Abstract

In this paper we propose analyse the apodisation or windowing of the coupling coefficients in the unit cells of coupled resonator waveguide devices (CROWs) as a means to reduce the level of secondary sidelobes in the bandpass characteristic of their transfer functions. This technique is regularly employed in the design of digital filters and has been applied as well in the design of other photonic devices such as corrugated waveguide filters and fiber Bragg gratings. The apodisation of both Type-I and Type-II structures is discussed for several windowing functions.

© 2007 Optical Society of America

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  1. T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, M. Yasu, "Ring resonators composed of GeO2-doped silica waveguides," J. Lightwave Technol. 12,1781-1788 (1992).
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    [CrossRef]
  7. V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, P. T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002)
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. B. E. Little, S. T. Chu, W Pan, and Y Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12,323-325 (2000)
    [CrossRef]
  12. K. J. Vahala, "Optical microcavities," Nature (London) 424,839-846, (2003)
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2007 (1)

F. Xia, L. Sekaric and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photon 1,65-71 (2007).
[CrossRef]

2006 (2)

2005 (2)

Y. Landobasa and M. Chin, "Defect modes in micro-ring resonator arrays," Opt. Express 13,7800-7815 (2005).
[CrossRef] [PubMed]

Y. Landobasa, S. Darmawan, M. Chin, "Matrix Analysis of 2-D Microresonator Lattice Optical Filters," IEEE J. Quantum Electron. 41,1410-1418 (2005)
[CrossRef]

2004 (2)

2003 (2)

2002 (2)

P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, "Polymer Micro-Ring Filters and Modulators," J. Lightwave Technol. 20,1968-1975 (2002)
[CrossRef]

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, P. T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002)
[CrossRef]

2001 (1)

2000 (2)

B. E. Little, S. T. Chu, W Pan, and Y Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12,323-325 (2000)
[CrossRef]

A. Yariv, "Universal relations for coupling of optical power between micro resonators and dielectric waveguides," Electron. Lett. 36,321-322 (2000)
[CrossRef]

1999 (1)

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11,1623-1625 (1999)
[CrossRef]

1996 (1)

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, "Design of apodised linearly chirped fiber gratings for dispersioncompensation," J. Light. Technol. 14,2581-2588 (1996)
[CrossRef]

1995 (1)

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: the corner mirrors of the future?," IEE Proc. Optoel 142,61-65 (1995).
[CrossRef]

1994 (1)

D. L. MacFarlane and E.M. Dowling, "Z-domain techniques in the analysis of Fabry-Perot etalons and multilayer structures," J. Opt. Soc. Am. 11,236-245, (1994).
[CrossRef]

1993 (1)

D. R. Rowland and J. D. Love, "Evanescent wave coupling of whispering gallery modes of a dielectric cylinder," IEE Proc. Optoel. 140,177-188 (1993).
[CrossRef]

1992 (1)

T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, M. Yasu, "Ring resonators composed of GeO2-doped silica waveguides," J. Lightwave Technol. 12,1781-1788 (1992).
[CrossRef]

1990 (1)

J. Capmany and M. A. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8,1904-1919, 1990.
[CrossRef]

1977 (1)

Electron. Lett. (1)

A. Yariv, "Universal relations for coupling of optical power between micro resonators and dielectric waveguides," Electron. Lett. 36,321-322 (2000)
[CrossRef]

IEE Proc. Optoel (1)

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: the corner mirrors of the future?," IEE Proc. Optoel 142,61-65 (1995).
[CrossRef]

IEE Proc. Optoel. (1)

D. R. Rowland and J. D. Love, "Evanescent wave coupling of whispering gallery modes of a dielectric cylinder," IEE Proc. Optoel. 140,177-188 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Landobasa, S. Darmawan, M. Chin, "Matrix Analysis of 2-D Microresonator Lattice Optical Filters," IEEE J. Quantum Electron. 41,1410-1418 (2005)
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, P. T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002)
[CrossRef]

IEEE Photon. Technol. Lett. (3)

H. Tazawa and W. H. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18,211-213 (2006).
[CrossRef]

C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11,1623-1625 (1999)
[CrossRef]

B. E. Little, S. T. Chu, W Pan, and Y Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12,323-325 (2000)
[CrossRef]

J. Light. Technol. (1)

D. Pastor, J. Capmany, D. Ortega, V. Tatay, J. Marti, "Design of apodised linearly chirped fiber gratings for dispersioncompensation," J. Light. Technol. 14,2581-2588 (1996)
[CrossRef]

J. Lightwave Technol. (3)

J. Capmany and M. A. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8,1904-1919, 1990.
[CrossRef]

P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, "Polymer Micro-Ring Filters and Modulators," J. Lightwave Technol. 20,1968-1975 (2002)
[CrossRef]

T. Kominato, Y. Ohmori, N. Takato, H. Okazaki, M. Yasu, "Ring resonators composed of GeO2-doped silica waveguides," J. Lightwave Technol. 12,1781-1788 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

D. L. MacFarlane and E.M. Dowling, "Z-domain techniques in the analysis of Fabry-Perot etalons and multilayer structures," J. Opt. Soc. Am. 11,236-245, (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Photon (1)

F. Xia, L. Sekaric and Y. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photon 1,65-71 (2007).
[CrossRef]

Nature (London) (1)

K. J. Vahala, "Optical microcavities," Nature (London) 424,839-846, (2003)
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Other (4)

P. Dumon, I. Christiaens, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, D. Van Thourhout and R. Baets, "Microring resonators on Silicon-on-Insulator," in Proc. of European Conf. on Integrated Optics, 2005.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing. Prentice-Hall (1999)

A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech: Norwood, MA, 2000).

