Interferometric amplitude apodization of integrated gratings

Transcription

1 Interferometrc ampltude apodzaton of ntegrated gratngs T. W. Mossberg, C. Grener, and D. Iazkov LghtSmyth Technologes, Inc., 860 W. Park St. Ste 250, Eugene, OR Abstract: Modern photolthography wth ts sub-hundred-nanometer-scale resoluton and cm-scale spatal coherence provdes for the creaton of powerful wavegude dffractve structures useful as ntegrated spectral flters, multplexers, spatal sgnal routers, nterconnects, etc. Applcaton of such structures s facltated by a lthographcally frendly means of ampltude apodzaton, whch allows for programmng of general spectral and spatal transfer functons. We descrbe here an approach to mplementng flexble bnary-etch-compatble dffractve ampltude control based on the decomposton of dffractve structures nto subregons each of whose dffractve contours are spatally postoned so as to nterferometrcally control the net dffractve ampltude and phase of the subregon. The present approach s unquely powerful because t allows for substantal decouplng of ampltude and phase apodzaton Optcal Socety of Amerca OCIS codes: ( ) Dffracton gratngs, ( ) Wavegudes, channeled, ( ) Guded waves, ( ) Mcrostructure fabrcaton, ( ) Bragg reflectors References and lnks 1. C. Grener, D. Iazkov, and T. W. Mossberg, Lthographcally-fabrcated planar holographc Bragg reflectors, J. Lghtwave Technol. 22, (2004). 2. J. L. Rebola and A. V. T. Cartaxo, Performance optmzaton of Gaussan apodzed fber Bragg gratng flters n WDM systems, J. Lghtwave Technol. 8, (2002). 3. T. Komuka, K. Tamura, and M. Nakazawa, An effcent 0.04-nm apodzed fber Bragg gratng and ts applcaton to narrow-band spectral flterng, IEEE Photoncs Technol. Lett. 9, (1997). 4. T. Erdogan, Fber gratng spectra, J. Lghtwave Technol. 15, (1997). 5. D. Wesmann, C. Davd, R. Germann, D. Ern, and G. L. Bona, Apodzed surface-corrugated gratngs wth varyng duty cycles, IEEE Photoncs Technol. Lett. 12, (2000). 6. D. Wesmann, R. Germann, G. L. Bona, C. Davd, D. Ern, and H. Jackel, Add-drop flter based on apodzed surface-corrugated gratngs, J. Opt. Soc. Am. B 20, (2003). 7. D. Iazkov, C. Grener, and T. W. Mossberg, Effectve gray scale n lthographcally scrbed planar holographc Bragg reflectors, Appl. Opt. 43, (2004). 8. C. Grener, T. W. Mossberg, and D. Iazkov, Bandpass engneerng of lthographcally-scrbed channel-wavegude Bragg gratngs, Opt. Lett. 29, (2004). 9. B. Malo, S. Therault, D. C. Johnson, F. Blodeau, J. Albert, K. O. Hll, Apodsaton of the spectral response of fbre Bragg gratngs usng a phase mask wth varable dffracton effcency, Electron. Lett. 31, (1995). 10. H. J. Deyerl, N. Plougmann, J. B. Jensen, F. Florean, H. R. Sørensen, M. Krstensen, Fabrcaton of Advanced Bragg Gratngs wth Complex Apodzaton Profles by Use of the Polarzaton Control Method, Appl. Opt. 43, (2004). 11. M. Ibsen, M. K. Durkn, M. J. Cole, R. I. Lamng, Snc-sampled fber Bragg gratngs for dentcal multple wavelength operaton, Photoncs Technology Lett. 10, (1998). (C) 2005 OSA 4 Aprl 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2419

