Accurate Diffraction Efficiency Control for Multiplexed Volume Holographic Gratings. Xuliang Han, Gicherl Kim, and Ray T. Chen

Accuate Diffaction Efficiency Contol fo Multiplexed Volume Hologaphic Gatings Xuliang Han, Gichel Kim, and Ray T. Chen Micoelectonic Reseach Cente Depatment of Electical and Compute Engineeing Univesity of Texas at Austin E-mail: hanxuliang@mail.utexas.edu Single and multiplexed volume hologaphic gatings have been suggested fo use in feespace [] and substate-guided-wave [2], [3] boad-level optical inteconnect systems. The photopolyme-based volume hologam is an attactive option fo making high efficiency gatings. The advantage of photopolymes ove othe types of emulsion, such as dichomated gelatin and silve halides, includes dy-pocessing capability, long shelf life, and good photospeed [4]. In this pape, fist, we biefly eview the theoetical model descibing gating fomation pocess in dy photopolyme films. Then, based on the expeimental evaluations of the gating fomation chaacteistics in dy photopolyme films, we pesent the way to develop the pactical ecoding schedules fo the fabication of hologaphic gatings unde accuate diffaction efficiency contol. Finally, we demonstate a pactical application by using the single and double hologaphic gatings we ecoded. The dy photopolyme film (DuPont HRF-600) consists of monomes, polymeic bindes, and photoinitiatos. The monomes ae polymeized when exposed to light of a specific wavelength and the pecentage of polymeized monomes is popotional to the exposue dosage. We study the fomation of double hologaphic gatings in which the two gatings ae

ecoded sequentially with non-paallel gating vecto oientations. Duing the fist exposue, a -D diffusion equation [5], [6] in the following descibes the monome concentation u (, t) ( x, t) u t = [ D( x, t) u( x, t) ] F [ + V cos( K x) ] u( x t) and a 2-D diffusion equation is equied duing the second exposue, whee K and K 2 u t (, t) = o, [ ] u( t) [ D(, t) u(, t) ] F + V cos( K ) o 2,,, (), (2) epesent, espectively, the gating vecto fomed by the fist and second exposue, D (, t) is the diffusion paamete, F o is the polymeization facto ( F o = κi, whee o κ is a constant and I o is the aveage iadiance), and V is the finge visibility. The initial conditions of equation (2) depend on the final conditions of equation (), and the final monome concentation afte ecoding can be witten in the fom of u (, t) = u ( t) cos( K ) + u () t ( K ) i= 0 i k cos k= 0 2. (3) If the two gatings ae othogonally multiplexed ( K ^ K 2 ), equation (2) can be decomposed into two uncoupled -D diffusion equations though a pope coodinate tansfomation. If the two gatings ae non-othogonally multiplexed, howeve, the two -D diffusion equations ae coupled with each othe, which implies that the fomation of the second gating is affected by the change of the fist gating duing the second exposue in a complicated way. We poposed a novel inteconnect achitectue called the centalized optical backplane [7]. This achitectue etains the advantages of bus achitectue while at the same time poviding unifom optical signal fan-outs. To achieve such fan-outs, single hologaphic gatings, as shown in Fig. (a), and equal-stength double hologaphic gatings, as shown in Fig. (b), ae equied [7]. Fo these hologaphic gatings, the econstuction wavelength is 850 nm, and the

