Abstract

We propose and demonstrate the application of concepts from digital filter design in order to optimize artificial optical resonant structures to produce a nearly ideal nonlinear phase shift response. Multistage autoregressive moving average (ARMA) optical filters (ring-resonator-based Mach–Zehnder interferometer lattices) are designed and studied. The filter group delay is used as a measure instead of finesse or quality factor to study the nonlinear sensitivity for multiple resonances. The nonlinearity of a four-stage ARMA filter is 17 times higher than that of the intrinsic material of the same group delay. We demonstrate that the nonlinear sensitivity can be increased within constant bandwidth by allocating more in-band phase or by using higher-order filter structures and that the nonlinear sensitivity enhancement improves with increasing group delay. We also investigate methods to precompensate the nonlinear response to reduce the occurrence of optical bistabilities. The effect of optical loss, including linear absorption and two-photon absorption, is discussed in postanalysis. In addition, we discuss how the improvement in nonlinear response scales with respect to various filter parameters.

© 2005 Optical Society of America

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2004 (1)

2003 (9)

A. Nahata, R. A. Linke, T. Ishi, K. Ohashi, “Enhanced nonlinear optical conversion from a periodically nanostructured metal film,” Opt. Lett. 28, 423–425 (2003).
[CrossRef] [PubMed]

M. Soljacic, C. Luo, J. D. Joannopoulos, S. Fan, “Nonlinear photonic crystal microcavities for optical integration,” Opt. Lett. 28, 637–637 (2003).
[CrossRef]

S. Blair, “Self-focusing of narrow 1-D beams in photonic microcavity arrays,” J. Opt. Soc. Am. B 20, 1520–1526 (2003).
[CrossRef]

Y. Chen, S. Blair, “Nonlinear phase shift of cascaded microring resonators,” J. Opt. Soc. Am. B 20, 2125–2132 (2003).
[CrossRef]

Y. Chen, G. Pasrija, B. Farhang-Boroujeny, S. Blair, “Engineering the nonlinear phase shift,” Opt. Lett. 28, 1945–1947 (2003).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

M. Bajcsy, A. S. Zibrov, M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638–641 (2003).
[CrossRef] [PubMed]

A. Melloni, F. Morichetti, M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365–379 (2003).
[CrossRef]

2002 (6)

2001 (1)

S. Nakamura, Y. Ueno, K. Tajima, “168-Gbit/s all-optical wavelength conversion with a symmetric Mach–Zehnder type switch,” IEEE Photon. Technol. Lett. 13, 1091–1093 (2001).
[CrossRef]

2000 (6)

S. E. Harris, “Pondermotive forces with slow light,” Phys. Rev. Lett. 85, 4032–4035 (2000).
[CrossRef] [PubMed]

L. Brzozowski, E. H. Sargent, “Optical signal processing using nonlinear distributed feedback structures,” IEEE J. Quantum Electron. 36, 550–555 (2000).
[CrossRef]

K. Stubkjaer, “Semiconductor optical amplifier based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6, 1428–1435 (2000).
[CrossRef]

G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spalter, R. E. Slusher, S.-W. Cheong, J. S. Sanghera, I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25, 254–256 (2000).
[CrossRef]

N. G. R. Broderick, D. J. Richardson, M. Ibsen, “Nonlinear switching in a 20-cm-long fiber Bragg grating,” Opt. Lett. 25, 536–538 (2000).
[CrossRef]

C. K. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18, 860–868 (2000).
[CrossRef]

1999 (6)

A. Yariv, Y. Xu, R. K. Lee, A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

J. E. Heebner, R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
[CrossRef]

N. G. R. Broderick, T. M. Monro, P. J. Bennett, D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
[CrossRef]

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

R. Fitzgerald, “Ultraslow light pulse propagation observed in atoms—both cold and hot,” Phys. Today 52(7), 17–18 (1999).
[CrossRef]

1998 (1)

C. K. Madsen, “Efficient architectures for exactly realizing optical filters with optimum bandpass designs,” IEEE Photon. Technol. Lett. 10, 1136–1138 (1998).
[CrossRef]

1997 (3)

1996 (4)

J. C. Knight, T. A. Birks, P. S. J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

K. Jinguji, “Synthesis of coherence two-port optical delay-line circuit with ring waveguides,” J. Lightwave Technol. 14, 1882–1898 (1996).
[CrossRef]

C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
[CrossRef]

V. M. Shalaev, E. Y. Poliakov, V. A. Markel, “Small-partical composites. II. Non-linear optical properties,” Phys. Rev. B 53, 2437–2449 (1996).
[CrossRef]