2 It has recently been demonstrated [1] that deep ultravolet (DUV) photolthography provdes a powerful means of producng dstrbuted dffractve or holographc structures n slab and channel wavegudes provdng for the fabrcaton of vrtually arbtrary computer-desgned patterns pxlated at the resoluton of <100 nm wth full spatal coherence on the centmeter scale. Such flexble fabrcaton means allow for the ncorporaton of powerful volume holographc desgn concepts nto dstrbuted dffractve structures provdng for general spatal and spectral sgnal processng, flterng, and routng n devce formats consstent wth hgh volume and low-cost producton. In the present work, we explore the applcaton of DUV photolthographc desgn flexblty to the realzaton of an ampltude and phase apodzaton means that s fully compatble wth fabrcaton frendly bnary etch methods and at the same tme unquely mnmzes the couplng of ampltude and phase effects. The present method, correlated-contour apodzaton, utlzes the precse placement of contours wthn dffractve contour subsets to nterferometrcally control the ampltude and phase of the net feld dffracted by the contour subset. We note that other apodzaton methods have been demonstrated n fber Bragg gratngs [2-4], channel wavegudes [5,6] and slab dffractve structures [7]. These prevously descrbed methods generally ntroduce a complex couplng between ampltude and phase apodzaton. Correlated-contour ampltude and phase control s applcable to many dstrbuted dffractve structures ncludng channel wavegude Bragg gratngs, slab wavegude holographc Bragg reflectors (HBRs), and even free-space reflecton and transmsson gratngs. A lthographcally-scrbed channel wavegude gratng s depcted schematcally n Fg. 1 from a top vew (1(a)) and sde vew (1(b)). The dffractve contours (lnes) of the gratng are patterned wth a deep ultravolet (DUV) stepper n resst, etched nto the channel wavegude core, and flled wth materal of dfferng refractve ndex. A top vew of a holographc Bragg reflector (HBR) s shown n Fg. 1(c). The HBR s a volume hologram mplemented n a slab wavegude. Lght typcally enters the slab regon through a channel wavegude and then expands freely (n the plane) to nteract wth the curved HBR dffractve contours. The shape of each contour may be computer-talored to create from the nput sgnal an output sgnal whose wavefront s optmally matched to the entry mode of the output channel wavegude. Smple geometrc curves lke crcles and ellpses may suffce for couplng between nput and output ports n some cases, but custom contours (lke aspherc Fg. 1. (a)-(b) Top and sde vews of channel wavegude gratng, respectvely. (c) Top-vew of slab-wavegude holographc Bragg reflector wth channel wavegude access. (d) Photograph of gratng contours for channel wavegude gratng pror to fll. (C) 2005 OSA 4 Aprl 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2420

3 (a) d o (c) N=5 z (b) δ d o /2- δ d o δ (d) d o d o z 0 ε = (z -z 0 ) z δ δ Fgure 2 ε Fg, 2. Basc concept of correlated-contour ampltude and phase control. (a) Unform gratng. (b) Blow-up of two adjacent gratng contours wth common and dfferental poston shfts. (c) Fvecontour subgroups wth center contour deleton to provde room for centerwse dsplacement of outer contours. (d) Common mode and dfferental dsplacements of contour set elements (N=5) used to adjust phase and ampltude, respectvely. magng optcs) wll provde more effcent sgnal couplng n general HBR desgns. Wth modern DUV photolthographc fabrcaton, asphercs are as easy to fabrcate as sphercs. The varous contours of the HBR are spaced so that generated output wavefronts from the ensemble arrve at the output port wth desgned phase relatonshps and typcally a common wavefront. Correlated-contour apodzaton comprses spatal repostonng of contours wthn contour subsets so that the coherent addton of ther scattered wavefronts s adjusted to desred values. Overall phase shfts can be mplemented through spatal shfts n the center of gravty of the varous contour subsets. Fgure 1(d) s a scannng-electron mcroscope pcture of dffractve contours lke those used n the channel wavegudes pror to fllng wth claddng. There are many ways a collecton of dffractve contours can be postonally dspersed to acheve a desred net reflectvty. We concentrate here on one specfc but systematc approach to contour postonng. In Fg. 2(a), we depct a gratng structure of constant spacng d o, whch wll backscatter lght at wavelength λ o = 2nd o, where n s the effectve wavegude refractve ndex. We assume that the overall bandwdth of the gratng λ s very small compared to λ o (. e. λ/λ o <<1). In Fg. 2(b), we show a two-member set of dffractve contours. If the central poston of the set s z o (z ) pror to (after) apodzaton, and the fnal separaton between lnes s d = d o -2δ, wth the contours symmetrc about z (see Fg. 2(b)), the net feld backscattered from the lne par wll be E ( δ, ε ) = Eo exp( 2k oε ) cos( 2koδ ), (1) where E o s the net backscattered feld magntude from the set of two correlated lnes for resonant lght wth δ =0, k o =2πn/λ o, ε = z - z o, and t s assumed that k o d o = mπ (m=1,2, ). The two parameters δ and ε, provde ndependent control over the net reflectve ampltude and phase, respectvely, of the correlated two-lne set. The resonant correlated-lne-set ampltude reflecton coeffcent may be wrtten as (C) 2005 OSA 4 Aprl 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2421

