Abstract

The phase modulation and dispersion property of a Fabry–Perot etalon are investigated analytically. It is demonstrated that within the resonant dispersion region in the etalon transmission spectrum, effective time delay of light pulse propagation can be achieved, and the maximum delay period can be simply related to the mirror reflectivity and optical length of the etalon. With a much simplified model, the influences of etalon parameters on the transmitted Gaussian pulse are evaluated, and simple relations regarding pulse distortion and energy loss are obtained to illustrate the temporal properties of the etalon.

© 2001 Optical Society of America

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References

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  1. M. O. Scully, M. Fleischhauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360–1363 (1992).
    [CrossRef] [PubMed]
  2. O. Schmidt, R. Wynands, Z. Hussein, D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
    [CrossRef] [PubMed]
  3. J. Marangos, “Slow light in cool atoms,” Nature 397, 559–560 (1999).
    [CrossRef]
  4. A. M. Steinberg, P. G. Kwiat, R. Y. Chiao, “Measurement of single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
    [CrossRef] [PubMed]
  5. A. M. Steinberg, R. Y. Chiao, “Subfemtosecond determination of transmission delay time for a dielectric mirror (photonic band gap) as a function of the angle of incidence,” Phys. Rev. A 51, 3525–3528 (1995).
    [CrossRef] [PubMed]
  6. Ch. Spielmann, R. Szipocs, A. Stingl, F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
    [CrossRef] [PubMed]
  7. M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
    [CrossRef]
  8. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
    [CrossRef] [PubMed]
  9. S. Zhu, N. Liu, H. Zheng, H. Chen, “Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures,” Opt. Commun. 174, 139–144 (2000).
    [CrossRef]
  10. D. Huber, J. B. Carroll, “Time domain response of an optically frequency swept Fabry–Perot interferometer,” Appl. Opt. 25, 2386–2390 (1986).
    [CrossRef]
  11. G. Cesini, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry–Perot interferometer to amplitude-modulated light beams,” Opt. Acta 24, 1217–1236 (1977).
    [CrossRef]
  12. C. Roychoudhuri, “Response of Fabry–Perot interferometers to light pulses of very short duration,” J. Opt. Soc. Am. 65, 1418–1426 (1975).
    [CrossRef]
  13. A. Giazatto, “Interferometric detection of gravitation waves,” Phys. Rep. 182, 365–425 (1989).
    [CrossRef]
  14. P. Grosse, V. Offermann, “Analysis of reflectance data using the Kramers–Kronig relations,” Appl. Phys. A 52, 138–144 (1991).
    [CrossRef]
  15. S. Maeda, G. Thyagarajan, P. N. Schatz, “Absolute infrared intensity measurement in thin films. II. Solids deposited on Halide plates,” J. Chem. Phys. 39, 3474–3481 (1963).
    [CrossRef]
  16. K. Kozima, W. Suëtaka, P. N. Schatz, “Optical constants of thin films by a Kramers–Kronig method,” J. Opt. Soc. Am. 56, 181–184 (1966).
    [CrossRef]
  17. J. P. Dowling, C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345–351 (1994).
    [CrossRef]
  18. E. H. Hauge, J. A. Støvneng, “Tunneling time: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
    [CrossRef]

2000 (1)

S. Zhu, N. Liu, H. Zheng, H. Chen, “Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures,” Opt. Commun. 174, 139–144 (2000).
[CrossRef]

1999 (1)

J. Marangos, “Slow light in cool atoms,” Nature 397, 559–560 (1999).
[CrossRef]

1996 (2)

O. Schmidt, R. Wynands, Z. Hussein, D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

1995 (1)

A. M. Steinberg, R. Y. Chiao, “Subfemtosecond determination of transmission delay time for a dielectric mirror (photonic band gap) as a function of the angle of incidence,” Phys. Rev. A 51, 3525–3528 (1995).
[CrossRef] [PubMed]

1994 (2)

Ch. Spielmann, R. Szipocs, A. Stingl, F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (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]

1993 (1)

A. M. Steinberg, P. G. Kwiat, R. Y. Chiao, “Measurement of single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

1992 (1)

M. O. Scully, M. Fleischhauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360–1363 (1992).
[CrossRef] [PubMed]

1991 (2)

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

P. Grosse, V. Offermann, “Analysis of reflectance data using the Kramers–Kronig relations,” Appl. Phys. A 52, 138–144 (1991).
[CrossRef]

1989 (2)