1995 (4)

K. I. Kang, T. G. Chang, I. Glesk, P. R. Prucnal, R. K. Boncek, “Demonstration of ultrafast, all-optical, low control energy, single wavelength, polarization independent, cascadable, and integrable switch,” Appl. Phys. Lett. 67, 605–607 (1995).
[CrossRef]

R. J. Manning, G. Sherlock, “Recovery of a π phase shift in ∼12.5 ps in a semiconductor laser amplifier,” Electron. Lett. 31, 307–308 (1995).
[CrossRef]

R. Orta, P. Savi, R. Tascone, D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

O. Dühr, F. Seifert, V. Petrov, “Ultrafast Kerr demultiplexing up to 460 Gbit/s in short optical fibers,” Appl. Opt. 34, 5297–5300 (1995).
[CrossRef]

1994 (2)

A. Huang, N. Whitaker, H. Avramopoulos, P. French, H. Hough, I. Chuang, “Sagnac fiber logic gates and their possible applications: a system perspective,” Appl. Opt. 33, 6254–6267 (1994).
[CrossRef] [PubMed]

E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
[CrossRef]

1993 (1)

1992 (2)

M. Jinno, T. Matsumoto, “Nonlinear Sagnac interferometer switch and its applications,” IEEE J. Quantum Electron. 28, 875–882 (1992).
[CrossRef]

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

1991 (1)

K.-J. Boller, A. Imamolu, S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

N. J. Doran, D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 311–313 (1988).
[CrossRef]

1987 (1)

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarization-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

Aggarwal, I. D.

Andrejco, M. J.

Andrekson, P. A.

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

Atkin, D. M.

Avramopoulos, H.

Bailey, R. J.

Bajcsy, M.

M. Bajcsy, A. S. Zibrov, M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638–641 (2003).
[CrossRef] [PubMed]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Bennett, P. J.

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

Birks, T. A.

Blair, B.

B. Blair, “Optical soliton-based logic gates,” Ph.D. thesis (University of Colorado, Boulder, Colo., 1998).

Blair, S.

Blow, K. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).
[CrossRef]

Boller, K.-J.

K.-J. Boller, A. Imamolu, S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Boncek, R. K.

K. I. Kang, T. G. Chang, I. Glesk, P. R. Prucnal, R. K. Boncek, “Demonstration of ultrafast, all-optical, low control energy, single wavelength, polarization independent, cascadable, and integrable switch,” Appl. Phys. Lett. 67, 605–607 (1995).
[CrossRef]

Boyd, R.

Boyd, R. W.

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

J. Heebner, R. W. Boyd, Q.-H. Park, “SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides,” J. Opt. Soc. Am. B 19, 722–731 (2002).
[CrossRef]

J. E. Heebner, R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
[CrossRef]

Broderick, N. G. R.

Brzozowski, L.

L. Brzozowski, E. H. Sargent, “Optical signal processing using nonlinear distributed feedback structures,” IEEE J. Quantum Electron. 36, 550–555 (2000).
[CrossRef]

Bures, J.

Chang, T. G.

K. I. Kang, T. G. Chang, I. Glesk, P. R. Prucnal, R. K. Boncek, “Demonstration of ultrafast, all-optical, low control energy, single wavelength, polarization independent, cascadable, and integrable switch,” Appl. Phys. Lett. 67, 605–607 (1995).
[CrossRef]

Chen, Y.

Cheong, S.-W.

Chuang, I.

DeLong, K. W.

Digiovanni, D. J.

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

Donnelly, J. P.

Doran, N. J.

N. J. Doran, D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 311–313 (1988).
[CrossRef]

Dowling, E. M.

E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
[CrossRef]

Dühr, O.

Dumais, P.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Fan, S.

Farhang-Boroujeny, B.

Fennelly, C. I.

Fitzgerald, R.

R. Fitzgerald, “Ultraslow light pulse propagation observed in atoms—both cold and hot,” Phys. Today 52(7), 17–18 (1999).
[CrossRef]

French, P.

Gilles, L.

Glesk, I.

K. I. Kang, T. G. Chang, I. Glesk, P. R. Prucnal, R. K. Boncek, “Demonstration of ultrafast, all-optical, low control energy, single wavelength, polarization independent, cascadable, and integrable switch,” Appl. Phys. Lett. 67, 605–607 (1995).
[CrossRef]

Gonthier, F.

Groves, S. H.

Hall, K. L.

