Abstract

We present a new iterative approach to obtain the electric field from the displacement field for a chiral medium with Kerr nonlinearity. In a study recently reported [P. Tran, J. Opt. Soc. Am. B 16, 70 (1999)], this is done by a Newton–Raphson root-finding approach, which requires the initial guess to be near the solution. The new approach eliminates this requirement, and therefore it is more robust. We also study an all-optical switch using a chiral nonlinear thin-film Bragg reflector with two defect layers. This switch has a lower switching threshold than one using a perfect Bragg reflector. Since the switching operation is dependent on the shifting of the defect mode and not on the band edge (as in the case of a perfect multilayer structure), it should be less susceptible to manufacturing errors.

© 2002 Optical Society of America

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2000 (2)

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circulariza tion filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[CrossRef]

I. J. Hodgkinson, A. Lakhtakia, and Q. H. Wu, “Experimental realization of sculptured thin film polarization-discriminatory light-handedness inverters,” Opt. Eng. 39, 2828–2831 (2000).

1999 (3)

P. Tran, “All-optical switching with a nonlinear chiral photonic bandgap structure,” J. Opt. Soc. Am. B 16, 70–73 (1999).
[CrossRef]

K. Robbie, J. Sit, D. J. Broer, and M. J. Brett, “Chiral porous thin film/liquid crystal hybrid materials,” Proc. SPIE 3803, 26–33 (1999).
[CrossRef]

Y.-C. Yang, C.-S. Kee, J.-E. Kim, H. Y. Park, J. C. Lee, and Y.-J. Jeon, “Photonic defect modes of cholesteric liquid crystals,” Phys. Rev. E 60, 6852–6854 (1999).
[CrossRef]

1997 (3)

1996 (6)

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

J. V. Selinger and R. L. B. Selinger, “Theory of chiral order in random copolymers,” Phys. Rev. Lett. 76, 58–61 (1996).
[CrossRef] [PubMed]

P. Tran, “Optical switching with a nonlinear photonic crystal: a numerical study,” Opt. Lett. 21, 1138–1140 (1996).
[CrossRef] [PubMed]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

V. V. Konotop and G. P. Tsironis, “Dynamics of coupled gap solitons,” Phys. Rev. E 53, 5393–5398 (1996).
[CrossRef]

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

1995 (5)

A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

V. V. Konotop, “Vector gap solitons,” Phys. Rev. A 51, R3422–R3425 (1995).
[CrossRef] [PubMed]

P. Tran, “Photonic band structure calculation of material possessing Kerr nonlinearity,” Phys. Rev. B 52, 10673–10676 (1995).
[CrossRef]

A. E. Bieber, T. G. Brown, and R. C. Tiberio, “Optical switching in phase-shifted metal-semiconductor-metal Bragg reflectors,” Opt. Lett. 20, 2216–2218 (1995).
[CrossRef] [PubMed]

R. Luebbers, H. S. Langdon, F. Hunsberger, C. F. Bohren, and S. Yoshikawa, “Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band,” IEEE Trans. Antennas Propag. 43, 123–129 (1995).
[CrossRef]

1994 (7)

R. C. Qiu and I.-Tai Lu, “Guided waves in chiral optical fibers,” J. Opt. Soc. Am. A 11, 3212–3219 (1994).
[CrossRef]

S. Radic, N. George, and G. P. Agrawal, “Optical switching in λ/4-shifted nonlinear periodic structures,” Opt. Lett. 19, 1789–1791 (1994).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrafast pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

C. Martijn De Sterke and J. E. Sipe, “Gap solitons,” Prog. Opt. 33, 203–260 (1994).
[CrossRef]

J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 811–812 (1994).
[CrossRef]

1993 (1)

1991 (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

1987 (4)

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, and J. H. English, “GaAs-AlAs monolithic microresonator arrays,” Appl. Phys. Lett. 51, 94–96 (1987).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

W. Chen and D. L. Mills, “Gap solitons in nonlinear periodic structures,” Phys. Rev. Lett. 58, 160–163 (1987).
[CrossRef] [PubMed]

D. L. Mills and S. E. Trullinger, “Gap solitons in nonlinear periodic structures,” Phys. Rev. B 36, 947–952 (1987).
[CrossRef]

1985 (1)

S. L. McCall and P. M. Platzman, “An optimized π/2 distributed feedback laser,” IEEE J. Quantum Electron. 21, 1899–1904 (1985).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–306 (1966).

