JP2004006567A - Point defect 3-dimensional photonic crystal optical resonator - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a point defect 3-dimensional photonic crystal which can control the resonant wavelength. <P>SOLUTION: A point defect 12 is formed by introducing a point defect material into a 3-dimensional photonic crystal. Accordingly, a point detect level is formed within a photonic band gap and only the light of the wavelength corresponding to the energy of the point defect level can exist within the point defect 12. In result, an optical resonator can play the role in the relevant wavelength. The loss of the optical energy from the point defect 12 is rather small and the efficiency of the resonator is high because of the 3-dimensional crystal. The resonant wavelength can be controlled by adequately setting the size, shape and location as the parameters of a defect member. Moreover, the light of a plurality of wavelengths may be resonated with only one 3-dimensional photonic crystal by introducing a plurality of point defects in which parameters of the defect member are different. These elements can contribute to reduction in size of a device for the wavelength multiplex communication or the like. <P>COPYRIGHT: (C)2004,JPO

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an optical resonator that can be applied to a light source for optical wavelength division multiplexing communication and the like.
[0002]
[Prior art]
In recent years, photonic crystals have attracted attention as new optical devices. A photonic crystal is an optical functional material having a periodic refractive index distribution, and forms a band structure with respect to photon energy. In particular, it is characterized in that an energy region (photonic band gap) where light cannot be propagated is formed.
[0003]
As an example of a field where photonic crystals are expected to be applied, the field of optical communication is taken up. In optical communication, wavelength division multiplexing (Wavelength Division Multiplexing: WDM) is used instead of the conventional optical time division multiplexing (OTDM). This WDM is a communication system in which light of a plurality of wavelengths is propagated in one transmission line, and a separate signal is carried on each. As a result, the amount of information that can be transmitted per unit time is dramatically improved.
[0004]
In this wavelength division multiplex communication, a light source is required for each of a plurality of wavelengths. At present, as a light source, a light source using a semiconductor laser having a different oscillation wavelength for each wavelength, a light source combining a white light source with an optical demultiplexer, and the like are used. However, all of these methods cannot avoid the increase in size of the apparatus and are inefficient.
[0005]
[Problems to be solved by the invention]
It is already known that a photonic crystal can be used as an optical resonator. Since the optical resonator can confine light, the optical resonator can be used as a light source by providing appropriate light extraction means. Therefore, by using a photonic crystal as a light source, the size of the wavelength division multiplex communication device can be significantly reduced.
[0006]
A photonic crystal as an optical resonator has been studied in a two-dimensional photonic crystal (for example, described in JP-A-2001-272555). In this document, the use of not only an optical resonator but also a wavelength demultiplexing / multiplexing device by introducing a point defect that disturbs the period of the photonic crystal has been studied.
[0007]
Although a two-dimensional photonic crystal has an advantage of being relatively easy to manufacture, a three-dimensional system having a high effect of confining light within the resonator is more desirable in consideration of the efficiency as an optical resonator.
[0008]
Regarding the three-dimensional photonic crystal, a waveguide in which a waveguide has been introduced (for example, Japanese Unexamined Patent Application Publication No. 2001-79555) or a point in which a point defect is introduced (Makoto Okano et al. Analysis of the Apparatus ”, Abstracts of the 2000 Autumn Meeting of the Japan Society of Applied Physics, and“ Analysis of Single-Defect Micro Optical Resonators in Three-Dimensional Photonic Crystals (II) ”, Abstracts of the 2001 Spring Meeting of the Japan Society of Applied Physics) Have been. However, no specific report has been made on the relationship between the structure of the defect and the characteristics of the resonator.
[0009]
Industrially, when an optical resonator is used as a light source for wavelength division multiplexing optical communication, for example, it is not practical if the emission wavelength cannot be set to an arbitrary desired value.
[0010]
The present invention has been made to solve such a problem, and an object of the present invention is to provide a specific control method of a resonance wavelength of an optical resonator using a point defect three-dimensional photonic crystal. Is to do.