Harris, S. E.

S. E. Harris, “Pondermotive forces with slow light,” Phys. Rev. Lett. 85, 4032–4035 (2000).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

K.-J. Boller, A. Imamolu, S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Heebner, J.

Heebner, J. E.

Hough, H.

Huang, A.

Hwang, H. Y.

Ibanescu, M.

Ibsen, M.

Imamoglu, A.

M. D. Lukin, A. Imamoglu, “Nonlinear optics and quantum entanglement of ultraslow photons,” in Quantum Electronics and Laser Science, Vol. 40 of Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 137–138.

Imamolu, A.

K.-J. Boller, A. Imamolu, S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Ippen, E.

Ishi, T.

Islam, M. N.

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, Cambridge, 1992).

Jinguji, K.

K. Jinguji, “Synthesis of coherence two-port optical delay-line circuit with ring waveguides,” J. Lightwave Technol. 14, 1882–1898 (1996).
[CrossRef]

Jinno, M.

M. Jinno, T. Matsumoto, “Nonlinear Sagnac interferometer switch and its applications,” IEEE J. Quantum Electron. 28, 875–882 (1992).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kang, K. I.

K. I. Kang, T. G. Chang, I. Glesk, P. R. Prucnal, R. K. Boncek, “Demonstration of ultrafast, all-optical, low control energy, single wavelength, polarization independent, cascadable, and integrable switch,” Appl. Phys. Lett. 67, 605–607 (1995).
[CrossRef]

Katsufuji, T.

Kelly, A. E.

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).
[CrossRef]

Khoo, I.-C.

I.-C. Khoo, Liquid Crystals. Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

Knight, J. C.

Lacroix, S.

Lee, R. K.

Lenz, G.

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

Lines, M. E.

Linke, R. A.

Logan, R. A.

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

Lukin, M. D.

M. Bajcsy, A. S. Zibrov, M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638–641 (2003).
[CrossRef] [PubMed]

M. D. Lukin, A. Imamoglu, “Nonlinear optics and quantum entanglement of ultraslow photons,” in Quantum Electronics and Laser Science, Vol. 40 of Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 137–138.

Luo, C.

MacFarlane, D. L.

E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
[CrossRef]

Madsen, C. K.

C. K. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18, 860–868 (2000).
[CrossRef]

C. K. Madsen, “Efficient architectures for exactly realizing optical filters with optimum bandpass designs,” IEEE Photon. Technol. Lett. 10, 1136–1138 (1998).
[CrossRef]

C. K. Madsen, J. H. Zhao, “Postfabrication optimization of an autoregressive planar waveguide lattice filter,” Appl. Opt. 36, 642–647 (1997).
[CrossRef] [PubMed]

C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
[CrossRef]

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

Manning, R. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).
[CrossRef]

R. J. Manning, G. Sherlock, “Recovery of a π phase shift in ∼12.5 ps in a semiconductor laser amplifier,” Electron. Lett. 31, 307–308 (1995).
[CrossRef]

Markel, V. A.

V. M. Shalaev, E. Y. Poliakov, V. A. Markel, “Small-partical composites. II. Non-linear optical properties,” Phys. Rev. B 53, 2437–2449 (1996).
[CrossRef]

Martinelli, M.

A. Melloni, F. Morichetti, M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365–379 (2003).
[CrossRef]

A. Melloni, M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296–303 (2002).
[CrossRef]

Matsumoto, T.

M. Jinno, T. Matsumoto, “Nonlinear Sagnac interferometer switch and its applications,” IEEE J. Quantum Electron. 28, 875–882 (1992).
[CrossRef]

Melloni, A.

A. Melloni, F. Morichetti, M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365–379 (2003).
[CrossRef]

A. Melloni, M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296–303 (2002).
[CrossRef]

Mizrahi, V.

Monro, T. M.

Morichetti, F.

A. Melloni, F. Morichetti, M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365–379 (2003).
[CrossRef]

Morioka, T.

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarization-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

Morton, P. A.

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

Nahata, A.

Nakamura, S.

S. Nakamura, Y. Ueno, K. Tajima, “168-Gbit/s all-optical wavelength conversion with a symmetric Mach–Zehnder type switch,” IEEE Photon. Technol. Lett. 13, 1091–1093 (2001).
[CrossRef]

Napoleon, A.

Ohashi, K.

Olsson, N. A.

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

Orta, R.

R. Orta, P. Savi, R. Tascone, D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Park, Q.-H.

Pasrija, G.

Petrov, V.

