Abstract

We studied the imaging performance of a chirped grating for a demultiplexer designed for coarse wavelength division multiplexing using a wavefront aberration analysis and the ray tracing simulation. The demultiplexer was composed of a chirped grating, cylindrical lenses, and a waveguide. The best image point and the spot shape focused by the chirped grating were effectively calculated with the wavefront aberration. We applied the aberration analysis to design a waveguide to connect branched beams to photodetectors, and we confirmed the demultiplexing performance experimentally.

© 2006 Optical Society of America

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  1. L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, "Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks," IEEE Photon. Technol. Lett. 14, 702-704 (2002).
    [CrossRef]
  2. H. Sasaki and Y. Okabe, "CWDM multi/demultiplexer consisting of stacked dielectric interference filters and off-axis diffractive lenses," IEEE Photon. Technol. Lett. 15, 551-553 (2003).
    [CrossRef]
  3. I. Nishi, T. Oguchi, and K. Kato, "Broad-passband-width optical filter for multi/demultiplexer using a diffraction grating and a retroreflector prism," Electron. Lett. 21, 423-424 (1985).
    [CrossRef]
  4. C. X. Yu, D. T. Neilson, C. R. Doerr, and M. Zimgibl, "Dispersion-free (De)mux with very high figure-of-merit," in Optical Fiber Communications Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 318-319.
    [CrossRef]
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    [CrossRef] [PubMed]
  6. T. Nakazawa, S. Kittaka, K. Tsunetomo, K. Kintaka, J. Nishii, and K. Hirao, "Compact and monolithic coarse wavelength-division multiplexer-demultiplexer fabricated by use of a high-spatial-frequency transmission grating buried in a slab waveguide," Opt. Lett. 29, 1188-1190 (2004).
    [CrossRef] [PubMed]
  7. Y. Fujii and J. Minowa, "Optical demultiplexer using a silicon concave diffraction grating," Appl. Opt. 22, 974-978 (1983).
    [CrossRef] [PubMed]
  8. T. Suhara, J. Viljanen, and M. Leppihalme, "Integrated-optic wavelength multi- and demultiplexers using a chirped grating and an ion-exchanged waveguide," Appl. Opt. 21, 2195-2198 (1982).
    [CrossRef] [PubMed]
  9. T. Shibata, T. Hoshino, H. Masuda, and Y. Sugimoto, Wavelength Division Demultiplexer for CWDM System, Technical Report OME2002-72 (IEICE, 2002), 35-39.
  10. K. Hirano, T. Sugita, H. Yasuda, T. Ushiwata, T. Abe, and Y. Itoh, "Coarse wavelength division demultiplexer using diffraction grating," in Proceedings of 30th European Conference on Optical Communication (ECOC2004), Stockholm (Kista Photonics Research Center, 2004), Tul. 4.6.
  11. E. B. Champagne, "Nonparaxial imaging, magnification, and aberration properties in holography," J. Opt. Soc. Am. 57, 51-55 (1967).
    [CrossRef]
  12. D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell Syst. Tech. J. 52, 1563-1578 (1973).
  13. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), pp. 517-532.
  14. Ref. 13, pp. 543-547.

2004

2003

H. Sasaki and Y. Okabe, "CWDM multi/demultiplexer consisting of stacked dielectric interference filters and off-axis diffractive lenses," IEEE Photon. Technol. Lett. 15, 551-553 (2003).
[CrossRef]

2002

L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, "Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks," IEEE Photon. Technol. Lett. 14, 702-704 (2002).
[CrossRef]

1993

1985

I. Nishi, T. Oguchi, and K. Kato, "Broad-passband-width optical filter for multi/demultiplexer using a diffraction grating and a retroreflector prism," Electron. Lett. 21, 423-424 (1985).
[CrossRef]

1983

1982

1973

D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell Syst. Tech. J. 52, 1563-1578 (1973).

1967

Abe, T.

