Patent Publication Number: US-7715668-B2

Title: Polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer

Description:
TECHNICAL FIELD 
     The present invention relates to a polarization-independent multiplexer/demultiplexer capable of demultiplexing both transverse-electric (TE) and transverse-magnetic (TM) components of light with a predetermined wavelength or multiplexing these two components of light. 
     BACKGROUND ART 
     Optical communication is a technique that could play a central role in future broadband communications. Accordingly, for widespread use of the optical communication, the optical components used in optical communication systems are required to be higher in performance, smaller in size and lower in price. Optical communication devices using photonic crystals are one of the leading candidates for the next-generation optical communication components that satisfy the aforementioned requirements. Some of these devices have already been put into practical use, an example of which is a photonic crystal fiber for polarization dispersion compensation. Furthermore, recent efforts have had the practical goal of developing optical multiplexers/demultiplexers and other devices that can be used in wavelength division multiplexing. 
     A photonic crystal consists of a dielectric body in which a periodic structure is formed. Typically, the periodic structure is created by providing the dielectric body with a periodic arrangement of modified refractive index areas, i.e. the areas whose refractive index differs from that of the dielectric body. Within the crystal, the periodic structure creates a band structure with respect to the energy of light and thereby produces an energy region in which the light cannot be propagated. Such an energy region is called the “photonic band gap” or “PBG.” 
     Providing an appropriate defect in the photonic crystal creates a specific energy level within the PBG (“defect level”), and only such light that has a wavelength (or frequency) corresponding to the defect level is allowed to be present in the vicinity of the defect. A defect that is shaped like a point can be used as a resonator for the light having the aforementioned wavelength, whereas a linearly shaped defect can be used as a waveguide. 
     As an example of the previously described technique, Patent Document 1 discloses a two-dimensional photonic crystal having a body (or slab) provided with a periodic arrangement of modified refractive index areas, in which a linear defect of the periodic arrangement is created to form a waveguide and a point-like defect is created adjacent to the waveguide to form a resonator. This two-dimensional photonic crystal functions as the following two devices: a demultiplexer for extracting a component of light whose wavelength equals the resonance frequency of the resonator from the components of light having various wavelengths and propagated through the waveguide and for sending the extracted light to the outside; and a multiplexer for introducing the same light from the outside into the waveguide. 
     Including the one disclosed in Patent Document 1, many two-dimensional photonic crystals are designed so that a wide PBG is created for either a TE-polarized light, in which the electric field oscillates in the direction parallel to the body, or a TM-polarized light, in which the magnetic field oscillates in the direction parallel to the body. In this case, it is possible that no PBG is created for the other polarized light, or a PBG may be created for this polarized light but only under non-optimal conditions. 
     For example, if the photonic crystal is designed so that a PBG for the TE polarization (TE-PBG) is created and a defect level (resonance wavelength) due to a point-like defect (resonator) is created within the TE-PBG, it is possible that a PBG for the TM polarization (TM-PBG) is not created within the wavelength range of the TE-PBG. In this case, a TM-polarized light having the resonance wavelength does not resonate at the resonator. Therefore, in an attempt to demultiplex light having the resonance wavelength from broadband light passing through a waveguide located in the vicinity of the resonator, though the TE-polarized light can be almost completely extracted, the demultiplexing efficiency will be low since the TM-polarized light cannot be extracted. A similar problem also arises in the case of multiplexing. 
     Patent Document 1: Japanese Unexamined Patent Application Publication No. 2001-272555 (Paragraphs [0023] through [0027] and [0032]; FIGS. 1 and 5 through 6) 
     DISCLOSURE OF THE INVENTION 
     Problem to be Solved by the Invention 
     The problem to be solved by the present invention is to provide a wavelength multiplexer/demultiplexer capable of multiplexing and demultiplexing light with a specific wavelength for both TE and TM polarizations and thereby achieving a high level of multiplexing/demultiplexing efficiency. 
     Means for Solving the Problems 
     (1) Configuration of First Mode of Polarization-Independent Two-Dimensional Photonic Crystal Multiplexer/Demultiplexer 
     To solve the aforementioned problem, the polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the first mode of the present invention is a wavelength multiplexer/demultiplexer created on a two-dimensional photonic crystal formed of a plate-shaped body with a periodic distribution of refractive index created therein and having a photonic band gap for the TE polarization, which is characterized by comprising: 
     a) a first waveguide and a second waveguide separately provided in the two-dimensional photonic crystal, each waveguide formed by creating a linear defect of the periodic distribution of the refractive index; 
     b) a first resonator and a second resonator separately provided between the first and second waveguides, both resonators having the same resonance wavelength, and each resonator formed by creating a point-like defect of the periodic distribution of the refractive index; 
     c) a first polarization converter provided on the first waveguide between a first closest point, which is the point closest to the first resonator on the first waveguide, and a second closest point, which is the point closest to the second resonator on the first waveguide, the first polarization converter being capable of converting a TM-polarized light propagated from the first closest point toward the second closest point to a TE-polarized light; and 
     d) a second polarization converter provided on the second waveguide between a third closest point, which is the point closest to the first resonator on the second waveguide, and a fourth point, which is the point closest to the second resonator on the second waveguide, the second polarization converter being capable of converting a TE-polarized light propagated from the third closest point toward the fourth closest point to a TM-polarized light. 
