Patent Publication Number: US-2010110546-A1

Title: Photonics device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This U.S. non-provisional patent application claims priority under 35 U.S.C. § 119 of Korean Patent Application No. 10-2008-010830, filed on Nov. 3, 2008, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     The present invention disclosed herein relates to a photonics device, and more particularly, to a multi-channel distribution Bragg reflector (DBR) filter. 
     In twenty-first century, optical communication technology has been highly developed, and much research is currently underway to apply optical communication technology to communication between computer boards, communication between chips of a board, or communication inside a complementary metal oxide semiconductor (CMOS) chip. In the case where optical signal communication technology is applied to a silicon very-large-scale-integration circuit (VLSI) chip, demerits of electric signal communication technology such as low-speed, high-resistance, excessive heat generation, and parasitic capacitance can be removed. Therefore, more research will be conducted on optical communication technology in semiconductor and information/communication fields. 
     Silicon optical waveguide devices such as silicon-based optical switches, optical modulators, and multiplexing/demultiplexing (MUX/DEMUX) filters are necessary to apply optical communication technology to silicon-based semiconductor chips. Since such optical switches, optical modulators, and MUX/DEMUX filters can be constituted using ring resonators or arrayed waveguide gratings (AWGs), much research is being conducted on the ring resonators or AWGs. 
     However, since a ring resonator or an AWG is highly sensitive to statistic errors caused by inevitable process condition variations, it is difficult to maintain wavelength spacing between channels of a ring resonator or an AWG at a constant level. Furthermore, since the ring resonator or the AWG includes a silicon waveguide of which the refractive index is largely dependent on temperature, a channel center wavelength can be largely varied even by a slight temperature variation. Moreover, since the ring resonator or the AWG has a minimum line width of about 100 nm, it is difficult to fabricate the ring resonator or the AWG stably through a photolithography process using an ArF excimer laser having a wavelength of 193 nm. 
     SUMMARY OF THE INVENTION 
     The present invention provides a photonics device capable of multi-channel multiplexing/demultiplexing (MUX/DEMUX). 
     The present invention also provides a photonics device having improved inter-channel wavelength spacing characteristics. 
     The present invention also provides a photonics device in which a channel center wavelength is less dependent on temperature. 
     The present invention also provides a photonics device that can have stable characteristics even when fabricated using an ArF excimer laser. 
     Embodiments of the present invention provide photonics devices including: a distribution Bragg reflector (DBR); a plurality of first waveguides disposed at a side of the DBR; a plurality of second waveguides disposed at the other side of the DBR; first lenses disposed between the DBR and the first waveguides; and second lenses disposed between the DBR and the second waveguides. 
     In some embodiments, the DBR may include three cavities. In this case, each of the cavities may have a length that is N times greater than λ/2, where N denotes an integer and λ denotes a center channel wavelength (for example, 1550 nm). That is, the length of the cavity can be expressed by L=N(λ/2n cos θ) where L denotes the length of the cavity, θ denotes an incident angle at a center channel, n denotes a refractive index of the cavity. 
     In even other embodiments, each of the first and second waveguides may be used as one of a discharging waveguide configured to guide signal light toward the DBR and a receiving waveguide configured to receive signal light from the DBR. In this case, end-portions of the first waveguides used as the discharging waveguides may be arranged at different angles with the DBR, and end-portions of the second waveguides used as the discharging waveguides may be arranged at different angles with the DBR. This arrangement angle difference may have influence on wavelengths to be filtered. 
     In yet other embodiments, both sidewalls of the DBR facing the first and second waveguides may be substantially flat and are uniformly spaced from each other. 
     In further embodiments, end-portions of the first and second waveguides adjacent to the DBR may be configured as spot size converters. In addition, each of the first and second lenses may be used to collimate light traveling from one of the first and second waveguides toward the DBR or to focus light discharged from the DBR onto one of the first and second waveguides. 