K. Hirano, T. Sugita, H. Yasuda, T. Ushiwata, T. Abe, and Y. Itoh, "Coarse wavelength division demultiplexer using diffraction grating," in Proceedings of 30th European Conference on Optical Communication (ECOC2004), Stockholm (Kista Photonics Research Center, 2004), Tul. 4.6.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), pp. 517-532.

Buckman, L. A.

L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, "Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks," IEEE Photon. Technol. Lett. 14, 702-704 (2002).
[CrossRef]

Champagne, E. B.

Doerr, C. R.

C. X. Yu, D. T. Neilson, C. R. Doerr, and M. Zimgibl, "Dispersion-free (De)mux with very high figure-of-merit," in Optical Fiber Communications Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 318-319.
[CrossRef]

Fujii, Y.

Gloge, D.

D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell Syst. Tech. J. 52, 1563-1578 (1973).

Gong, W.

L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, "Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks," IEEE Photon. Technol. Lett. 14, 702-704 (2002).
[CrossRef]

Hirano, K.

K. Hirano, T. Sugita, H. Yasuda, T. Ushiwata, T. Abe, and Y. Itoh, "Coarse wavelength division demultiplexer using diffraction grating," in Proceedings of 30th European Conference on Optical Communication (ECOC2004), Stockholm (Kista Photonics Research Center, 2004), Tul. 4.6.

Hirao, K.

Hoshino, T.

T. Shibata, T. Hoshino, H. Masuda, and Y. Sugimoto, Wavelength Division Demultiplexer for CWDM System, Technical Report OME2002-72 (IEICE, 2002), 35-39.

Ishii, Y.

Itoh, Y.

K. Hirano, T. Sugita, H. Yasuda, T. Ushiwata, T. Abe, and Y. Itoh, "Coarse wavelength division demultiplexer using diffraction grating," in Proceedings of 30th European Conference on Optical Communication (ECOC2004), Stockholm (Kista Photonics Research Center, 2004), Tul. 4.6.

Kato, K.

I. Nishi, T. Oguchi, and K. Kato, "Broad-passband-width optical filter for multi/demultiplexer using a diffraction grating and a retroreflector prism," Electron. Lett. 21, 423-424 (1985).
[CrossRef]

Kintaka, K.

Kittaka, S.

Kubota, T.

Lemoff, B. E.

L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, "Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks," IEEE Photon. Technol. Lett. 14, 702-704 (2002).
[CrossRef]

Leppihalme, M.

Marcatili, E. A. J.

D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell Syst. Tech. J. 52, 1563-1578 (1973).

Masuda, H.

T. Shibata, T. Hoshino, H. Masuda, and Y. Sugimoto, Wavelength Division Demultiplexer for CWDM System, Technical Report OME2002-72 (IEICE, 2002), 35-39.

Minowa, J.

Nakazawa, T.

Neilson, D. T.

C. X. Yu, D. T. Neilson, C. R. Doerr, and M. Zimgibl, "Dispersion-free (De)mux with very high figure-of-merit," in Optical Fiber Communications Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 318-319.
[CrossRef]

Nishi, I.

I. Nishi, T. Oguchi, and K. Kato, "Broad-passband-width optical filter for multi/demultiplexer using a diffraction grating and a retroreflector prism," Electron. Lett. 21, 423-424 (1985).
[CrossRef]

Nishii, J.

Oguchi, T.

I. Nishi, T. Oguchi, and K. Kato, "Broad-passband-width optical filter for multi/demultiplexer using a diffraction grating and a retroreflector prism," Electron. Lett. 21, 423-424 (1985).
[CrossRef]

Okabe, Y.

H. Sasaki and Y. Okabe, "CWDM multi/demultiplexer consisting of stacked dielectric interference filters and off-axis diffractive lenses," IEEE Photon. Technol. Lett. 15, 551-553 (2003).
[CrossRef]

Sasaki, H.

