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US008835204B2 (12) United States Patent sm et a]. (54) METHOD FOR MANUFACTURING (52) Sep. 16, 2014 vs. C]. MULTI-DIMENSIONAL TARGET WAVEGUIDE GRATING AND VOLUME GRATING WITH MICRO-STRUCTURE CPC .......... .. H01S 5/2031 (2013.01); G021; 5/1057 QUASI-PHASE-MATCHING USPC (2013.01); G021; 5/1023 (2013.01); G021; 6/1225 (2013.01) (58) 438/32;438/31;385/27;385/37; Field of Classi?cation Search USPC ........... .. 438/32, 31; 385/27, 37, 15; 359/578, Chen, Nanjing (CN) 359/579; 708/400 See application ?le for complete search history. (73) Assignee: Nanjing University, Nanjing (CN) Notice: ................. .. 385/15; 359/578; 359/579; 708/400 (75) Inventors: Yuechun Shi, Nanjing (CN); Xiangfei (*) US 8,835,204 B2 (10) Patent N0.: (45) Date of Patent: Subject to any disclaimer, the term of this patent is extended or adjusted under 35 (56) References Cited U.S. PATENT DOCUMENTS U.S.C. 154(b) by 0 days. 5,852,688 A * 12/1998 Brinkman et a1. ............ .. 385/16 (21) Appl. No.: 13/977,718 6,067,391 A * 5/2000 Land 6,285,813 B1* 9/2001 Schultz et al. (22) PCT Filed: Dec. 30, 2011 6,640,034 B1* 10/2003 Charlton et al. (86) PCT No.: PCT/CN2011/085067 § 371 (0X1)’ (2), (4) Date: Jun. 30, 2013 6,393,172 B1* 7,454,103 (87) . . . .. 385/27 . . . .. 385/37 5/2002 Brinkman et a1. . 11/2008 Parriaux . . . . . . . . . . . . . 2005/0033787 A1* 2/2005 Stepanov et al. 2008/0069497 A1* 3/2008 CN CN CN CN PCT Pub. Date: Jul. 12, 2012 2004100075305 2004100091670 101924326 102147492 Tissot et al. 385/16 385/122 . . . .. 385/37 708/400 .... .. 385/37 Nov. 7, 2013 A A A A 1/2005 2/2005 12/2010 8/2011 OTHER PUBLICATIONS Prior Publication Data US 2013/0295703 A1 ..... FOREIGN PATENT DOCUMENTS PCT Pub. No.: WO2012/092828 (65) B2* . . . . . . . . . . . . . . . . . . Yating Zhou et al. Equivalent A-/4 Phase Shift to Improve the Single Longitudinal Mode Property of Asymmetric Sampled Bragg Grating (30) Foreign Application Priority Data Jan. 6, 2011 (51) (CN) ........................ .. 2011 1 0001786 Int. Cl. Greiner, Dmitri IaZikov, and Thomas W. Mossberg, Optical add-drop multiplexers based on the antisymmetric waveguide Bragg grating, (2006.01) (2006.01) (2006.01) (2006.01) (2006.01) (2006.01) (2006.01) (2006.01) H01L 21/00 G021; 6/26 G021; 6/42 G021; 6/34 G021; 27/00 G021; 5/10 H01S 5/20 G021; 6/122 Semiconductor Laser. Microwave Photonics, 2010 IEEE Topical Meeting. pp. 89-92, ISBN 978-1-4244-7825-5. Xu Mai, Research Progress on Waveguide Gratings for integrated Optics “Chinese Journal of Luminescence ”,2005, 26 (4) ; 415-425. Jose M. Castro, David F. Geraghty, Seppo Honkanen, Christoph M. Applied Optics, 2006,45(6); 1236-1243. Ming Li,Yaming Wu, Jiangyi Yang, and Hongchang Qu, Return loss reduction of integrated grating-assisted optical Add/Drop multi plexer by control the re?ective spectrum, Journal of lightwave tech nology , 2005, 23(3): 1403-1409. Jose M. Castro, David F. Geraghty, Demonstration of mode conver sion using anti-symmetric waveguide Bragg gratings, Optics Express, 2005, 13(11): 4180-4184. WAVE vector ummampm Phase matching condition is satisfied Wveacvtoer ofstWveahcvteodr Wave vector of the target equivalent grating Incident light US 8,835,204 B2 Page 2 Yitang Dai, Xiangfei Chen, Li Xia, Yejin Zhang, and ShiZhong Xie, (57) ABSTRACT Sampled Bragg grating with desired response in one channel by use of reconstruction algorithm and equivalent chirp, Optics Letters, 2004, 29(12): 1333-1335. Yitang Dai and Xiangfei Chen, DFB semiconductor lasers based on reconstruction-equivalent-chirp technologyOptics Express, 2007,15(5) : 2348-2353. Jingsi Li,Huan Wang, Xiangfei Chen, Zuowei Yin, Yuechun Shi, Yanqing Lu, Yitang Dai and Hongliang Zhu, Experimental demon A method for manufacturing a multi-dimensional target waveguide grating and volume grating with micro-structure quasi-phase-matching. An ordinary waveguide grating is used as a seed grating, and on this basis, a two-dimensional or three-dimensional sampling structure modulated with a refractive index, that is, a sampling grating, is formed. The stration of distributed feedback semiconductor lasers based on recon sampling grating comprises multiple shadow gratings, and struction-equivalent-chirp technology. Optics Express, 2009, 17(7) : one of the shadow gratings is selected as a target equivalent 5240-5245. grating. A sampled grating comprises Fourier components in Jingsi Li, Xiangfei Chen, NingZhou, etc, Monolithically integrated many orders, that is, shadow gratings, a corresponding grat ing wave vector is [Formula 1], and the grating pro?le of all the shadow gratings changes with the sampling structure 30-wavelength DFB laser array, Proc.of SPIE-OSA-IEEE, 2009, SPIE 7631, 763104. J .A. Armstrong, N. Bloembergen, J .Ducuing, and P.S.Pershan. Inter actions between light waves in a nonlinear dielectric, Physical review, 1962, 127(6) : 