Abstract

Theoretical models of photon traversal through quarter-wave dielectric stack barriers that arise due to Bragg reflection predict the saturation of the propagation time with the barrier length, known as the Hartman effect. This saturation is sensitive to the addition of single dielectric layers, varying significantly from sub-luminal to apparently super-luminal and vice versa. Our research tests the suitability of photonic bandgaps as an optical model for the tunneling process. Of particular importance is our observation of subtle structural changes in dielectric stacks drastically affecting photon traversal times, allowing for apparent sub- and super-luminal effects. We also introduce a simple model to link HOM visibility to wavepacket distortion that allows us to exclude this as a possible cause of the loss of contrast in the barrier penetration process.

© 2010 OSA

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References

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  1. T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33(12), 3427–3433 (1962).
    [CrossRef]
  2. V. Laude and P. Tournois, “Superluminal asymptotic tunneling times through one-dimensional photonic bandgap in quarter-wave-stack dielectric mirrors,” J. Opt. Soc. Am. B 16(1), 194–198 (1999).
    [CrossRef]
  3. D. L. Solli, J. J. Morehead, C. F. McCormick, and J. M. Hickman, “Comparative study of the propagation of light in bandgaps of photonic crystals and the tunneling of matter waves,” J. Opt. A 10, 075204 (2008).
  4. W. Yun-ping and Z. Dian-lin, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52(4), 2597–2600 (1995).
    [CrossRef] [PubMed]
  5. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
    [CrossRef] [PubMed]
  6. N. Brunner, V. Scarani, M. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93(20), 203902 (2004).
    [CrossRef] [PubMed]
  7. Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73(17), 2308–2311 (1994).
    [CrossRef] [PubMed]
  8. R. Y. Chiao and A. M. Steinberg, “Quantum optical studies of tunneling and other superluminal phenomena,” Phys. Scr. T76(1), 61–66 (1998).
    [CrossRef]
  9. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
    [CrossRef] [PubMed]
  10. S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007).
    [CrossRef] [PubMed]
  11. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68(16), 2421–2424 (1992).
    [CrossRef] [PubMed]
  12. D. Strekalov, A. B. Matsko, A. Savchenkov, and L. Maleki, “Quantum-correlation metrology with biphotons: where is the limit?” J. Mod. Opt. 52(16), 2233–2243 (2005).
    [CrossRef]
  13. N.B. Rutter, S.V. Polyakov, P. Lett, A. Migdall, and CLEO/QELS Conference Proceedings (2008).
  14. D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Opt. Express 16, 16005–16012 (2008), http://www.opticsinfobase.org/abstract.cfm?uri=oe-16-20-16005
    [CrossRef] [PubMed]
  15. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
    [CrossRef] [PubMed]
  16. N. Malkova, S. V. Polyakov, G. Bryant, and A. Migdall, “Effect of Surface Modes on Photon Propagation through Dielectric Bandgaps”, CLEO/QELS Conference Proceedings (2009).
  17. N. Malkova, G. Bryant, S. Polyakov, and A. Migdall, “Effect of surface modes on photon traversal through stop bands of dielectric stacks,” Phys. Rev. B 80(16), 165127 (2009).
    [CrossRef]
  18. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).
  19. N. Borjemscaia, S.V. Polyakov, P. Lett, and A. Migdall, in preparation.
  20. H. G. Winful, “Energy storage in superluminal barrier tunneling: Origins of the Hartman effect,” Opt. Express 10, 1491–1496 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-10-25-1491
    [PubMed]
  21. H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep. 436(1-2), 1–69 (2006).
    [CrossRef]

2009

N. Malkova, G. Bryant, S. Polyakov, and A. Migdall, “Effect of surface modes on photon traversal through stop bands of dielectric stacks,” Phys. Rev. B 80(16), 165127 (2009).
[CrossRef]

2008

D. L. Solli, J. J. Morehead, C. F. McCormick, and J. M. Hickman, “Comparative study of the propagation of light in bandgaps of photonic crystals and the tunneling of matter waves,” J. Opt. A 10, 075204 (2008).

