Abstract

Several one-dimensional arrays of focusing grating couplers are designed for uniform distribution of incident optical powers to several processing boards in a backboard interconnection scheme. As main design parameters, both the length and the duty cycle of each focusing grating coupler are determined on the bases of ray-optic propagation-mode analysis in a slab waveguide and of rigorous coupled-wave diffraction analysis for out-coupled radiation modes. The backboard interconnection scheme incorporating the one-dimensional focusing-grating-coupler arrays, when used to distribute a guided optical power of TE0 mode to several converging waves radiated only toward a glass substrate, displayed a power uniformity of 5% and a total coupling efficiency of 99.1%, which can be highly acceptable in practical use.

© 1995 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. W. Hunziker, W. Vogt, H. Melchior, “Optoelectronic integrated-circuit packaging with self-aligned fiber to waveguide array coupling by Si V-groove flip-chip technique,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper SaC3.
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  9. GLAD is a registered trademark of Applied Optics Research, Tucson, Arizona.
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    [CrossRef]
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    [CrossRef]
  12. S. Y. Park, S. D. Jung, S. H. Song, “Highly accurate fabrication of binary phase levels in gratings by using Langmuir–Blodgett technique,” presented at the Fourth Micro-optics Conference and Eleventh Topical Meeting on Gradient-Index Optical Systems, Japan Society of Applied Physics, Kawasaki, Japan, 20–22 October 1993.
  13. S. D. Jung, J. J. Kim, W. Y. Hwang, T. Zyung, “Transfer characteristics of Langmuir–Blodgett films of stereoregular poly(methyl methacrylates),” Mol. Cryst. Liq. Cryst. 247, 281–291 (1994).
    [CrossRef]

1994 (2)

M. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

S. D. Jung, J. J. Kim, W. Y. Hwang, T. Zyung, “Transfer characteristics of Langmuir–Blodgett films of stereoregular poly(methyl methacrylates),” Mol. Cryst. Liq. Cryst. 247, 281–291 (1994).
[CrossRef]

1992 (1)

1991 (1)

1984 (1)

1982 (1)

1977 (2)

W. Y. Wang, T. J. DiLaura, “Bragg-effect waveguide coupler analysis,” Appl. Opt. 16, 3230–3236 (1977).
[CrossRef] [PubMed]

T. Tamir, S. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

1973 (1)

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Chang, W. S. C.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

DiLaura, T. J.

Fujima, H.

Gale, M.

M. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Gaylord, T. K.

Goto, K.

Hatakoshi, G.

Hubbard, W. M.

Hunziker, W.

W. Hunziker, W. Vogt, H. Melchior, “Optoelectronic integrated-circuit packaging with self-aligned fiber to waveguide array coupling by Si V-groove flip-chip technique,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper SaC3.

Hwang, W. Y.

S. D. Jung, J. J. Kim, W. Y. Hwang, T. Zyung, “Transfer characteristics of Langmuir–Blodgett films of stereoregular poly(methyl methacrylates),” Mol. Cryst. Liq. Cryst. 247, 281–291 (1994).
[CrossRef]

Jung, S. D.

S. D. Jung, J. J. Kim, W. Y. Hwang, T. Zyung, “Transfer characteristics of Langmuir–Blodgett films of stereoregular poly(methyl methacrylates),” Mol. Cryst. Liq. Cryst. 247, 281–291 (1994).
[CrossRef]

S. Y. Park, S. D. Jung, S. H. Song, “Highly accurate fabrication of binary phase levels in gratings by using Langmuir–Blodgett technique,” presented at the Fourth Micro-optics Conference and Eleventh Topical Meeting on Gradient-Index Optical Systems, Japan Society of Applied Physics, Kawasaki, Japan, 20–22 October 1993.

Kim, J. J.

S. D. Jung, J. J. Kim, W. Y. Hwang, T. Zyung, “Transfer characteristics of Langmuir–Blodgett films of stereoregular poly(methyl methacrylates),” Mol. Cryst. Liq. Cryst. 247, 281–291 (1994).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, Berlin, 1975), pp. 15–29.

Kubota, T.

Melchior, H.

W. Hunziker, W. Vogt, H. Melchior, “Optoelectronic integrated-circuit packaging with self-aligned fiber to waveguide array coupling by Si V-groove flip-chip technique,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper SaC3.

Moharam, M. G.

Ogawa, K.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Park, S. Y.

S. Y. Park, S. D. Jung, S. H. Song, “Highly accurate fabrication of binary phase levels in gratings by using Langmuir–Blodgett technique,” presented at the Fourth Micro-optics Conference and Eleventh Topical Meeting on Gradient-Index Optical Systems, Japan Society of Applied Physics, Kawasaki, Japan, 20–22 October 1993.

Pedersen, J.

M. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Peng, S.

T. Tamir, S. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Rastani, K.

Rosenbaum, F. J.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Rossi, M.

M. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Schutz, H.

M. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Song, S. H.

S. Y. Park, S. D. Jung, S. H. Song, “Highly accurate fabrication of binary phase levels in gratings by using Langmuir–Blodgett technique,” presented at the Fourth Micro-optics Conference and Eleventh Topical Meeting on Gradient-Index Optical Systems, Japan Society of Applied Physics, Kawasaki, Japan, 20–22 October 1993.

Sopori, B. L.

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

Takeda, M.

Tamir, T.

T. Tamir, S. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Vogt, W.

W. Hunziker, W. Vogt, H. Melchior, “Optoelectronic integrated-circuit packaging with self-aligned fiber to waveguide array coupling by Si V-groove flip-chip technique,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper SaC3.