A. Giazatto, “Interferometric detection of gravitation waves,” Phys. Rep. 182, 365–425 (1989).
[CrossRef]

E. H. Hauge, J. A. Støvneng, “Tunneling time: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
[CrossRef]

1986 (1)

1977 (1)

G. Cesini, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry–Perot interferometer to amplitude-modulated light beams,” Opt. Acta 24, 1217–1236 (1977).
[CrossRef]

1975 (1)

1966 (1)

1963 (1)

S. Maeda, G. Thyagarajan, P. N. Schatz, “Absolute infrared intensity measurement in thin films. II. Solids deposited on Halide plates,” J. Chem. Phys. 39, 3474–3481 (1963).
[CrossRef]

Bendickson, J. M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Boemer, M. J.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Bowden, C. M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

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

Brommer, K. D.

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

Carroll, J. B.

Cesini, G.

G. Cesini, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry–Perot interferometer to amplitude-modulated light beams,” Opt. Acta 24, 1217–1236 (1977).
[CrossRef]

Chen, H.

S. Zhu, N. Liu, H. Zheng, H. Chen, “Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures,” Opt. Commun. 174, 139–144 (2000).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg, R. Y. Chiao, “Subfemtosecond determination of transmission delay time for a dielectric mirror (photonic band gap) as a function of the angle of incidence,” Phys. Rev. A 51, 3525–3528 (1995).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, R. Y. Chiao, “Measurement of single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

Dowling, J. P.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

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

Fleischhauer, M.

M. O. Scully, M. Fleischhauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360–1363 (1992).
[CrossRef] [PubMed]

Flynn, R. J.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Fork, R. L.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Giazatto, A.

A. Giazatto, “Interferometric detection of gravitation waves,” Phys. Rep. 182, 365–425 (1989).
[CrossRef]

Gmitter, T. J.

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

Grosse, P.

P. Grosse, V. Offermann, “Analysis of reflectance data using the Kramers–Kronig relations,” Appl. Phys. A 52, 138–144 (1991).
[CrossRef]

Guattari, G.

G. Cesini, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry–Perot interferometer to amplitude-modulated light beams,” Opt. Acta 24, 1217–1236 (1977).
[CrossRef]

Hauge, E. H.

E. H. Hauge, J. A. Støvneng, “Tunneling time: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
[CrossRef]

Huber, D.

Hussein, Z.

O. Schmidt, R. Wynands, Z. Hussein, D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

Joannopoulos, J. D.

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

Kozima, K.

Krausz, F.

Ch. Spielmann, R. Szipocs, A. Stingl, F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef] [PubMed]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, R. Y. Chiao, “Measurement of single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

Leavitt, R. P.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Ledbetter, H. S.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Liu, N.

S. Zhu, N. Liu, H. Zheng, H. Chen, “Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures,” Opt. Commun. 174, 139–144 (2000).
[CrossRef]

Lucarini, G.

G. Cesini, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry–Perot interferometer to amplitude-modulated light beams,” Opt. Acta 24, 1217–1236 (1977).
[CrossRef]

Maeda, S.

S. Maeda, G. Thyagarajan, P. N. Schatz, “Absolute infrared intensity measurement in thin films. II. Solids deposited on Halide plates,” J. Chem. Phys. 39, 3474–3481 (1963).
[CrossRef]

Marangos, J.

J. Marangos, “Slow light in cool atoms,” Nature 397, 559–560 (1999).
[CrossRef]

Meade, R. D.

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

Meschede, D.

O. Schmidt, R. Wynands, Z. Hussein, D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

Offermann, V.

P. Grosse, V. Offermann, “Analysis of reflectance data using the Kramers–Kronig relations,” Appl. Phys. A 52, 138–144 (1991).
[CrossRef]

Palma, C.

G. Cesini, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry–Perot interferometer to amplitude-modulated light beams,” Opt. Acta 24, 1217–1236 (1977).
[CrossRef]

Rappe, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, 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. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Roychoudhuri, C.

Scalora, M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Schatz, P. N.

K. Kozima, W. Suëtaka, P. N. Schatz, “Optical constants of thin films by a Kramers–Kronig method,” J. Opt. Soc. Am. 56, 181–184 (1966).
[CrossRef]

S. Maeda, G. Thyagarajan, P. N. Schatz, “Absolute infrared intensity measurement in thin films. II. Solids deposited on Halide plates,” J. Chem. Phys. 39, 3474–3481 (1963).
[CrossRef]

Schmidt, O.

O. Schmidt, R. Wynands, Z. Hussein, D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

Scully, M. O.