     The configuration of the polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the first mode of the present invention (which will be referred to as the “first mode multiplexer/demultiplexer”) is hereinafter described in detail with reference to the conceptual diagram of  FIG. 1 . 
     The first mode multiplexer/demultiplexer is created on a two-dimensional photonic crystal  11 . The two-dimensional photonic crystal  11  is a plate-shaped body in which a periodic distribution of the refractive index is created. As explained earlier, there are two types of two-dimensional photonic crystals: One type has a PBG created for the TE polarization, and the other type has a PBG created for the TM polarization. The first mode multiplexer/demultiplexer uses the former type. (The latter type will be used in the second mode, which will be described later.) A PBG for the TM polarization may or may not be created. 
     In this two-dimensional photonic crystal  11 , a first waveguide  121  and second waveguide  122  are separately provided. Each of these waveguides can be formed by creating a linear defect in the periodic diffraction index distribution of the two-dimensional photonic crystal  11 . 
     A first resonator  131  and second resonator  132  are separately provided between the first and second waveguides. Each of these resonators can be formed by creating a point-like defect in the periodic diffraction index distribution of the two-dimensional photonic crystal  11 . The resonance wavelength of the resonators can be regulated by changing various parameters as described in Patent Document 1, such as the shape of the point-like defect and the period distance of the refractive index distribution. In the present invention, the first and second resonators  131  and  132  have the same resonance wavelength, which is adjusted at the wavelength of the light that should be multiplexed and/or demultiplexed. In the first mode, since the two-dimensional photonic crystal  11  is designed to have a PBG for the TE polarization, these resonators effectively work only on the TE-polarized light (i.e. multiplex/demultiplex this light with high efficiency). 
     A first polarization converter  151  is provided on the first waveguide  121  between a first closest point  141 , which is the point closest from the first resonator  131  on the first waveguide  121 , and a second closest point  142 , which is the point closest from the second resonator  132  on the first waveguide  121 . This converter is capable of converting a TM-polarized light propagated from the first closest point  141  toward the second closest point  142  to a TE-polarized light. Similarly, a second polarization converter  152  is provided on the second waveguide  122  between a third closest point  143 , which is the point closest from the first resonator  131  on the second waveguide  122 , and a fourth closest point  144 , which is the point closest from the second resonator  132  on the second waveguide  122 . This converter is capable of converting a TE-polarized light propagated from the third closest point  143  toward the fourth closest point  144  to a TM-polarized light. It has been already known that such polarization converters for converting a TE-polarized light to a TM-polarized light or vice versa can be created using a two-dimensional photonic crystal (examples of which are disclosed in Sei-ichi Takayama et al,  Preprints of the  52 th Spring Meeting of the Japan Society of Applied Physics  2005, vol. 3, Lecture No. 30a-YV-11, and Yoshinori Tanaka et al,  Preprints of the  66 th Autumn Meeting of the Japan Society of Applied Physics  2005, vol. 3, Lecture No. 8p-H-5). Those two-dimensional photonic crystal polarization converters can be directly used in the present invention. 
     (1) Operation of First Mode Multiplexer/Demultiplexer 
     An operation of the first mode multiplexer/demultiplexer is hereinafter described with reference to  FIG. 1 . The following description initially deals with the use of the device as a demultiplexer for extracting light whose wavelength equals the resonance wavelength (labeled λr) of the first and second resonators  131  and  132  from superimposed light containing a large number of wavelength components. In this demultiplexer, the end of the first waveguide  121  closer to the first closest point  141  becomes an input port  161  for the introduction of superimposed light into the first waveguide  121 . The end of the second waveguide  122  close to the fourth closest point  144  becomes an output port  162  for the output of demultiplexed light with wavelength λr. 
     When superimposed light is introduced from the input port  161  into the first waveguide  121 , a TE-polarized light with wavelength λr contained in the superimposed light resonates with the first resonator  131  and is captured by the same resonator, to be demultiplexed into the second waveguide  122 . The demultiplexed TE-polarized light is propagated through the second waveguide  122  toward the output port  162 . If this light maintains its original mode (TE polarization) while propagating through the second waveguide, it will be captured by the second resonator  132  and returned to the first waveguide  121 . To avoid this situation, the TE-polarized light with wavelength λr that has been demultiplexed into the second waveguide  122  is converted to a TM-polarized light by the second polarization converter  152 . The resultant TM-polarized light with wavelength λr passes through the fourth closest point  144  without being captured by the second resonator  132 , to be extracted from the output port  162 . 
     Meanwhile, the superimposed light excluding the TE-polarized light with wavelength λr (but including a TM-polarized light with wavelength λr) passes through the first closest point  141  without being captured by the first resonator  131  and continues through the first waveguide  121 . Then, at the first polarization converter  151 , the TM-polarized light with wavelength λr contained in the superimposed light is converted to a TE-polarized light. The resultant TE-polarized light with wavelength λr resonates with the second resonator  132  and is captured by the same resonator, to be demultiplexed into the second waveguide  122 . 
     The components of light that have been introduced from the input port  161  with wavelengths different from λr pass through both of the first and second closest points  141  and  142  on the first waveguide  121 ; they will not be demultiplexed into the second waveguide  122 . 
     Thus, the first mode multiplexer/demultiplexer can extract both TE and TM polarized lights with wavelength λr from superimposed light introduced from the input port  161  into the first waveguide  121  and demultiplex them into the second waveguide  122 . 