1918-1939. Shi-ning Zhu, Yong-yuan Zhu, Nai-ben Ming, Quasi-Phase-Matched third-harmonic generation in a quasi-periodic optical superlattice, Science, 1997, 278 (843). The ?rst of?ce action for corresponding Chinese application CN 2011101048752, dated Nov. 30, 2011. * cited by examiner Primary Examiner * Evan Pert [Formula 2]. In a case where a seed grating wave vector [Formula 3] and a required two-dimensional or three-dimen sional grating wave vector do not match, a certain Fourier periodic structure component of the Fourier components of the sampling structure is used to compensate for the wave vector mismatch. The manufacturing method may be applied to design and manufacture a multi-dimensional target waveguide grating and volume grating for any grating pro?le, and may simplify the grating manufacturing process and also make possible a variety of grating-based photon devices. Assistant Examiner * Gustavo Ramallo (74) Attorney, Agent, or Firm * Treasure 1P Group 13 Claims, 13 Drawing Sheets US. Patent Sep.16,2014 Sheet10f13 US 8,835,204 B2 wave vactor of the sampling strunture’s Faurim subgrating m5>2 ;> U Seed grating a w FIG. 1 US. Patent Sep. 16, 2014 Sheet 2 0f 13 US 8,835,204 B2 Phase matching condition is satisfied 1: cu cu 0: cu .C u|-l 5 e o l 8 o\ x, . ‘0 a? > m v a“ “‘* a: a, m C <6 i“ Q" a. ,Q E m J i Wavs vest-m? cf the target i» s 33* 539 v9. *2? Q in 4:» 0 ' l. ? ‘1", w " f ' squivaient grating Incident light FIG. 2 if: 3i" ' ' i '1? 2*? é" Q US. Patent Sep. 16, 2014 Sheet 3 0f 13 US 8,835,204 B2 Samgiing straautrez Samgiing strumtrei ' FIG. 3 ¢ incident ?ghts US. Patent Sep. 16, 2014 Sheet 4 0f 13 US 8,835,204 B2 %. Chirped. seed A: :3 v A A 21 A “ FIG. 4 gmii?g US. Patent Sep. 16, 2014 Sheet 5 0f 13 US 8,835,204 B2 LM "x, iwn {i pimw giaiff in 3am?!ng ,l 1 FIG. 5 structure. US. Patent Sep.16,2014 Sheet60f13 + 3$2%; FIG. 6 US 8,835,204 B2 US. Patent Sep.16,2014 Imammw58%Z?mm:.ma9w. Sheet70f13 ,7 v M W,if A,» 7 w / i, ff, ./ \ FIG. 7 ,\ US 8,835,204 B2 US. Patent Sep. 16, 2014 Sheet 8 0f 13 US 8,835,204 B2 Re?ected. with W. anglal getqrauiv entg \ ‘Re?eeted with angieZ HM! incident ?ght FIG. 8 US. Patent Sep. 16, 2014 g3%ang “bEMwa Sheet 9 0f 13 US 8,835,204 B2 US. Patent Sep. 16, 2014 Sheet 10 0f 13 (c)Phase matching condition Wave water of m target a-quivaimt garati?g imam sigh: FIG. 9c US 8,835,204 B2 US. Patent Sep. 16, 2014 Sheet 11 0f 13 Z1.1m; FIG. 9d US 8,835,204 B2 US. Patent Sep. 16, 2014 Sheet120f13 3.»5?% FIG. 10 US 8,835,204 B2 US. Patent Sep. 16, 2014 Sheet 13 0f 13 US 8,835,204 B2 US 8,835,204 B2 1 2 METHOD FOR MANUFACTURING MULTI-DIMENSIONAL TARGET WAVEGUIDE GRATING AND VOLUME GRATING WITH MICRO-STRUCTURE [4] are achieved. In actual design, it is necessary to achieve different functions of the waveguide grating in a single pho tonic chip, which means different grating pro?les have to be written individually for different functions. In particular, in QUASI-PHASE-MATCHING order to achieve different grating directions, cycles, phase CROSS REFERENCE TO RELATED APPLICATION This application is a National Phase application of, and claims priority to, PCT Application No. PCT/CN2011/ 10 consuming properties of E-Beam lithography have increased the dif?culty and cost of fabrication and limited its large-scale 085067, ?led on Dec. 30, 2011, entitled “METHOD FOR implementation. MANUFACTURING MULTI-DIMENSIONAL TARGET WAVEGUIDE GRATING AND VOLUME GRATING In order to solve this practical problem, Chen Xiangfei et al ?rst proposed an effective solution to simplify the fabrication WITH MICRO-STRUCTURE QUASI-PHASE-MATCH ING”, which claimed priority to Chinese Application No 2011100017865, ?led on Jan. 6, 201 1. Both the PCT Appli cation and Chinese Application are incorporated herein by of ?ber gratings, and they called it “Reconstruction-Equiva lent-Chirp (REC) technology” [5-6]. With this technology, we can fabricate a nano-scale grating structure with micron reference in their entireties. 20 TECHNICAL FIELD This invention belongs to the ?eld of optoelectronic tech nology involving ?ber-optic communications, photonic inte gration, photoelectric sensing as well as other optoelectronic information processing technologies. The main idea of the 25 invention is to propose the micro-structure of quasi-phase matching technology (i.e. MS-QPM) with which we can equivalently realize any target grating structure for the two dimensional planar waveguide Bragg grating or three-dimen scale precision. This method has also been successfully applied to the design and fabrication of the distributed feed back (DFB) semiconductor laser and the DFB laser array [7-9], which provides an effective solution for high perfor mance of semiconductor laser array in photonic integration. In order to further solve the monolithic integration problem of different waveguide gratings with complex structure in the planar photonic integration and to lower the