     In even further embodiments, the photonics device may further include: a lower clad layer; lower core patterns disposed on the lower clad layer to define shapes of the first and second lenses and the DBR; an upper core layer disposed on the lower core patterns to form an optical waveguide between the first waveguides and the second waveguides; and an upper clad layer covering the upper core layer. In this case, the lower core patterns may be formed of a material having a refractive index greater than a refractive index of the upper core layer so as to increase an effective refractive index of the upper core layer, and the upper core layer may form a slab waveguide between the first waveguides and the second waveguide. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The accompanying figures are included to provide a further understanding of the present invention, and are incorporated in and constitute a part of this specification. The drawings illustrate exemplary embodiments of the present invention and, together with the description, serve to explain principles of the present invention. In the figures: 
         FIG. 1  is a plan view illustrating a multi-channel distribution Bragg reflector (DBR) filter according to an embodiment of the present invention; 
         FIG. 2  is a plan view illustrating one of the channel regions of the multi-channel DBR filter according to an embodiment of the present invention; 
         FIG. 3  is a plan view for explaining waveguides and lenses of the multi-channel DBR filter according to an embodiment of the present invention; 
         FIGS. 4 and 5  are sectional views illustrating a multi-channel DBR filter according to an embodiment of the present invention; 
         FIG. 6  is a plan view illustrating a DBR according to an embodiment of the present invention; 
         FIG. 7  is a graph showing a channel wavelength spectrum according to an embodiment of the present invention; and 
         FIG. 8  is a graph showing an eight-channel-wavelength spectrum according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention will be described below in more detail with reference to the accompanying drawings. The present invention may, however, be embodied in different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art. 
     In the specification, the dimensions of layers and regions are exaggerated for clarity of illustration. It will also be understood that when a layer (or film) is referred to as being ‘on’ another layer or substrate, it can be directly on the other layer or substrate, or intervening layers may also be present. Also, though terms like a first, a second, and a third are used to describe various regions and layers in various embodiments of the present invention, the regions and the layers are not limited to these terms. These terms are used only to tell one region or layer from another region or layer. Therefore, a layer referred to as a first layer in one embodiment can be referred to as a second layer in another embodiment. An embodiment described and exemplified herein includes a complementary embodiment thereof. 
       FIG. 1  is a plan view illustrating a multi-channel distribution Bragg reflector (DBR) filter according to an embodiment of the present invention. 
     Referring to  FIG. 1 , the multi-channel DBR filter of the current embodiment may include: a connection waveguide structure  200 ; an output waveguide structure  210 ; a DBR  100  disposed between the connection waveguide structure  200  and the output waveguide structure  210 ; and lens structures ( 300 ,  310 ) disposed among the connection waveguide structure  200 , the DBR  100 , and the output waveguide structure  210 . In addition, an input waveguide  201  and a through-waveguide  220  may be disposed at sides of the connection waveguide structure  200 . 
     The DBR  100  includes high refraction regions and low refraction regions that are arranged in turns, and the widths of the high and low refraction regions may vary according to wavelengths of light to be selected. The DBR  100  will be described later in more detail with reference to  FIGS. 5 and 6 . In the current embodiment, the DBR  100  may be disposed between the connection waveguide structure  200  and the output waveguide structure  210  and have a uniform width (that is, the distance between both sidewalls of the DBR  100  may be uniform). In other words, both sidewalls of the DBR  100  may be flat along the whole length of the DBR  100 . 
     The lens structures may include a first lens structure  300  disposed at a side of the DBR  100  and a second lens structure  310  disposed at the other side of the DBR  100 . The first lens structure  300  may include a plurality of first lenses arranged between the DBR  100  and the connection waveguide structure  200 . The second lens structure  310  may include a plurality of second lenses arranged between the DBR  100  and the output waveguide structure  210 . Technical characteristics of the first and second lenses will be described later in detail with reference to  FIGS. 2 through 5 . 