[0011]
[Means for Solving the Problems]
The first aspect of the point defect three-dimensional photonic crystal optical resonator according to the present invention, which has been made to solve the above problems, is as follows.
a) A plurality of stripe layers in which a plurality of rods are arranged in parallel and periodically at a predetermined in-plane period are stacked in parallel, and each rod belonging to each stripe layer is orthogonal to each rod belonging to the nearest stripe layer. A main body made of a three-dimensional photonic crystal in which each rod belonging to each stripe layer is parallel to each rod belonging to a stripe layer separated by two layers and is shifted by ず れ of the in-plane period;
b) a point defect provided on one of the rods and having a ratio Δx / Δy of a size Δx in the rod width direction and a size Δy in the rod longitudinal direction larger than 1;
It is characterized by having.
[0012]
In a second aspect of the point defect three-dimensional photonic crystal optical resonator according to the present invention,
a) A plurality of stripe layers in which a plurality of rods are arranged in parallel and periodically at a predetermined in-plane period are stacked in parallel, and each rod belonging to each stripe layer is orthogonal to each rod belonging to the nearest stripe layer. A main body made of a three-dimensional photonic crystal in which each rod belonging to each stripe layer is parallel to each rod belonging to a stripe layer separated by two layers and is shifted by ず れ of the in-plane period;
b) a point defect provided in one of the rods, wherein the center of the point defect is determined from the center axis of the nearest rod belonging to the stripe layer adjacent to the point defect; Point defects arranged displaced in the longitudinal direction;
It is characterized by having.
[0013]
BEST MODE FOR CARRYING OUT THE INVENTION
First, a three-dimensional photonic crystal serving as a base of the optical resonator of the present invention will be described. A three-dimensional photonic crystal is composed of a set of rods. By arranging such rods in parallel at a predetermined period (in-plane period) a, one layer is formed. This is called a stripe layer. A three-dimensional crystal is formed by laminating stripe layers. In order to form a photonic band gap, the positional relationship between rods belonging to each stripe layer and rods belonging to other stripe layers is important. is there. In the three-dimensional photonic crystal used in the present invention, each rod belonging to each stripe layer is arranged so as to be orthogonal to each rod belonging to the nearest stripe layer. Further, each rod belonging to each stripe layer is parallel to each rod belonging to a stripe layer next to the nearest adjacent stripe layer (that is, a stripe layer separated by two layers), and has a length a / a in the width direction of the rod. By being displaced by two, a periodic refractive index distribution is formed. Such a periodic refractive index distribution forms an energy range (photonic band gap) where light cannot exist in the three-dimensional photonic crystal.
[0014]
Point defects are introduced into one rod in a three-dimensional photonic crystal having such periodicity. The point defects introduced in this way cause disturbances in the periodic refractive index distribution in the three-dimensional photonic crystal, and energy levels (defect levels) where light can exist are formed in the photonic band gap. That is, the three-dimensional photonic crystal having such a point defect becomes an optical resonator. If a light emitter is introduced into this point defect, this optical resonator becomes a light source.
[0015]
There are various methods for introducing a point defect. For example, a method of removing a part of a rod and disposing an object having a different shape, a different refractive index, or the like, a method of attaching a member to the rod without causing the rod to be lost, or a method of changing the shape of the rod itself (thickness). Or thinning). These are collectively called defective members. When a point defect is used as a light source, it is necessary to introduce a luminous body into a defective portion, but the luminous body itself may be used as a defective member.
[0016]
When a three-dimensional photonic crystal having a point defect introduced therein is used as an optical resonator, three characteristics of an energy value of a defect level, an interval between defect levels, and an optical confinement effect are important. In order to obtain the necessary characteristics for these, it is necessary to appropriately select parameters relating to the point defect, such as the size, shape, and displacement of the point defect.
[0017]
The energy value of the defect level can be set with a high degree of freedom depending on the size of the defect member among the parameters relating to the point defect. However, simply controlling the size of the defective member may reduce the resonance frequency interval. That is, a level used as a resonator (hereinafter, referred to as a used level) is close to an adjacent level, and the used level may be affected by the adjacent level. Therefore, in the present invention, it has been clarified that the influence of the adjacent level can be avoided by adjusting the shape and displacement of the defective member by the following method.