H. Sasaki and Y. Okabe, "CWDM multi/demultiplexer consisting of stacked dielectric interference filters and off-axis diffractive lenses," IEEE Photon. Technol. Lett. 15, 551-553 (2003).
[CrossRef]

Schmit, A. J.

L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, "Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks," IEEE Photon. Technol. Lett. 14, 702-704 (2002).
[CrossRef]

Shibata, T.

T. Shibata, T. Hoshino, H. Masuda, and Y. Sugimoto, Wavelength Division Demultiplexer for CWDM System, Technical Report OME2002-72 (IEICE, 2002), 35-39.

Sugimoto, Y.

T. Shibata, T. Hoshino, H. Masuda, and Y. Sugimoto, Wavelength Division Demultiplexer for CWDM System, Technical Report OME2002-72 (IEICE, 2002), 35-39.

Sugita, T.

K. Hirano, T. Sugita, H. Yasuda, T. Ushiwata, T. Abe, and Y. Itoh, "Coarse wavelength division demultiplexer using diffraction grating," in Proceedings of 30th European Conference on Optical Communication (ECOC2004), Stockholm (Kista Photonics Research Center, 2004), Tul. 4.6.

Suhara, T.

Tella, R. P.

L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, "Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks," IEEE Photon. Technol. Lett. 14, 702-704 (2002).
[CrossRef]

Tsunetomo, K.

Ushiwata, T.

K. Hirano, T. Sugita, H. Yasuda, T. Ushiwata, T. Abe, and Y. Itoh, "Coarse wavelength division demultiplexer using diffraction grating," in Proceedings of 30th European Conference on Optical Communication (ECOC2004), Stockholm (Kista Photonics Research Center, 2004), Tul. 4.6.

Viljanen, J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), pp. 517-532.

Yasuda, H.

K. Hirano, T. Sugita, H. Yasuda, T. Ushiwata, T. Abe, and Y. Itoh, "Coarse wavelength division demultiplexer using diffraction grating," in Proceedings of 30th European Conference on Optical Communication (ECOC2004), Stockholm (Kista Photonics Research Center, 2004), Tul. 4.6.

Yu, C. X.

C. X. Yu, D. T. Neilson, C. R. Doerr, and M. Zimgibl, "Dispersion-free (De)mux with very high figure-of-merit," in Optical Fiber Communications Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 318-319.
[CrossRef]

Zimgibl, M.

C. X. Yu, D. T. Neilson, C. R. Doerr, and M. Zimgibl, "Dispersion-free (De)mux with very high figure-of-merit," in Optical Fiber Communications Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 318-319.
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

D. Gloge and E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell Syst. Tech. J. 52, 1563-1578 (1973).

Electron. Lett.

I. Nishi, T. Oguchi, and K. Kato, "Broad-passband-width optical filter for multi/demultiplexer using a diffraction grating and a retroreflector prism," Electron. Lett. 21, 423-424 (1985).
[CrossRef]

IEEE Photon. Technol. Lett.

L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, "Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks," IEEE Photon. Technol. Lett. 14, 702-704 (2002).
[CrossRef]

H. Sasaki and Y. Okabe, "CWDM multi/demultiplexer consisting of stacked dielectric interference filters and off-axis diffractive lenses," IEEE Photon. Technol. Lett. 15, 551-553 (2003).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Other

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), pp. 517-532.

Ref. 13, pp. 543-547.

C. X. Yu, D. T. Neilson, C. R. Doerr, and M. Zimgibl, "Dispersion-free (De)mux with very high figure-of-merit," in Optical Fiber Communications Conference (OFC), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 318-319.
[CrossRef]

T. Shibata, T. Hoshino, H. Masuda, and Y. Sugimoto, Wavelength Division Demultiplexer for CWDM System, Technical Report OME2002-72 (IEICE, 2002), 35-39.

K. Hirano, T. Sugita, H. Yasuda, T. Ushiwata, T. Abe, and Y. Itoh, "Coarse wavelength division demultiplexer using diffraction grating," in Proceedings of 30th European Conference on Optical Communication (ECOC2004), Stockholm (Kista Photonics Research Center, 2004), Tul. 4.6.