     The connection waveguide structure  200  includes a plurality of connection waveguides  202 ,  203 ,  204 ,  205 ,  206 ,  207 , and  208  configured to connect the first lenses optically. Both end-portions of each of the connection waveguides  202  to  208  may be pointed toward the DBR  100  or the first lenses. For this, each of the connection waveguides  202  to  208  may be U-shaped. In the current embodiment of the present invention, the connection waveguides  202  to  208  may have different shapes so that both end-portions of the connection waveguides  202  to  208  are pointed toward the DBR  100  at different angles. Technical features of this structure will be described later in detail with reference to  FIGS. 2 through 5 . 
     The output waveguide structure  210  includes a plurality of output waveguides  211 ,  212 ,  213 ,  214 ,  215 ,  216 ,  217 , and  218 , which are configured to transmit signal light incident from the second lenses to other optical devices (not shown). An end-portion of one of the output waveguides  211  to  218  adjacent to one of the second lenses may be parallel with an end-portion of one of the input waveguide  201  and the connection waveguides  202  to  208  and may be disposed on an extension line of the end-portion of the one of the input waveguide  201  and the connection waveguides  202  to  208 . This will be described later with reference to  FIG. 2 . 
     The multi-channel DBR filter of the current embodiment may be divided into a plurality of channel regions G 1 , G 2 , G 3 , G 4 , G 5 , G 6 , G 7 , and G 8 . Each of the channel regions G 1  to G 8  may include a pair of the first lenses, a pair of the second lenses, and a portion of the DBR  100  disposed therebetween. Each of the channel regions G 1  to G 8  may further include an end-portion of one of the connection waveguides  202  to  208  and an end-portion of one of the input waveguide  201  and the output waveguides  211  to  218 . In the current embodiment of the present invention, the channel regions G 1  to G 8  may be configured such that input light including optical signals having different wavelength bands can be distributed to the different output waveguides  211  to  218 . For this purpose, the lenses and waveguides constituting the channel regions G 1  to G 8  may have different geometric structures. One of the channel regions G 1  to G 8  will be exemplarily described in detail with reference to  FIG. 2 . 
       FIG. 2  is a detailed plan view illustrating one of the channel regions of the multi-channel DBR filter according to an embodiment of the present invention. 
     Referring to  FIG. 2 , the first lens structure  300  may include a pair of the first lenses  301  and  302  disposed among the DBR  100 , the input waveguide  201 , and the connection waveguide  202 , and the second lens structure  310  may include a pair of the second lenses  311  and  312  disposed between the DBR  100  and the output waveguide  211 . In another embodiment of the present invention, the second lens structure  310  may not include the second lens  311  but include the second lens  312  disposed on an extension line of an end-portion of the output waveguide  211 . 
     In embodiments of the present invention, wavelengths (hereinafter also referred to as channel wavelengths) to be distributed to the output waveguides  211  to  218  through the channel regions G 1  to G 8  may be determined by the angle of incident of signal light on the DBR  100 . In detail, if light incident onto the DBR  100  at right angle can pass through the DBR  100  when the light has a wavelength λo (reference wavelength), light incident onto the DBR  100  at an incident angle θ 1  can pass through the DBR  100  when the light have a wavelength λ expressed by Equation 1 below. 
       λ˜λ o  cos θ1   [Equation 1] 
     Therefore, signal light can be selectively distributed by adjusting the angle of incident of the signal light. For this adjustment, optical paths formed by the first and second lenses  301 ,  302 ,  311 , and  312 , and end-portions of the input, connection, and output waveguides  201 ,  202 , and  211  are angled with respect to the DBR  100  at different angles according to the channel regions G 1  to G 8 . Table 1 below shows an exemplary angle-wavelength relationship for distributing a wavelength band of 1544 nm to 1588 nm to eight channels according to an embodiment of the present invention. In this embodiment, the angle-wavelength relationship is obtained by calculation using a Transfer matrix. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Channel 
                 Angle (degrees) 
                 wavelength (nm) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 channel 1 
                 10.31 
                 1544 
               