[0018]
First, the shape of the defective member will be described. Considering the use of the lithography method when manufacturing the rod and the defective member, the defective member has the same height (in the stacking direction) as the rod, and the planar shape at the point defect point is different from the rod portion (rectangular shape, elliptical shape). Etc.).
[0019]
Next, considering the relationship between the width Δx and the length Δy in such a planar shape of the defective member, (i) when Δx and Δy are equal (Δx / Δy = 1), (ii) Δx is larger than Δy (Δx / Δy> 1) and (iii) a case where Δx is smaller than Δy (Δx / Δy <1). Since the electromagnetic field distribution has direction dependency, the energy value of the defect level due to the point defect depends on Δx / Δy of the defective member. Therefore, when the energy difference ΔE between the used level and the adjacent level was examined, it was found that the energy difference ΔE was largest when the shape of the defective member was Δx / Δy> 1. Therefore, in order to avoid the influence of the adjacent level on the used level, the defective member has a shape anisotropy in which the width Δx is larger than the length Δy. The value of Δx / Δy is preferably 1.5 or more, and more preferably 2 or more.
[0020]
Next, the displacement of the point defect will be described. The displacement of a point defect indicates a positional relationship between the point defect and rods of upper and lower stripe layers (hereinafter, referred to as adjacent layers) adjacent to the stripe layer to which the point defect belongs.
[0021]
As can be easily understood in consideration of the influence of the electromagnetic field distribution, the energy value of the defect level also depends on the displacement. The larger the displacement, the larger the distance between the defect level and the adjacent level. By setting the displacement to 0.1a or more, the energy difference becomes practically sufficient. Since the rods of the upper and lower adjacent layers are shifted from each other by the length a / 2, when the displacement with respect to one adjacent layer exceeds 0.25a, the displacement with respect to the other adjacent layer is 0.25a or less. become. That is, the maximum value of the displacement is 0.25a, and at that time, the interval between the defect level and the adjacent level becomes maximum.
[0022]
As the parameter of the point defect, not the position in the whole crystal but the above “displacement” is significant. This is because the same defect level can be obtained even at different positions in the crystal by applying the same displacement.
[0023]
The advantage of the displacement is obtained independently of the shape of the point defect (defective member).
[0024]
As described above, the energy value of the defect level can be set with a high degree of freedom by appropriately setting the size, shape, and displacement of the point defect (defective member). If a plurality of point defects (defect members) having different sizes and / or shapes and / or displacements are introduced at different positions in the three-dimensional photonic crystal, a plurality of point defects each having a different defect level energy value are introduced. Can be manufactured.
[0025]
Next, the Q value in the optical resonator will be described. The Q value is obtained by dividing the energy of light stored in the optical resonator by the energy of light lost from the resonator per unit time and multiplying the result by the resonance angular frequency. When this value exceeds about 1000, laser oscillation can be obtained at room temperature.
[0026]
In order to improve the Q value of the optical resonator, it is necessary to suppress the loss of light energy from the optical resonator. For that purpose, the size of the crystal should be sufficiently large in all three-dimensional directions. However, it is necessary to pay attention to the following points.
[0027]
Since the three-dimensional photonic crystal of the present invention is manufactured by forming stripe layers one by one and stacking them, it is relatively easy to enlarge the crystal in the in-plane direction of the stripe layer. Enlarging the crystal in the stacking direction increases the manufacturing cost by increasing the number of stacking steps. From this point, it is not preferable to increase the number of stripe layers too much.
[0028]
In the present invention, in order to suppress the loss of light energy from the optical resonator, it is desirable that the number of the stripe layers is four or more both above and below the stripe layer to which the point defect belongs. Furthermore, when the number of the stripe layers is six or more in both the upper and lower portions of the stripe layer to which the point defect belongs, the Q value reaches nearly 1,000. The appropriate number of layers may be determined in consideration of the result and the manufacturing cost.