4 ( δ ) E ρ( δ (2) ) = = cos( 2k o δ ) Eo The reflected feld ampltude, beng nterferometrcally determned, exhbts chromatc varaton. But n the lmt of λ/λ o <<1, the ampltude of the apodzed lne par wll be essentally constant over the reflecton bandwdth of the overall gratng. To provde a manylne gratng wth smooth reflectve ampltude varaton along ts length, all dffractve contours n the gratng are grouped nto lne pars wth δ and ε varable from par to par. A unque feature of the correlated-contour apodzaton method s that the surface-etch percentage, averaged over dstances >>λ o, remans nomnally constant allowng the guded waves to experence a constant average materal composton. Ths deal stuaton can be complcated by fabrcaton mperfectons, for example nvolvng etch-profle changes wth neghbor separaton. Such effects are shown here to be small. Owng to the nomnally constant materal composton, the effectve wavegude refractve ndex n may be expected to reman essentally constant as the dffractve ampltude s changed. In ths case, phase modulaton s not ntrnscally coupled to ampltude apodzaton. In prevously descrbed ampltude apodzaton methods applcable to etched gratngs [2-8], ampltude changes typcally ntroduce changes n average materal composton and hence n n. Changes n n, unless compensated n desgn, have the effect of ntroducng poston-dependent phase shfts concomtant to ntended ampltude apodzaton. Couplng of phase and ampltude apodzaton can sgnfcantly complcate the problem of achevng desred gratng response. We note that decouplng of ampltude apodzaton from ndex varaton has been developed prevously for gratngs based on photo-wrtten ndex varatons [9-11]. In some cases, the spacng between gratng lnes, d o, may be at the level of lthographc resoluton, whch mples that dsplacements of contours toward one another cannot be correctly rendered. In ths scenaro (applcable to our experments), correlated-contour ampltude apodzaton can be mplemented as shown n Fgs. 2(c-d). The contours, n the case shown, are dvded nto groupngs of 5 lnes each. The center lne of each set s deleted (Fg. 2(c)). Deleton of the center lne provdes room for the lnes on each sde to be moved toward the center of the orgnal group, as shown n Fg. 2(d), whle leavng a lthographcally renderable gap. The center-lne deleton approach can be extended to correlated lne sets nvolvng an arbtrary (ntally) odd number, N, of dffractve contours. As we mplement the method, all lnes on ether sde of the center are dsplaced symmetrcally n a manner analogous to that shown n Fg. 2(d). The reflected ampltude and phase of the groupngs then stll vares as n Eqs. (1-2), where E o represents the δ =0 reflecton ampltude of a correlated set regardless of the number of lnes nvolved. Deleton of the center lne of each contour groupng may ntroduce addtonal gratng resonances. Wth deleted lnes, the gratng can be vewed as a frst-order gratng as n Fg. 2(a) combned wth an oppostely sgned N th -order gratng wth the latter havng resonances spaced about k o by k o /N. For small values of N and thus wde spectral spacng the addtonal resonances can typcally be gnored. Alternatvely, by varyng N throughout the dffractve structure, the addtonal resonances may be reduced n ampltude as needed. We have tested correlated-contour dffractve ampltude control n both channel wavegudes and HBRs. All gudng structures fabrcated are multlayer slca-on-slcon. The HBR structures have a 2-µm thck core wth blateral 15 µm claddng and core-claddng refractve ndex contrast of 0.8 percent. Dffractve structures are patterned (va DUV photolthography) and etched on the top of the core layer to a depth of about 450 nm and flled wth claddng. HBR dffractve contours are crcular wth nput and output wavegudes at common conjugate mage ponts. The HBR contours span an area of approxmately 2 2 mm and contan about 4000 contours. The channel wavegude structures employed have core dmensons of approxmately 2 6 µm and dffered from the HBR structures n that the (C) 2005 OSA 4 Aprl 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2422