M. O. Scully, M. Fleischhauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360–1363 (1992).
[CrossRef] [PubMed]

Spielmann, Ch.

Ch. Spielmann, R. Szipocs, A. Stingl, F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef] [PubMed]

Steinberg, A. M.

A. M. Steinberg, R. Y. Chiao, “Subfemtosecond determination of transmission delay time for a dielectric mirror (photonic band gap) as a function of the angle of incidence,” Phys. Rev. A 51, 3525–3528 (1995).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, R. Y. Chiao, “Measurement of single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

Stingl, A.

Ch. Spielmann, R. Szipocs, A. Stingl, F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef] [PubMed]

Støvneng, J. A.

E. H. Hauge, J. A. Støvneng, “Tunneling time: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
[CrossRef]

Suëtaka, W.

Szipocs, R.

Ch. Spielmann, R. Szipocs, A. Stingl, F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef] [PubMed]

Thyagarajan, G.

S. Maeda, G. Thyagarajan, P. N. Schatz, “Absolute infrared intensity measurement in thin films. II. Solids deposited on Halide plates,” J. Chem. Phys. 39, 3474–3481 (1963).
[CrossRef]

Tocci, M. D.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Wynands, R.

O. Schmidt, R. Wynands, Z. Hussein, D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

Yablonovitch, E.

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

Zheng, H.

S. Zhu, N. Liu, H. Zheng, H. Chen, “Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures,” Opt. Commun. 174, 139–144 (2000).
[CrossRef]

Zhu, S.

S. Zhu, N. Liu, H. Zheng, H. Chen, “Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures,” Opt. Commun. 174, 139–144 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

P. Grosse, V. Offermann, “Analysis of reflectance data using the Kramers–Kronig relations,” Appl. Phys. A 52, 138–144 (1991).
[CrossRef]

J. Chem. Phys. (1)

S. Maeda, G. Thyagarajan, P. N. Schatz, “Absolute infrared intensity measurement in thin films. II. Solids deposited on Halide plates,” J. Chem. Phys. 39, 3474–3481 (1963).
[CrossRef]

J. Mod. Opt. (1)

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. (2)

Nature (1)

J. Marangos, “Slow light in cool atoms,” Nature 397, 559–560 (1999).
[CrossRef]

Opt. Acta (1)

G. Cesini, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry–Perot interferometer to amplitude-modulated light beams,” Opt. Acta 24, 1217–1236 (1977).
[CrossRef]

Opt. Commun. (1)

S. Zhu, N. Liu, H. Zheng, H. Chen, “Time delay of light propagation through defect modes of one-dimensional photonic band-gap structures,” Opt. Commun. 174, 139–144 (2000).
[CrossRef]

Phys. Rep. (1)

A. Giazatto, “Interferometric detection of gravitation waves,” Phys. Rep. 182, 365–425 (1989).
[CrossRef]

Phys. Rev. A (2)

O. Schmidt, R. Wynands, Z. Hussein, D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

A. M. Steinberg, R. Y. Chiao, “Subfemtosecond determination of transmission delay time for a dielectric mirror (photonic band gap) as a function of the angle of incidence,” Phys. Rev. A 51, 3525–3528 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Boemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tun-able group delay with minimal distortion and loss,” Phys. Rev. E 54, R1078–R1081 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

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

Ch. Spielmann, R. Szipocs, A. Stingl, F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef] [PubMed]

M. O. Scully, M. Fleischhauer, “High-sensitivity magnetometer based on index-enhanced media,” Phys. Rev. Lett. 69, 1360–1363 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, R. Y. Chiao, “Measurement of single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

E. H. Hauge, J. A. Støvneng, “Tunneling time: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Typical F–P etalon with nominal refractive index n0, reflectivity R, and thickness L. The incident and transmitted electric fields are denoted by Ei(ω) and Et(ω), respectively, where ω is the angular frequency of the waves.

Fig. 2
Fig. 2

(a) Power transmission T (ω), (b) effective real refractive index n (ω), and (c) effective extinction coefficient κ(ω) around the resonant frequency ωt0=π for three reflectivities, R=0.999, 0.99, and 0.9.

Fig. 3
Fig. 3

(a) Effective dispersion dn(ω)/dω and (b) effective group index ng of the etalon around the resonant frequency ωt0=π for R=0.999, 0.99, and 0.9.