     When the first mode multiplexer/demultiplexer is used as a multiplexer, TE and TM-polarized lights with wavelength λr are introduced from the input port  161  into the first waveguide  121 , and the light into which those lights should be multiplexed is introduced into the second waveguide  122  through the end of the second waveguide  122  closer to the third closest point  143 . As in the case of the demultiplexer, the TE and TM-polarized lights with wavelength λr that have been introduced into the first waveguide  121  are introduced into the second waveguide  122  through the first and second resonators  131  and  132 , respectively, and multiplexed into the light within the second waveguide  122 . 
     The first and second polarization converters may be a polarization converter capable of both TE-to-TM and TM-to-TE conversions. The use of such a polarization converter eliminates the distinction between the first and second waveguides, enabling any one of these waveguides to serve as a waveguide for the introduction of superimposed light and the other to serve as an output waveguide for the demultiplexed light with wavelength λr. This discussion also holds true for the operation as a multiplexer. 
     (3) Configuration for Improving Efficiency of First Mode Multiplexer/Demultiplexer 
     The TE-polarized light with wavelength λr introduced from the input port  161  is not entirely captured by the first and second resonators  131  and  132  while passing through the first waveguide  121 ; a portion of this light can pass through the first and closest points  141  and  142 . This deteriorates the multiplexing or demultiplexing efficiency. Additionally, a portion of the TE-polarized light with wavelength λr multiplexed or demultiplexed into the second waveguide  122  is propagated in the direction opposite to the output port  162 , which also deteriorates the multiplexing or demultiplexing efficiency. To address these problems and improve the multiplexing and demultiplexing efficiencies, the first mode multiplexer/demultiplexer may be configured as follows: 
     As shown in  FIG. 2 , a first reflector  171  for reflecting a TE-polarized light with wavelength λr is provided on the first waveguide  121  between the first closest point  141  and the first polarization converter  151 . In this configuration, a TE-polarized light with wavelength λr that has passed through without being captured by the first resonator  131  will be reflected by the first reflector  171  toward the first resonator  131  and captured by the same resonator  131 , to be introduced into the second waveguide  122 . Thus, the multiplexing or demultiplexing efficiency is improved. Similarly, a second reflector  172  may be provided on the first waveguide  121  downstream from the second closest point  142  (i.e. on the side opposite to the input port  161 ). 
     Additionally, a third reflector  173  may be provided on the second waveguide  122  within the section upstream from the third closest point  143  (i.e. on the side opposite to the output port  162 ). In this configuration, a TE-polarized light with wavelength λr being propagated away from the output port  162  will be reflected by the third reflector  173  toward the output port  162 . Thus, the multiplexing or demultiplexing efficiency is improved. Similarly, a fourth reflector  174  may be provided on the second waveguide  122  between the fourth closest point  144  and the second polarization converter  152 . 
     To achieve the highest possible multiplexing and demultiplexing efficiencies, it is preferable to provide all of these four reflectors, although the provision of only one, two or three of the four reflectors can certainly improve the efficiency to levels higher than that of the multiplexer/demultiplexer of  FIG. 1 . 
     Such a reflector can be created in the following manner: The wavelength range of light that is allowed to transmit through the waveguide changes according to the cycle distance of the refractive index distribution of the two-dimensional photonic crystal. Given this knowledge, the refractive index distribution of the two-dimensional photonic crystal is designed in such a manner that the cycle distance of the refractive index distribution in the reflector differs from that in the sections other than the reflector so that the wavelength λr will not be included in the transmission wavelength band of the waveguide within the reflector. As a result, the TE-polarized light with wavelength λr will be reflected by the boundary between the reflector and the surrounding two-dimensional photonic crystal. A detailed description of this reflector is available in Japanese Unexamined Patent Application Publication No. 2004-233941. 
     (4) Second Mode of Polarization-Independent Two-Dimensional Photonic Crystal Multiplexer/Demultiplexer 
     The preceding discussion dealt with the first mode multiplexer/demultiplexer using a two-dimensional photonic crystal having a PBG for the TE polarization. It is also possible to use a two-dimensional photonic crystal having a PBG for the TM polarization to create a polarization-independent multiplexer/demultiplexer similar to the first mode. Thus, the polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the second mode of the present invention is a wavelength multiplexer/demultiplexer created on a two-dimensional photonic crystal formed of a plate-shaped body with a periodic distribution of refractive index created therein and having a photonic band gap for the TM polarization, which is characterized by comprising: 
     a) a first waveguide and a second waveguide separately provided in the two-dimensional photonic crystal, each waveguide formed by creating a linear defect of the periodic distribution of the refractive index; 
     b) a first resonator and a second resonator separately provided between the first and second waveguides, both resonators having the same resonance wavelength, and each resonator formed by creating a point-like defect of the periodic distribution of the refractive index; 
     c) a first polarization converter provided on the first waveguide between a first closest point, which is the point closest from the first resonator on the first waveguide, and a second closest point, which is the point closest from the second resonator on the first waveguide, the first polarization converter being capable of converting a TE-polarized light propagated from the first closest point toward the second closest point to a TM-polarized light; and 
     d) a second polarization converter provided on the second waveguide between a third closest point, which is the point closest from the first resonator on the second waveguide, and a fourth point, which is the point closest from the second resonator on the second waveguide, the second polarization converter being capable of converting a TM-polarized light propagated from the third closest point toward the fourth closest point to a TE-polarized light. 