               
                   
                 channel 2 
                 10.04 
                 1546 
               
               
                   
                 channel 3 
                 9.77 
                 1548 
               
               
                   
                 channel 4 
                 9.49 
                 1550 
               
               
                   
                 channel 5 
                 9.20 
                 1552 
               
               
                   
                 channel 6 
                 8.90 
                 1554 
               
               
                   
                 channel 7 
                 8.60 
                 1556 
               
               
                   
                 channel 8 
                 8.28 
                 1558 
               
               
                   
                   
               
            
           
         
       
     
     Referring to  FIG. 1  and Table 1, in the current embodiment, a 1544-nm wavelength λ 1  of signal light is output through the output waveguide  211  of a channel  1 , and wavelengths λ 2  to λn of the signal light are reflected by the DBR  100  to the connection waveguide  202  through the first lens  302 . Then, the wavelengths λ 2  to λn are selectively output to the output waveguides  212  to  218  through the channel regions G 1  to G 8  in the same manner. Wavelengths of the signal light different from channel wavelengths λ 1  to λ 8  of the channel regions G 1  to G 8  may be transmitted to the through-waveguide  220  and processed by an optical device (not shown). The distribution of the wavelengths of the signal light is a demultiplexing (DEMUX) process. 
     On the other hand, in the current embodiment, signal light beams having wavelengths corresponding to the channel wavelengths λ 1  to λ 8  of the channel regions G 1  to G 8  can be incident onto the channel regions G 1  to G 8  through the output waveguides  211  to  218 . In this case, optical signals having different wavelengths can be combined. This combining process of optical signals is a multiplexing (MUX) process. 
       FIG. 3  is a plan view for explaining waveguides and lenses of the multi-channel DBR filter according to an embodiment of the present invention. 
     Referring to  FIG. 3 , in the current embodiment, end-portions of the waveguides of the multi-channel DBR filter may have a spot size converter structure. In detail, as shown in  FIG. 3 , the end-portions of the waveguides  201  and  211  may be tapered toward the DBR  100 . In this case, an optical beam output from the input waveguide  201  may diverge to a width w 2  greater than a width w 1  of the input waveguide  201  as shown in  FIG. 3 . 
     The first lens  301  is configured to collimate light emitted from the spot size convert structure; that is, the diverged optical beam emitted from the spot size convert structure is collimated by the first lens  301  and is converted into a parallel optical beam having a width w 3 . For this end, the first lens  301  may be a two-dimensional convex lens. 
     The second lens  312  focuses the parallel optical beam received from the first lens  301  onto the output waveguide  211 . For this, the second lens  312  may be a two-dimensional convex lens like the first lens  301 . However, it may be unnecessary that the first and second lenses  301  and  312  have the same shape. For example, if the distance between the first lens  301  and the input waveguide  201  is different from the distance between the second lens  312  and the output waveguide  211 , the first and second lenses  301  and  312  may have different sizes or surface curvatures. This difference or modification may be apparent to those of ordinary skill in the art. 
     Table 2 below shows exemplary geometric sizes and related features of a propagating beam, a lens, and a waveguide according to an embodiment of the present invention. These geometric sizes (dimensions) are obtained by computer modeling. In the present invention, however, the geometric sizes can be variously changed. That is, the present invention is not limited to the geometric sizes of Table 2. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
             
            
               
                   
                 Waveguide width (w1) 
                 0.560 
                 μm 
               
               
                   
                 Beam width (w2) at end of waveguide 
                 3.41 
                 μm 
               
               
                   
                 Parallel beam width (w3) 
                 5.232 
                 μm 
               
               
                   
                 Length (d1) of tapered end portion of waveguide 
                 6.1 
                 μm 
               
               
                   
                 Distance (d2) between waveguide and lens 
                 10 
                 μm 
               
               
                   
                   
               
            
           
         
       