Agrawal, G. P.

Baek, Y.

Baumann, I.

Bendikson, J.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

Bieber, A. E.

Bloemer, M. J.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrafast pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Bohren, C. F.

R. Luebbers, H. S. Langdon, F. Hunsberger, C. F. Bohren, and S. Yoshikawa, “Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band,” IEEE Trans. Antennas Propag. 43, 123–129 (1995).
[CrossRef]

Bowden, C. M.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrafast pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

Brett, M. J.

K. Robbie, J. Sit, D. J. Broer, and M. J. Brett, “Chiral porous thin film/liquid crystal hybrid materials,” Proc. SPIE 3803, 26–33 (1999).
[CrossRef]

Broer, D. J.

K. Robbie, J. Sit, D. J. Broer, and M. J. Brett, “Chiral porous thin film/liquid crystal hybrid materials,” Proc. SPIE 3803, 26–33 (1999).
[CrossRef]

Brommer, K. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Brown, T. G.

Chen, W.

W. Chen and D. L. Mills, “Gap solitons in nonlinear periodic structures,” Phys. Rev. Lett. 58, 160–163 (1987).
[CrossRef] [PubMed]

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

DeLong, K. W.

Dowling, J. P.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrafast pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

English, J. H.

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, and J. H. English, “GaAs-AlAs monolithic microresonator arrays,” Appl. Phys. Lett. 51, 94–96 (1987).
[CrossRef]

Fittinghoff, D. N.

Flynn, R. L.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

Fork, R. L.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

George, N.

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Gossard, A. C.

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, and J. H. English, “GaAs-AlAs monolithic microresonator arrays,” Appl. Phys. Lett. 51, 94–96 (1987).
[CrossRef]

Ho, S. T.

Hodgkinson, I. J.

I. J. Hodgkinson, A. Lakhtakia, and Q. H. Wu, “Experimental realization of sculptured thin film polarization-discriminatory light-handedness inverters,” Opt. Eng. 39, 2828–2831 (2000).

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circulariza tion filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[CrossRef]

Hunsberger, F.

R. Luebbers, H. S. Langdon, F. Hunsberger, C. F. Bohren, and S. Yoshikawa, “Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band,” IEEE Trans. Antennas Propag. 43, 123–129 (1995).
[CrossRef]

Jeon, Y.-J.

Y.-C. Yang, C.-S. Kee, J.-E. Kim, H. Y. Park, J. C. Lee, and Y.-J. Jeon, “Photonic defect modes of cholesteric liquid crystals,” Phys. Rev. E 60, 6852–6854 (1999).
[CrossRef]

Jewell, J. L.

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, and J. H. English, “GaAs-AlAs monolithic microresonator arrays,” Appl. Phys. Lett. 51, 94–96 (1987).
[CrossRef]

Joannopoulos, J. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Kee, C.-S.

Y.-C. Yang, C.-S. Kee, J.-E. Kim, H. Y. Park, J. C. Lee, and Y.-J. Jeon, “Photonic defect modes of cholesteric liquid crystals,” Phys. Rev. E 60, 6852–6854 (1999).
[CrossRef]

Kim, J.-E.

Y.-C. Yang, C.-S. Kee, J.-E. Kim, H. Y. Park, J. C. Lee, and Y.-J. Jeon, “Photonic defect modes of cholesteric liquid crystals,” Phys. Rev. E 60, 6852–6854 (1999).
[CrossRef]

Konotop, V. V.

V. V. Konotop and G. P. Tsironis, “Dynamics of coupled gap solitons,” Phys. Rev. E 53, 5393–5398 (1996).
[CrossRef]

V. V. Konotop, “Vector gap solitons,” Phys. Rev. A 51, R3422–R3425 (1995).
[CrossRef] [PubMed]

Kozhekin, A.

A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

Krijnen, G.

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Krumbugel, M. A.

Kurizki, G.

A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

Lakhtakia, A.