Wang, W. Y.

Zyung, T.

S. D. Jung, J. J. Kim, W. Y. Hwang, T. Zyung, “Transfer characteristics of Langmuir–Blodgett films of stereoregular poly(methyl methacrylates),” Mol. Cryst. Liq. Cryst. 247, 281–291 (1994).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. (1)

T. Tamir, S. Peng, “Analysis and design of grating couplers,” Appl. Phys. 14, 235–254 (1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Ogawa, W. S. C. Chang, B. L. Sopori, F. J. Rosenbaum, “A theoretical analysis of etched grating couplers for integrated optics,” IEEE J. Quantum Electron. QE-9, 29–42 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Mol. Cryst. Liq. Cryst. (1)

S. D. Jung, J. J. Kim, W. Y. Hwang, T. Zyung, “Transfer characteristics of Langmuir–Blodgett films of stereoregular poly(methyl methacrylates),” Mol. Cryst. Liq. Cryst. 247, 281–291 (1994).
[CrossRef]

Opt. Eng. (1)

M. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Other (4)

S. Y. Park, S. D. Jung, S. H. Song, “Highly accurate fabrication of binary phase levels in gratings by using Langmuir–Blodgett technique,” presented at the Fourth Micro-optics Conference and Eleventh Topical Meeting on Gradient-Index Optical Systems, Japan Society of Applied Physics, Kawasaki, Japan, 20–22 October 1993.

W. Hunziker, W. Vogt, H. Melchior, “Optoelectronic integrated-circuit packaging with self-aligned fiber to waveguide array coupling by Si V-groove flip-chip technique,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper SaC3.

H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, Berlin, 1975), pp. 15–29.

GLAD is a registered trademark of Applied Optics Research, Tucson, Arizona.

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Figures (11)

Fig. 1
Fig. 1

Backboard interconnection scheme with 1-D arrays of FGC's: (a) three-dimensional view, (b) bottom view, and (c) side view.

Fig. 2
Fig. 2

Phase diagram for guided-mode to radiation-mode coupling.

Fig. 3
Fig. 3

Out-coupled polarization produced by a FGC for TE and TM polarization states of guided modes: polarization plots of out-coupled (a) TE and (c) TM radiation modes; far-field intensity plots of out-coupled (b) TE and (d) TM radiation-modes. The size of the arrow or the ellipse represents the complex amplitude of out-coupled modes.

Fig. 4
Fig. 4

Ray-optic concept for radiation-mode analysis showing that the zig-zag wave of the TE0 mode guided in a slab waveguide is out coupled by multiple diffraction from a FGC.

Fig. 5
Fig. 5

Diffraction efficiency of radiation modes from a FGC with a square grating profile (duty cycle = 0.5). S(i) and C(i) denote the efficiencies of the ith order of the substrate mode and the air mode, respectively.

Fig. 6
Fig. 6

Out-coupling efficiency (OCE) of the FGC for several lengths.

Fig. 7
Fig. 7

Dependence of the radiation decay coefficient on the grating thickness, where 4 α p S ( 1 ) is the coefficient obtained from the approximate perturbation analysis.

Fig. 8
Fig. 8

Multiple beam distribution with a varying out-coupling efficiency, η n .

Fig. 9
Fig. 9

Dependence of OCE on the length of a FGC, and the distribution of OCE's for generating N (equal to 10, 20, and 50) uniform beams.

Fig. 10
Fig. 10

Dependence of the OCE on the duty cycle, D, of gratings in a FGC.

Fig. 11
Fig. 11

Design result of the lengths and the duty cycles of ten FGC's for a uniform power distribution. Black dots represent results of the FGC's with a grating thickness of 50 nm.

Equations (13)

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y = 1 ( N 2 n s 2 ) ( m λ N + N n s f n s 2 f sin θ n s A ) , A = ( N 2 n s 2 ) x 2 + m 2 λ 2 + 2 m λ f ( n s 2 N sin θ ) + f 2 ( N n s 2 sin θ ) 2 , m = 0 , ± 1 , ± 2 , ,
n s k sin θ q = N k + q κ , q = 0 , ± 1 , ± 2 , ,
n c / n s < sin θ 1 < 1 .
M = L 2 T eff tan θ 0 ,
η i , q tot = i q + i q t + i q t 2 + + i q t ( M 1 ) = i q ( 1 t M ) ( 1 t ) , i = { C for air modes S for substrate modes ,
A ( L ) = exp ( α r L ) = t M .
α r = M 2 L ln ( t ) = 1 ( 4 T eff tan θ 0 ) m = 1 ( 1 t ) m m ( 1 t ) 4 T eff tan θ 0 , t 1 .
d d y p ( y ) = 2 α r | A ( y ) | 2 = 2 α r P ( y ) ,
p r i ( q ) ( y ) = 2 α r i ( q ) | A ( y ) | 2 , α r = q , i α r i ( q ) .
p r i ( q ) ( L ) = 0 L p r i ( q ) ( y ) d y = α r i ( q ) α r [ 1 exp ( 2 α r L ) ] .
α r i ( q ) α r = i q ( 1 t M ) ( 1 t ) | M or α r i ( q ) = α r i q ( 1 t ) .
η n = η 1 [ 1 ( n 1 ) η 1 ] , n = 1 , 2 , , N .
L n = 1 2 α r ln S 1 [ S 1 ( 1 t ) η n ] , n = 1 , 2 , , N .

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