     
       FIGS. 4 and 5  are sectional views illustrating the multi-channel DBR filter according to an embodiment of the present invention.  FIG. 4  is a sectional view taken along line I-I′ of  FIG. 3 , and  FIG. 5  is a sectional view taken along line II-II′ of  FIG. 3 . That is,  FIG. 4  illustrates sections of the second lens  312  and a portion of the output waveguide  211 , and  FIG. 5  illustrates a section of the DBR  100 . 
     Referring to  FIGS. 4 and 5 , an upper core layer  30  and an upper clad layer  40  are sequentially disposed on a lower clad layer  10 . Lower core patterns  20   20  are disposed between the lower clad layer  10  and the upper core layer  30 . The lower core patterns  20  include the connection waveguide structure  200 , the output waveguide structure  210 , the input waveguide  201 , the through-waveguide  220 , the first lens structure  300 , and the second lens structure  310 . 
     The upper core layer  30  is formed of a material having a refractive index higher than refractive indexes of the lower clad layer  10  and the upper clad layer  40 , so as to form a slab waveguide. The lower core patterns  20  including waveguides and lenses as described above may be formed of a material having a refractive index higher than the refractive index of the upper core layer  30 . For example, the lower clad layer  10 , the lower core patterns  20 , the upper core layer  30 , and the upper clad layer  40  may be formed of silicon oxide, silicon, silicon nitride, and silicon oxide, respectively. The thicknesses t 1 , t 2 , and t 3  of the lower core patterns  20 , the upper core layer  30 , and the upper clad layer  40  may be about 2200 Å, 4000 Å, and 2 μm, respectively. 
     In this case, the refractive indexes of the lower clad layer  10 , the upper core layer  30 , and the upper clad layer  40  may be about 1.45, 2.0, and 1.45, respectively. The effective refractive index of the lower core patterns  20  may be about 2.27, and the effective refractive index of the upper core layer  30  may be about 1.65 when the thickness t 2  of the upper core layer  30  is about 4000 Å. 
     In the current embodiment, an optical signal may be vertically guided by the upper core layer  30 . In addition, the horizontal shape of the optical signal is varied at an end portion of the second lens  312  or the output waveguide  211  according to the shapes and arrangement of the lower core patterns  20 . 
     Referring to  FIG. 5 , the DBR  100  includes high refraction regions and low refraction regions that are arranged in turns. In an embodiment of the present invention, the upper core layer  30  forms the low refraction regions, and the lower core patterns  20  form the high refraction regions. 
     The sum of the width w 4  of the high refraction region and the width w 5  of the low refraction region may be about ½ of a wavelength (λ/ 2 ). For example, when a channel wavelength is 1550 nm, the width w 4  of the high refraction region and the width w 5  of the low refraction region may be about 160 nm and 230 nm, respectively. In this case (channel wavelength=1550 nm), the lower core patterns  20  may be disposed in a manner such that the incident angle of light on the DBR  100  can be about 9.49° as described above. 
     In a typical ring resonator filter, the distance between two waveguides forming an optical coupling region is about 100 nm. Therefore, it is difficult to guarantee the distance between the two waveguides in the case where the typical ring resonator filter is fabricated through a photolithography process using an ArF excimer laser having a wavelength of 193 nm. However, as explained above, in the current embodiment, since the minimum line width (minimum distance) of the patterns forming the DBR  100  is the width w 4  (that is, about 160 nm) of the high refraction regions, the minimum line width can be surely guaranteed as compared with the case of the typical ring resonator filter. 
     In the case of an arrayed waveguide grating (AWG) (filtering device), waveguide length differences are used for filtering. Therefore, the AWG has a relatively large effective area as compared with that of the DBR filter or a typical ring resonator filter. That is, the DBR filter of the present invention can have an effective area similar to that of a typical ring resonator filter, while providing more stable optical characteristics than the typical ring resonator filter. 
       FIG. 6  is a plan view illustrating a DBR according to an embodiment of the present invention. 
     Referring to  FIG. 6 , the DBR of the current embodiment may include a plurality of region clusters that are sequentially and continuously arranged. Each of the region clusters may include high refraction regions (H) and low refraction regions (L) that are arranged in turns, or each of the region clusters may include a pair of low refraction regions (L). 
     In an embodiment, the DBR includes first to fifth region clusters R 1  to R 5  that are sequentially and continuously arranged. As shown in  FIG. 6 , each of the first and fourth region clusters R 1  and R 4  may include high refraction regions (H) and low refraction regions (L) that are arranged sequentially and alternately. Each of the second and fifth region clusters R 2  and R 5  may include low refraction regions (L) and high refraction regions (H) that are arranged sequentially and alternately. The third region cluster R 3  may include a pair of low refraction regions (L)  99 . 
     In this case, low refraction regions  99  are disposed between the first and second region clusters R 1  and R 2  and between the fourth and fifth region clusters R 4  and R 5 , respectively, and therefore, totally, three pairs of low refraction regions  99  are arranged. 
     Since the sum of the width w 4  of the high refraction region (H) and the width w 5  of the low refraction region (L) is ½ of a wavelength (λ/2) as described above, an optical mirror structure can be formed. On the other hand, the pair of low refraction regions  99  forms a λ/2 cavity. That is, in the current embodiment, the DBR has three cavities. 
