Abstract

We demonstrate how to design thin-film multilayer structures that separate multiple wavelength channels with a single stack by spatial dispersion, thus allowing compact manufacturable wavelength multiplexers and demultiplexers and possibly beam-steering or dispersion-control devices. We discuss four types of structure—periodic one-dimensional photonic crystal superprism structures, double-chirped structures exploiting wavelength-dependent penetration depth, coupled-cavity structures with dispersion that is due to stored energy, and numerically optimized nonperiodic structures utilizing a mixture of the other dispersion effects. We experimentally test the spatial dispersion of a 200-layer periodic structure and a 66-layer nonperiodic structure. Probably because of its greater design freedom, the nonperiodic structure can give both a linear shift with wavelength and a larger usable shift than the thicker periodic structure gives.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  43. V. Narayan, E. M. Dowling, D. L. MacFarlane, “Design of multimirror structures for high-frequency bursts and codes of ultrashort pulses,” IEEE J. Quantum Electron. 30, 1671–1680 (1994).
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2002 (1)

2001 (4)

M. Jablonski, Y. Takushima, K. Kikuchi, “The realization of all-pass filters for third-order dispersion compensation in ultrafast optical fiber transmission systems,” J. Lightwave Technol. 19, 1194–1205 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Lett. 87, 253902-1–253902-4 (2001).
[CrossRef]

T. Ochiai, J. Sanchez-Dehesa, “Superprism effect in opal-based photonic crystals,” Phys. Rev. B 64, 245113-1–245113-7 (2001).
[CrossRef]

I. Walmsley, L. Waxer, C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

2000 (4)

B. Gralak, S. Enoch, G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012–1020 (2000).
[CrossRef]

B. E. Nelson, M. Gerken, D. A. B. Miller, R. Piestun, C.-C. Lin, J. S. Harris, “Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting,” Opt. Lett. 25, 1502–1504 (2000).
[CrossRef]

E. Silvestre, J. M. Pottage, P. St. J. Russell, P. J. Roberts, “Design of thin-film photonic crystal waveguides,” Appl. Phys. Lett. 77, 942–944 (2000).
[CrossRef]

A. N. Naumov, R. B. Miles, P. Barker, A. M. Zheltikov, “Ultradispersive prisms and narrow-band tunable filters combining dispersion of atomic resonances and photonic band-gap structures,” Laser Phys. 10, 622–626 (2000).

1999 (5)

S. Enoch, G. Tayeb, D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[CrossRef]

G. Lenz, C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. 17, 1248–1254 (1999).
[CrossRef]

K. Rajamani, Y.-S. Lai, “A novel method for designing allpass digital filters,” IEEE Signal Process Lett. 6, 207–209 (1999).
[CrossRef]

1998 (2)

N. Matuschek, F. X. Kärtner, U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

1997 (2)

N. Matuschek, F. X. Kärtner, U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1997).
[CrossRef]

B. J. Eggleton, G. Lenz, N. Litchinitser, D. B. Patterson, R. E. Slusher, “Implications of fiber grating dispersion for WDM communication systems,” IEEE Photon. Technol. Lett. 9, 1403–1405 (1997).
[CrossRef]

1996 (1)

1995 (1)

P. Tournois, P. Hartemann, “Bulk chirped Bragg reflectors for light pulse compression and expansion,” Opt. Commun. 119, 569–575 (1995).
[CrossRef]

1994 (5)

R. Szipöcs, K. Ferencz, C. Spielmann, F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203 (1994).
[CrossRef] [PubMed]

J. P. Dowling, C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345–351 (1994).
[CrossRef]

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

M. Lang, T. I. Laakso, “Simple and robust method for the design of allpass filters using least-squares phase error criterion,” IEEE Trans. Circuits Syst. II 41, 40–48 (1994).
[CrossRef]

V. Narayan, E. M. Dowling, D. L. MacFarlane, “Design of multimirror structures for high-frequency bursts and codes of ultrashort pulses,” IEEE J. Quantum Electron. 30, 1671–1680 (1994).
[CrossRef]

1992 (1)

1990 (1)

1989 (1)

1987 (2)

F. Oullette, “Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,” Opt. Lett. 12, 847–849 (1987).
[CrossRef]

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

1977 (2)

1973 (1)

A. H. Gray, J. D. Markel, “Digital lattice and ladder filter synthesis,” IEEE Trans. Audio Electroacoust. AU-21, 491–500 (1973).
[CrossRef]

1965 (1)

1958 (1)

Barker, P.