[0029]
In order to widen the usable wavelength range of light, it is desirable that the photonic band gap width is large. Up to this point, parameters relating to point defects have been mainly discussed, but in the following, in order to control the size of the photonic band gap, parameters of a three-dimensional photonic crystal serving as a base are discussed. The parameters to be considered include the in-plane / out-of-plane period ratio and the in-plane rod filling factor. The in-plane / out-of-plane period ratio is a ratio z / a of a magnitude (out-of-plane period) z of one period (one period corresponds to four layers of the stripe layer) in the stacking direction with respect to an in-plane period a in the stripe layer. The rod filling rate is a value w / a obtained by dividing the rod width w by the in-plane period a.
[0030]
When the filling ratio w / a is variously changed with respect to various values of the in-plane / out-of-plane periodic ratio z / a, the filling ratio w / a is 0.275 to 0, regardless of the in-plane / out-of-plane period ratio z / a. In the range of 0.30, the photonic band gap width becomes maximum. When the filling ratio w / a is out of the range of 0.20 to 0.40, the photonic band gap width sharply decreases as the filling ratio w / a departs from the range.
[0031]
On the other hand, when the value of the in-plane / out-of-plane periodic ratio z / a is variously changed with respect to various values of the filling rate w / a, when the in-plane / out-of-plane period ratio z / a is 0.20 to 0.30, When a = 1.2, when the filling ratio w / a is 0.30 to 0.40, the photonic band gap width becomes maximum when the in-plane / out-of-plane period ratio z / a = 1.3.
[0032]
When the value of the in-plane / out-of-plane period ratio z / a is increased, the Q value is improved. In particular, z / a is 2 which has not been studied so far in three-dimensional photonic crystals. ^0.5 If it is larger than the above, a high Q value is obtained.
[0033]
【The invention's effect】
A point defect is introduced into a three-dimensional photonic crystal, and the size, shape, and displacement of the point defect (defect member) arranged therein, and the in-plane / out-of-plane period ratio z / a and the filling factor w / a of the three-dimensional photonic crystal By changing the parameters such as these, the resonance frequency can be set arbitrarily, and the unity of the frequency can be improved. In particular, laser oscillation can be performed by appropriately setting these parameters. Therefore, for example, when the optical resonator according to the present invention is used as a light source, the light source has a desired emission wavelength and a high wavelength uniformity, and is optimal as a light source for wavelength division multiplexing optical communication. Of course, other light sources can be used as light sources for various optical devices.
[0034]
【Example】
First, FIG. 1 shows a configuration example of a three-dimensional photonic crystal serving as a base. The rod 11 is shown as a rod in the figure. One of the arrows shown at the right end of the figure corresponds to one stripe layer. “A” in the drawing is the length (in-plane period) of one period of the rod array in the stripe layer. z is the length (out-of-plane period) of one cycle in the stacking direction composed of four stripe layers. w represents the width of the rod, and h represents the height of the rod. As a material of the rod, for example, a III-V group semiconductor (for example, GaAs, InP, or the like) which is a substance which is transparent to infrared rays often used in optical communication and is a dielectric capable of introducing a light emitting body is used. be able to.
[0035]
FIG. 2 shows the result of calculating the energy band using the plane wave expansion method in order to confirm that the crystal as shown in FIG. 1 has a photonic band gap. Here, the in-plane / out-of-plane periodic ratio z / a = 1.2, the filling rate w / a = 0.25, and the refractive index of the rod was 3.309. The vertical axis on the left side of FIG. 2 represents a normalized frequency obtained by multiplying the frequency of light by a / c (c is the speed of light) to make it dimensionless, and the vertical axis on the right side represents the center energy of the photonic band gap at 0.8 eV ( It represents the photon energy when it is assumed to be energy of light having a wavelength of 1.55 μm generally used in optical multiplex communication. The horizontal axis in FIG. 2 represents the direction in the wave number space. From this figure, it can be seen that when the normalized frequency is in the range of 0.38 to 0.45, the energy gap is open in all directions in the wavenumber space. This is the photonic band gap.