     In the second mode, since the PBG of the two-dimensional photonic crystal  11  is created for the TM-polarization, both of the first and second resonators effectively operate only for the TM-polarization (i.e. efficiently perform the multiplexing/demultiplexing only for the TM polarization). Therefore, the polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the second mode operates as follows (refer to  FIG. 3 ): When a TM-polarized light with wavelength λr is introduced from the input port  161 , the light will be captured by the first resonator  131 , to be introduced into the second waveguide  122 . Subsequently, this light is converted to a TE-polarized light by the second polarization converter  152  so that it will not be captured by the second resonator  132 , and then extracted from the output port  162 . When a TE-polarized light with wavelength λr is introduced from the input port  161 , the light will be converted to a TM-polarized light by the first polarization converter  151  and then captured by the second resonator  132 , to be introduced into the second waveguide  122  and eventually extracted from the output port  162 . 
     As in the first mode, the polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer in the second mode may be provided with one or more reflectors. The reflector in the second mode should reflect TM-polarized light. The location of the reflector is the same as in the first mode. 
     (5) Polarization-Independent Two-Dimensional Photonic Crystal Multistage Multiplexer/Demultiplexer 
     A polarization-independent two-dimensional photonic crystal multistage multiplexer and demultiplexer capable of multiplexing and demultiplexing at each of different wavelengths are hereinafter described. The polarization-independent two-dimensional photonic crystal multistage demultiplexer (which will be hereinafter called the “multistage demultiplexer”) includes a plurality of polarization-independent two-dimensional photonic crystal multiplexers/demultiplexers according to the first or second mode of the present invention (multiplexer/demultiplexer units  10 A,  10 B, . . . ), which are arranged so that the first waveguides of the multiplexer/demultiplexer units are connected in series. The polarization-independent two-dimensional photonic crystal multistage multiplexer (the “multistage multiplexer”) includes a plurality of multiplexer/demultiplexer units  10 A,  10 B and so on, which are arranged so that the second waveguides of the multiplexer/demultiplexer units are connected in series. 
     The configuration of the multistage demultiplexer  20  is hereinafter described with reference to  FIG. 4 . The first waveguide  121  is in the form of a single line connecting the multiplexer/demultiplexer units  10 A,  10 B and so on. The second waveguides ( 122 A,  122 B, . . . ) are separately provided in each of the multiplexer/demultiplexer units  10 A,  10 B and so on. The first resonators  131 A,  131 B, . . . of the multiplexer/demultiplexer units  10 A,  10 B, . . . have resonance wavelengths of λr 1 , λr 2  and so on, which differ from each other. The second resonators  132 A,  132 B, . . . of the multiplexer/demultiplexer units  10 A,  10 B, . . . also have resonance wavelengths of λr 1 , λr 2  and so on. Accordingly, the first and second resonators located in the same multiplexer/demultiplexer unit has the same resonance wavelength, and the value of this resonance wavelength of the first and second resonators changes from one multiplexer/demultiplexer unit to another. The configurations and locations of the first polarization converters  151 A,  151 B, . . . and second polarization converters  152 A,  152 B, . . . within each multiplexer/demultiplexer unit are identical to those of the already described first or second mode multiplexer/demultiplexer. 
     An operation of the multistage demultiplexer  20  is hereinafter described. The following description assumes that each of the multiplexer/demultiplexer units  10 A and  10 B is a first mode multiplexer/demultiplexer. However, the same explanation holds true of the case where each of the multiplexer/demultiplexer units  10 A and  10 B is a second mode multiplexer/demultiplexer. 
     Superimposed light containing wavelengths of λr 1 , λr 2  . . . is introduced from the input port  161  of the multiplexer/demultiplexer unit  10 A into the first waveguide  121 . The TE-polarized light with wavelength λr 1  contained in the superimposed light resonates with the first resonator  131 A and is captured by the same resonator, to be demultiplexed into the second waveguide  122 A. Subsequently, this light is converted to a TM-polarized light so that it will not be captured by the second resonator  132 A. The superimposed light excluding the TE-polarized light with wavelength λr 1  (but including a TM-polarized light with wavelength λr 1 ) passes by the first resonator  131 A. 
     The TM-polarized light with wavelength λr 1  contained in the superimposed light that has passed by the first resonator  131 A is converted to a TE-polarized light when it passes through the first polarization converter  151 A. The resultant TE-polarized light with wavelength λr 1  is captured by the second resonator  132 A, to be demultiplexed into the second waveguide  122 A. The superimposed light excluding light with wavelength λr 1  (but including TE and TM-polarized lights with wavelength λr 2 ) passes by the second resonator  132 A. By the operations described to this point, all modes of light with wavelength λr 1  originally contained in the superimposed light have been demultiplexed into the second waveguide  122 A. 
     The TE-polarized light with wavelength λr 2  contained in the superimposed light that has passed by the second resonator  132 A is captured by the first resonator  131 B, to be demultiplexed into the second waveguide  122 B. Subsequently, this TE-polarized light is converted to a TM-polarized light by the second polarization converter  152 B. The superimposed light excluding the light with wavelength λr 1  and the TE-polarized light with wavelength λr 2  (but including the TM-polarized light with wavelength λr 2 ) passes by the first resonator  131 B. 