fabrication costs, based on the previous research of the applicants of this inven tion, the applicants propose a micro-structure quasi-phase matching (MS-QPM) technology. This technology not only 30 sional volume grating using the sampling structure. Based on this design idea, the applicants also propose a variety of new provides a new method of design and fabrication of the waveguide grating with two or three dimensions, but also gives some novel grating structure and corresponding optical properties of waveguide gratings or volume gratings. For photonic devices such as new wavelength division multi plexer or ?lter without retro -re?ection, tilted waveguide grat ing, DFB semiconductor lasers with suppressed 0th channel based on the reconstruction equivalent chirp technology as well as directional coupler and power splitters. shifts, chirps and even arbitrary structures in the same chip, the traditional low-cost holographic exposure is almost impossible to actualize. Therefore, more advanced nano-fab rication technology, such as electron beam (E-Beam) lithog raphy, is often utilized. However, the high cost and time instance, we can change the grating period and even rotate the 35 grating directions equivalently and simultaneously by sam pling in the same seed grating. The REC technology is a special one-dimensional case of the micro-structure of quasi phase matching (MS-QPM) [5]. The mathematical expres sion of this technology shares some similarities with the BACKGROUND 40 famous quasi-phase matching (QPM) described in non-linear With the advancement of computer network technology, the demand for information is increasing exponentially. Over the past decade, the fast development of Internet and the optical materials [10,11], and therefore it can be considered as a new discovery and development of quasi-phase matching technology. In summary, this technology can achieve arbi accompanying huge requirement for information transmis sion not only call for a more advanced ?ber communication trary shape of two or three-dimensional gratings by changing the large-scale sampling structure while keeping the seed system, but also demands the development of advanced ?ber communication technology. This is especially true for optical two or three-dimensional grating structure can be achieved as grating period unchanged. Any of the physical achievable of long as the two or three dimensional gratings design is used by sampling structure with micrometer scale and uniform communication devices. This new demand requires new theo ries and cost-effective devices to support the further develop ment of optical networks. Fortunately, the photonic integra tion circuits (PICs) technology developed in recent years 50 conforms to the development of times and is opening a new era of optical networks. PICs technology is considered to be the cutting-edge and the most promising technology of opti cal communications. In the SiliconValley of the United States seed grating. With this structure we can achieve a variety of optical properties of the waveguide grating or volume grating 55 with the ?ne grating structures. We only need to change the sampling structure while keep the seed grating uniform. The sampling structure size is normally a few micrometers, the implementation of this method only requires a standard holo graphic exposure technique with conventional photolithogra of America, In?nera Corporation has realized the integration of a large number of complex optoelectronic integrated devices with indium phosphide and other materials, lowering phy technique. This greatly eases fabrication process and the cost of optical communication while increasing its capac idea of two or three-dimensional sampled grating structures ity. In the ?eld of passive optical devices, Bragg grating substantially improves productivity and product quality. The 60 waveguide shows an excellent property of wavelength selec tivity and has been used in a variety of optical communication devices and photonic integrated devices, such as planar inte can be used to design new photonic devices, such as wave length division multiplexer, which until now are array waveguide grating (AWG) and multimode interference wavelengths waveguide grating assisted components (MMI) in the mainstream market. These existing devices have high requirement for waveguide accuracy, aside from relatively large size. Based on this two-dimensional sampling structure, combined with Bragg grating re?ection principle, (OADM) [2-3], tilted waveguide grating mode converter, etc. we can make a new compact wavelength division multiplexer. grated Bragg grating waveguide ?lter [1] with which multi plexer/demultiplexer or ?lter of light signal with different 65 US 8,835,204 B2 4 3 coe?icient, n denotes the nth Fourier order and describes all the Fourier components of the sampled In addition, some other photonic devices such as ?lter without retrore?ection, DFB semiconductor lasers with suppressed 0th channel resonance based on the Reconstruction-Equiva grating, i.e. the ghost gratings or sub-gratings. lent-Chirp technology, directional coupler and power splitters According to Eq.