A. N. Naumov, R. B. Miles, P. Barker, A. M. Zheltikov, “Ultradispersive prisms and narrow-band tunable filters combining dispersion of atomic resonances and photonic band-gap structures,” Laser Phys. 10, 622–626 (2000).

Baumeister, P.

Belkind, A.

Bowden, C. M.

J. P. Dowling, C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345–351 (1994).
[CrossRef]

Chong, E. K. P.

E. K. P. Chong, S. H. Zak, An Introduction to Optimization (Wiley, New York, 1996).

de Sterke, C. M.

Dobrowolski, J. A.

Dorrer, C.

I. Walmsley, L. Waxer, C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Dowling, E. M.

V. Narayan, E. M. Dowling, D. L. MacFarlane, “Design of multimirror structures for high-frequency bursts and codes of ultrashort pulses,” IEEE J. Quantum Electron. 30, 1671–1680 (1994).
[CrossRef]

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

Dowling, J. P.

J. P. Dowling, C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345–351 (1994).
[CrossRef]

Eggleton, B. J.

M. Sumetsky, B. J. Eggleton, C. M. de Sterke, “Theory of group delay ripple generated by chirped fiber gratings,” Opt. Express 10, 332–340 (2002).
[CrossRef] [PubMed]

B. J. Eggleton, G. Lenz, N. Litchinitser, D. B. Patterson, R. E. Slusher, “Implications of fiber grating dispersion for WDM communication systems,” IEEE Photon. Technol. Lett. 9, 1403–1405 (1997).
[CrossRef]

Enoch, S.

B. Gralak, S. Enoch, G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012–1020 (2000).
[CrossRef]

S. Enoch, G. Tayeb, D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

Ferencz, K.

Gerken, M.

B. E. Nelson, M. Gerken, D. A. B. Miller, R. Piestun, C.-C. Lin, J. S. Harris, “Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting,” Opt. Lett. 25, 1502–1504 (2000).
[CrossRef]

M. Gerken, D. A. B. Miller, “Thin-Film (DE)MUX based on group-velocity effects,” in Proceedings of the Twenty-Eighth European Conference on Optical Communication ECOC 2002, P. Danielsen, ed. (ECOC, Copenhagen, Denmark, 2002), paper 11.3.3.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Gralak, B.

Gray, A. H.

A. H. Gray, J. D. Markel, “Digital lattice and ladder filter synthesis,” IEEE Trans. Audio Electroacoust. AU-21, 491–500 (1973).
[CrossRef]

Harris, J. S.

Hartemann, P.

P. Tournois, P. Hartemann, “Bulk chirped Bragg reflectors for light pulse compression and expansion,” Opt. Commun. 119, 569–575 (1995).
[CrossRef]

Hecht, E.

E. Hecht, Optik (Addison-Wesley, Bonn, Germany, 1989).

Hietala, V. M.

Ho, F. C.

Hong, C.-S.

Hong, J.-S.

J.-S. Hong, M. J. Lancaster, Microstrip Filters for RF/Microwave Applications (Wiley-Interscience, New York, 2001).
[CrossRef]

Hunter, J.

J. Hunter, Theory and Design of Microwave Filters (Institution of Electrical Engineers, London, 2001).
[CrossRef]

Jablonski, M.

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Jones, E. D.

Jones, E. M. T.

G. Matthaei, E. M. T. Jones, L. Young, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, Norwood, Mass., 1980).

Kärtner, F. X.

N. Matuschek, F. X. Kärtner, U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1997).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Keller, U.

N. Matuschek, F. X. Kärtner, U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1997).
[CrossRef]

Kemp, R. A.

Kikuchi, K.

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Koss, V. A.

Krausz, F.

Laakso, T. I.

M. Lang, T. I. Laakso, “Simple and robust method for the design of allpass filters using least-squares phase error criterion,” IEEE Trans. Circuits Syst. II 41, 40–48 (1994).
[CrossRef]

Lai, Y.-S.

K. Rajamani, Y.-S. Lai, “A novel method for designing allpass digital filters,” IEEE Signal Process Lett. 6, 207–209 (1999).
[CrossRef]

Lancaster, M. J.