5 Fg. 3. Reflecton spectra of two channel wavegudes (left and rght) each contanng four separate gratngs. Top and bottom rows show dfferent nput polarzatons. Each ndvdual gratng s wrtten wth dentcal contour sets adjusted to specfc feld reflectvty and gratng lengths are adjusted to provde nearly unform net reflectvty (see text). core was comprsed of two sublayers wth dffractve contours etched 850 nm deep nto the top of the 1-µm thck lower core layer (2 percent ndex contrast relatve to the claddng) and flled wth the upper core layer (0.8 percent contrast relatve to the claddng). Channel dffractve contours are straght segments orented normal to the channel propagaton drecton and spannng the entre transverse extent of the gude. The channel wavegude core was surrounded by lower ndex claddng. All dffractve structures were desgned to operate n the weak reflecton lmt (< 10 percent power reflecton) to elmnate saturaton effects. Operaton n the weak reflecton lmt s for expermental convenence only. Measurement n ths lmt allows for strct proportonalty between the reflectvty of ndvdual correlatedlne sets and the easly measured reflectvty of a whole gratng comprsed of many correlated sets. To test the varaton of reflectvty and refractve ndex wth lne dsplacement (δ ), eght separate channel wavegude gratngs were fabrcated. The channel wavegude gratngs utlzed 5-lne (center-lne-deleted) correlated-lne-set ampltude control (see Fg. 2(d)). Wthn each gratng, δ (the lne dsplacement) was held constant. The number of correlated lne sets wthn each gratng was vared so that the overall gratng reflectvty (number of correlated sets ndvdual set reflectvty) was held approxmately constant provdng a convenent nearly constant reflected power level for measurement. The gratngs were located sequentally, wthout spatal overlap, along two channel wavegudes wth gratngs (ad) n one channel and (e-h) n the other. Gratngs wthn a sngle channel were dsplaced n wavelength so that they could be dstngushed n the reflectve measurement. Wavelength separaton was set large to avod nterference. More generally, wavelength separaton may be vared contnuously n ncrements down to the transform lmt. In Fg. 3, we show the reflecton spectra of the gratngs. Reflected powers nclude a 7 db excess nput couplng loss unque to the test setup. The top and bottom of Fg. 3 detal the gratng responses to TE and TM nput polarzatons, respectvely. The desgn physcal characterstcs of the varous (C) 2005 OSA 4 Aprl 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2423

6 gratngs are gven n Table 1. Note the varatons n gratng resonance wdth resultng from the varaton n overall length from gratng to gratng. Ths wdth varaton s expected for spatally coherent gratngs. Table 1. Channel Wavegude Gratng Propertes Gratng Lne Spacng d 0 (µm) Lne Set Number δ /d 0 Relatve Ampltude Reflectvty ρ Expected Gratng Reflectvty (Power (db)) Measured Wavelength (nm) a b c d e f g h The observed reflected powers are converted to felds and are normalzed by the number of contour sets n each gratng to arrve at a measured correlated-set ampltude reflectvty. Identcal gratngs appearng n both channel wavegudes are used to normalze out reflectvty varatons ntroduced by dfferences n fber-to-channel couplng. In Fg. 4, measured ampltude reflectvty s plotted versus Eq. (2) reflectvty. The agreement between desgned and measured contour-set ampltude reflectvtes s qute good ndcatng that the fabrcaton process provdes hgh fdelty and that the underlyng theory s sound. Some devaton from Eq. (2) s expected because the lthographc process exhbts some fdelty Measured Reflecton Coeffcent 1.0 TE TM Fgure Desgn Reflecton Coeffcent Fg. 4. Plot of measured ampltude reflecton coeffcent versus desgn reflecton coeffcent for the gratngs of Table 1. (C) 2005 OSA 4 Aprl 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2424

