in the optical resonator can also be reduced to the minimum as the lattice constant of the photonic crystal. It is also possible to prevent a phase shift from occurring in the photonic crystal structure despite the introduction of the heterointerface.

  Here, a sufficient condition for realizing a high Q value exceeding 1 million in an optical resonator due to a point defect or a line defect in a photonic crystal slab is that the refractive index is abruptly around the optical resonator and the period of the crystal It does not change with sex. This is because such a sudden change in refractive index disturbs a smooth change in the electromagnetic field at the boundary of the optical resonator, resulting in an increase in the electromagnetic field distribution above the light line.

  In addition, by configuring the optical resonator with a line defect instead of a point defect, the direction in which the refractive index change leading to light leakage becomes a problem can be limited to the longitudinal direction of the line defect waveguide 3. However, the method of realizing the optical confinement in the longitudinal direction of the line defect waveguide 3 by the band gap confinement, that is, the photonic crystal barrier cannot fundamentally solve the above-described change in the refractive index. Resonance mode penetrates deeply into the barrier region by slowing down the height of the mode gap barrier while suppressing the refractive index change and periodicity to a negligible level by giving a small width change to the line defect waveguide As a result, the Q value of the resonator can be significantly increased as compared with the case of the photonic crystal barrier.

  Further, the first hole A on both sides facing the line defect in the central portion in the longitudinal direction of the line defect waveguide 3 and the second hole B adjacent thereto are shifted in a direction away from the center of the line defect, By making the shift amount of one hole A larger than the shift amount of the second hole B, it is possible to reduce light leakage more effectively and to increase the Q value of the optical resonator to the limit. Become.

  Photonic crystal optical resonators capable of realizing Q values exceeding 1 million have double heterojunctions formed by using lattice constant differences from those using a hexapole mode in point defects (see Non-Patent Document 6). Although there was only a thing (refer nonpatent literature 5), it becomes possible to implement | achieve Q value exceeding 1 million theoretically also in this embodiment.

  In the present embodiment, the optical resonator is realized by shifting the holes around the line defect waveguide 3 only in a very narrow region near the center of the optical resonator 4. An optical resonator can be realized with a minimum number of holes to be shifted, and a larger Q value can be realized by changing from several to ten or more. The region where these vacancies exist is extremely small, with one side being several times the lattice constant. This is not achievable with a technique that realizes a double heterojunction by a lattice constant difference.

  In the present embodiment, the portion where the structure of the photonic crystal needs to be changed can be limited to an extremely small size by the arrangement of the optical resonator 4, so that it is difficult to structurally affect the peripheral waveguide and other photonic crystal devices. In particular, in the case of the optical resonator 4 according to the present embodiment, the design is easy and the degree of freedom is high when a coupling operation with another adjacent optical resonator or waveguide is attempted.

  On the other hand, in the optical resonator 4 in which a double heterojunction is formed by a lattice constant difference, a region having a specified lattice constant must be secured in the periphery, so that the peripheral optical resonator and the waveguide are structurally We cannot avoid being restricted. Also, when the lattice constant in the direction along the longitudinal direction (Z-axis direction) of the line defect waveguide is changed and the region is limited to the lateral direction (X-axis direction) when viewed from the line defect waveguide As shown in FIG. 6, a structural phase shift occurs. However, according to the present embodiment, the lateral region can be limited without generating a structural phase shift.

  In the present embodiment, the basic width W of the line defect waveguide 3 used in the optical resonator 4 can be changed in a range of 0.5 to 1.2 times with respect to √3 times the lattice constant a. By changing the width of the line defect waveguide 3, the wavelength of the resonance level of the optical resonator 4 and the Q value of the optical resonator can be adjusted widely and with high accuracy. This is very advantageous when integrating optical resonators or performing linking operations with other devices.

  When the basic width of the line defect waveguide 3 is set to a value other than √3 times the lattice constant, the structural phase of the photonic crystals on both sides of the line defect waveguide 3 is shifted, so that the line defect guide In the case of forming a waveguide straddling the extended line of the waveguide 3, the characteristics are restricted.

  However, in this embodiment, in most applications, it is possible to realize a photonic crystal optical integrated circuit without impairing the function by designing so that the waveguide does not straddle the extension line of the line defect waveguide 3. Is possible. Further, since the optical resonator 4 having an extremely high Q value can be realized even if the basic width W of the line defect waveguide 3 is set to √3 times the lattice constant, the whole has a single lattice constant and a phase. It becomes possible to arrange a plurality of optical resonators having different resonance frequencies in a photonic crystal having no deviation.