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Figures (14)

Fig. 1
Fig. 1

Schematic of the demultiplexer.

Fig. 2
Fig. 2

Geometry of (a) the recording and (b) the reproduction of the chirped grating.

Fig. 3
Fig. 3

Output power distribution model of a GI MMF.

Fig. 4
Fig. 4

Simulated output distribution from the 62.5 μm core GI MMF: (a) simulated and measured far-field patterns and (b) simulated near-field pattern.

Fig. 5
Fig. 5

Distances of the image points from the chirped grating origin as a function of the normalized wavelength.

Fig. 6
Fig. 6

Spot widths of the chirped grating as a function of the normalized wavelength.

Fig. 7
Fig. 7

Distance difference Δz from the Gaussian image point to the best image point corrected with third-order aberrations: (a) R c = 14.4 (design configuration) and (b) R c = 13.3 mm.

Fig. 8
Fig. 8

Total wavefront aberrations, the third-order aberrations, and the residual error of the third-order aberrations as a function of the position on the chirped grating: (a) R c = 14.4 mm (design configuration) and λ = 1.03λ0 and (b) R c = 13.3 mm and λ = λ0.

Fig. 9
Fig. 9

Deformation of the focused spot of the chirped grating under the design configuration condition: (a) the spot diagrams and (b) the spot width as a function of the wavelength calculated with the third-order aberrations and the ray tracing.

Fig. 10
Fig. 10

Wavelength dependence of the coma and the spherical aberration coefficients of R c = 14.4 mm (design configuration) and the exchange condition of the input and output positions (R c  = 16.8 mm).

Fig. 11
Fig. 11

Spot widths as a function of the coma aberration coefficient.

Fig. 12
Fig. 12

Simulated and measured transmission spectra of the four-channel demultiplexer.

Fig. 13
Fig. 13

Wavelength dependence of the spherical and coma aberration coefficients: (a) R c = 14.4 mm and (b) the low coma aberration condition.

Fig. 14
Fig. 14

Spot width of R c = 14.4 mm and the low coma aberration condition as a function of the wavelength.

Equations (148)