     Subsequently, the TM-polarized light with wavelength λr 2  contained in the superimposed light is converted to a TE-polarized light when it passes through the first polarization converter  151 B. The resultant TE-polarized light with wavelength λr 2  is captured by the second resonator  132 B, to be demultiplexed into the second waveguide  122 B. Thus, all modes of light with wavelength λr 2  originally contained in the superimposed light have been demultiplexed into the second waveguide  122 B. 
     In a similar manner, any component of light whose wavelength differs from λr 1  and λr 2  can be demultiplexed into the second waveguide of the multiplexer/demultiplexer unit by using a multiplexer/demultiplexer unit having the first and second resonators that resonate at the wavelength concerned. 
       FIG. 5  is a conceptual diagram showing a polarization-independent two-dimensional photonic crystal multistage multiplexer  30  according to the present invention (which will be hereinafter called the “multistage multiplexer  30 ”). The same elements as used in the previously described multistage demultiplexer  20  are denoted by the same numerals. In the multistage multiplexer  30 , the second waveguide  122  is in the form of a single line passing through the multistage multiplexer  30  to connect the multiplexer/demultiplexer units  10 A,  10 B and so on. The first waveguides  121 A,  121 B and so on are separately provided in each of the multiplexer/demultiplexer units  10 A,  10 B and so on. Except for these points, the configuration of the multistage multiplexer  30  is identical to that of the multistage demultiplexer  20 . Such common elements are denoted by the same numerals as used for the elements of the multistage demultiplexer  20 . 
     The multistage multiplexer  30  is capable of multiplexing the components of light with wavelengths of λr 1 , λr 2 , . . . from the first waveguides  121 A,  121 B, . . . into the second waveguide  122  at the multiplexer/demultiplexer units  10 A,  10 B, . . . , respectively. The operations of the resonators and polarization converters in each multiplexer/demultiplexer unit during the multiplexing process are the same as those of the first or second mode multiplexer/demultiplexer. 
     In the multistage demultiplexer  20  or multistage demultiplexer  30 , the first and second polarization converters used in each of the multiplexer/demultiplexer units  10 A and  10 B may be a polarization converter capable of both TE-to-TM and TM-to-TE conversions. In this case, the configuration of the multistage demultiplexer  20  is the same as that of the multistage multiplexer  30 . Use of such a polarization converter makes it possible to create a polarization-independent two-dimensional photonic crystal multistage multiplexer/demultiplexer capable of both multiplexing and demultiplexing the components of light with different wavelengths λr 1 , λr 2  and so on. 
     EFFECT OF THE INVENTION 
     The polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the present invention makes it possible to multiplex and demultiplex both TE and TM-polarized lights with a predetermined wavelength, whereby the multiplexing and demultiplexing efficiencies can be enhanced to a level higher than those of many conventional types of two-dimensional photonic crystal multiplexer/demultiplexer that can only multiplex and demultiplex either a TE or TM-polarized light. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a conceptual diagram of a first mode polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the present invention. 
         FIG. 2  is a conceptual diagram of the first mode polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer having reflectors  171  to  174 . 
         FIG. 3  is a conceptual diagram of a second mode polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the present invention. 
         FIG. 4  is a conceptual diagram of a polarization-independent two-dimensional photonic crystal multistage multiplexer/demultiplexer according to the present invention. 
         FIG. 5  is a conceptual diagram of a polarization-independent two-dimensional photonic crystal multistage multiplexer/demultiplexer according to the present invention. 
         FIG. 6  is a top view showing an embodiment of a polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the present invention. 
         FIG. 7  is a top view showing the configuration of a first polarization converter  451  and a second polarization converter  452 , and vertical sectional views at sections A-A′ and B-B′ shown in the top view. 
         FIG. 8  is a top view showing the configuration of a multiplexer/demultiplexer  50  which is an embodiment of the polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer provided with reflectors. 
         FIG. 9  shows a calculated result of the intensity distribution of TE and TM-polarized lights within a waveguide in the case of introducing a TE-polarized light into the input port  461  of the multiplexer/demultiplexer  50 . 
         FIG. 10  is shows a calculated result of the intensity distribution of TE and TM-polarized lights within a waveguide in the case of introducing a TM-polarized light into the input port  461  of the multiplexer/demultiplexer  50 . 
         FIG. 11  is a top view showing an embodiment of the polarization-independent two-dimensional photonic crystal multistage multiplexer/demultiplexer according to the present invention. 