diffaction angles ae 45 o. Equation (2) is difficult to solve in the case of non-othogonal multiplexing. Moeove, the diffusion model involves some mateial paametes [6] that ae not available at this stage. Theefoe, this model cannot be used diectly fo diffaction efficiency contol, especially in the case of non-othogonal multiplexing. Expeimental evaluations of gating fomation chaacteistics ae equied to develop the pactical ecoding schedules fo the fabication of hologaphic gatings unde accuate diffaction efficiency contol [8]. Hologaphic gatings wee ecoded in DuPont HRF-600X04 photopolyme films. The film s thickness is 20 µm, which along with the 850 nm econstuction wavelength and the 45 o diffaction angle as shown in Fig. satisfies the equiement fo a thick phase hologam [9]. The 532 nm line of 0.2 W fom a Vedi lase was used fo making all exposues. The mateial has little esponse at 850 nm, which allows in situ monitoing at this wavelength. The diffacted light fom an 850 nm pobe lase was monitoed to measue the dynamic diffaction efficiency. To examine the dynamic popeties of single gating fomation in dy photopolyme films, a seies of single-gating hologams, as shown in Fig. (a), was ecoded with the exposing illumination was stopped befoe the maximum satuation in the diffaction efficiency was eached. Fig. 2 shows the nomalized diffaction efficiency as a function of post-theshold exposue time duing and afte the exposue. Afte the temination of the exposue, the diffaction efficiency continues to incease until a satuation value is eached. This incement depends on the diffaction efficiency η stop at which the exposing illumination is stopped. The data in Fig. 2 show that the value of diffaction efficiency inceased, espectively, 5%, 0%, 3%, 3%, 0%, and 8% afte the exposing illumination was stopped at 26%, 37%, 48%, 62%, 73%, and 87%. At elatively low diffaction efficiencies, monome concentation gadients ae still weak. When eaching elatively high diffaction efficiencies,

the monome content available fo futhe diffusion becomes low. Theefoe, the postillumination diffaction efficiency incement is elatively small in these cases. To make a single-gating hologam with the desied diffaction efficiency, η stop is a key paamete to contol. Fig. 2 can be used as a guide to find the coesponding η stop fo the desied diffaction efficiency. To examine the dynamic popeties of double gating fomation in dy photopolyme films, a seies of double-gating hologams, as shown in Fig. (b), was ecoded. The expeiments wee conducted as follows: () the fist exposue was stopped when the fist gating s diffaction efficiency, η stop, eached a value, e.g., 30%; (2) the substate was otated 80 o ; (3) the film was exposed to the ecoding beams again to fom the second gating. To ensue the stability of the fist gating and the epeatability of the expeiments, some waiting time is equied to guaantee that the second step takes 30 seconds. Fig. 3 shows the nomalized diffaction efficiency of the two gatings as a function of second-exposue time. The calculated cuves by solving two uncoupled -D diffusion equations using the paametes fom cuve fitting [5], [6] ae also shown in Fig. 3 as efeences. Duing the second exposue, the diffaction efficiency of the fist gating inceases to a satuation value, and then olls down with futhe exposue. The second gating shows the same behavio but lags behind that of the fist gating. Ou taget is to chaacteize the cossing point whee the two gatings have the same diffaction efficiency η equal, which depends on the fist gating s diffaction efficiency η ( 0) at which the second exposue is stated. As discussed peviously, ( 0) η is detemined by η stop. The data in Fig. 3 (a), (b), and (c) show that η equal was, espectively, 26%, 43%, and 47% in the case that ( 0) η was 6%, 30%, and 37%. In these cases, the monome content left

afte the fist exposue is enough fo the second gating to catch up with the fist gating, and η inceases with η ( 0) equal exist in the case that ( 0). On the othe hand, the data in Fig. 3 (d) show that η equal did not η was 52%, because the monome content available fo the second gating fomation was too low. To make a high-efficiency equal-stength double-gating hologam, ( 0) η is a key paamete to contol. Fig. 3 can be used as a guide to find the optimal η ( 0), and then Fig. 2 can be used to find stop η fo the coesponding ( 0) η. Followed the pocedue descibed above, we obtained the hologaphic gatings fo the demonstation of unifom optical signal fan-outs in a five-boad centalized optical backplane as shown in Fig. 4. An 850 nm VCSEL was used at cente as the tansmitte. As specified by the centalized optical backplane achitectue [7], an equal-stength (47%/47%) double-gating hologam was attached to the cente of the optical waveguiding plate. The diffaction angles of the hologaphic gatings wee 45 o. Each end of the plate had a 22.5 o bevel coated with aluminum to povide a nealy 00% eflection efficiency. The fan-out vaiation was measued to be within 2.5%. This method is staightfowad and achieves bette unifomity compaed with the method that contols the diffaction efficiency by setting exposue time [0]. In this pape, the diffusion model descibing the pocess of gating fomation in dy photopolyme films is biefly eviewed. If two gatings ae non-othogonally multiplexed, the pocess of the second gating fomation is coupled with the change of the fist gating duing the second exposue. Due to the complexity of solving the diffusion equation and the lack of infomation about mateial paametes [6], this model cannot be used diectly fo diffaction efficiency contol, especially in the case of non-othogonal multiplexing. Based on the expeimental evaluations of the gating fomation chaacteistics in dy photopolyme films, we develop the pactical ecoding schedules fo the fabication of hologaphic gatings unde