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circulariza tion filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[CrossRef]

I. J. Hodgkinson, A. Lakhtakia, and Q. H. Wu, “Experimental realization of sculptured thin film polarization-discriminatory light-handedness inverters,” Opt. Eng. 39, 2828–2831 (2000).

Langdon, H. S.

R. Luebbers, H. S. Langdon, F. Hunsberger, C. F. Bohren, and S. Yoshikawa, “Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band,” IEEE Trans. Antennas Propag. 43, 123–129 (1995).
[CrossRef]

Leavitt, R. P.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

Ledbetter, H.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

Lee, J. C.

Y.-C. Yang, C.-S. Kee, J.-E. Kim, H. Y. Park, J. C. Lee, and Y.-J. Jeon, “Photonic defect modes of cholesteric liquid crystals,” Phys. Rev. E 60, 6852–6854 (1999).
[CrossRef]

Lee, S.

Lu, I.-Tai

Luebbers, R.

R. Luebbers, H. S. Langdon, F. Hunsberger, C. F. Bohren, and S. Yoshikawa, “Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band,” IEEE Trans. Antennas Propag. 43, 123–129 (1995).
[CrossRef]

Martijn De Sterke, C.

C. Martijn De Sterke and J. E. Sipe, “Gap solitons,” Prog. Opt. 33, 203–260 (1994).
[CrossRef]

Martin, J.

J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 811–812 (1994).
[CrossRef]

McCall, S. L.

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, and J. H. English, “GaAs-AlAs monolithic microresonator arrays,” Appl. Phys. Lett. 51, 94–96 (1987).
[CrossRef]

S. L. McCall and P. M. Platzman, “An optimized π/2 distributed feedback laser,” IEEE J. Quantum Electron. 21, 1899–1904 (1985).
[CrossRef]

Meade, R. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Mills, D. L.

W. Chen and D. L. Mills, “Gap solitons in nonlinear periodic structures,” Phys. Rev. Lett. 58, 160–163 (1987).
[CrossRef] [PubMed]

D. L. Mills and S. E. Trullinger, “Gap solitons in nonlinear periodic structures,” Phys. Rev. B 36, 947–952 (1987).
[CrossRef]

Ouellette, F.

J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 811–812 (1994).
[CrossRef]

Park, H. Y.

Y.-C. Yang, C.-S. Kee, J.-E. Kim, H. Y. Park, J. C. Lee, and Y.-J. Jeon, “Photonic defect modes of cholesteric liquid crystals,” Phys. Rev. E 60, 6852–6854 (1999).
[CrossRef]

Platzman, P. M.

S. L. McCall and P. M. Platzman, “An optimized π/2 distributed feedback laser,” IEEE J. Quantum Electron. 21, 1899–1904 (1985).
[CrossRef]

Qiu, R. C.

Radic, S.

Rapper, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Reinhardt, S. B.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

Robbie, K.

K. Robbie, J. Sit, D. J. Broer, and M. J. Brett, “Chiral porous thin film/liquid crystal hybrid materials,” Proc. SPIE 3803, 26–33 (1999).
[CrossRef]

Scalora, M.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrafast pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

Scherer, A.

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, and J. H. English, “GaAs-AlAs monolithic microresonator arrays,” Appl. Phys. Lett. 51, 94–96 (1987).
[CrossRef]

Schiek, R.

Selinger, J. V.

J. V. Selinger and R. L. B. Selinger, “Cooperative chiral order in copolymers of chiral and achiral units,” Phys. Rev. E 55, 1728–1731 (1997).
[CrossRef]

J. V. Selinger and R. L. B. Selinger, “Theory of chiral order in random copolymers,” Phys. Rev. Lett. 76, 58–61 (1996).
[CrossRef] [PubMed]

Selinger, R. L. B.

J. V. Selinger and R. L. B. Selinger, “Cooperative chiral order in copolymers of chiral and achiral units,” Phys. Rev. E 55, 1728–1731 (1997).
[CrossRef]

J. V. Selinger and R. L. B. Selinger, “Theory of chiral order in random copolymers,” Phys. Rev. Lett. 76, 58–61 (1996).
[CrossRef] [PubMed]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

C. Martijn De Sterke and J. E. Sipe, “Gap solitons,” Prog. Opt. 33, 203–260 (1994).
[CrossRef]

Sit, J.