(3), there are a series of ghost gratins of any angle, optical waveguide mode converter, any other photonic devices based on waveguide grating and the volume All in the ofsampled these ghost grating gratings with their can be wave-vector changed with the grating, can be achieved. We believe this method can open a new avenue and bring a new dawn to the design of planar sampling structure S[?]. And nth order wave-vector of the ghost grating FA?) corresponds to the sum mation of the wave-vectors of the seed grating Koand photonic integration and other relative photonic devices. The main idea of this invention is to propose the micro structure of quasi-phase matching technology. Based on this technology, the target waveguide grating or volume waveguide grating with any grating shape and the corre sponding photonic devices can be achieved by two or three dimensional sampling structures using a uniform grating. of the nth order sampling structure’ s Fourier sub-grat ing 654?). According to equation (3), the wave vector of the target equivalent grating) TgN (Y) can be expressed as, SUMMARY OF THE INVENTION If the wave-vector of the target equivalent grating T<>N( A method to fabricate a multi-dimensional target waveguide and volume grating. Any kind of two or three ~> 20 dimensional (2D or 3D) target grating with arbitrary grating . ~> r ) equals to the wave-vector of the target grating k d structure can be realized if it is physically realizable. The (Y), that is, YN (Y) :Yd (Y). Y, (Y) is the wave common waveguide Bragg grating or volume grating is used vector of the seed grating, 65A, (Y) is the wave-vector as the seed grating. Its period can be uniform and varies from 50 nm to 1000 nm. The 2D or 3D sampled grating is then formed with refractive-index-modulated sampling structure. of the target sampling structure’ s Fourier sub-grating, 25 Among the multiple ghost gratings or sub-gratings in the sampled grating structure, one is selected as the target equiva lent grating.The wave-vector of the seed grating is KO(?), the wave-vector of the light is Kand the wave vector difference 30 vector of the seed grating F0 (Y) mismatches the expressed as AnS(Y):5[Y]-An(Y) (2) ied, then the arbitrary target grating structure can be equivalently realized. In other words, when the wave wave-vector of the required 2D or 3D target grating , one of the Fourier sub-gratings in the sampling struc ture i.e., the wave-vector of the target sampling struc between light and the seed grating is Algwhich can be AY:Y-FO(Y) (1) The refractive index modulation of the sampled grating with arbitrary sampling structure and uniform seed grat ing can be expressed as, TgN (Y) can be changed with the sampling structure: By changing the periodic distribution of the sampling structure S[?], the wave-vector 65A, (Y) can be var 35 ture’ s Fourier sub-grating 65A, (Y) is used to compen sate this mismatch. Therefore, an additional target sampling structure’s Fourier sub-grating is employed 40 here to keep the phase difference equals to zero during the optical transmission process, and the following phase match is also satis?ed. Here S[?]is the sampling structure and An(?) is the refractive index modulation depth of the seed grating ; According to Eq.(3), the phase of the sampled grating is Ydenotes the space vector. Based on the Fourier analysis, equation (2) can be further expressed as, 45 also a function of space. Specially the phase of the uniform ghost grating can be expressed as, expvfin-YiexpW'O-Y» (6) If there is a phase shift in the sampling structure, and the 50 shift value is A? , a phase shift will also exist in the sampling structure’s Fourier sub-grating. The corre sponding phase of the ghost grating can be described as, exp U6..-<Y+AY'>1expo<K’O-Y>>IeXpU6..-<Y>1expo< Here j denotes an imaginary number, 65,4?) is the 55 wave-vector of the nth order Fourier component of the . ‘> . sampling structure; KO ( r ) is the wave-vector of the seed grating and it can be further expressed as 60 7307))6XPUE’M'A7') (7) The corresponding phase shift of the ghost-grating has a magnitude of exp?asnAf'). For a uniform seed grating, G’sn-AY':¢. So a phase shift ¢is introduced in the nth order ghost grating of the sampled grating. (7) is the period of the seed grating and Y0 denotes the direction of the seed grating. Cn(?) is the Fourier 65 The refractive-index modulation, which corresponds to the Fourier coe?icient Cn(?), can also be changed with the pattern or shape in one sampling period, such as the duty cycle. In the 2D case, the refractive-index modulation can also be equivalently changed by this method. The US 8,835,204 B2 