     
    
    
     EXPLANATION OF NUMERALS 
     
         
           10 A,  10 B,  40 A,  40 B . . . Multiplexer/Demultiplexer Unit 
           11 ,  41  . . . Two-Dimensional Photonic Crystal 
           121 ,  121 A,  121 B,  421 ,  62  . . . First Waveguide 
           122 ,  122 A,  122 B,  422 ,  422 A,  422 B . . . Second Waveguide 
           131 ,  131 A,  131 B,  431 ,  431 A,  431 B . . . First Resonator 
           132 ,  132 A,  132 B,  432 ,  432 A,  432 B . . . Second Resonator 
           141  . . . First Closest Point 
           142  . . . Second Closest Point 
           143  . . . Third Closest Point 
           144  . . . Fourth Closest Point 
           151 ,  151 A,  151 B,  451 ,  451 A,  451 B . . . First Polarization Converter 
           152 ,  152 A,  152 B,  452 ,  452 A,  452 B . . . Second Polarization Converter 
           161 ,  461  . . . Input Port 
           162 ,  462  . . . Output Port 
           171 ,  471  . . . First Reflector 
           172 ,  472  . . . Second Reflector 
           173 ,  473  . . . Third Reflector 
           174 ,  474  . . . Fourth Reflector 
           20  . . . Polarization-Independent Two-Dimensional Photonic Crystal Multistage Demultiplexer (Multistage Demultiplexer) 
           30  . . . Polarization-Independent Two-Dimensional Photonic Crystal Multistage Multiplexer (Multistage Multiplexer) 
           40 ,  50  . . . Multiplexer/Demultiplexer 
           411  . . . Slab 
           412  . . . Air Hole 
           412 A,  412 B . . . Oblique Air Hole 
           48  . . . Section Including Polarization Converters 
           511 ,  512 ,  515 ,  516  . . . Area Where TE-Polarized Light Is Present 
           513 ,  514  . . . Area Where TM-Polarized Light Is Present 
           60  . . . Multistage Multiplexer/Demultiplexer 
           62 A,  62 B . . . Bending Portion 
       
    
     BEST MODES FOR CARRYING OUT THE INVENTION 
     (1) First Embodiment of Polarization-Independent Two-Dimensional Photonic Crystal Multiplexer/Demultiplexer According to Present Invention 
     The first embodiment of the polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer according to the present invention is hereinafter described with reference to  FIGS. 6 and 7 .  FIG. 6  is a top view of the multiplexer/demultiplexer  40  in the present embodiment. The two-dimensional photonic crystal  41  used in this multiplexer/demultiplexer is similar to the one shown in Patent Document 1; it is made of a slab  411  in which a periodic distribution of refractive index is created by arranging circular air holes (modified refractive index areas)  412  in a triangular lattice pattern. This two-dimensional photonic crystal  41  has a PBG created for the TE polarization. 
     A first waveguide  421  is formed by omitting one row of air holes  412  (i.e. by not providing air holes  412  along one line of the triangular lattice). Similarly, a second waveguide  422  is formed separately from the first waveguide  421 . A first resonator  431  is created between the first and second waveguides  421  and  422  by omitting three air holes  412  aligned parallel to the first and second waveguides  421  and  422 . Similarly, a second resonator  432  is created separately from the first resonator  431  between the first and second waveguides  421  and  422 . 
     A first polarization converter  451  is provided between the point closest from the first resonator  431  on the first waveguide  421  and the point closest from the second resonator  432 . Similarly, a second polarization converter  452  is provided between the point closest from the first resonator  431  on the second waveguide  422  and the point closest from the second resonator  432 . As shown in  FIG. 7 , among the air holes located on both sides of the first waveguide  421  in the first polarization converter  451 , the two pairs of air holes located on the side closer to the first resonator  431  extend perpendicularly to the first waveguide  421  and obliquely at an angle of 45° to the plane of the slab  411 . (These pairs are hereinafter called the “oblique air holes  412 A.”) The other two pairs of air holes on both sides of the first waveguide  421 , which are located closer to the second resonator  432  and next to the oblique air holes  412 A, are shaped like a mirror image of the oblique air holes  412 A with respect to a plane of mirror symmetry parallel to the extending direction of the first waveguide  421 . (These pairs are hereinafter called the “oblique air holes  412 B.”) Additionally, another set of oblique air holes having the same configuration as those of the oblique air holes  412 A and  412 B is provided on the side closer to the second resonator  432  from the air holes  412 A and  412 B. The second polarization converter  452  is identical in configuration to the first polarization converter  451 . 
     The oblique air holes can be created by an anisotropic etching process. An example of the anisotropic etching process is a plasma-etching method using an electric field by which a plasma gas is made to move in a specific direction and collide with the slab  411 ; another example is a method using a focused ion beam. 
     These first and second polarization converters  451  and  452  are each capable of both TE-to-TM and TM-to-TE conversions, regardless of the direction of the light propagating through the waveguide within the polarization converter. That is, a TE-polarized light propagated from the first resonator  431  toward the second resonator  432  is converted to a TM-polarized light, and a TM-polarized light to a TE-polarized light. Similarly, a TE-polarized light propagated from the second resonator  432  toward the first resonator  431  is converted to a TM-polarized light, and a TM-polarized light to a TE-polarized light. 
     However, the first and second polarization converters  451  and  452  have a limited frequency range within which they can convert the polarization. The range is between 0.270c/a to 0.274c/a, where a is the cycle distance of the triangular lattice and c is the speed of light. By contrast, the resonance frequency of the first resonator  431  and the second resonator is 0.261c/a. Accordingly, if the cycle distance of the triangular lattice is uniform over the entire two-dimensional photonic crystal  41 , it is impossible to convert the polarization because the light whose frequency equals the resonance frequency of the resonators (i.e. the frequency of the light to be multiplexed or demultiplexed) is not included within the conversion-capable frequency band of the polarization converters. Given this problem, in the present embodiment, the cycle distance of the triangular lattice is varied: the value is a 0  within the regions except for the section  48  including the first and second polarization converters  451  and  452 , and 1.041a 0  within this section  48 . This configuration gives the polarization converter a conversion-capable frequency band of 0.259c/a 0  to 0.263c/a 0 , which includes the frequency of the light to be multiplexed or demultiplexed: 0.261c/a 0 . 