Poliakov, E. Y.

V. M. Shalaev, E. Y. Poliakov, V. A. Markel, “Small-partical composites. II. Non-linear optical properties,” Phys. Rev. B 53, 2437–2449 (1996).
[CrossRef]

Poustie, A. J.

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).
[CrossRef]

Prasad, P. N.

P. N. Prasad, D. J. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991).

Prucnal, P. R.

K. I. Kang, T. G. Chang, I. Glesk, P. R. Prucnal, R. K. Boncek, “Demonstration of ultrafast, all-optical, low control energy, single wavelength, polarization independent, cascadable, and integrable switch,” Appl. Phys. Lett. 67, 605–607 (1995).
[CrossRef]

Richardson, D. J.

Russell, P. S. J.

Saifi, M. A.

Sanghera, J. S.

Sargent, E. H.

L. Brzozowski, E. H. Sargent, “Optical signal processing using nonlinear distributed feedback structures,” IEEE J. Quantum Electron. 36, 550–555 (2000).
[CrossRef]

Saruwatari, M.

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarization-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

Savi, P.

R. Orta, P. Savi, R. Tascone, D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Scherer, A.

Seifert, F.

Shalaev, V. M.

V. M. Shalaev, E. Y. Poliakov, V. A. Markel, “Small-partical composites. II. Non-linear optical properties,” Phys. Rev. B 53, 2437–2449 (1996).
[CrossRef]

Sherlock, G.

R. J. Manning, G. Sherlock, “Recovery of a π phase shift in ∼12.5 ps in a semiconductor laser amplifier,” Electron. Lett. 31, 307–308 (1995).
[CrossRef]

Slusher, R. E.

Soljacic, M.

Spalter, S.

Stegeman, G. I.

Stubkjaer, K.

K. Stubkjaer, “Semiconductor optical amplifier based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6, 1428–1435 (2000).
[CrossRef]

Tajima, K.

S. Nakamura, Y. Ueno, K. Tajima, “168-Gbit/s all-optical wavelength conversion with a symmetric Mach–Zehnder type switch,” IEEE Photon. Technol. Lett. 13, 1091–1093 (2001).
[CrossRef]

Takada, A.

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarization-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

Tanbun-Ek, T.

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

Tascone, R.

R. Orta, P. Savi, R. Tascone, D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Tran, P.

Trinchero, D.

R. Orta, P. Savi, R. Tascone, D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Ueno, Y.

S. Nakamura, Y. Ueno, K. Tajima, “168-Gbit/s all-optical wavelength conversion with a symmetric Mach–Zehnder type switch,” IEEE Photon. Technol. Lett. 13, 1091–1093 (2001).
[CrossRef]

Villeneuve, A.

Wecht, K. W.

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

Whitaker, N.

Wigley, P. G. J.

Williams, D. J.

P. N. Prasad, D. J. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991).

Wood, D.

N. J. Doran, D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 311–313 (1988).
[CrossRef]

Xu, Y.

Yariv, A.

Zhao, J. H.

C. K. Madsen, J. H. Zhao, “Postfabrication optimization of an autoregressive planar waveguide lattice filter,” Appl. Opt. 36, 642–647 (1997).
[CrossRef] [PubMed]

C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
[CrossRef]

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

Zibrov, A. S.

M. Bajcsy, A. S. Zibrov, M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638–641 (2003).
[CrossRef] [PubMed]

Zimmermann, J.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

K. I. Kang, T. G. Chang, I. Glesk, P. R. Prucnal, R. K. Boncek, “Demonstration of ultrafast, all-optical, low control energy, single wavelength, polarization independent, cascadable, and integrable switch,” Appl. Phys. Lett. 67, 605–607 (1995).
[CrossRef]

Electron. Lett. (2)

T. Morioka, M. Saruwatari, A. Takada, “Ultrafast optical multi/demultiplexer utilising optical Kerr effect in polarization-maintaining single-mode fibers,” Electron. Lett. 23, 453–454 (1987).
[CrossRef]

R. J. Manning, G. Sherlock, “Recovery of a π phase shift in ∼12.5 ps in a semiconductor laser amplifier,” Electron. Lett. 31, 307–308 (1995).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Jinno, T. Matsumoto, “Nonlinear Sagnac interferometer switch and its applications,” IEEE J. Quantum Electron. 28, 875–882 (1992).
[CrossRef]

L. Brzozowski, E. H. Sargent, “Optical signal processing using nonlinear distributed feedback structures,” IEEE J. Quantum Electron. 36, 550–555 (2000).
[CrossRef]