[0036]
Next, as shown in FIG. 3A, a point defect 12 is introduced into the base crystal. The point defect is formed by disposing a defective member on a part of the rod. In this embodiment, the defective member is a rectangular parallelepiped having the same height as the rod, and the material is the same as the rod. Even when the material (refractive index) is different from that of the rod, the results shown below are the same. In the following, the effects of various parameters of the defective member on various characteristics such as the energy level of a point defect will be examined. The planar shape of the defective member was examined when the width Δx and the length Δy shown in FIG. 3 (2) were equal and when Δx> Δy shown in FIG. 3 (3). In the case of Δx <Δy, as a result of the examination, it has been found that the interval between the defect levels tends to be narrower than that in the case of Δx = Δy, and the description is omitted below. Hereinafter, the point defect of Δx = Δy is referred to as “square defect”, and the point defect of Δx> Δy is referred to as “rectangular defect”.
[0037]
Next, the displacement of the defective member will be examined. As shown in FIG. 4, the displacement in the y direction between the center of the defective member and the center of the nearest rod in the stripe layer immediately above was examined. FIG. 4A shows the case where there is no shift in the y direction, and FIGS. 4B and 4C show the case where the shift is in the y direction. In addition, although the displacement in the x direction was also examined, it was found that in this case, the gap between the defect levels tends to be narrowed by increasing the displacement. Therefore, only the displacement in the y direction will be discussed below.
[0038]
The calculation results of the effect of the size, shape, and displacement of the defective member on the defect level of the point defect are shown below. First, FIG. 5 shows calculation results when the shape is fixed to a square and the displacement is changed in three ways of 0.0a, 0.125a, and 0.25a. In this calculation, a time-domain difference method that is more accurate than the plane wave expansion method is used. The horizontal axis in FIG. 5 represents the size of the defective member. The white area in the background of the figure is an area having a photonic band gap. When the displacement is 0.0a, the two defect levels on the low energy (low frequency) side intersect near the magnitude Δx = 0.6. It is not preferable to use a defect level near this intersection because the unity of wavelength is lost. When the displacements are 0.125a and 0.25a, no such intersection is seen.
[0039]
FIG. 6 shows the minimum value Δν of the interval between the defect level having the lowest frequency and the other levels. _min Is shown. The “other levels” are the band edge on the high frequency side on the left side of the × mark, the adjacent levels between the × mark and the + mark, Also on the right side is the band edge on the low frequency side. The dashed line indicates the distance between the defect level and the band edge on the side close to the defect level. Note that, within the calculated range, when the displacement is 0.0a, the "other levels" are all adjacent levels, and when the displacement is 0.125a, the "other levels" are the band edges on the high frequency side. It does not become.
[0040]
In FIG. 6, when the displacement is 0.25a, Δν _min Is shown to be the largest. Here, when considering the introduction of a luminescent material made of an InGaAsP-based material into a point defect, the full width at half maximum of the multiple quantum well at room temperature is experimentally 60 meV (0.0315 c / a) is observed, and judging from this value, Δν _min Is desirably 30 half meV or more. When the displacement is 0.25a, this condition is satisfied, and a single-mode strong light emission is obtained.
[0041]
Next, FIGS. 7 to 9 show the results of calculation using a plane wave expansion method for rectangular defects with Δx / Δy of 1.5, 2.0, and 2.5. In each case, it can be seen that the difference between the defect level having the lowest frequency and the defect level adjacent thereto is larger than that of the square defect. As Δx / Δy increases, the difference increases. At the time of the square defect, the intersection of the defect levels was observed. When the displacement was 0.0a, the difference from the adjacent defect level increased with the increase of Δx / Δy, and when Δx / Δy = 2.5, The intersection has disappeared.
[0042]
FIG. 10 shows a result of the above calculation at Δx / Δy = 2.0 using the time domain difference method. Comparing FIG. 5 with FIG. 5 in order to compare the difference between the rectangular defect and the square defect, it can be seen that it is very similar to FIG. 5 from which adjacent levels have been removed. This is because, when the value of Δx / Δy is larger than 1, the adjacent level is suppressed and shifted to the high frequency side, but such a shift does not occur in the used level and the next adjacent level. by. The difference between the adjacent level and the used level is that the electromagnetic field distribution in the adjacent level spreads in the y direction, whereas the electromagnetic field distribution in the used level is strongly localized at the center of the point defect. by.