7 Effectve Refractve Index Fgure 5 (a) Reflecton coeffcent (b) Reflecton coeffcent Fg. 5. (a) Measured effectve refractve ndex as a functon of ampltude reflecton coeffcent for correlated-lne-set gratngs (sold crcles) and a reference gratng set (open trangles) whose reflectvty s controlled va the partal scrbe method of Ref. 8. (b) Effectve refractve ndex of the two gratng sets after extractng ntrnsc wavelength dependence. varaton as the pattern rendered s vared. As seen from Fg. 4, complcatons of ths knd are relatvely small. Ultmately, an emprcal replacement for Eq. (2) may be devsed that accounts for fabrcaton subtletes as necessary. The data of Fg. 4 ndcates that correlated-contour apodzaton s effectve n controllng the reflectve ampltude of gratngs. We now examne how effectve refractve ndex vares wth the reflectve ampltude. To nvestgate ths ssue, we plot ndex values derved from the eght test gratngs as determned by measurng the peak reflected wavelength, λ o, for each channel wavegude gratng, usng the parameters of Table I, and applyng the relaton n =λ o /2d o. Resultng ndex values are plotted (sold ponts) n Fg. 5(a) as a functon of desgn gratng reflectvty. Also plotted as the open trangles, are the smlarly derved effectve ndces for a reference set of channel wavegude gratngs whose reflecton ampltude s vared usng the partal-fll grayscale method [8]. In the partal-fll grayscale method, reflectve ampltude s vared by adjustng the wdth of the gratng lnes across the channel wavegude. As the wdth of gratng lnes vares, the amount of fll materal added vares. Thus the average materal composton seen by sgnals changes wth reflectve ampltude and a sgnfcant correlaton of ampltude and ndex may be expected. Ths reference set of gratngs spans a range of wavelengths and reflectvtes smlar to the correlated-lne-set gratngs. Geometrc and materal propertes lead to a natural varaton of effectve wavegude ndex as a functon of sgnal wavelength. Snce the test gratngs are dsplaced n wavelength, the raw ndex data of Fg. 5(a) should be corrected to remove natural wavelength related changes. We have done ths usng measured materal and estmated geometrc ndex effects and plot the corrected gratng ndces n Fg. 5(b). It s clear that the couplng between reflectve ampltude and effectve ndex s much weaker for gratngs apodzed usng the correlated-contour ampltude control method than for those apodzed usng the partal-fll method. Wth correlated-contour ampltude control, absolute ndex changes on the level of only a few parts n 10 4 are observed when reflectve ampltude s vared over an order of magntude. It should be noted that the desgn reflectvty of the correlated-contour test gratngs does not vary monotoncally wth wavelength (see Table I). It s for ths reason that (C) 2005 OSA 4 Aprl 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2425

8 Fg. 6. Reflecton spectra of HBRs apodzed wth 3-lne (N=3) correlated-contour ampltude and phase control. In (a), the lower trace depcts the calculated reflectve spectrum of a lnearly chrped gratng wth no ampltude apodzaton, the mddle (sold) trace s a measured reflecton spectrum of an apodzed HBR, the top trace (dashed) s the smulated HBR response, whch s dsplaced upward by 5 db for clarty. (b) s a blow-up of the measured reflecton spectrum of part (a) wth traces (TE top) for both polarzatons and scalar smulated spectrum (flattest). The ampltude and phase apodzaton functons employed n the HBR of (a-b) are shown n (c) and (d), respectvely. the wggles n the ndex data of Fg. 5(a) are smoothed (as shown n Fg. 5(b)) when one corrects for the natural wavegude chromatc ndex varaton. In Fg. 6, we show the reflecton spectra of HBR flters desgned to produce flat-top passbands approxmately sutable for course WDM multplexng. Fg. 6(a) (sold lne), depcts the TM reflecton spectrum of an HBR apodzed wth correlated-contour apodzaton (N=3). The dashed lne s the desgn bandpass functon (dsplaced by 5 db above the measurement for dsplay). The vertcal scale of Fg. 6(a) s expanded n Fg. 6(b) where TE (top), TM (bottom), and desgn (flattest) bandpass functons are shown. Fgure 6(c) (6(d)) shows the radal ampltude (phase) apodzaton functon employed n the HBR. The phase functon shown corresponds approxmately to a lnear perod chrp. Measurements of empty channel wavegudes ndcate that couplng to the rectangular access channels accounted for nearly all of the change n reflected power wth polarzaton observed n Fg. 6(b). Slght rpple n the observed passband may have occurred because of coherent backscatterng from edges and other structures wthn the test de. The oscllatng bandpass functon (lowest curve) shown n Fg. 6(a) shows the calculated reflecton spectrum from a lnearly chrped gratng of constant ampltude (unapodzed). Overall, t s clear that the correlated contour apodzaton approach allows for powerful passband control. We have descrbed an approach to ntroducng poston-dependent dffractve ampltude and phase nto dstrbuted dffractve structures. The method s enabled by the precse and arbtrary postonng control afforded to desgners by DUV photolthography and wavegude deposton technques. Advanced ntegrated flterng and sgnal processng devces of dverse character are enabled by the spectral and spatal programmablty the present apodzaton approach allows. We note that the present apodzaton method may be appled even n the case of free-space surface gratngs. (C) 2005 OSA 4 Aprl 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2426