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

1 R i = 1 R c + 1 m g 2 μ ( 1 R o 1 R r ) ,
sin   θ i = sin   θ c + 1 m g μ ( sin   θ o sin   θ r ) ,
R q
θ q
Q ( Q = O , R , C , or   I )
m g
μ = λ / λ 0
λ 0
R q
R q
θ q
R q
θ q
R i
θ i
θ c
p d θ i d λ R i λ p = sin   θ c sin   θ i cos   θ i λ p λ 0 R i ,
λ p
B p α M ϕ p λ p ,
M = R i d θ i R c d θ c = R i / cos   θ i R c / cos   θ c .
R c
R c / cos   θ c = R i / cos   θ i )
θ i
R i
N × ( n s n s ) = m λ λ 0 N  × Φ ( r ) ,
s
Φ ( r )
ν ( r )
Φ ( r ) = λ m ν ( r )
( r )
θ max ( r )
NA ( r ) = sin   θ max ( r ) = NA 0 n ( r ) n 0 1 ( r r 0 ) 2 ,
NA 0
n 0
r 0
n ( r )
n ( r ) = n 0 [ 1 NA 0 2 2 n 0 2 ( r r 0 ) 2 ] .
θ max
I ( r , θ )
NA ( r ) 2
62.5 μ m
1307   nm
62.5 μ m
( R i )
1312.5   nm
R r
R o
θ r = 35 °
θ o = 18 °
R i
θ c
R c
( R r = 14.4   mm )
62.5 μ m
1 / e 2
R r = R c = 14.4   mm
R r = 14.4   mm
R c = 14.0   mm
R r = 14.4   mm
R c = 16.8   mm
3 %
40   nm
W = r c ± μ ( r o r r ) r i ,
r q ( q = o , r , c , i )
Q ( Q = O , R , C , I )
ρ = x / a
W = n = 0 W n ρ n .
Φ 3
Φ 3 = W 4 ρ 4 + W 3 ρ 3 + W 2 ρ 2 = a 4 8 w 4 ρ 4 + a 3 2 w 3 ρ 3 a 2 2 w 2 ρ 2 .
w p
w p = x c p R c 3 ± μ m g     4 p ( x o p R o 3 x r p R r 3 ) x i p R i 3 ,
x q = R q   sin   θ q
W 4
W 3
W 4
W 5
W 2
P n ( x )
W = n = 0 W n P n ( x ) .
W n
W n
W 4 = ( 8 / 35 ) W 4
W 3 = ( 2 / 5 ) W 3
W 2 = ( 2 / 3 ) W 2
Φ = Φ + H ρ 2 + L ρ + M ,
Δ z = 2 ( R a ) 2 H , Δ x = ( R a ) L ,
Φ 3 = [ 8 35 W 4 P 4 ( ρ ) + 2 5 W 3 P 3 ( ρ ) ] + [ ( 6 7 W 4 + W 2 ) ρ 2 + 3 5 W 3 ρ 3 35 ] .
Δ z
Δ z = 2 ( R i a ) 2 ( 6 7 W 4 + W 2 )
= 2 ( R i a ) 2 ( 3 a 4 28 w 4 + a 2 2 w 2 ) .
Δ z
w 2
Δ x
w 3
Δ x
F ( u )
F ( u ) = f ( ρ ) exp ( 2 π i u ρ ) d ρ .
f ( ρ )
W ( ρ )
τ ( ρ )
f ( ρ ) = τ ( ρ ) exp [ 2 π i W ( ρ ) ] , | ρ | 1 ,
= 0 , | ρ | 1 ,
ρ = x / a
u = ( NA / λ ) ξ
I ( u )
I 0 ( v )
I ( u ) = I 0 ( v ) | F ( u v ) | 2 d v ,
v = M V
I 0 ( v x ) = r 0 2 v x 2 r 0 2 v x 2 exp [ ( v x 2 + v y 2 ) 2 σ 0 4 ] d v u .
Δ z
0.03 μ m
λ / λ 0
1 %
λ / λ 0 = 1.03
I ( v )
σ 0 = 12.5 μ m
( R c = 16.8 mm )
7.5 λ
62.5 μ m
R r = R c = 14.4   mm
62.5 μ m
1310   nm
25   nm
250 μ m
62.5 μ m
13   nm
15   nm
α = 1.5
20   dB
m g = 1
μ = 1 + Δ μ
w 3 = α r α 0 R c 2 α c + α 0 R r 2 α c α r R 0 2 + 2 ( α c α r + α 0 ) × ( 1 R c R r 1 R c R 0 + 1 R r R 0 ) + { ( α 0 R 0 2 α r R r 2 α 0 α r R c 2 ) [ 4 α 0 α r R r + 2 α c R c + ( 3 α 0 α r ) ( 1 R 0 1 R r ) ] ( 1 R 0 1 R r ) } Δ μ + O ( Δ μ 2 ) ,
α q = sin   θ q
Δ μ
R c = R r , α c = α r
w 3 = Δ μ ( 1 R 0 1 R r ) ( α r 2 α 0 R 0 + α r R r ) + O ( μ 2 ) .
1 + R 0 R r = 2 sin   θ 0 sin   θ r .
w 4 = [ ( 1 R 0 3 1 R r 3 ) 3 R c 3 ( 1 R 0 1 R r ) ] μ 3 R c ( 1 R 0 1 R r ) 2 μ 2 ( 1 R 0 1 R r ) 3 μ 3 .
R r = R 0
R 0 = R r
θ 0 = 0
| θ 0 |
| θ 0 |
| R 0 |
| R 0 |
R c = 14.4   mm
1 / n 4
1 / n 3

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