6 5 suitable shape in one sampling period to get the largest corresponding refractive index modulation intensity is 0.2 or larger. The stopband of the transmission light is up to 40 nm refractive-index modulation intensity can be obtained from the Fourier analysis. The characteristic of the MS-QPM technology as described in claim 1: the target equivalent grating with arbi trary structures, such as the tilted/arc grating or chirped/phase based on Reconstruction-equivalent-chirp (REC) technology shifted grating is realized by the MS-QPM technology, as with the suppressed 0th order resonance can be fabricated. long as the grating structure is physically realizable. There are a series of Fourier components, which are called ghost grat The period of the seed grating keeps uniform but tilted with an included angle (2° to 1 5° ) between the direction of the wave ings, with their wave-vectors Of kn (f) in the sampled grat vector KO(?) and the axial direction of the waveguide work ing as resonant cavity. Correspondingly, the designed sam pling structure is also tilted with some tilted angle, Therefore, according to Eq.(4), the direction of the target equivalent grating’s wave-vector kN (F) Will be rotated to be parallel to the axial direction of the resonant cavity. When designing, the Fourier order N is usually equal to :1. The speci?c tilted angle of the seed grating wave-vector k0 (Y) can be deter mined according to the effect on the suppression of Oth order or even wider, which can cover one whole optical communi cation window. In the present invention, the DFB semiconductor laser ing structure. According to Eq.(4) and (5), in order to obtain a speci?c target equivalent grating, i.e., the ghost grating with a certain Fourier order, the corresponding sampling structure, i.e., sampling period distribution, should be designed via compo sing the grating wave-vectors. Furthermore, according to Eq.(4), to change the direction of the grating, the target equivalent grating with arbitrary directions or arc pro?les can be realized by changing the direction of the wave-vector of sampling structure’s Fourier sub-grating In addi 20 tion, to realize the multiple-dimension phase shifted grating, only the phase shift in the sampling structure is required according to Eq.(5)-(7). In contrast, to realize the chirped grating, the sampling period and direction of the sampling structure are needed to be changed in space. For the fabrica 25 tion process, the period of the uniform seed grating is usually in the order of several hundred nanometers, thus it facilitates the fabrication process via the traditional holographic expo sure by interference method, or by means of the near ?eld holographic exposure. In contrast, the scale of the sampling structure is usually in the order of several micrometers, which is also very straightforward to be fabricated using the com mon photolithography technology. In the present invention, the characteristics of the MS QPM technology as applied to fabricate the WDM multi plexer/demultiplexer based on the waveguide grating or the volume grating are the two methods to design the multiplexer/ demultiplexer. The ?rst method is the cascade sampling struc 30 of the corresponding wave-vector. So the target equivalent grating in each section of the sampled grating diffracts a light beam with certain frequency (Bragg wavelength), while the seed grating keeps uniform. The second method is adopting sampling period is also uniform but there is a tilted angle between the wave-vector of the target sampling structure’s 35 target equivalent grating kN (f) and the axial direction of the waveguide according to Eq.(4). This tilted angle is usually 40 trary coupling direction, can be fabricated based on the MS QPM technology. The sampling structures are different in 45 gratings with different directions in different sections of the waveguide will re?ect incident light with a speci?c wave length along different directions. Each of the re?ective direc 50 tions can be designed on purpose. The detailed parameters can be calculated according to Eq.(4). Therefore, the direc tional coupler can be realized. If the refractive-index modu lation is properly designed, the sampled grating only re?ects re?ected in the same direction and couple into one single a portion of the incident light power. Then, the power divider 55 can be obtained. The refractive-index modulation intensity is usually designed multiplexer/demultiplexer devices are determined by the number of the channels. Usually, the sampling period of the multiplexer/demultiplexer grating varies from 0.5 to 20 pm from 0.001 to 0.2. The larger refractive-index modulation intensity of the target equivalent grating will lead to a higher 60 In the present invention, Bragg grating ?lter can be fabri diffractive e?iciency. In the present invention, the arbitrary volume grating ?lter and volume grating