  By the way, a two-dimensional structure comprising a light confinement layer and upper and lower light guide layers having a lower refractive index, and at least holes having an arbitrary cross-sectional shape penetrating the light confinement layer vertically are arranged in a triangular lattice or a square lattice. In the photonic crystal structure (lattice constant a), the distance between the centers of the vacancies on both sides facing the defect in the linear line defect waveguide is 0.5 times 1.2 times or less of √3 × a. An optical resonator provided on a line-defect waveguide having a basic width, in a region surrounding the optical resonator, a single standard hole is uniformly arranged at each lattice point, The optical confinement in the direction along the longitudinal direction of the defect waveguide is performed by a mode gap barrier introduced into the line defect waveguide by changing the cross-sectional area of the vacancies around the line defect waveguide. To appear The holes whose cross-sectional area is changed are present only in the third row counting from the line defect waveguide, and the cross-sectional area of the holes on both sides facing the defect at the center of the optical resonator is that of the standard hole. Even in the case of an optical resonator that is made smaller, it is possible in principle to obtain the same effects as those of the present embodiment.

  However, when a heterojunction is formed by changing the hole diameter, the amount of change in the refractive index with respect to the size of the introduced mode gap barrier is much larger than when the waveguide width and lattice constant are changed. Constraints on characteristic design become stricter.

  In existing nanolithography such as electron beam exposure and light exposure, it is difficult to control the pore diameter on the nanometer order. In that respect, if the position of the holes used in the present embodiment is controlled, the accuracy in the nanometer order is obtained by the existing nanolithography, which is excellent in terms of compatibility with the lithography and realistic.

  A first embodiment of the present invention will be described with reference to FIGS.

  FIG. 9 shows a photonic crystal structure of the first embodiment of the optical resonator of the present invention. In the figure, the basic structure is that a cylindrical hole 11 having a radius of 0.5a (= 216 nm) is provided in a Si substrate 10 having a thickness of 204 nm in a regular triangular lattice arrangement with a lattice constant a (= 432 nm). The top and bottom of the Si substrate 10 and the holes are photonic crystal slabs of air (refractive index 1). The ΓK axis in the crystal coordination direction of the holes 11 in the triangular lattice arrangement is a direction connecting the centers of two adjacent air holes, and the three sides of the triangular lattice correspond to the ΓK axis. The ΓM axis is perpendicular to the straight line connecting the centers of two adjacent air holes (ΓK axis) and is directed toward the center of the shortest air hole.

  Here, a line defect waveguide 12 having a basic width of 0.9 × √3a (= 674 nm) extending in the Z-axis direction overlapping with the ΓK axis is provided. The four first air holes A facing each other on both sides of the line defect waveguide 12 at the substantially central position in the Z-axis direction of the line defect waveguide 12 are X outward from the line defect waveguide 12 as indicated by arrows. The ten second holes B adjacent to the hole A are shifted by 12 nm in the axial direction, and shifted 6 nm in the X-axis direction from the line defect waveguide 12 to the outside as indicated by arrows. Further, the four third holes C having the same Z-axis coordinate as the hole A and adjacent to the hole B are shifted by 4 nm in the X-axis direction outward from the line defect waveguide 12 as indicated by arrows. ing. Due to the shift of the holes A, B, and C, a double heterojunction optical resonator 14 is formed in which the line defect waveguide 12 having a basic width (674 nm) without shift is used as a mode gap barrier.

  The electromagnetic field (Y-axis direction magnetic field) distribution calculation result near the center of the optical resonator 14 in the electromagnetic field numerical simulation performed by the three-dimensional finite difference time domain (FDTD) method for the structure of FIG. Is shown in FIG.

  FIG. 10A is the XZ plane of the calculation model, and shows the right half from the line defect waveguide 12 here. 10B shows the magnetic field power distribution in the XZ plane, FIG. 10C shows the magnetic field power distribution in the YZ plane, and FIG. 10D shows the magnetic field power distribution in the XY plane. The magnetic field power distribution is standardized so that the magnetic field power at the point of maximum intensity is 1.

FIG. 10 shows that an electromagnetic field, that is, light is confined in the vicinity of the optical resonator, and this structure functions as an optical resonator. The mode volume of the resonance mode is 0.12 [μm ³ ], which is the same value as that of the point defect optical resonator. In addition, the Q value of this resonance mode is as extremely high as about 4.2 million. The wavelength of the resonance mode is 1553 nm, and this is the only mode with a high Q value in this optical resonator structure.