accuate diffaction efficiency contol. The method pesented in this pape is staightfowad and can also be used fo accuate diffaction efficiency contol fo othe types of multiplexed volume hologaphic gatings. Acknowledgements The authos thank BMDO, DARPA, ONR, AFOSR, and the ATP pogam of the State of Texas fo suppoting this study. Refeences []. R. K. Kostuk, J. Yeh, and M. Fink, Distibuted Optical Data Bus fo Boad-Level Inteconnects, Applied Optics, 32, 500, (993). [2]. K. Benne, F. Saue, Diffactive-Reflective Optical Inteconnects, Applied Optics, 27, 425, (988). [3]. S. Nataajan, C. Zhao, and R. T. Chen, Bi-Diectional Optical Backplane Bus fo Geneal Pupose Multi-Pocesso Boad-to-Boad Optoelectonic Inteconnects, Jounal of Lightwave Technology, 3, 03, (995). [4]. W. J. Gambogi, A. M. Webe, and T. J. Tout, Advances and Applications of DuPont Hologaphic Photopolymes, Poc. SPIE 2043, 2, (993). [5]. G. Zhao, P. Mououlis, Diffusion Model of Hologam Fomation in Dy Photopolyme Mateials, Jounal of Moden Optics, 4, 929, (994). [6]. V. Moeau, J. R. Lawence, S. Sole Henandez, B. Tilkens, Y. Renotte, and Y. Lion, Optimization of Hologams Recoded in DuPont Photopolyme, Poc. SPIE 4089, 822, (2000).

[7]. G. Kim, X. Han, and R. T. Chen, A Method fo Reboadcasting Signals in an Optical Backplane Bus System, Jounal of Lightwave Technology, 9, 959, (200). [8]. R. K. Kostuk, Dynamic Hologam Recoding Chaacteistics in DuPont Photopolymes, Applied Optics, 38, 357, (999). [9]. H. Kogelnik, Coupled Wave Theoy fo Thick Hologam Gatings, Bell System Technical Jounal, 48, 2909, (969). [0]. J. Liu, C. Zhao, R. Lee, and R. T. Chen, Coss-link optimized cascaded volume hologam aay with enegy-equalized one-to-many suface-nomal fan-outs, Optics Lettes, 22, 024, (997).

Figue Captions Fig. The vecto diagam of the (a) single-gating hologam, (b) double-gating hologam. R epesents the wave vecto of the econstuction beam. S epesents the wave vecto of the diffaction beam. K epesents the gating vecto fomed by the exposue. Fig. 2 Diffaction efficiency vesus post-theshold exposue time duing and afte the exposue. The monitoed diffaction efficiency was, espectively, 26%, 37%, 48%, 62%, + 73%, and 87%, when the exposing illumination was stopped. Fig. 3 Diffaction efficiency vesus second-exposue time duing the second exposue. At the beginning of the second exposue, the diffaction efficiency of the fist gating was, espectively, (a) 6%, (b) 30%, (c) 37%, and (d) 52%. * Cuves epesent the calculated solutions. Fig. 4 Unifom optical signal fan-outs in a five-boad centalized optical backplane. SH epesents single-gating hologam. DH epesents double-gating hologam.

(a) (b) Fig.

00 nomalized diffaction efficiency (%) 90 80 70 60 50 40 30 20 0 0 0 5 0 5 20 25 30 35 40 post-theshold exposue time (s) Fig. 2

(a) (b) (c) Fig. 3 (d)

Fig. 4