based photonic device can be fabricated based on the MS-QPM technology, The seed grating keeps uniform and the sampling structure can be realized by photo cated based on the MS-QPM technology. If there are two equivalent rcphase shifts inserted in the 1/4 and 3/ 4 positions of the target equivalent grating, a narrow pass-band will be established in the middle of the stopband. The equivalent rcphase shift can be realized by Eq. (5) to (7). Usually the cavity length varies from about 50.0 pm to 5000.0 pm, the different sections of the waveguide for the power divider or the directional coupler. The corresponding target equivalent other hand, the lights with different frequencies (wave lengths) propagating in given directions and positions, will be for a two-dimensional waveguide. designed to be from 2° to 15°. In the present invention, the power divider with arbitrary power division ratio, and the directional coupler with arbi directions. Hence, the demultiplexer can be achieved. On the waveguide, following the Bragg diffraction conditions. So the multiplexer can be realized. The total cavity length of the Fourier sub-grating USA, (T) and the seed grating. Hence, there will be a tilted angle between the wave-vector of the the sampled grating with chirped seed gating. The seed grat ing is chirped and the sampling structure keeps uniform. Therefore, by the aid of different target equivalent gratings in different sections of the sampled grating, the light with dif ferent frequencies (wavelengths) will be re?ected in different parameters of the seed grating and the sampling structure can be determined according to Eq.(4). The period of the sam pling structure usually varies from 0.5 to 20 pm. The larger title angle will lead to a better suppression effect. When the tilted angle is larger than 10° , the light resonance of the Oth order channel can be fully suppressed. In the present invention, the tilted waveguide grating can be fabricated with the following characteristic: The uniform seed grating is used and the direction of the wave-vector k0 (F) is designed according to the actual requirement. The ture which consists of several sections in the two dimensional waveguide grating. Each section is of the particular sampling structure including particular sampling period and direction channel’ s resonance. Usually the tilted angle is from 2° to 15° , which enables a good suppression. The detailed designing mask using the common photolithography method. The sam 65 pling structure can be designed according to the equations from Eq.(3) to Eq.(7). Therefore, the required target grating structure can be realized by the target equivalent grating. US 8,835,204 B2 8 7 In the present invention, the waveguide grating based pho effective refractive index of 1.455. The thickness of the core layer is 2 pm. The wave-vector of the seed grating tonic device with ?ne grating structure can be fabricated based on the MS-QPM technology. The uniform seed grating can be fabricated by holographic exposure. The required tar get equivalent grating can be obtained by designing the sam pling structure according to the equations from Eq.(3) to Eq.(7). The sampled grating can be realized by the common k0 (Y) is parallel to the +Z direction with the period of 485 nm. The incident light with the wavelength of 1545 .5 nm and the beam width of 30 um propagate along the +Z direction. There is a diffractive beam with the diffractive ef?ciency of about 50% propagating along photolithography method. Therefore, various waveguide the designed direction with an angle of 15.740 between the direction of re?ective direction and the -Z axial direction, while the rest 50% propagates along +Z direc grating based photonic devices can be easily realized. In the present invention, the photonic integrated circuits with DFB semiconductor laser array based on REC technol tion, the corresponding refractive index modulation intensity is about 0.001. The sampling pattern is square wave with the duty cycle of 0.5. The included angle is ogy, the waveguide grating ?lters, coupler and multiplexer/ demultiplexer can be monolithically integrated on the same chip, All the devices listed above can share the same seed 50° between the wave-vector of the sampling structure grating, while the sampling structure can be designed sepa rately according to the equations Eq. (3) to Eq.