     The operation of the multiplexer/demultiplexer  40  in the present embodiment as a demultiplexer is as follows: When superimposed light containing a wavelength that equals the resonance wavelength λr (or resonance frequency) of the first resonator  431  and the second resonator is introduced into the first waveguide  421  from the end of the same waveguide  421  closer to the first resonator  431  (i.e. from the input port  461 ), the TE-polarized light with wavelength λr contained in the superimposed light resonates with the first resonator  431  and is captured by the same resonator, to be demultiplexed into the second waveguide  422 . The demultiplexed TE-polarized light is converted to a TM-polarized light by the second polarization converter  452  and extracted from the end of the second waveguide  422  closer to the second resonator  432  (i.e. from the output port  462 ) without being captured by the same resonator  432 . The superimposed light excluding the TE-polarized light with wavelength λr (but including a TM-polarized light with wavelength λr) passes through without being captured by the first resonator  431 . Among this superimposed light, the TM-polarized light with wavelength λr is converted to a TE-polarized light by the first polarization converter  451 . The resultant TE-polarized light resonates with the second resonator  432  and is captured by the same resonator, to be demultiplexed into the second waveguide  422 . 
     The operation of the multiplexer/demultiplexer  40  as a multiplexer is as follows: When superimposed light is introduced into the second waveguide and TE and TM-polarized lights with wavelength λr are introduced into the first waveguide  421 , the TE-polarized light with wavelength λr is captured by the first resonator  431 , to be multiplexed into the second waveguide  422 . Subsequently, this TE-polarized light with wavelength λr is converted to a TM-polarized light by the second polarization converter  452  and so will not be captured by the second resonator  432 . This TM-polarized light with wavelength λr will not be captured by the first resonator  431  but converted to a TE-polarized light by the first polarization converter  451 . The resultant TE-polarized light with wavelength λr is captured by the second resonator  432 , to be multiplexed into the second waveguide  422 . 
     In the two-dimensional photonic crystal  41 , it is possible to use equilateral-triangular air holes in place of the circular air holes  412  to obtain a two-dimensional photonic crystal having a PBG created for the TM polarization. Providing this two-dimensional photonic crystal with waveguides, resonators and polarization converters as in the multiplexer/demultiplexer  40  results in a second mode polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer. 
     (2) Embodiment of Polarization-Independent Two-Dimensional Photonic Crystal Multiplexer/Demultiplexer with Reflectors 
     With reference to  FIG. 8 , one embodiment of the polarization-independent two-dimensional photonic crystal multiplexer/demultiplexer with reflectors is hereinafter described. This multiplexer/demultiplexer  50  has an area  471  within which air holes  412  are arrayed with a cycle distance of 0.965a 0 , which is shorter than that in the surrounding area, between the point closest from the first resonator  431  on the first waveguide  421  and the first polarization converter  451  of the previously described multiplexer/demultiplexer  40 . Arraying the air holes  412  with such a cycle distance causes the transmission wavelength band in the area  471  (i.e. the wavelength band within which a TE-polarized light can pass through the first waveguide  421 ) to be shifted toward the shorter-wavelength side from the wavelength band of the other area of the first waveguide  421  so that the wavelength λr is excluded from the transmission wavelength band. Therefore, the area  471  functions as a first reflector  471  for reflecting the TE-polarized light with wavelength λr propagated through the first waveguide  421 . 
     Also provided in a similar manner are a second reflector  472  between the point closest from the second resonator  432  on the first waveguide  421  and the end of the first waveguide, a third reflector  473  between the point closest from the first resonator  431  on the second waveguide  422  and the end of the second waveguide, and a fourth reflector  474  between the point closest from the second resonator  432  on the second waveguide  422  and the second polarization converter  452 . 
     In the multiplexer/demultiplexer  50 , a TE-polarized light with wavelength λr that has passed without being captured by the first resonator  431  is reflected by the first reflector  471  toward the first resonator  431  and captured by the same resonator  431 , to be introduced into the second waveguide  422 , whereby the multiplexing or demultiplexing efficiency is improved. The second reflector  472  also operates in a similar manner. 
     Among the TE-polarized light with wavelength λr introduced from the first resonator  431  into the second waveguide  422 , the portion propagating toward the output port  462  is reflected by the third resonator  473  toward the output port  462 , whereby the multiplexing or demultiplexing efficiency is improved. The fourth reflector  474  also operates in a similar manner. 
       FIG. 9  shows the distribution of TE and TM-polarized lights with wavelength λr in the case of introducing a TE-polarized light with wavelength λr from the input port  461  of the multiplexer/demultiplexer  50 , calculated by a three-dimensional FDTD (finite difference time domain) method. Similarly,  FIG. 10  shows a similarly calculated distribution of TE and TM-polarized lights with wavelength λr within the multiplexer/demultiplexer  50  in the case of introducing a TM-polarized light with wavelength λr from the input port  461 . In these figures, the areas surrounded by the dashed lines on the waveguide indicate the areas where light is present. The magnitude of the amplitude of the light is indicated by the density of the stripe patterns in the figure. 
     In the case of introducing a TE-polarized light with wavelength λr into the input port  461 , the TE-polarized light is present in the area  511  located upstream from the first reflector  471  on the first waveguide  421  and the area  512  between the third reflector  473  and the second polarization converter  452  on the second waveguide  422  ( FIG. 9(   a )). This demonstrates that the TE-polarized light with wavelength λr supplied from the input port  461  is introduced from the first waveguide  421  into the second waveguide  422 , and reflected by the first reflector  471  and the third reflector  473 . Since this TE-polarized light is converted to a TM-polarized light by the second polarization converter  452 , a TM-polarized light is present within the area  513  downstream from the second polarization converter  452  on the second waveguide  422  ( FIG. 9(   b )); no TE-polarized light exists in this area. Neither TE nor TM polarized light is observed in the area downstream from the first polarization converter  451 . 