J.-S. Hong, M. J. Lancaster, Microstrip Filters for RF/Microwave Applications (Wiley-Interscience, New York, 2001).
[CrossRef]

Lang, M.

M. Lang, T. I. Laakso, “Simple and robust method for the design of allpass filters using least-squares phase error criterion,” IEEE Trans. Circuits Syst. II 41, 40–48 (1994).
[CrossRef]

Lenz, G.

G. Lenz, C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. 17, 1248–1254 (1999).
[CrossRef]

B. J. Eggleton, G. Lenz, N. Litchinitser, D. B. Patterson, R. E. Slusher, “Implications of fiber grating dispersion for WDM communication systems,” IEEE Photon. Technol. Lett. 9, 1403–1405 (1997).
[CrossRef]

Li, L.

Lin, C.-C.

Lin, S.-Y.

Litchinitser, N.

B. J. Eggleton, G. Lenz, N. Litchinitser, D. B. Patterson, R. E. Slusher, “Implications of fiber grating dispersion for WDM communication systems,” IEEE Photon. Technol. Lett. 9, 1403–1405 (1997).
[CrossRef]

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]

V. Narayan, E. M. Dowling, D. L. MacFarlane, “Design of multimirror structures for high-frequency bursts and codes of ultrashort pulses,” IEEE J. Quantum Electron. 30, 1671–1680 (1994).
[CrossRef]

MacLeod, H. A.

H. A. MacLeod, Thin-Film Optical Filters (Institute of Physics Publishing, Philadelphia, Pa., 2001).
[CrossRef]

Madsen, C. K.

G. Lenz, C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. 17, 1248–1254 (1999).
[CrossRef]

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

Markel, J. D.

A. H. Gray, J. D. Markel, “Digital lattice and ladder filter synthesis,” IEEE Trans. Audio Electroacoust. AU-21, 491–500 (1973).
[CrossRef]

Matthaei, G.

G. Matthaei, E. M. T. Jones, L. Young, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, Norwood, Mass., 1980).

Matuschek, N.

N. Matuschek, F. X. Kärtner, U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1997).
[CrossRef]

Maystre, D.

S. Enoch, G. Tayeb, D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Miles, R. B.

A. N. Naumov, R. B. Miles, P. Barker, A. M. Zheltikov, “Ultradispersive prisms and narrow-band tunable filters combining dispersion of atomic resonances and photonic band-gap structures,” Laser Phys. 10, 622–626 (2000).

Miller, D. A. B.

B. E. Nelson, M. Gerken, D. A. B. Miller, R. Piestun, C.-C. Lin, J. S. Harris, “Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting,” Opt. Lett. 25, 1502–1504 (2000).
[CrossRef]

M. Gerken, D. A. B. Miller, “Thin-Film (DE)MUX based on group-velocity effects,” in Proceedings of the Twenty-Eighth European Conference on Optical Communication ECOC 2002, P. Danielsen, ed. (ECOC, Copenhagen, Denmark, 2002), paper 11.3.3.

Mistree, F.

T. E. Shoup, F. Mistree, Optimization Methods with Applications for Personal Computers (Prentice-Hall, Englewood Cliffs, N.J., 1987).

Narayan, V.

V. Narayan, E. M. Dowling, D. L. MacFarlane, “Design of multimirror structures for high-frequency bursts and codes of ultrashort pulses,” IEEE J. Quantum Electron. 30, 1671–1680 (1994).
[CrossRef]

Naumov, A. N.

A. N. Naumov, R. B. Miles, P. Barker, A. M. Zheltikov, “Ultradispersive prisms and narrow-band tunable filters combining dispersion of atomic resonances and photonic band-gap structures,” Laser Phys. 10, 622–626 (2000).

Nelson, B. E.

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Lett. 87, 253902-1–253902-4 (2001).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Ochiai, T.

T. Ochiai, J. Sanchez-Dehesa, “Superprism effect in opal-based photonic crystals,” Phys. Rev. B 64, 245113-1–245113-7 (2001).
[CrossRef]

Oullette, F.

Patterson, D. B.

B. J. Eggleton, G. Lenz, N. Litchinitser, D. B. Patterson, R. E. Slusher, “Implications of fiber grating dispersion for WDM communication systems,” IEEE Photon. Technol. Lett. 9, 1403–1405 (1997).
[CrossRef]

Piestun, R.

Pottage, J. M.