(7). Conse quently, the whole sampling structure can be fabricated on the same mask. Therefore, the whole sampled grating on that chip can be realized at the same time to achieve the monolithic integration of different photonic elements. In the present invention, 8-channel WDM Multiplexer/ Demultiplexer based on the multiple sections (layers) 20 sampled grating structure can be fabricated. The core of the two-dimensional planar waveguide is made of Ge:Si02 with the effective refractive index equal to 1.455. The refractive index modulation of the seed grating is 0.006. The width of the device is 40 um along X direction. The length of each section is 100 pm. The total length of the device is 1200 um 25 and that of the seed grating. In the present invention, the DFB semiconductor laser based on the Reconstruction-Equivalent-Chirp technology with suppressed 0” channel can be fabricated. The effective refractive index is 3.1. The cavity length is 400 pm. The width of the ridge waveguide is 2 pm. The period of the seed grating is 238 nm. The sampling period is 3 pm. The angle between the wave-vector @SA, (Y) and the axial direction of the waveguide is 53.67°. The angle between the seed grating wave-vector k0 (Y) and the axial direction of the laser waveguide is 3.67° Both ofthe angle of GSA, (Y) and k0 (Y) with the axial direction of waveguide are clockwise or anti clockwise. The direction of the wave-vector of —lst order along Z axis. The direction of the wave-vector k0 (Y) of the seed grating is parallel to the +Z direction with the grating target equivalent grating is parallel to the waveguide axial period of 500 nm. The channel spacing is 2 nm and the operating wavelength is from 1544 nm to 1558 nm. The sponding Bragg wavelength is 1551 .71nm. direction and its grating period is 250.27 nm, and the corre DESCRIPTION OF THE INVENTION incident polychromatic light is also parallel to the +Z direc tion. The detailed design parameters are listed in the follow ing Table. 1. Table.l. the channel wavelength/ sampling period/ The 35 fabricate the two dimensional (2-D) planar waveguide grating and the three dimensional (3-D) volume grating with complex included angle between wave-vector 65A, (Y) of the sampling structure and the wave-vector of the seed grat ing/the Corresponding re?ective angle between the —Z grating corrugation pro?le. The arbitrary grating corrugation 40 direction. Included angle between the Included angle Re?ective Channel Sampling betweenGSN ) Light and —Z wavelength period andK O (7') direction 55° 56° 56° 57° 58° 58° 58° 58° ll.95° 12.7l° l3.42° l4.36° l5.90° l6.44° l7.00° l7.62° 1544 1546 1548 1550 1552 1554 1556 1558 nm nm nm nm nm nm nm nm 4.20 4.00 3.85 3 60 3 30 3 20 310 3.00 pm pm pm pm pm pm pm pm 45 cess and lowers the cost of production for the various photo nic devices. The description of the present invention are as follows: The main characteristic of the invention is to use uniform as the seed grating with grating period between 50 nm and 1000 nm. Then the sampling structure further modulates the 50 seed grating’s index corrugation to form the sampled grating structure. This sampled grating with speci?c sampling struc ture can equivalently realize the arbitrary 2-D or 3-D grating structure. Based on the Fourier series analysis, such a sampled grating contains a series of Fourier components. 55 Each of these Fourier components can also be considered as a grating which is called ghost grating or sub-grating. If one of these ghost gratings is selected to perform a speci?c func grating. As the wave-vector of the seed grating and the incident light are all parallel to the +Z direction, all of appear to be of mirror symmetry regarding to +Z direc tion. A directional coupler with power division ratio of 0.5 can be fabricated: The width of the device is 30 um along the X axis and the length of the device is 50 um along the Z axis. The material of the core layer is Ge:SiO2 with the pro?le can also be equivalently achieved by designing the sampling structure and the seed grating with relatively small grating period. This technology simpli?es the fabrication pro grating period and uniform grating index modulation strength Here, the +1“ ghost grating works as the target equivalent these included angles can be either clockwise or coun terclockwise. The sampling structures of these two cases This invention proposes a technology named the micro structure quasi-phase-matching. This technology is used to tion, this ghost grating is called the target equivalent grating. 60 When the wave-vector of the seed grating is described as KO (Y), the wave-vector difference Ak between the light k and the seed grating can be expressed as, 65 When a light beam hit on a grating based device (either two or three dimensional), strong coupling will happen if some certain condition is satis?ed. This condition is usually called US 8,835,204 B2 10 the phase matching condition. Speci?cally, it can be written changed accordingly. According to Equ. (4), the wave-vector as AF:T<’-KO(Y):0. If it is satis?ed, the light will have the largest diffractive ef?ciency. This phenomenon is also called the Bragg diffraction. of the target equivalent grating can also be changed. To carefully pre-design the sampling structure, the target equivalent grating can be same as the target grating. There fore, the arbitrary grating pro?le can be realized equivalently only by changing the sampling pattern under a certain seed Usually, the index corrugation of the seed grating can be expressed as An(?):1/2An eprKO~?)