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

K. Stubkjaer, “Semiconductor optical amplifier based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6, 1428–1435 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

S. Nakamura, Y. Ueno, K. Tajima, “168-Gbit/s all-optical wavelength conversion with a symmetric Mach–Zehnder type switch,” IEEE Photon. Technol. Lett. 13, 1091–1093 (2001).
[CrossRef]

P. A. Andrekson, N. A. Olsson, D. J. Digiovanni, P. A. Morton, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, “64 Gbit/s all-optical demultiplexing with the nonlinear optical-loop mirror,” IEEE Photon. Technol. Lett. 4, 644–647 (1992).
[CrossRef]

R. Orta, P. Savi, R. Tascone, D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

C. K. Madsen, “Efficient architectures for exactly realizing optical filters with optimum bandpass designs,” IEEE Photon. Technol. Lett. 10, 1136–1138 (1998).
[CrossRef]

J. Lightwave Technol. (5)

K. Jinguji, “Synthesis of coherence two-port optical delay-line circuit with ring waveguides,” J. Lightwave Technol. 14, 1882–1898 (1996).
[CrossRef]

C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
[CrossRef]

E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
[CrossRef]

C. K. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18, 860–868 (2000).
[CrossRef]

A. Melloni, M. Martinelli, “Synthesis of direct-coupled-resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296–303 (2002).
[CrossRef]

J. Mod. Opt. (1)

A. J. Poustie, K. J. Blow, A. E. Kelly, R. J. Manning, “Temporal evolution of amplitude restoration and thresholding in an all-optical regenerative memory,” J. Mod. Opt. 46, 1251–1254 (1999).
[CrossRef]

J. Opt. Soc. Am. B (5)

Nature (2)

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

M. Bajcsy, A. S. Zibrov, M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638–641 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (16)

Y. Chen, G. Pasrija, B. Farhang-Boroujeny, S. Blair, “Engineering the nonlinear phase shift,” Opt. Lett. 28, 1945–1947 (2003).
[CrossRef] [PubMed]

A. Nahata, R. A. Linke, T. Ishi, K. Ohashi, “Enhanced nonlinear optical conversion from a periodically nanostructured metal film,” Opt. Lett. 28, 423–425 (2003).
[CrossRef] [PubMed]

M. Soljacic, C. Luo, J. D. Joannopoulos, S. Fan, “Nonlinear photonic crystal microcavities for optical integration,” Opt. Lett. 28, 637–637 (2003).
[CrossRef]

S. Blair, “Nonlinear sensitivity enhancement with one-dimensional photonic bandgap microcavity arrays,” Opt. Lett. 27, 613–615 (2002).
[CrossRef]

J. C. Knight, T. A. Birks, P. S. J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

S. Blair, J. Heebner, R. Boyd, “Beyond the absorption-limited nonlinear phase shift with microring resonators,” Opt. Lett. 27, 357–359 (2002).
[CrossRef]

N. J. Doran, D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 311–313 (1988).
[CrossRef]

G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spalter, R. E. Slusher, S.-W. Cheong, J. S. Sanghera, I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25, 254–256 (2000).
[CrossRef]

N. G. R. Broderick, D. J. Richardson, M. Ibsen, “Nonlinear switching in a 20-cm-long fiber Bragg grating,” Opt. Lett. 25, 536–538 (2000).
[CrossRef]

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140–1142 (1989).
[CrossRef] [PubMed]

P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wigley, G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett. 18, 1996–1998 (1993).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, P. S. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

K. L. Hall, J. P. Donnelly, S. H. Groves, C. I. Fennelly, R. J. Bailey, A. Napoleon, “40-Gbit/s all-optical circulating shift register with an inverter,” Opt. Lett. 22, 1479–1481 (1997).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

J. E. Heebner, R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
[CrossRef]

N. G. R. Broderick, T. M. Monro, P. J. Bennett, D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
[CrossRef]

Opt. Quantum Electron. (1)

A. Melloni, F. Morichetti, M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365–379 (2003).
[CrossRef]

Phys. Rev. B (1)

V. M. Shalaev, E. Y. Poliakov, V. A. Markel, “Small-partical composites. II. Non-linear optical properties,” Phys. Rev. B 53, 2437–2449 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

K.-J. Boller, A. Imamolu, S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

S. E. Harris, “Pondermotive forces with slow light,” Phys. Rev. Lett. 85, 4032–4035 (2000).
[CrossRef] [PubMed]

Phys. Today (1)

R. Fitzgerald, “Ultraslow light pulse propagation observed in atoms—both cold and hot,” Phys. Today 52(7), 17–18 (1999).
[CrossRef]

Science (1)

M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef] [PubMed]

Other (6)

M. D. Lukin, A. Imamoglu, “Nonlinear optics and quantum entanglement of ultraslow photons,” in Quantum Electronics and Laser Science, Vol. 40 of Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 137–138.