Fig. 4
Fig. 4

Transmitted signal for an incident Gaussian pulse through 1, equal-length free space; 2, one etalon with 50-mm optical thickness; 3, five etalons with 10-mm optical thickness; 4, ten etalons with 5-mm optical thickness; and 5, fifty etalons with 1-mm optical thickness, with the input pulse FWHM width of (a) 100 ns and (b) 80 ns, where the etalon mirrors have reflectivity of R=0.999.

Fig. 5
Fig. 5

Amplitude filtering function (solid curves) and the approximate Gaussian function (dashed curves) around a resonant angular frequency ω0 for (a) R=0.999 and (b) R=0.99.

Fig. 6
Fig. 6

Comparison of the numerical result in Section 4 and the approximate result in Section 5. The input Gaussian pulse is assumed to have a FWHM width of (a) 100 ns and (b) 50 ns. Curve 1 is the output with propagation in a 10-mm free space and 2 and 3 are results after ten 1-mm optical length etalons, where 2 is from the numerical method and 3 is from the approximate approach.

Equations (40)

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t(ω)=Et(ω)Ei(ω)=exp(-iωt0) 1-R1-R exp(-i2ωt0),
|t(ω)| =1-R[1+R2-2R cos(2ωt0)]1/2,
ϕ(ω)=ωt0+arctanR sin(2ωt0)1-R cos(2ωt0).
n(ω)=cωL ϕ(ω)=n0ωt0 ϕ(ω),
κ(ω)=-cωLln|t(ω)| =-n0ωt0ln|t(ω)|.
n(ω)=n01+1ωt0arctanR sin(2ωt0)1-R cos(2ωt0),
κ(ω)=-n0ωt0ln1-R[1+R2-2R cos(2ωt0)]1/2,
n(ω)=n0+2ωπPV0κ(ω)ω2-ω2dω,
dn(ω)dω=n0ωt0-1ωarctanR sin(2ωt0)1-R cos(2ωt0)+2Rt0[cos(2ωt0)-R]1+R2-2R cos(2ωt0)
ng(ω)=n(ω)+ω dn(ω)dω=n01+2R[cos(2ωt0)-R]1+R2-2R cos(2ωt0).
η=1+R2-2R cos(2ωt0)1-R2.
η0=1-R1+R,
ΔωFWHM=πt0F,
τ=ngLc=t01-R21+R2+2R cos(2ωt0).
τ=1NTiNiti=1Pipiti,
P=(1-R)21+R2-2R cos(2ωt0).
pi=R2(i-1)(1-R)2.
τ=t01-R21+R2-2R cos(2ωt0),
vt=cn01+R2-2R cos(2ωt0)1-R2
Ei(t)=E0exp[-(t/a)2]exp(iω0t),
E˜i(ω)=aE02exp-a24 (ω-ω0)2,
E˜t(ω)=(1-R) aE02exp-a24 (ω-ω0)2×exp(-iωt0)1-R exp(-2iωt0),
Et(t)=12π-+E˜t(ω)dω
=1-R2π aE0exp[iω0(t-t0)]×-+dω exp(-a2ω2/4)exp[iω(t-t0)]1-R exp[-2i(ω+ω0)t0],
Et(t)|R=0=E0exp[-(t-t0)2/a2]×exp[iω0(t-t0)],
Et(t)=1-R2π aE0exp[iω0(t-t0)]×-+FG1dω+i-+FG2dω,
F=exp(-a2ω2/4)1+R2-2R cos[2(ω+ω0)t0],
G1=cos[ω(t-t0)]-R cos[ω(t+t0)+2ω0t0],
G2=sin[ω(t-t0)]-R sin[ω(t+t0)+2ω0t0].
It(t)=(1-R)24π a2I0-+FG1dω2+-+FG2dω2,
AG(ω)=exp[-(ω-ω0)2/Ω2],
ϕ(ω)=ϕ(ω0)+ϕ(ω0)(ω-ω0)+12! ϕ(ω0)(ω-ω0)2+13! ϕ(ω0)(ω-ω0)3+ ,
ϕ(ω0)=ω0t0ϕ(ω0)=t0/η0,
ϕ(ω0)=0 ϕ(ω0)=-8Rt03/(1-R)3.
t(ω)=AG(ω)exp[-iϕT(ω)],
Et(t)=aΩE0[4+a2Ω2]1/2exp[iω0(t-t0)]×exp-Ω2t-t0η024+a2Ω2
It(t)=a2Ω024+a2Ω2 I0exp-2Ω2t-t0η024+a2Ω2,
ξW=1+4a2Ω21/2,
ξP=1+4a2Ω2-1,
ξE=1+4a2Ω2-1/2.

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