+c.c. The correspond grating. In other words, we use one of the Fourier components of the sampling structure to compensate the wave-vector dif ing sampled grating with arbitrary sampling structure can be expressed as, ference between the seed grating wave-vector KO(?) and the target grating wave-vector KAY) when KO(?) and KAY) is not equal. In general, this method is similar to the Quasi Here, S[?] describes the sampling structure, An(?) is the phase-matching technology of the nonlinear optics for high amplitude of the index modulation of the seed grating, Y denotes the spatial vector. If the Fourier analysis is applied here, the Eq. (2) can be further expressed as order harmonic generation. In the nonlinear medium, an addi tional periodic structure is provided to compensate the wave vector mismatch between the incident fundmental and the output high order harmonic light frequency. This transforma tion can contribute an additional momentum to satisfy the (3) necessary of momentum conservation. By contrast, the 20 "Iiee Micro-structure Quasi-phase-matching technology has the similar physical picture and mathematical expression that can be expressed as follows: "Iiee A?:T<’d-FO<?>-@SN<Y>:O (5) 25 Here, Kd can be usually expressed as KdIFre—Tgm. Furthermore, according to Eq. (3), the phase of the sampled Here j denotes imaginary unit, 39‘?) are the wave-vec tors of the nth Fourier components of the sampling structure. These Fourier components are called sampling structure’s grating is also a function of the space. For a certain ghost grating, the phase change can be expressed as Fourier sub-grating. KO(?) is the grating wave-vector of the seed grating and can be written as 30 Assuming there is a phase shift in the sampling structure, and the value of the shift is AY', the phase of the sampled (7) 35 grating will be, is the period of the seed grating. 30 denotes the direction of the seed grating. C” is the Fourier coef?cients of each Fourier Then, a phase shift is easily introduced into the ghost component. n denotes the order of the Fourier components. Therefore, nth order of the ghost gratings is characterized by wave-vector Obviously, all of these ghost gratings can be manipulated by changing the sampling structure S[?]. This is because KAY) is only composed by seed grating’s 40 wave-vector KO(?) and the wave-vector of sampling struc ture’s Fourier sub-grating 654?). For a certain order of the Fourier components of the sampled grating, i.e. nIN, the wave-vector transformation relation according to Eq. (3) can 45 be expressed as 50 grating. The corresponding phase shift is exp?asnAf'). For example, if the seed grating is uniform and G’s” AY'Iq), a phase shift value 4) is then introduced in the nth order ghost grating. The index modulation strength of the target equivalent grating can be changed by changing the sampling structure shape in one sampling period such as the duty cycle. In the case of 2-D, we can continuously change the duty cycle of sampling structure along the grating, the equivalent apodiza tion can be realized. The relation between the index modula tion of a certain sub-grating and the duty cycle can be deter mined by the Fourier analysis. Let KM?) be equal to Kd(?) of our desired grating or target grating, i.e. KMYFKAY), then KN (Y) can be called 55 as target equivalent grating wave-vector. Then, we call 65A, (Y) target sampling structure’s Fourier sub-grating wave vector. Kdis the wave-vector of the target grating correspond ing to the speci?c grating corrugation that we select to per form a speci?c function. The target equivalent grating is When an optical signal is actually transmitted and pro cessed, this optical signal has a certain bandwidth instead of a single frequency. That means this optical signal has a certain wavelength within a certain bandwidth. So the corresponding grating structures should be designed according to the pro cess of the realistic optical signal to obtain the largest ef? ciency. For an actual optical signal, the speci?c grating is 60 called as the target grating if we can get the best ef?ciency of denoted by KN (Y) and can be easily manipulated by chang single process. The wave-vector of the target grating is called as the wave-vector of the target grating K ing the sampling structure S[?]. The detailed wave-vector grating. The period of the target grating is usually in the transform procedure can be summarized as follows: We ?rst change the sampling pattern or sampling structure S[?] on purpose. Then, the wave-vector 352%?) can be In most of the cases, the target grating is not a uniform 65 magnitude of a few hundreds of nanometers. Nanotechnology is needed to fabricate this grating. Meanwhile, the wave length space of two channels of signals is usually smaller than