K. Okamoto. Fundamentals of Optical Waveguides. (Academic Press, 2nd ed, 2005).

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Figures (11)

Fig. 1.
Fig. 1.

Type I CROW structure layout.

Fig. 2.
Fig. 2.

Type-I CROW unit cell and closing cell.

Fig. 3.
Fig. 3.

Type-I CROWreflection transfer function for Gauss window apodisation (parameter G=0, 3 and 4) on (a) one bus and (b) two buses

Fig. 4.
Fig. 4.

Type-I CROW reflection transfer function for Hamming window apodisation (parameter H=0, 0.15 and 0.3) on (a) one bus and (b) two buses

Fig. 5.
Fig. 5.

Type-I CROWreflection transfer function for Kaiser window apodisation (parameter βk =0, 0.15 and 0.3) on (a) one bus and (b) two buses

Fig. 6.
Fig. 6.

Type-I CROW reflection transfer comparison for Gauss, Hamming and Kaiser window apodisation (effective number of rings 6.9), on (a) one bus and (b) two buses

Fig. 7.
Fig. 7.

Type-I CROWreflection normalised delay for Gauss and Kaiser window apodisation

Fig. 8.
Fig. 8.

Type II CROW structure layout.

Fig. 9.
Fig. 9.

Type-II CROW unit cell, opening and closing sections.

Fig. 10.
Fig. 10.

Type-II CROW transmission transfer function for (a) Hamming, (b) Gauss, (c) Kaiser window apodisation (window parameters as in Figs. 35) and (d) comparison for an effective number of rings 6.6.

Fig. 11.
Fig. 11.

Type-II CROW FDTD analysis, (a) power coupling coefficient K vs distance for an InP w=0.3 microns deep-etched waveguide, and (b) model vs FDTD simulation for a 6 ring CROW with Hamming windowing, H=0.12.

Equations (34)

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M UCi = 1 R 2 i ( ( R 1 i R 2 i T 1 i T 2 i ) e j Δ T 2 i e T 1 i e j Δ e j Δ )
M CN = 1 R 2 N ( R 1 N R 2 N T 1 N T 2 N T 2 N T 1 N 1 )
R 1 i = t 1 i t 2 i * ( t 1 i 2 + κ 1 i 2 ) τ i e j δ 1 τ i t 1 i * t 2 i * e j δ
R 2 i = t 2 i t 1 i * ( t 2 i 2 + κ 2 i 2 ) τ i e j δ 1 τ i t 1 i * t 2 i * e j δ
T 1 i = κ 1 i * κ 2 i τ i e j δ 2 1 τ i t 1 i * t 2 i * e j δ
T 2 i = κ 2 i * κ 1 i τ i e j δ 2 1 τ i t 1 i * t 2 i * e j δ
δ = β L c
τ = exp ( α L c )
Δ = β L b
( E N + E N ) = ( T 11 T 12 T 21 T 22 ) ( E 1 + E 1 )
M T = ( T 11 T 12 T 21 T 22 ) = M CN i = N 1 1 M UCi
T = E N + E 1 + E N = 0 = 1 T 22
R = E 1 E 1 + E N = 0 = T 21 T 22
t = 1 K
κ = j K
w ( i ) = exp ( G ( i N 2 N ) 2 )
i = 0 , 1 , , N 1
K = 0 . 1
G = 0 , 3 , 4
w ( i ) = 1 + H cos ( 2 π n ) 1 + H
i = 0 , 1 , , N 1
K = 0.1
H = 0 , 0.15 , 0.3
w ( i ) = β k sinh ( β k ) I 0 ( β k 1 4 n 2 )
i = 0 , 1 , , N 1
n = ( i N 2 ) N
K = 0.1
β k = 1 , 2 , 3
N eff = N Σ i = 0 N 1 i w ( i ) Σ i = 0 N 1 i
τ d T c = ϕ ( δ ) δ
M UCi = 1 κ i ( τ i 1 2 ( κ i 2 + t i 2 ) e j δ 2 t i * t i τ i 1 2 e j δ 2 )
M OS = 1 κ 0 ( ( κ 0 2 + t 0 2 ) τ 0 1 4 e j δ 4 t 0 * τ 0 1 4 e j δ 4 t 0 τ 0 1 4 e j δ 4 τ i 1 4 e j δ 4 )
M CS = 1 κ N ( ( κ N 2 + t N 2 ) τ N 1 4 e j δ 4 t N * τ N 1 4 e j δ 4 t N τ N 1 4 e j δ 4 τ i 1 4 e j δ 4 )
M T = M CS [ i = N 1 1 M UCi ] M OS

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