E. Silvestre, J. M. Pottage, P. St. J. Russell, P. J. Roberts, “Design of thin-film photonic crystal waveguides,” Appl. Phys. Lett. 77, 942–944 (2000).
[CrossRef]

Rajamani, K.

K. Rajamani, Y.-S. Lai, “A novel method for designing allpass digital filters,” IEEE Signal Process Lett. 6, 207–209 (1999).
[CrossRef]

Roberts, P. J.

E. Silvestre, J. M. Pottage, P. St. J. Russell, P. J. Roberts, “Design of thin-film photonic crystal waveguides,” Appl. Phys. Lett. 77, 942–944 (2000).
[CrossRef]

Russell, P. St. J.

E. Silvestre, J. M. Pottage, P. St. J. Russell, P. J. Roberts, “Design of thin-film photonic crystal waveguides,” Appl. Phys. Lett. 77, 942–944 (2000).
[CrossRef]

Sanchez-Dehesa, J.

T. Ochiai, J. Sanchez-Dehesa, “Superprism effect in opal-based photonic crystals,” Phys. Rev. B 64, 245113-1–245113-7 (2001).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Lett. 87, 253902-1–253902-4 (2001).
[CrossRef]

Shoup, T. E.

T. E. Shoup, F. Mistree, Optimization Methods with Applications for Personal Computers (Prentice-Hall, Englewood Cliffs, N.J., 1987).

Silvestre, E.

E. Silvestre, J. M. Pottage, P. St. J. Russell, P. J. Roberts, “Design of thin-film photonic crystal waveguides,” Appl. Phys. Lett. 77, 942–944 (2000).
[CrossRef]

Slusher, R. E.

B. J. Eggleton, G. Lenz, N. Litchinitser, D. B. Patterson, R. E. Slusher, “Implications of fiber grating dispersion for WDM communication systems,” IEEE Photon. Technol. Lett. 9, 1403–1405 (1997).
[CrossRef]

Spielmann, C.

Sumetsky, M.

Szipöcs, R.

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Lett. 87, 253902-1–253902-4 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Lett. 87, 253902-1–253902-4 (2001).
[CrossRef]

Takushima, Y.

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Tayeb, G.

B. Gralak, S. Enoch, G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012–1020 (2000).
[CrossRef]

S. Enoch, G. Tayeb, D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals: toward microscale lightwave circuits,” J. Lightwave Technol. 17, 2032–2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Tournois, P.

P. Tournois, P. Hartemann, “Bulk chirped Bragg reflectors for light pulse compression and expansion,” Opt. Commun. 119, 569–575 (1995).
[CrossRef]

Walmsley, I.

I. Walmsley, L. Waxer, C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Wang, L.

Waxer, L.

I. Walmsley, L. Waxer, C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Lett. 87, 253902-1–253902-4 (2001).
[CrossRef]

Yariv, A.

Yeh, P.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Lett. 87, 253902-1–253902-4 (2001).
[CrossRef]

Young, L.

G. Matthaei, E. M. T. Jones, L. Young, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, Norwood, Mass., 1980).

Zak, S. H.

E. K. P. Chong, S. H. Zak, An Introduction to Optimization (Wiley, New York, 1996).

Zengerle, R.

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

Zhao, J. H.

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

Zheltikov, A. M.

A. N. Naumov, R. B. Miles, P. Barker, A. M. Zheltikov, “Ultradispersive prisms and narrow-band tunable filters combining dispersion of atomic resonances and photonic band-gap structures,” Laser Phys. 10, 622–626 (2000).

Appl. Opt. (4)

Appl. Phys. Lett. (1)

E. Silvestre, J. M. Pottage, P. St. J. Russell, P. J. Roberts, “Design of thin-film photonic crystal waveguides,” Appl. Phys. Lett. 77, 942–944 (2000).
[CrossRef]

IEEE J. Quantum Electron. (3)

N. Matuschek, F. X. Kärtner, U. Keller, “Exact coupled-mode theories for multilayer interference coatings with arbitrary strong index modulations,” IEEE J. Quantum Electron. 33, 295–302 (1997).
[CrossRef]

N. Matuschek, F. X. Kärtner, U. Keller, “Analytical design of double-chirped mirrors with custom-tailored dispersion characteristics,” IEEE J. Quantum Electron. 35, 129–137 (1999).
[CrossRef]