2007

S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007).
[CrossRef] [PubMed]

2006

H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep. 436(1-2), 1–69 (2006).
[CrossRef]

2005

D. Strekalov, A. B. Matsko, A. Savchenkov, and L. Maleki, “Quantum-correlation metrology with biphotons: where is the limit?” J. Mod. Opt. 52(16), 2233–2243 (2005).
[CrossRef]

2004

N. Brunner, V. Scarani, M. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93(20), 203902 (2004).
[CrossRef] [PubMed]

1999

V. Laude and P. Tournois, “Superluminal asymptotic tunneling times through one-dimensional photonic bandgap in quarter-wave-stack dielectric mirrors,” J. Opt. Soc. Am. B 16(1), 194–198 (1999).
[CrossRef]

1998

R. Y. Chiao and A. M. Steinberg, “Quantum optical studies of tunneling and other superluminal phenomena,” Phys. Scr. T76(1), 61–66 (1998).
[CrossRef]

1996

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[CrossRef] [PubMed]

1995

W. Yun-ping and Z. Dian-lin, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52(4), 2597–2600 (1995).
[CrossRef] [PubMed]

1994

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73(17), 2308–2311 (1994).
[CrossRef] [PubMed]

1993

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

1992

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68(16), 2421–2424 (1992).
[CrossRef] [PubMed]

1987

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

1962

T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33(12), 3427–3433 (1962).
[CrossRef]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[CrossRef] [PubMed]

Brunner, N.

N. Brunner, V. Scarani, M. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93(20), 203902 (2004).
[CrossRef] [PubMed]

Bryant, G.

N. Malkova, G. Bryant, S. Polyakov, and A. Migdall, “Effect of surface modes on photon traversal through stop bands of dielectric stacks,” Phys. Rev. B 80(16), 165127 (2009).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao and A. M. Steinberg, “Quantum optical studies of tunneling and other superluminal phenomena,” Phys. Scr. T76(1), 61–66 (1998).
[CrossRef]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68(16), 2421–2424 (1992).
[CrossRef] [PubMed]

Dian-lin, Z.

W. Yun-ping and Z. Dian-lin, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52(4), 2597–2600 (1995).
[CrossRef] [PubMed]

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[CrossRef] [PubMed]

Gisin, N.

N. Brunner, V. Scarani, M. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93(20), 203902 (2004).
[CrossRef] [PubMed]

Hartman, T. E.

T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33(12), 3427–3433 (1962).
[CrossRef]

Hickman, J. M.

D. L. Solli, J. J. Morehead, C. F. McCormick, and J. M. Hickman, “Comparative study of the propagation of light in bandgaps of photonic crystals and the tunneling of matter waves,” J. Opt. A 10, 075204 (2008).

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Krausz, F.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73(17), 2308–2311 (1994).
[CrossRef] [PubMed]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68(16), 2421–2424 (1992).
[CrossRef] [PubMed]

Laude, V.

V. Laude and P. Tournois, “Superluminal asymptotic tunneling times through one-dimensional photonic bandgap in quarter-wave-stack dielectric mirrors,” J. Opt. Soc. Am. B 16(1), 194–198 (1999).
[CrossRef]

Legré, M.

N. Brunner, V. Scarani, M. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93(20), 203902 (2004).
[CrossRef] [PubMed]

Maleki, L.

D. Strekalov, A. B. Matsko, A. Savchenkov, and L. Maleki, “Quantum-correlation metrology with biphotons: where is the limit?” J. Mod. Opt. 52(16), 2233–2243 (2005).
[CrossRef]

Malkova, N.

N. Malkova, G. Bryant, S. Polyakov, and A. Migdall, “Effect of surface modes on photon traversal through stop bands of dielectric stacks,” Phys. Rev. B 80(16), 165127 (2009).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Matsko, A. B.

D. Strekalov, A. B. Matsko, A. Savchenkov, and L. Maleki, “Quantum-correlation metrology with biphotons: where is the limit?” J. Mod. Opt. 52(16), 2233–2243 (2005).
[CrossRef]

McCormick, C. F.