  The structure shown in FIG. 9 was actually prototyped by electron beam lithography. The structure shown in FIG. 9 can be realized by using a commercially available electron beam lithography apparatus, resist, developer, silicon-on-insulator substrate, dry etching apparatus, hydrofluoric acid / ammonium fluoride for removing a silicon oxide film, and the like.

  FIG. 11 shows an electron microscope image of the prototype structure. Since the amount of shift of the holes in the optical resonator is as small as 12 nm at the maximum, it is unclear which hole is shifted at the magnification shown in FIG. 11. Therefore, the optical resonator 14 is surrounded by a solid line, and the mode gap barrier is shown. The line defect waveguide 12 is surrounded by a broken line.

  The ends of the optical input line defect waveguides 16 and 18 are provided at the hole positions of the sixth column in the X-axis direction from the line defect waveguide 12 constituting the optical resonator 14. Each of the line defect waveguides 16 and 18 is coupled.

  Resonant mode was measured for the prototyped sample using a measurement system with a combination of a tunable laser, an optical attenuator, and a photodetector. In the optical resonator 14, a nonlinear phenomenon due to two-photon absorption and a peak shift and broadening due to heat generation are likely to occur. Therefore, the input light intensity was set to not more than 150 dBm by an optical attenuator and measurement was performed at a weak light intensity.

  The measured resonance mode signals are shown in FIG. The full width at half maximum of the resonance peak is about 4 pm, which corresponds to a Q value of about 400,000. The reason why the measured value is an order of magnitude smaller than the theoretical value needs to be clarified in the future, but the Q value of 400,000 has already reached the theoretical limit value in the conventional single and multi-point defect type optical resonators. This value is not possible, and the effect of the present invention is clear.

  A second embodiment of the present invention will be described with reference to FIGS.

  FIG. 13 shows a photonic crystal structure of a second embodiment of the optical resonator of the present invention. In the figure, the basic structure is such that a cylindrical hole 21 having a radius of 0.5a (= 210 nm) is provided in a Si substrate 20 having a thickness of 204 nm in a regular triangular lattice arrangement with a lattice constant a (= 420 nm). The upper and lower sides and the holes of the Si substrate 20 are photonic crystal slabs of air (refractive index 1). The ΓK axis in the crystal coordination direction of the holes 21 in the triangular lattice arrangement is a direction connecting the centers of two adjacent air holes, and the three sides of the triangular lattice correspond to the ΓK axis. The ΓM axis is perpendicular to the straight line connecting the centers of two adjacent air holes (ΓK axis) and is directed toward the center of the shortest air hole.

  Here, a line defect waveguide 22 having a basic width of 1.0 × √3a (= 728 nm) extending in the Z-axis direction overlapping the ΓK-axis is provided. Two holes A facing each other on both sides of the line defect waveguide 22 at approximately the center position in the Z axis direction of the line defect waveguide 22 are directed outward from the line defect waveguide 22 in the X axis direction as indicated by arrows. Shifted by 12 nm. Due to the shift of the holes A, a double heterojunction optical resonator 24 is formed in which the line defect waveguide 22 having a basic width (728 nm) without a shift is used as a mode gap barrier. This structure is characterized in that only two holes A are shifted to form the optical resonator 22.

  FIG. 14 shows an electromagnetic field (Y-axis direction magnetic field) distribution calculation result in the vicinity of the center of the optical resonator 24 in the electromagnetic field numerical simulation executed by the three-dimensional FDTD method for the structure of FIG.

  FIG. 14A is the XZ plane of the calculation model, and shows the right half from the line defect waveguide 22 here. 14B shows the magnetic field power distribution in the XZ plane, FIG. 14C shows the magnetic field power distribution in the YZ plane, and FIG. 14D shows the magnetic field power distribution in the XY plane. The magnetic field power distribution is standardized so that the magnetic field power at the point of maximum intensity is 1.

FIG. 14 shows that an electromagnetic field, that is, light is confined in the vicinity of the optical resonator, and this structure acts as an optical resonator. The mode volume of the resonance mode was 0.20 [μm ³ ], the Q value of the resonance mode was about 1 million, and the wavelength of the resonance mode was 1560 nm.

  The structure shown in FIG. 13 was actually fabricated by electron beam lithography. FIG. 15 shows an electron microscope image of the prototype structure. Since the shift amount of the holes of the optical resonator 24 is as small as 12 nm, it is unclear which hole is shifted at the magnification of FIG. 15. Therefore, the optical resonator 24 is surrounded by a solid line to indicate the mode gap barrier. The line defect waveguide 22 is surrounded by a broken line.

  The ends of the optical input line defect waveguides 26 and 28 are provided at the hole positions in the fifth column in the X-axis direction from the line defect waveguide 22 constituting the optical resonator 24. Each of the line defect waveguides 26 and 28 is coupled.