[0043]
FIG. 11 shows Δν at Δx / Δy = 2.0 calculated from FIG. _min Is shown. The symbols x and + in the figure and the meaning of the broken lines are the same as those in FIG. In any case, the displacement was Δν more than that of the square defect. _min It can be seen that has increased.
[0044]
FIG. 12 shows a calculation result of the Q value when the displacement is 0.25a for each of the square defect and the rectangular defect (Δx / Δy = 2.0). Each Δx is Δx = 0.65a (square defect) and Δx = 0.80a (rectangular defect) when the defect level is near the center of the photonic band gap. The horizontal axis in FIG. 12 represents the total number of stacked stripe layers. If there are n layers of stripe layers above and below the layer to which the point defect belongs, the value on the horizontal axis is 2n + 1. From this figure, in both cases of the square defect and the rectangular defect, when n = 6, the Q value reaches 1000 which is a value at which laser oscillation can be obtained at room temperature.
[0045]
FIG. 13 shows the results of calculating the Δx dependence of the Q value for the square defects and the rectangular defects (Δx / Δy = 2.0) for the cases of n = 4 and n = 8. From this figure, it can be seen that when n = 8, a high Q value is obtained for any value of Δx. Therefore, a defect level having a high Q value can be formed over a wide wavelength range within the photonic band gap, and a high degree of freedom in designing can be obtained.
[0046]
FIG. 14 shows the displacement dependence of the Q value for a rectangular defect (Δx / Δy = 2.0) when n = 8. A high Q value is maintained at any displacement.
[0047]
From the calculation results so far, it is found that by appropriately setting the parameters of the defective member to be arranged at the point defect, the interval between the defect levels can be widened and a high Q value can be obtained in a wide frequency range. Was. From this, if a plurality of defect members having different shapes, sizes, and / or displacements are introduced into one three-dimensional photonic crystal, a plurality of point defect resonators having a plurality of different resonance frequencies will cause each other to have a different frequency. Regions do not overlap and all are obtained with high Q values. As described above, since a plurality of optical resonators can be realized using only one three-dimensional photonic crystal, the resonator according to the present invention contributes to downsizing of a device such as wavelength division multiplexing optical communication.
[0048]
Here, as shown in FIG. 15, a three-dimensional photonic crystal provided with a plurality of defect members having the same shape and size and different displacements will be examined. Such a configuration is advantageous in mass production because there is only one type of defective member. In this figure, an example is given in which the displacement of each defect differs by a constant interval Δd, but it goes without saying that only the displacement corresponding to the target wavelength may be introduced. FIG. 16 shows an example of the normalized frequency of each point defect when a plurality of point defects having different displacements are introduced when Δx = 0.8 and Δx / Δy = 2.0. When the standardized frequency is applied to the 1.55 μm band (C band) used in optical multiplex communication or the like, it can be seen that the wavelength can be controlled over a range of 1.525 μm to 1.565 μm and a bandwidth of 0.04 μm. At present, the wavelength band actually used in the optical multiplex communication is 1.530 μm to 1.565 μm. Therefore, the optical resonator according to the present invention can cope with it only by adjusting the displacement of the point defect.
[0049]
When N point defects having the same shape and the same size but different displacements are introduced as shown in FIG. 15, if the displacements are set so as to be equally spaced within a range of 0.0a to 0.25a, Light of a plurality of wavelengths in which the wavelengths are equally spaced in the entire wavelength band can be obtained. With such a configuration, as described above, light of a plurality of wavelengths within a given wavelength band in optical multiplex communication can be generated by one light source, and the wavelengths are equally spaced. Thus, the wavelength band can be used effectively.
[0050]
In practical use, it is convenient to set the displacements so as to be evenly spaced within the range of 0.0a to 0.5a. In this way, as shown by the ranges A and B in FIG. 17, the entire wavelength band is always covered regardless of the position of the range (ie, even if the range is shifted by ΔL in the y direction as a whole). Will be able to do it. This structure is very useful in consideration of manufacturing misalignment.