V. Narayan, E. M. Dowling, D. L. MacFarlane, “Design of multimirror structures for high-frequency bursts and codes of ultrashort pulses,” IEEE J. Quantum Electron. 30, 1671–1680 (1994).
[CrossRef]

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

N. Matuschek, F. X. Kärtner, U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. J. Eggleton, G. Lenz, N. Litchinitser, D. B. Patterson, R. E. Slusher, “Implications of fiber grating dispersion for WDM communication systems,” IEEE Photon. Technol. Lett. 9, 1403–1405 (1997).
[CrossRef]

IEEE Signal Process Lett. (1)

K. Rajamani, Y.-S. Lai, “A novel method for designing allpass digital filters,” IEEE Signal Process Lett. 6, 207–209 (1999).
[CrossRef]

IEEE Trans. Audio Electroacoust. (1)

A. H. Gray, J. D. Markel, “Digital lattice and ladder filter synthesis,” IEEE Trans. Audio Electroacoust. AU-21, 491–500 (1973).
[CrossRef]

IEEE Trans. Circuits Syst. II (1)

M. Lang, T. I. Laakso, “Simple and robust method for the design of allpass filters using least-squares phase error criterion,” IEEE Trans. Circuits Syst. II 41, 40–48 (1994).
[CrossRef]

J. Lightwave Technol. (4)

J. Mod. Opt. (2)

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

J. P. Dowling, C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345–351 (1994).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Laser Phys. (1)

A. N. Naumov, R. B. Miles, P. Barker, A. M. Zheltikov, “Ultradispersive prisms and narrow-band tunable filters combining dispersion of atomic resonances and photonic band-gap structures,” Laser Phys. 10, 622–626 (2000).

Opt. Commun. (2)

S. Enoch, G. Tayeb, D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171–176 (1999).
[CrossRef]

P. Tournois, P. Hartemann, “Bulk chirped Bragg reflectors for light pulse compression and expansion,” Opt. Commun. 119, 569–575 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Lett. 87, 253902-1–253902-4 (2001).
[CrossRef]

Phys. Rev. B (2)

T. Ochiai, J. Sanchez-Dehesa, “Superprism effect in opal-based photonic crystals,” Phys. Rev. B 64, 245113-1–245113-7 (2001).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Rev. Sci. Instrum. (1)

I. Walmsley, L. Waxer, C. Dorrer, “The role of dispersion in ultrafast optics,” Rev. Sci. Instrum. 72, 1–29 (2001).
[CrossRef]

Other (12)

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

E. Hecht, Optik (Addison-Wesley, Bonn, Germany, 1989).

H. A. MacLeod, Thin-Film Optical Filters (Institute of Physics Publishing, Philadelphia, Pa., 2001).
[CrossRef]

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989).

G. Matthaei, E. M. T. Jones, L. Young, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, Norwood, Mass., 1980).

J. Hunter, Theory and Design of Microwave Filters (Institution of Electrical Engineers, London, 2001).
[CrossRef]

J.-S. Hong, M. J. Lancaster, Microstrip Filters for RF/Microwave Applications (Wiley-Interscience, New York, 2001).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

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

E. K. P. Chong, S. H. Zak, An Introduction to Optimization (Wiley, New York, 1996).

T. E. Shoup, F. Mistree, Optimization Methods with Applications for Personal Computers (Prentice-Hall, Englewood Cliffs, N.J., 1987).

M. Gerken, D. A. B. Miller, “Thin-Film (DE)MUX based on group-velocity effects,” in Proceedings of the Twenty-Eighth European Conference on Optical Communication ECOC 2002, P. Danielsen, ed. (ECOC, Copenhagen, Denmark, 2002), paper 11.3.3.

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Figures (11)

Fig. 1
Fig. 1

Operating schematics of four types of thin-film structures that can be used for demultiplexing different wavelengths by spatial beam shifting. The structure in (a) is periodic, and those in (b)–(d) are nonperiodic. Polychromatic light is incident at an angle from the top left corner. All structures are operated in reflection and demultiplex light by a wavelength-dependent shift along the x axis. After exiting the structures, beams of different wavelengths propagate in parallel once again. For clarity, only two different wavelengths are pictured in the schematics. (a) The superprism effect for a one-dimensional photonic crystal (combined here with a simple reflection off the right face). Different wavelengths propagate at different group-velocity angles within the structure and are thus spatially shifted along the x axis. The nonperiodic structure in (b) reflects different wavelengths at different positions along the z axis. Because the structure is operated at an angle, this wavelength-dependent penetration depth leads to a spatial shift along the x axis. The structure in (c) exhibits wavelength-dependent stored energy. Stored energy is loosely equivalent to multiple bounces in the structure as indicated here. Again, because of the operation at an angle, beams of different wavelengths are shifted by different amounts along the x axis. Finally, the structure in (d) utilizes a combination of wavelength-dependent penetration depth and stored energy to demultiplex polychromatic light.