  FIG. 16 shows the measurement result of the resonance mode measured for the prototype sample. The full width at half maximum of the resonance peak is about 13.7 pm, which corresponds to a Q value exceeding 110,000. In the present embodiment, an optical resonator 24 having a high Q value can be realized by shifting only two cavities A with respect to the line defect waveguide 22, and the optical resonator-based optical element is densely arranged at a narrow interval. This is very advantageous for the purpose of integrating the

  As described above, in the present invention, in the photonic crystal slab, by modulating the line defect waveguide width by shifting the line defect waveguide and a specific hole around the line defect waveguide, a mode gap barrier double heterojunction is configured. An optical resonator having a high Q value far exceeding 100,000 was realized. The method of realizing the present invention is very simple and easy, and an optical resonator having a high Q value can be realized by a slight shift of only a few to a dozen holes. As a result, an optical resonator having a high Q value can be integrated on the photonic crystal with almost no restrictions on the design of peripheral photonic crystals and device performance.

It is a figure which shows the relationship between the band structure and light line in a typical photonic crystal slab. It is a figure for demonstrating the light line of an optical resonator. It is a figure which shows the fundamental propagation mode of the typical 1 line | wire open line defect waveguide in a photonic crystal slab. It is a figure which shows the fundamental propagation mode of the double heterojunction in a line defect waveguide. The structure of the line defect double heterojunction optical resonator by the conventional mode gap barrier is shown. It is a figure which shows the structure which introduced the hetero interface from which a lattice constant differs. It is a figure which shows the photonic crystal structure of one Embodiment of the optical resonator of this invention. It is a figure which shows the relationship between the fundamental width of a line defect waveguide, and waveguide mode. It is a figure which shows the photonic crystal structure of 1st Example of the optical resonator of this invention. It is a figure which shows the electromagnetic field distribution calculation result near the center of the optical resonator in the electromagnetic field numerical simulation of 1st Example of this invention. It is a figure which shows the electron microscope image of the structure of 1st Example made as an experiment by electron beam lithography. It is a figure which shows the signal of the resonance mode measured with the structure of FIG. It is a figure which shows the photonic crystal structure of 2nd Example of the optical resonator of this invention. It is a figure which shows the electromagnetic field distribution calculation result of the center vicinity of the optical resonator in the electromagnetic field numerical simulation of 2nd Example of this invention. It is a figure which shows the electron microscope image of the structure of 2nd Example made as an experiment by electron beam lithography. It is a figure which shows the signal of the resonance mode measured with the structure of FIG.

Explanation of symbols

1,10,20 Si substrate 2,11,21 Air hole 3,12,16,18,22 Line defect waveguide 4,14,24 Optical resonator

Claims (6)

In an optical resonator composed of a two-dimensional photonic crystal,
Forming a line defect waveguide based on a line defect in which one row of vacancies in the crystal coordination direction is removed, and having a basic width as the distance between the centers of vacancies on both sides facing the defect
At least the vacancies on both sides facing the line defect in the central portion in the longitudinal direction of the line defect waveguide are shifted from the lattice point of the crystal lattice in a direction away from the center of the line defect, Introducing a mode gap barrier into the line defect waveguide with a center spacing larger than the basic width;
An optical resonator characterized in that light confinement in a direction along a longitudinal direction of the line defect is performed by the mode gap barrier. The optical resonator according to claim 1.
The holes that are shifted to introduce the mode gap barrier are arranged so that the shift amount becomes larger toward the center of the optical resonator in the longitudinal direction of the line defect, and passes through the center of the optical resonator. The optical resonator is disposed so as to be plane-symmetric with respect to a plane orthogonal to the line defect. The optical resonator according to claim 1 or 2,
The basic width of the line defect waveguide is 0.5 times or more and 1.2 times or less of √3 × a when the lattice constant a is used. The optical resonator according to any one of claims 1 to 3,
The length of the line defect in the basic width portion in the longitudinal direction of the line defect waveguide is at least five times the lattice constant a. The optical resonator according to any one of claims 2 to 4,
The optical resonator is characterized in that vacancies shifted to introduce a mode gap barrier into the line defect waveguide are up to a third row counting from vacancies on both sides facing the line defect waveguide. The optical resonator according to claim 5, wherein
The holes that are shifted to introduce a mode gap barrier into the line defect waveguide have a shift amount of holes in the first row counted from holes on both sides facing the line defect waveguide. An optical resonator, wherein the shift amount of the holes in the second row is greater than the shift amount of the holes in the third row and is greater than the shift amount of the holes.