K. Robbie, J. Sit, D. J. Broer, and M. J. Brett, “Chiral porous thin film/liquid crystal hybrid materials,” Proc. SPIE 3803, 26–33 (1999).
[CrossRef]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Sohler, W.

Stegeman, G. I.

Sweetser, J. N.

Tiberio, R. C.

Tocci, M. D.

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

Tran, P.

Trebino, R.

Trullinger, S. E.

D. L. Mills and S. E. Trullinger, “Gap solitons in nonlinear periodic structures,” Phys. Rev. B 36, 947–952 (1987).
[CrossRef]

Tsironis, G. P.

V. V. Konotop and G. P. Tsironis, “Dynamics of coupled gap solitons,” Phys. Rev. E 53, 5393–5398 (1996).
[CrossRef]

Wu, Q. H.

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circulariza tion filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[CrossRef]

I. J. Hodgkinson, A. Lakhtakia, and Q. H. Wu, “Experimental realization of sculptured thin film polarization-discriminatory light-handedness inverters,” Opt. Eng. 39, 2828–2831 (2000).

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yang, Y.-C.

Y.-C. Yang, C.-S. Kee, J.-E. Kim, H. Y. Park, J. C. Lee, and Y.-J. Jeon, “Photonic defect modes of cholesteric liquid crystals,” Phys. Rev. E 60, 6852–6854 (1999).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–306 (1966).

Yoshikawa, S.

R. Luebbers, H. S. Langdon, F. Hunsberger, C. F. Bohren, and S. Yoshikawa, “Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band,” IEEE Trans. Antennas Propag. 43, 123–129 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

J. L. Jewell, A. Scherer, S. L. McCall, A. C. Gossard, and J. H. English, “GaAs-AlAs monolithic microresonator arrays,” Appl. Phys. Lett. 51, 94–96 (1987).
[CrossRef]

Electron. Lett. (1)

J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 811–812 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. L. McCall and P. M. Platzman, “An optimized π/2 distributed feedback laser,” IEEE J. Quantum Electron. 21, 1899–1904 (1985).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

K. S. Yee, “Numerical solution of initial value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–306 (1966).

R. Luebbers, H. S. Langdon, F. Hunsberger, C. F. Bohren, and S. Yoshikawa, “Calculation and measurement of the effective chirality parameter of a composite chiral material over a wide frequency band,” IEEE Trans. Antennas Propag. 43, 123–129 (1995).
[CrossRef]

J. Appl. Phys. (2)

M. Scalora, J. P. Dowling, M. J. Bloemer, and C. M. Bowden, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: a new approach to gain enhancement,” J. Appl. Phys. 75, 1896–1899 (1994).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

Opt. Eng. (2)

Q. H. Wu, I. J. Hodgkinson, and A. Lakhtakia, “Circulariza tion filters made of chiral sculptured thin films: experimental and simulation results,” Opt. Eng. 39, 1863–1868 (2000).
[CrossRef]

I. J. Hodgkinson, A. Lakhtakia, and Q. H. Wu, “Experimental realization of sculptured thin film polarization-discriminatory light-handedness inverters,” Opt. Eng. 39, 2828–2831 (2000).

Opt. Lett. (6)

Phys. Rev. A (1)

V. V. Konotop, “Vector gap solitons,” Phys. Rev. A 51, R3422–R3425 (1995).
[CrossRef] [PubMed]

Phys. Rev. B (2)

D. L. Mills and S. E. Trullinger, “Gap solitons in nonlinear periodic structures,” Phys. Rev. B 36, 947–952 (1987).
[CrossRef]

P. Tran, “Photonic band structure calculation of material possessing Kerr nonlinearity,” Phys. Rev. B 52, 10673–10676 (1995).
[CrossRef]

Phys. Rev. E (4)

Y.-C. Yang, C.-S. Kee, J.-E. Kim, H. Y. Park, J. C. Lee, and Y.-J. Jeon, “Photonic defect modes of cholesteric liquid crystals,” Phys. Rev. E 60, 6852–6854 (1999).
[CrossRef]