     In other embodiments, the DBR may have one cavity or two cavities. In theses cases, however, it is difficult to obtain a desirable spectrum such as a rectangular shaped spectrum of  FIG. 7  which was obtained by simulating the case where the DBR has three cavities. 
     In other embodiments, the DBR may have four or more cavities. In these cases, however, since the area of the DBR increases with the number of cavities, it may be less efficient as compared with the case where the DBR has three cavities. 
     In other embodiments, the length (width) of the cavity of the DBR may be nλ/2 (where n is a natural number equal to or greater than 2) such as 1λ and 3λ/2. However, in the present invention, since signal light is incident from each of the channel regions G 1  to G 8  onto the DBR at an oblique angle, according to simulation results, the spectrum of the signal can be distorted with increased ripples in the case where the length of the cavity has a value greater than λ/2 such as 1λ or 3λ/2. Here, λ denotes the wavelength of a center channel (for example, 1550 nm). The length of the cavity may be expressed by L=N(λ/2n cos θ) where N denotes a natural number such as 1, 2, 3, and 4, θ denotes the incident angle at the center channel, and n denotes the refractive index of the cavity. 
     In another embodiment, the first, second, fourth, and fifth region clusters R 1 , R 2 , R 4 , and R 5  may include eight pairs, 16 pairs, 16 pairs, and 8 pairs of high and low refraction regions (H) and (L), respectively. The number of pairs may be varied according to a filter bandwidth. 
       FIG. 7  is a graph showing a channel wavelength spectrum according to an embodiment of the present invention.  FIG. 7  shows a channel wavelength spectrum including a 1550-nm channel wavelength, which was obtained by performing a computer simulation using a transfer matrix on a multi-channel DBR filter including the DBR of  FIG. 6 . As shown in  FIG. 7 , a transmission bandwidth was about 1.6 nm, and ripples were smaller than about 0.2 dB. Therefore, it may be understood from the simulation results that the multi-channel DBR filter of the present invention has good spectrum characteristics. 
       FIG. 8  is a graph showing an eight-channel-wavelength spectrum according to an embodiment of the present invention. The graph of  FIG. 8  was obtained by performing a computer simulation using a transfer matrix on the multi-channel DBR filter shown in  FIG. 1 . Referring to  FIG. 8 , although the incident angle of light varied with the channel regions G 1  to G 8 , substantially the same spectrum characteristics are presented at the respective channel regions G 1  to G 8  of the multi-channel DBR filter. Therefore, the multi-channel DBR filter of the present invention can be used for constituting a multi-channel multiplexing/demultiplexing filter. 
     The multi-channel DBR filter described in the above embodiments can be used as a multiplexing/demultiplexing device as mentioned above, and can also be used for constituting an optical switch and an optical modulator. It will be apparent to those skilled in the art that such modifications and variations can be made in the present invention. 
     As described above, since the refractive index of silicon is largely dependent on temperature, in the case of a ring resonator filter or AWG including filtering silicon patterns, a channel center wavelength is largely varied with temperature at about 6 nm/100° C. However, since the refractive index of a silicon nitride is less varied with temperature at a rate equal to or less than ⅕ that of silicon, the multi-channel DBR filter of the present invention, which includes a waveguide formed of a silicon nitride layer, can have a channel center wavelength that is less variable with temperature (at about 1.7 nm/100° C.) as compared with a ring resonator filter or AWG. 
     Furthermore, according to the present invention, since the minimum line width or spacing of patterns of the multi-channel DBR filter (the length of a high refraction region) is about 160 nm, the minimum line width can be stably maintained when the multi-channel DBR filter is fabricated through a photolithography process using an ArF excimer laser having a wavelength of 193 nm. In addition, the multi-channel DBR filter can have an effective area which is similar to that of a typical resonator filter but much smaller than that of an AWG (filtering device). 
     In the case of a ring resonator filter or an AWG, inter-channel wavelength spacing is dependent on the size and distance of patterns which are largely varied according to variation errors of manufacturing processes. Therefore, the inter-channel wavelength spacing of the ring resonator filter or AWG is sensitively varied according to statistic errors caused by manufacturing process condition errors. 
     However, in the case of the multi-channel DBR filter of the present invention, each channel wavelength is dependent on the incident angle of signal light which is determined by orientations of lenses or waveguides. Since the orientations of the lenses or waveguides are not sensitive to variation errors of a manufacturing process because the lenses or waveguides are formed through a transferring process using a photomask, the multi-channel DBR filter of the present invention is relatively less affected by statistic errors caused by manufacturing process errors. For example, even when the size of a lens of the multi-channel DBR filter is varied due to a process error, this variation does not affect inter-channel wavelength spacing significantly although it can affect the intensity of an output signal. Therefore, the multi-channel DBR filter of the present invention can have good inter-channel wavelength spacing characteristics even when there are statistic errors. 
     The above-disclosed subject matter is to be considered illustrative, and not restrictive, and the appended claims are intended to cover all such modifications, enhancements, and other embodiments, which fall within the true spirit and scope of the present invention. Thus, to the maximum extent allowed by law, the scope of the present invention is to be determined by the broadest permissible interpretation of the following claims and their equivalents, and shall not be restricted or limited by the foregoing detailed description.