[0051]
By appropriately setting the size of the point defect other than the displacement of the point defect, it is possible to introduce a point defect optical resonator having a plurality of different resonance frequencies in a wider bandwidth. However, a bandwidth wider than the photonic band gap cannot be created. Here, in order to control the size of the photonic band gap, it is necessary to adjust parameters in the host crystal.
[0052]
Therefore, the structural parameters of the parent three-dimensional photonic crystal for controlling the size of the photonic band gap will be examined. The target parameters are the in-plane / out-of-plane period ratio z / a relating to the lamination period of the stripe layer, and the rod filling ratio w / a in the stripe layer.
[0053]
FIG. 18 shows the dependence of the photonic band gap width on the in-plane / out-of-plane period ratio z / a and the filling factor w / a. Here, the vertical axis shows the photonic band gap width divided by its center frequency in percentage. Focusing on the filling rate w / a, if the in-plane / out-of-plane period ratio z / a is any value, if the filling rate w / a is out of the range of 0.2 to 0.4, the photonic becomes farther away from the range. The band gap width decreases sharply. From this result, it is understood that the filling ratio w / a is preferably set to 0.2 to 0.4.
[0054]
FIG. 19 shows the dependency of the photonic band gap width on the in-plane / out-of-plane period ratio z / a using the filling factor w / a when the photonic band gap width is maximized at each value of the in-plane / out-of-plane period ratio z / a. Show. The filling ratio w / a used here is 0.275 at 1.05 <z / a <1.225 and 1.70 <z / a, and 0.30 at 1.25 <z / a <1.65. It is. From FIG. 19, it can be seen that the photonic band gap width is largest when z / a = 1.225.
[Brief description of the drawings]
FIG. 1 is a configuration example of a three-dimensional photonic crystal serving as a base of a three-dimensional photonic crystal optical resonator of the present invention.
FIG. 2 is a graph showing a photonic band structure of a base three-dimensional photonic crystal.
FIG. 3 is a diagram illustrating an example of a shape of a defective member introduced into a three-dimensional photonic crystal.
FIG. 4 is a diagram illustrating an example of displacement of a defective member introduced into a three-dimensional photonic crystal.
FIG. 5 is a graph showing displacement dependence of a relationship between the size of a square defect and a resonance frequency.
FIG. 6 shows Δν in a square defect _min A graph representing.
FIG. 7 is a graph showing the displacement dependence of the relationship between the size of a defective member and the resonance frequency in the case of a rectangular defect where Δx / Δy is 1.5.
FIG. 8 is a graph showing the displacement dependence of the relationship between the size of a defective member and the resonance frequency in the case of a rectangular defect having Δx / Δy of 2.0.
FIG. 9 is a graph showing the displacement dependence of the relationship between the size of a defective member and the resonance frequency in the case of a rectangular defect where Δx / Δy is 2.5.
FIG. 10 is a graph showing the result of calculating the displacement dependence of the relationship between the size of a defective member and the resonance frequency in the case of a rectangular defect having Δx / Δy of 2.0 by the time domain difference method.
FIG. 11 shows Δν in a rectangular defect _min A graph representing.
FIG. 12 is a graph showing a calculation result of a Q value when a displacement is 0.25a for each of a square defect and a rectangular defect (Δx / Δy = 2.0).
FIG. 13 is a graph showing the Δx dependency of the Q value for each of a square defect and a rectangular defect (Δx / Δy = 2.0).
FIG. 14 is a graph showing displacement dependence of a Q value in a rectangular defect (Δx / Δy = 2.0).
FIG. 15 is a configuration diagram of a resonator having a plurality of point defects arranged at different displacements.
FIG. 16 is a table showing a normalized frequency of each point defect when a plurality of point defects having different displacements are arranged.
FIG. 17 is a diagram schematically illustrating a resonance wavelength of each point defect when a plurality of point defects having different displacements are arranged.
FIG. 18 is a graph showing the dependency of the photonic band gap width on the in-plane / out-of-plane period ratio z / a and the filling factor w / a.
FIG. 19 is a graph showing the dependence of the photonic band gap width on the in-plane / out-of-plane period ratio z / a.