M. Scalora, R. L. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, J. Bendikson, H. Ledbetter, C. M. Bowden, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 76, R1078–R1081 (1996).
[CrossRef]

J. V. Selinger and R. L. B. Selinger, “Cooperative chiral order in copolymers of chiral and achiral units,” Phys. Rev. E 55, 1728–1731 (1997).
[CrossRef]

V. V. Konotop and G. P. Tsironis, “Dynamics of coupled gap solitons,” Phys. Rev. E 53, 5393–5398 (1996).
[CrossRef]

Phys. Rev. Lett. (7)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrafast pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rapper, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

W. Chen and D. L. Mills, “Gap solitons in nonlinear periodic structures,” Phys. Rev. Lett. 58, 160–163 (1987).
[CrossRef] [PubMed]

J. V. Selinger and R. L. B. Selinger, “Theory of chiral order in random copolymers,” Phys. Rev. Lett. 76, 58–61 (1996).
[CrossRef] [PubMed]

Proc. SPIE (1)

K. Robbie, J. Sit, D. J. Broer, and M. J. Brett, “Chiral porous thin film/liquid crystal hybrid materials,” Proc. SPIE 3803, 26–33 (1999).
[CrossRef]

Prog. Opt. (1)

C. Martijn De Sterke and J. E. Sipe, “Gap solitons,” Prog. Opt. 33, 203–260 (1994).
[CrossRef]

Other (11)

http://home.earthlink.net/~jpdowling/pbgbib.html; http://www.neci.nj.nec.com/homepages/vlasov/photonic.html; “Photonic band structures,” G. Kurizki and J. W. Hauss eds., J. Mod. Opt. 41, (1994), special issue; C. M. Bowden, J. P. Dowling, and H. O. Everitt, eds., “Development and applications of materials exhibiting photonic band gaps,” feature issue, J. Opt. Soc. Am. B 10, 280–413 (1993).

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, Orlando, Fla., 1985).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984).

B. A. Saleh and T. M. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge University, Cambridge, England, 1982).

W. S. Weiglhofer, ed., Proceedings of Bianisotropics ’97, http://www.maths.gla.ac.uk/~tropics/.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Time-harmonic electromagnetic fields in chiral media,” Lect. Notes Phys. 335 (1989).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Nonwood, Mass., 1994).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).

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Figures (5)

Fig. 1
Fig. 1

Transmission spectra for right-circularly polarized (RCP) (dashed curve) and left-circularly polarized (LCP) (solid curve) light of a linear 22-period chiral DBR with chirality parameter β=0.12. (a) Perfect DBR and (b) defect DBR. The defect structure was constructed by stacking together two 22-layer structures, each one with the 12th layer (air) replaced by a dielectric layer with index n0 H=1.4 and thickness 0.4λb. The dotted curve is for the initial Gaussian pulse traveling from air of carrier frequency ω0/ωb=0.906 for the perfect structure and ω0/ωb=0.9915 for the defect-induced one, with spectral width Δω0/ωb=2×10-2 in both cases. The arrows in (b) indicate the shift direction of the defect modes in the nonlinear regime. (c) The probe field intensity inside the perfect DBR is shown when χ=10-3 and when there is no pump (E0=0) (scale on the left). Also shown is the refractive-index profile of the corresponding structure (scale on the right). (d) Same as (c) but for the defect DBR.

Fig. 2
Fig. 2

LCP transmission spectrum of a 44-layer chiral DBR with a single-defect mode (dotted curve) and a coupled-defect pair (solid curve). Same material parameters as in Fig. 1.

Fig. 3
Fig. 3

Illustration of the fixed-point method. The crossing point between the functions F± at (x-=16, x+=116) corresponds to the peak probe intensity inside the first defect layer at t=710 and for an initial pump amplitude E0=30, as depicted on the lower left panel of Fig. 4. The arrows indicate how the iteration will converge to the fixed-point solution.

