Abstract

Holographic gratings are modeled and designed for path-reversed substrate-guided-wave wavelength-division demultiplexing (WDDM) as a continuation of earlier research [Appl. Opt. 38, 3046 (1999)]. An efficient and practical method is developed to simulate the slanted volume holographic gratings. The trade-off between dispersion and the bandwidth of the holograms is analyzed. A 60° (incident angle of the grating)/60° (diffraction angle of the grating in air) grating structure is selected to demultiplex optical signals in the 1555-nm spectral region, and a 45°/45° grating structure is chosen for the spectral region near 800 nm. Experimental results are consistent with the simulation results for these two WDDM devices. A four-channel WDDM is also demonstrated at a center wavelength of 1555 nm and with a channel spacing of 2 nm.

© 1999 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1999 (1)

1996 (1)

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 11, 1024–1035 (1996).
[CrossRef]

1995 (3)

1991 (2)

1985 (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Awada, K. A.

Caulfield, H. J.

Chateau, N.

Chen, R. T.

Duzik, T.

W. Gambogi, K. Steijn, S. Mackara, T. Duzik, B. Hamzavy, J. Kelly, “HOE imaging in DuPont holographic photopolymers,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Gambogi, W.

W. Gambogi, K. Steijn, S. Mackara, T. Duzik, B. Hamzavy, J. Kelly, “HOE imaging in DuPont holographic photopolymers,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Hamzavy, B.

W. Gambogi, K. Steijn, S. Mackara, T. Duzik, B. Hamzavy, J. Kelly, “HOE imaging in DuPont holographic photopolymers,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Huang, Y. T.

Hugonin, J. P.

Kaminow, I. P.

I. P. Kaminow, T. L. Koch, Optical Fiber Telecommunications (Academic, New York, 1997), Vol. IIIA.

Kelly, J.

W. Gambogi, K. Steijn, S. Mackara, T. Duzik, B. Hamzavy, J. Kelly, “HOE imaging in DuPont holographic photopolymers,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Koch, T. L.

I. P. Kaminow, T. L. Koch, Optical Fiber Telecommunications (Academic, New York, 1997), Vol. IIIA.

Li, L.

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 11, 1024–1035 (1996).
[CrossRef]

Li, M. M.

Liu, J.

J. Liu, R. T. Chen, “Path-reversed photopolymer-based substrate-guided-wave optical interconnects for wavelength division demultiplexing,” Appl. Opt. 38, 3046–3052 (1999).
[CrossRef]

J. Liu, “Multi-wavelength planar optoelectronic interconnections,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1999).

Mackara, S.

W. Gambogi, K. Steijn, S. Mackara, T. Duzik, B. Hamzavy, J. Kelly, “HOE imaging in DuPont holographic photopolymers,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Pai, D. M.

Rhee, U.

Shamir, J.

Steijn, K.

W. Gambogi, K. Steijn, S. Mackara, T. Duzik, B. Hamzavy, J. Kelly, “HOE imaging in DuPont holographic photopolymers,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 282–293 (1994).
[CrossRef]

Su, D. C.

Tsai, Y. K.

Vikram, C. S.

Appl. Opt. (3)

J. Opt. Soc. Am. A (3)

Opt. Lett. (1)

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Other (3)

I. P. Kaminow, T. L. Koch, Optical Fiber Telecommunications (Academic, New York, 1997), Vol. IIIA.

J. Liu, “Multi-wavelength planar optoelectronic interconnections,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1999).

W. Gambogi, K. Steijn, S. Mackara, T. Duzik, B. Hamzavy, J. Kelly, “HOE imaging in DuPont holographic photopolymers,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 282–293 (1994).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Configuration of a path-reversed substrate-guided wave holographic grating.

Fig. 2
Fig. 2

Grating structure and coordinate systems used for RCWA.

Fig. 3
Fig. 3

Dispersion and approximate bandwidth of planar volume holographic gratings at a center wavelength of 1555 nm.

Fig. 4
Fig. 4

RCWA simulation results for a 60°/60° grating structure at a center wavelength of 1555 nm.

Fig. 5
Fig. 5

RCWA simulation results for a 45°/45° grating structure at a center wavelength of 800 nm.

Fig. 6
Fig. 6

Measured diffraction efficiency as a function of wavelength shift from 1555 nm. The RCWA simulation result is given at Δn = 0.0128.

Fig. 7
Fig. 7

CCD image taken at a focal plane of a focusing lens with a 20-cm focal length.

Fig. 8
Fig. 8

Measured diffraction efficiency as a function of wavelength shift from 800 nm. The RCWA simulation result is given at Δn = 0.012.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

x1=x-y tan ζ=X/cos ζ, x2=y/cos ζ=Y-X tan ζ.
2E3=i k0μcos ζH1-sin ζH2,-1E3=i k0μcos ζH2-sin ζH1,1H2-2H1=-ik0ε cos ζE3
2H3=-i k0εcos ζE1-sin ζE2,-1H3=-i k0εcos ζE2-sin ζE1,1E2-2E1=ik0μ cos ζH3
2iE3H1=sin ζ 1ik0μ cos ζcos ζk0μk02εμ-1i2sin ζ 1iE3H1,
2iH3E1=sin ζ 1i-k0ε cos ζ-cos ζk0k02μ-1i1ε1isin ζ 1iH3E1.
F3x1, x2=expiα0x1+iβ0+1-x2+n Rn expiαnx1+iβn+1+x2,
F3x1, x2=n Tn expiαnx1+iβn-1-x2,
αn=α0+nK,  α0=k0ε+1μ sin θ0,K=2π/p,
βn±1±=αn sin ζ±k02ε±1μ-αn21/2 cos ζ,×Rek02ε±1μ-αn21/2+Imk02ε±1μ-αn21/2>0.
ηnr=-βn+1+-αn sin ζβ0+1--α0 sin ζ |Rn|2,  nU+,
ηnt=βn-1--αn sin ζβ0+1--α0 sin ζ |Tn|2,    nU-,
ηnt=ε+1ε-1βn-1--αn sin ζβ0+1--α0 sin ζ |Tn|2,  nU-.
θn±1=arcsinαnk0ε±1μ,  nU±.
Flx1, x2=n Flnx2expiαnx1,
εx1=n εn expinKx1,ax1=n an expinKx1,
α sin ζk0μ cos ζcos ζk0μk02εμ-α2α sin ζE3H1=ρE3H1,
α sin ζ-k0εcos ζ-cos ζk0k02μ-αaαα sin ζH3E1=ρH3E1.
E3x1, x2H1x1, x2=n,qexpiαnx1E3nq+H1nq+expiρq+x2Cq++E3nq-H1nq-expiρq-x2Cq-
Rn=S12n0,  Tn=S22n0,
εX=ε0+ε1 cos2πXΛ.

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