Fig. 2
Fig. 2

Experimentally observed superprism effect for a 100-period dielectric stack for an incidence angle of 40°, p polarization, and a spot size of 4.7 μm. Two exiting beams are observed. The center positions of both beams are plotted as a function of wavelength. One beam (crosses) is reflected off the front of the dielectric stack owing to impedance mismatch and does not change position as a function of wavelength. The second beam (circles) is the real signal beam that propagates through the dielectric stack twice. This beam shifts as a function of wavelength. The solid curve shows the theoretically expected shift with wavelength calculated by use of Bloch theory.

Fig. 3
Fig. 3

Schematic of the experimental setup.

Fig. 4
Fig. 4

Group-propagation angle as a function of wavelength calculated by use of Bloch theory with incidence angles of 40° (solid), 36.5° (dashed), and 43.5° (dash-dotted). For a Gaussian beam with a spot size of 4.7 μm at 880 nm and a center incidence angle of 40°, the intensity has decreased to 1/e 2 for beam components at incidence angles of 36.5° and 43.5°.

Fig. 5
Fig. 5

(a) Bragg wavelength as a function of the position in the structure for five different 60-layer SiO2–Ta2O5 double-chirped mirror designs. Layer data represented as follows: f = 0.5 (exes), f = 0.33 (crosses), f = 0.2 (squares), f = 0.1 (diamonds), f = 0 (circles). (b) The theoretical spatial shift as a function of wavelength is plotted for an incidence angle of 45° and p-polarized light. An approximately linear shift is observed for all five designs. The dispersion increases with decreasing chirp in the Bragg wavelength. The maximum dispersion is achieved with a single-chirped Bragg stack (circles).

Fig. 6
Fig. 6

(a) Physical layer thicknesses for a 200-layer SiO2–Ta2O5 double-chirped structure. Layer data represented as follows: SiO2 [squares] and Ta2O5 (circles). (b) Theoretically calculated shift as a function of wavelength at a 40° incidence angle and p polarization. (c) E fields parallel to the interfaces of the forward-propagating waves as a function of the position in the structure for four wavelengths—780, 830, 880, and 930 nm. The vertical lines indicate the position of the interfaces between layers. Light is incident from the left, and the structure extends from 0 to 28 μm. It can clearly be seen that light of longer wavelengths penetrates deeper into the structure, leading to temporal and spatial dispersions. Furthermore, the larger-than-unity field amplitudes for the longer wavelengths indicate additional dispersion that is due to stored energy.

Fig. 7
Fig. 7

Expected shift for a four-cavity structure is plotted as a function of wavelength for three different cavity optical thicknesses (dash-dotted curve, L c = 1.7 μm; solid curve, L c = 2.9 μm; dashed curve, L c = 5.8 μm). The same transfer function H AP(z) is used for all calculations, and a group-propagation angle of 20° is assumed in the cavity.

Fig. 8
Fig. 8

(a) Physical layer thicknesses for a 33-layer SiO2–Ta2O5 four-cavity structure (SiO2 data, squares; Ta2O5 data, circles). (b) Theoretically calculated shift as a function of wavelength structure at a 54° incidence angle and s polarization. The reflectance of the structure is 100%. (c) E fields parallel to the interfaces of the forward-propagating waves as a function of the position in the structure for four wavelengths—842, 846, 850, and 854 nm. The vertical lines indicate the position of the interfaces between layers. Light is incident from the left, and the structure extends from 0 to 15.4 μm. For longer wavelengths a larger amount of energy buildup occurs in the structure. This causes spatial and temporal dispersion. We also see that part of the dispersion can be attributed to a wavelength-dependent penetration depth.