     In the case of introducing a TM-polarized light with wavelength λr into the input port  461 , the TM-polarized light is present only in the area  514  located upstream from the first converter  451  on the first waveguide  421 . On the other hand, the TE-polarized light is present in the area  515  between the first polarization converter  451  and the second reflector  472  on the first waveguide  421  and the area  516  located downstream from the fourth reflector  474  on the second waveguide  422 . This demonstrates that the TM-polarized light with wavelength λr is converted to a TE-polarized light by the first polarization converter  451 , the TE-polarized light resulting from the polarization conversion is introduced into the second waveguide  422 , and the TE-polarized light resulting from the polarization conversion is reflected by the second reflector  472  and the fourth reflector  474 . 
     (3) Embodiment of Polarization-Independent Two-Dimensional Photonic Crystal Multistage Multiplexer/Demultiplexer 
     One embodiment of the polarization-independent two-dimensional photonic crystal multistage multiplexer/demultiplexer according to the present invention is hereinafter described with reference to  FIG. 11 . The multistage multiplexer/demultiplexer  60  in the present embodiment consists of a multiplexer/demultiplexer unit  40 A connected to another multiplexer/demultiplexer unit  40 B. The multiplexer/demultiplexer unit  40 A is structurally identical to the previously described multiplexer/demultiplexer  40  except for the second waveguide  422 . The multiplexer/demultiplexer unit  40 B is a reduced version of the multiplexer/demultiplexer unit  40 A. That is, the two multiplexer/demultiplexer units  40 A and  40 B are similar. In this case, the wavelength λr 1  at which the first and second resonators  431 A and  432 A of the multiplexer/demultiplexer unit  40 A resonate with the TE-polarized light differs from the wavelength λr 2  at which the first and second resonators  431 B and  432 B of the multiplexer/demultiplexer unit  40 B resonate with the TE-polarized light. 
     The first waveguide of the multiplexer/demultiplexer unit  40 A is connected to that of the multiplexer/demultiplexer unit  40 B to form a single waveguide  62 . On the other hand, the second waveguide  422 A of the multiplexer/demultiplexer unit  40 A and the second waveguide  422 B of the multiplexer/demultiplexer unit  40 B are separately provided and not connected to each other. The second waveguides  422 A and  422 B have bending portions  62 A and  62 B, respectively. Within the sections downstream from these bending portions, the second waveguides  422 A and  422 B become more distant from the first waveguide  62  as they extend downstream. 
     The operation of the multistage multiplexer/demultiplexer  60  as a demultiplexer is as follows: When superimposed light containing TE and TM polarized lights with wavelength λr 1  and TE and TM polarized lights with wavelength λr 2  is introduced from the end of the first waveguide  62  closer to the multiplexer/demultiplexer unit  40 A, the TE-polarized light with wavelength λr 1  is captured by the first resonator  431 A of the multiplexer/demultiplexer unit  40 A, to be demultiplexed into the second waveguide  422 A. Subsequently, this TE-polarized light is converted to a TM-polarized light by the second polarization converter  452 A of the multiplexer/demultiplexer unit  40 A. 
     The superimposed light excluding the TE-polarized light with wavelength λr 1  (but including the TM polarized light with wavelength λr 1  and the TE and TM polarized lights with wavelength λr 2 ) passes through without being captured by the first resonator  431 A. Among this superimposed light, the TM-polarized light with wavelength λr 1  is converted to a TE-polarized light by the first polarization converter  451 A of the multiplexer/demultiplexer unit  40 A. The resultant TE-polarized light with wavelength λr 1  is captured by the second resonator  432 A of the multiplexer/demultiplexer unit  40 A, to be demultiplexed into the second waveguide  422 A. 
     The superimposed light containing the TE and TM polarized lights with wavelength λr 2  passes through without being captured by the second resonator  432 A. Among this superimposed light, the TE-polarized light with wavelength λr 2  is captured by the first resonator  431 B of the multiplexer/demultiplexer unit  40 B, to be demultiplexed into the second waveguide  422 B. Subsequently, this TE-polarized light is converted to a TM-polarized light by the second polarization converter  452 B of the multiplexer/demultiplexer unit  40 B. 
     The superimposed light containing the TM polarized light with wavelength λr 2  passes through without being captured by the second resonator  431 B. Among this superimposed light, the TM-polarized light with wavelength λr 2  is converted to a TE-polarized light by the first polarization converter  451 B of the multiplexer/demultiplexer unit  40 B. The resultant TE-polarized light with wavelength λr 2  is captured by the second resonator  432 B of the multiplexer/demultiplexer unit  40 B, to be demultiplexed into the second waveguide  422 B. 
     Among the superimposed light, the components whose wavelengths differ from λr 1  and λr 2  are allowed to pass through the first waveguide  62 . 
     As already stated, the polarization converters used in the multistage multiplexer/demultiplexer  60  in the present embodiment are capable of both TE-to-TM and TM-to-TE conversions, regardless of the direction of propagation. Therefore, the operation of the multistage multiplexer/demultiplexer  60  as a multiplexer is the same as that of the demultiplexer when the flow of light is reversed for any wavelength and polarization.