D. L. Solli, J. J. Morehead, C. F. McCormick, and J. M. Hickman, “Comparative study of the propagation of light in bandgaps of photonic crystals and the tunneling of matter waves,” J. Opt. A 10, 075204 (2008).

Migdall, A.

N. Malkova, G. Bryant, S. Polyakov, and A. Migdall, “Effect of surface modes on photon traversal through stop bands of dielectric stacks,” Phys. Rev. B 80(16), 165127 (2009).
[CrossRef]

Migdall, A. L.

S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007).
[CrossRef] [PubMed]

Morehead, J. J.

D. L. Solli, J. J. Morehead, C. F. McCormick, and J. M. Hickman, “Comparative study of the propagation of light in bandgaps of photonic crystals and the tunneling of matter waves,” J. Opt. A 10, 075204 (2008).

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Polyakov, S.

N. Malkova, G. Bryant, S. Polyakov, and A. Migdall, “Effect of surface modes on photon traversal through stop bands of dielectric stacks,” Phys. Rev. B 80(16), 165127 (2009).
[CrossRef]

Polyakov, S. V.

S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007).
[CrossRef] [PubMed]

Savchenkov, A.

D. Strekalov, A. B. Matsko, A. Savchenkov, and L. Maleki, “Quantum-correlation metrology with biphotons: where is the limit?” J. Mod. Opt. 52(16), 2233–2243 (2005).
[CrossRef]

Scalora, M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[CrossRef] [PubMed]

Scarani, V.

N. Brunner, V. Scarani, M. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93(20), 203902 (2004).
[CrossRef] [PubMed]

Solli, D. L.

D. L. Solli, J. J. Morehead, C. F. McCormick, and J. M. Hickman, “Comparative study of the propagation of light in bandgaps of photonic crystals and the tunneling of matter waves,” J. Opt. A 10, 075204 (2008).

Spielmann, Ch.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73(17), 2308–2311 (1994).
[CrossRef] [PubMed]

Steinberg, A. M.

R. Y. Chiao and A. M. Steinberg, “Quantum optical studies of tunneling and other superluminal phenomena,” Phys. Scr. T76(1), 61–66 (1998).
[CrossRef]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68(16), 2421–2424 (1992).
[CrossRef] [PubMed]

Stingl, A.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73(17), 2308–2311 (1994).
[CrossRef] [PubMed]

Strekalov, D.

D. Strekalov, A. B. Matsko, A. Savchenkov, and L. Maleki, “Quantum-correlation metrology with biphotons: where is the limit?” J. Mod. Opt. 52(16), 2233–2243 (2005).
[CrossRef]

Szipöcs, R.

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73(17), 2308–2311 (1994).
[CrossRef] [PubMed]

Tournois, P.

V. Laude and P. Tournois, “Superluminal asymptotic tunneling times through one-dimensional photonic bandgap in quarter-wave-stack dielectric mirrors,” J. Opt. Soc. Am. B 16(1), 194–198 (1999).
[CrossRef]

Wegmüller, M.

N. Brunner, V. Scarani, M. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93(20), 203902 (2004).
[CrossRef] [PubMed]

Winful, H. G.

H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep. 436(1-2), 1–69 (2006).
[CrossRef]

Yun-ping, W.

W. Yun-ping and Z. Dian-lin, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52(4), 2597–2600 (1995).
[CrossRef] [PubMed]

J. Appl. Phys.

T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33(12), 3427–3433 (1962).
[CrossRef]

J. Mod. Opt.

D. Strekalov, A. B. Matsko, A. Savchenkov, and L. Maleki, “Quantum-correlation metrology with biphotons: where is the limit?” J. Mod. Opt. 52(16), 2233–2243 (2005).
[CrossRef]

J. Opt. A

D. L. Solli, J. J. Morehead, C. F. McCormick, and J. M. Hickman, “Comparative study of the propagation of light in bandgaps of photonic crystals and the tunneling of matter waves,” J. Opt. A 10, 075204 (2008).