[Explanation of symbols]
11… Rod
12 ... Point defect

Claims (18)

a) A plurality of stripe layers in which a plurality of rods are arranged in parallel and periodically at a predetermined in-plane period are stacked in parallel, and each rod belonging to each stripe layer is orthogonal to each rod belonging to the nearest stripe layer. A main body made of a three-dimensional photonic crystal in which each rod belonging to each stripe layer is parallel to each rod belonging to a stripe layer separated by two layers and is shifted by ず れ of the in-plane period;
b) a point defect provided on one of the rods and having a ratio Δx / Δy of a size Δx in the rod width direction and a size Δy in the rod longitudinal direction larger than 1;
A point-defect three-dimensional photonic crystal optical resonator, comprising: a) A plurality of stripe layers in which a plurality of rods are arranged in parallel and periodically at a predetermined in-plane period are stacked in parallel, and each rod belonging to each stripe layer is orthogonal to each rod belonging to the nearest stripe layer. A main body made of a three-dimensional photonic crystal in which each rod belonging to each stripe layer is parallel to each rod belonging to a stripe layer separated by two layers and is shifted by ず れ of the in-plane period;
b) a point defect provided in one of the rods, wherein the center of the point defect is determined from the center axis of the nearest rod belonging to the stripe layer adjacent to the point defect; Point defects arranged displaced in the longitudinal direction;
A point-defect three-dimensional photonic crystal optical resonator, comprising: 3. The point defect three-dimensional photonic crystal optical resonator according to claim 2, wherein the displacement is at least 0.1 times the in-plane period. 4. The point-defect three-dimensional photonic crystal optical resonator according to claim 3, wherein the displacement is 0.25 times the in-plane period. 5. The point defect three-dimensional photonic according to claim 2, wherein a ratio [Delta] x / [Delta] y of the size [Delta] x in the rod width direction and the size [Delta] y in the rod longitudinal direction of the point defect is larger than 1. Crystal optical resonator. 6. The point defect three-dimensional photonic crystal optical resonator according to claim 5, wherein the ratio Δx / Δy is 1.5 to 2.5. 7. The point-defect three-dimensional photonic crystal optical resonator according to claim 6, wherein the ratio [Delta] x / [Delta] y is 2.0 to 2.5. The point defect three-dimensional photonic crystal optical resonator according to any one of claims 1 to 7, wherein the point defect is formed of a rectangular parallelepiped defect member having the same height as a rod. 9. The point defect three-dimensional photonic crystal optical resonator according to claim 1, wherein four or more stripe layers are provided above and below the stripe layer to which the point defect belongs. 10. The point defect three-dimensional photonic crystal optical resonator according to claim 9, wherein six or more stripe layers are provided above and below the stripe layer to which the point defect belongs. 11. The method according to claim 1, wherein an out-of-plane period, which is a length of one period in the stacking direction including four stripe layers, is 1.1 to 1.7 times the in-plane period. The point defect three-dimensional photonic crystal optical resonator according to the above. Point defects wherein one period of the lamination direction consisting stripe layer of four layers plane period is the length in claim 11, characterized in that the 2 ^{0.5 to 1.7} times the surface within a period Three-dimensional photonic crystal optical resonator. The point defect three-dimensional photonic crystal optical resonator according to claim 1, wherein a ratio of a width of the rod to the in-plane period is 0.2 to 0.4. 14. The point defect three-dimensional photonic crystal optical resonator according to claim 1, wherein a plurality of point defects are provided in the main body. 15. The point defect three-dimensional photonic crystal optical resonator according to claim 14, wherein a plurality of point defects having the same shape and different displacements are provided in the main body. The point defect three-dimensional photo according to claim 15, wherein a plurality of point defects having the same shape are provided in the main body such that the displacements are equally spaced within a range of 0.0a to 0.25a. Nick crystal optical resonator. The point defect three-dimensional photo according to claim 15, wherein a plurality of point defects having the same shape are provided in the main body such that the displacements are equally spaced within a range of 0.0a to 0.5a. Nick crystal optical resonator. 18. The point-defect three-dimensional photonic crystal optical resonator according to claim 1, wherein a light emitter is introduced into the point-defect portion.

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