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, Cambridge, 1992).

P. N. Prasad, D. J. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991).

I.-C. Khoo, Liquid Crystals. Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

B. Blair, “Optical soliton-based logic gates,” Ph.D. thesis (University of Colorado, Boulder, Colo., 1998).

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, New York, 1999).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Artificial optical resonant structures.

Fig. 2
Fig. 2

Ideal linear filter response for nonlinear phase shift.

Fig. 3
Fig. 3

Z-plane plot of poles and zeros; poles are represented by ×, and zeros by ○.

Fig. 4
Fig. 4

One unit cell of an optical ARMA lattice filter.

Fig. 5
Fig. 5

One FSR of an optical ring lattice implementation of an ARMA discrete-time filter with four poles and four zeros: top, intensity transmission; middle, phase; bottom, group-delay response. The in-band phase change is approximately 4π, with a bandwidth δν = 100 GHz.

Fig. 6
Fig. 6

Nonlinear filter response versus incident intensity n2Iin.

Fig. 7
Fig. 7

Linear filter response versus frequency of an ARMA filter under various incident intensities showing transmission distortions: curve 0, low incident intensity; curves 1–4, incident intensities of n2Iπ/4, n2Iπ/2, n2I3π/4, n2Iπ, respectively.

Fig. 8
Fig. 8

Bistability hysteresis loop at frequency νm.

Fig. 9
Fig. 9

Precompensation of the nonlinear response by modifying the coupling coefficient of the ring-to-waveguide couplers.

Fig. 10
Fig. 10

Precompensation of the nonlinear response by slightly changing the circumference of the ring resonators.

Fig. 11
Fig. 11

Spectral distortion after precompensation.

Fig. 12
Fig. 12

Precompensation of the nonlinear response by blueshifting the filter spectrum.

Fig. 13
Fig. 13

Nonlinear sensitivity of multiple resonances having constant bandwidth and FSR: (a) a sixth-order filter (ΦFSR = 12π) with Φib = (2, 4, 6, 8)π and δν = 0.3FSR; (b) ϕibFSR = 0.5 with filter order of (2, 4, 6, 8) and δν = 0.3FSR.

Fig. 14
Fig. 14

Effect of optical loss. The linear absorption is α = 1 cm−1; the normalized TPA coefficients are K = 0, 0.03, 0.1.

Tables (2)

Tables Icon

Table 1 Physical Parameters of the Four-Stage ARMA Lattice Optical Filter

Tables Icon

Table 2 Scaling Properties of Nonlinear Response

Equations (11)

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

F ( z ) G ( z ) = 0.0643 0.3202 z 1 + 0.5830 z 2 0.4630 z 3 + 0.1360 z 4 1.0000 3.8431 z 1 + 5.5446 z 2 3.5590 z 3 + 0.8576 z 4 ,
S ( z ) = 1 G ( z ) [ H ( z ) j F ( z ) j F ( z ) H ( z ) ] ,
S 0 = [ cos θ S 0 j sin θ S 0 j sin θ S 0 cos θ S 0 ]
S i = [ cos θ S i j sin θ S i j sin θ S i cos θ S i ] × [ cos θ R i a i exp ( j ϕ i ) 1 a i cos θ R i exp ( j ϕ i ) 0 0 exp ( j ϕ S i ) ]
H ( z ) H ( z ) = G ( z ) G ( z ) F ( z ) F ( z )
ϕ i = ϕ i L + ϕ i NL = n k f C i + n 2 k f I i , ring C i ,
d Δ Φ d ( n 2 I in ) = k f L eff ( n 2 eff n 2 ) π / 4 ( n 2 I π / 4 ) ,
δ κ i = γ k gd , i 2 k gd , avg 2 i = 1 N k gd , i 2 ,
δ C i = β k gd , i 2 i 1 N k gd , i 2 ,
a i 2 = exp ( α C i ) 1 + 2 k f n 2 K | E ( 0 ) | 2 C i , eff ,
ϕ i = n k f c i + 1 2 K ln ( 1 + 2 k f n 2 K | E ( 0 ) | 2 C i , eff ) .

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