Fig. 4
Fig. 4

Illustration of the switching performance of a chiral nonlinear 44-layer DBR with a defect layer at the 12th and 34th layers, whose linear transmission spectrum is depicted in Fig. 1. (a) The transmitted and reflected pulse profiles in the nonlinear regime χ=10-3 for various pump-beam strengths. The solid curve is for no pump beam, and the dotted curve is for E0=30. Initial pulses are launched at x/λb=300. (b) The output spectra normalized by the peak transmitted probe spectral intensity in the absence of the pump (E0=0). (c) The probe and (d) the pump field intensity inside the defect DBR at t=710 and for an initial pump amplitude E0=30.

Fig. 5
Fig. 5

Same as Fig. 4 but for a perfect 44-layer chiral DBR.

Equations (66)

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

nH=n0 H+n2I,
D(0)=0¯¯rE,B=μ0H,
¯¯r=r+iβ00000+10-10=¯¯r,
t B=-×E,
t D=×H.
B=μ0H,
D=D(0)+D(3)=0(¯¯r+χ|E2|)E,
(H/Eref)μ0/0H,D/(0/Eref)D,
E/ErefE,χEref2χ,
1ctHy=xEz,
1ctHz=-xEy,
1ctDy=-xHz,
1ctDz=xHy,
Dy=rEy+iβEz+χ(|Ey|2+|Ez|2)Ey,
Dz=rEz-iβEy+χ(|Ey|2+|Ez|2)Ez.
1ct H±=x E±,
1ct D±=-x H±,
D±=(r±β+χ[|E+|2|+|E-|2])E±.
E±=E0f(x, t)exp(iϕ)eˆ±,
H±=i0μ0 E0f(x, t)exp(iϕ)eˆ±,
Hy|j+1/2n+1/2-Hy|j+1/2n-1/2cΔt=Ez|j+1n-Ez|jnΔx,
Hz|j+1/2n+1/2-Hz|j+1/2n-1/2cΔt=-Ey|j+1n-Ey|jnΔx,
Dy|jn+1-Dy|jncΔt=-Hz|j+1/2n+1/2-Hz|j-1/2n+1/2Δx,
Dz|jn+1-Dz|jncΔt=Hy|j+1/2n+1/2-Hy|j-1/2n+1/2Δx,
Dy|jn+1=(r j+qj)Ey|jn+1+iβjEz|jn+1,
Dz|jn+1=(r j+qj)Ez|jn+1-iβjEy|jn+1,
qj=χj(|Ey|jn+1|2+|Ez|jn+1|2),
qj[(r j+qj)2-βj2]2
-χj(|uj|2+|vj|2)[(r j+qj)2+βj2]
+4χjβj(r j+qj)Im{ujvj*}=0,
qj(r j+qj)2-χj(|uj|2+|vj|2)=0,
x±3+x±2a±+x±b±-c±=0,
x±=F±(x),
F±(x)=A±(x)+19A±r±βχ+x2-23r±βχ+x,
A±(x)=127r±βχ+x3+12D±χ2+14D±χ4+127r±βχ+x3D±χ21/3.
x±2+x±a˜±+b˜±-c˜±=0,
 x±=G±(x),
G±(x)=-rβχ+x+Dχ21x.
E(x, t)=E+pump+E-probe=f(x, t)exp(iϕ)[E0eˆ+eˆ-].
2Ext1c2E2t=0,
D=E-iαH,
B=μH+iαE,
1cBt=-×E,
1cDt=×H.
Ez=-ωckBy,
Ey=ωckBz,
Hz=ωckDy,
Hy=-ωckDz.
DyDz=1-β21iβ-iβ1EyEz,
ByBz=μ1-β21iβ-iβ1HyHz,
D+D-=/(1-β)00/(1+β)E+E-,
B+B-=μ/(1-β)00μ/(1+β)H+H-.
B±=±ickωE±,
D±=ickωH±.
μ(1β)2E±=ckω2E±.
k±=1(1β) μωc,
k±=(μ±α)ωc.
DxDyDz=xx000˜iα˜0-iα˜˜ExEyEz,
B=μH,
DyDz=˜iα˜-iα˜˜EyEz.
D+D-=˜+α˜00˜-α˜E+E-.
k±=μ(˜±α˜)ωc.
μ(˜-α˜)=μ-α,
μ(˜+α˜)=μ+α,
˜=+α2μ,
α˜=2αμ.

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