J. Opt. Soc. Am. B

V. Laude and P. Tournois, “Superluminal asymptotic tunneling times through one-dimensional photonic bandgap in quarter-wave-stack dielectric mirrors,” J. Opt. Soc. Am. B 16(1), 194–198 (1999).
[CrossRef]

Opt. Express

S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon- based method for determining photoncounting detection efficiency,” Opt. Express 15(4), 1390–1407 (2007).
[CrossRef] [PubMed]

Phys. Rep.

H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox,” Phys. Rep. 436(1-2), 1–69 (2006).
[CrossRef]

Phys. Rev. A

W. Yun-ping and Z. Dian-lin, “Reshaping, path uncertainty, and superluminal traveling,” Phys. Rev. A 52(4), 2597–2600 (1995).
[CrossRef] [PubMed]

Phys. Rev. B

N. Malkova, G. Bryant, S. Polyakov, and A. Migdall, “Effect of surface modes on photon traversal through stop bands of dielectric stacks,” Phys. Rev. B 80(16), 165127 (2009).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71(5), 708–711 (1993).
[CrossRef] [PubMed]

N. Brunner, V. Scarani, M. Wegmüller, M. Legré, and N. Gisin, “Direct measurement of superluminal group velocity and signal velocity in an optical fiber,” Phys. Rev. Lett. 93(20), 203902 (2004).
[CrossRef] [PubMed]

Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73(17), 2308–2311 (1994).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68(16), 2421–2424 (1992).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Phys. Scr.

R. Y. Chiao and A. M. Steinberg, “Quantum optical studies of tunneling and other superluminal phenomena,” Phys. Scr. T76(1), 61–66 (1998).
[CrossRef]

Other

N. Malkova, S. V. Polyakov, G. Bryant, and A. Migdall, “Effect of Surface Modes on Photon Propagation through Dielectric Bandgaps”, CLEO/QELS Conference Proceedings (2009).

N.B. Rutter, S.V. Polyakov, P. Lett, A. Migdall, and CLEO/QELS Conference Proceedings (2008).

D. J. Papoular, P. Clade, S. V. Polyakov, C. F. McCormick, A. L. Migdall, and P. D. Lett, “Measuring optical tunneling times using a Hong-Ou-Mandel interferometer,” Opt. Express 16, 16005–16012 (2008), http://www.opticsinfobase.org/abstract.cfm?uri=oe-16-20-16005
[CrossRef] [PubMed]

L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).

N. Borjemscaia, S.V. Polyakov, P. Lett, and A. Migdall, in preparation.

H. G. Winful, “Energy storage in superluminal barrier tunneling: Origins of the Hartman effect,” Opt. Express 10, 1491–1496 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-10-25-1491
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

Experimental apparatus. Two photons created via parametric down conversion are sent to a Hong-Ou-Mandel interferometer. The sample holder positions the reference and sample regions into and out of the beam. A mirror on a piezo actuator (PZT) provides fine motion control of the path length for scanning over the Hong-Ou-Mandel dip.

Fig. 2
Fig. 2

Stop-bands of the four structures studied, measured with a spectrophotometer. The photons are filtered, before entering HOM interferometer by the two filters, whose measured normalized transmittances are also shown.

Fig. 3
Fig. 3

a) Theoretical prediction of propagation delay times for different dielectric stack configurations. Each of the structures is responsible for a different propagation delay branch of the graph. The line represents propagation delay of a photon in an equivalent thickness of vacuum. Values below this luminal line represent superluminal propagation. Values above the luminal line represent subluminal propagation. Large symbols show experimental measurements with uncertainties being about half the size of the symbols; b) Relative HOM dip visibilities for the four stack types.

Fig. 4
Fig. 4

Measured HOM dip profiles. Propagation (group) delays are the mean difference between minima of the fits (indicated by vertical lines). The reference is an uncoated substrate (open circles and dotted lines). Sample regions are a) (LH)15L and b) (HL)15H (closed circles and solid lines). The sample profiles are scaled as indicated on the figures. The uncertainties associated with the datapoints are smaller than the size of the symbols

Tables (1)

Tables Icon

Table 1 Predicted and measured delays and dip visibilities

Metrics