Fig. 9
Fig. 9

(a) Physical layer thicknesses for a 66-layer, numerically optimized SiO2–Ta2O5 structure (SiO2 data, squares; Ta2O5 data, circles). (b) Theoretically calculated shift as a function of wavelength structure at a 54° incidence angle and p polarization. The reflectance of the structure is improved to nearly 100% by a gold layer on the extreme right. (c) E fields parallel to the interfaces of the forward-propagating waves as a function of the position in the structure for four wavelengths—821, 828, 835, and 842 nm. The vertical lines indicate the position of the interfaces between layers. Light is incident from the left, and the structure extends from 0 to 13.4 μm. We see that the dispersion is due to both a wavelength-dependent penetration depth and a wavelength-dependent amount of stored energy.

Fig. 10
Fig. 10

Experimentally observed spatial dispersion of a 66-layer SiO2–Ta2O5 dielectric stack with a total thickness of 13.4 μm on a quartz substrate for an incidence angle of 54° and p polarization. The experimental shift of the peak (circles) as a function of wavelength shows excellent agreement with the theoretical calculation (solid curve).

Fig. 11
Fig. 11

Comparison of the results for the 200-layer periodic structure in Section 2 and the 66-layer nonperiodic structure in Section 6. The results are scaled to the 1550-nm wavelength range for better comparison [circles, 200-layer periodic (experiment); solid curve, 200-layer periodic (theory); exes, 66-layer nonperiodic (experiment); dashed curve, 66-layer nonperiodic (theory)].

Tables (1)

Tables Icon

Table 1 Composition of the Designs Discussed in Sections 5 and 6

Equations (35)

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

vg=kωk=vgxx+vgzz,
vgx=ωβK=const,
vgz=ωKβ=const.
θgrω, β, K=tan-1vgx/vgz.
θgrθ, ω=tan-1-Kθ, ωθβθ, ωθ.
n=-Kθ, ωθx+βθ, ωθz.
sx=2L tanθgr=2Lvgx/vgz.
τgroup=svgx=sKωK=const=2L Kωβ=const=ϕrefl∂ωβ=const.
λB=2nHdH1-sinθnH21/2+nLdL1-sinθnL21/2.
λBp=800 nm1-0.02541 fp.
dHSCp=λBp4nH1-sinθnH21/2,
dLSCp=λBp4nL1-sinθnL21/2.
dHDCp=λBPDC4nH1-sinθnH21/2pPDC1.05,
dLDCp=λBp2-dHDCpnH1-sinθnH21/24nL1-sinθnL21/2.
HAPz=z-N1+n=1N anzn1+n=1N anz-n=ANRzANz.
rN+1-m=-am,m,
Am-1z=Amz-am,mAmz-1z-m1-am,m2.
MF=1Ni=1NQiT-QiΔQip1/p.
cosKla+lb=cosωc na2-β21/2la×cosωc nb2-β21/2lb-Δβ, ωsinωc na2-β21/2la×sinωc nb2-β21/2lb.
ΔTEβ, ω=12ωc nb2-β21/2ωc na2-β21/2+ωc na2-β21/2ωc nb2-β21/2,
ΔTMβ, ω=12na2ωc nb2-β21/2nb2ωc na2-β21/2+nb2ωc na2-β21/2na2ωc nb2-β21/2.
EincErefl=D0,1P1D1,2P2D2,3PN-1DN-1,N10.
Piβ, ω=expiωc ni2-β21/2di00exp-iωc ni2-β21/2di.
Di,i+1β, ω=1ti,i+1β, ω1ri,i+1β, ωri,i+1β, ω1,
ri,i+1β, ω=neff,iβ, ω-neff,i+1β, ωneff,iβ, ω+neff,i+1β, ω,
ti,i+1β, ω=2neff,iβ, ωneff,iβ, ω+neff,i+1β, ω.
neff,TE,iβ, ω=ni1-cβωni21/2,
neff,TM,iβ, ω=ni1-cβωni21/2.
ϕreflβ, ω=argEreflβ, ω-argEincβ, ω.
Kβ, ω=ϕreflβ, ω2L.
ϕapprβ, ω-2 iωc ni2-β21/2di.
ϕapprβ, ωωβ=const2 ini2c dini2-βcω21/2,
ϕapprβ, ωβω=const-2 iβcω dini2-βcω21/2.
βωapprK=const=-ϕappr/ωϕappr/βωβc2ini2dini2-βcω21/2idini2-βcω21/2.
βωapprK=const1c sinθ×ini2di/ni2-sinθ21/2idi/ni2-sinθ21/2.

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