Abstract

Pulse reshaping effects that give rise to fast and slow light phenomena are inextricably linked to the dynamics of energy exchange between the pulse and the propagation medium. Energy that is dissipated from the pulse can no longer participate in this exchange process, but previous methods of calculating real-time dissipation are not valid for extended propagation media. We present a method for calculating real-time dissipation that is valid for electromagnetic pulse propagation in extended media. This method allows one to divide the energy stored in an extended medium into the portion that can be later transmitted out of the medium, and that portion which must be lost to either dissipation or reflection.

© 2014 Optical Society of America

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References

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  1. L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
    [CrossRef]
  2. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
    [CrossRef]
  3. S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
    [CrossRef] [PubMed]
  4. S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
    [CrossRef]
  5. J. Sharping, Y. Okawachi, A. Gaeta, “Wide bandwidth slow light using a raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005).
    [CrossRef] [PubMed]
  6. R. Camacho, M. Pack, J. Howell, R. Boyd, “Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor,” Phys. Rev. Lett. 98, 153601 (2007).
    [CrossRef] [PubMed]
  7. R. W. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908–1915 (2009).
    [CrossRef]
  8. Z. Shi, R. W. Boyd, D. J. Gauthier, C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32, 915–917 (2007).
    [CrossRef] [PubMed]
  9. F. Xia, L. Skaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
    [CrossRef]
  10. M. Ware, S. Glasgow, J. Peatross, “Role of group velocity in tracking field energy in linear dielectrics,” Opt. Express 9, 506–518 (2001).
    [CrossRef] [PubMed]
  11. V. S. Zapasskii, G. G. Kozlov, “A saturable absorber, coherent population oscillations, and slow light,” Opt. Spectrosc. 100, 419–424 (2006).
    [CrossRef]
  12. M. Ware, S. Glasgow, J. Peatross, “Energy transport in linear dielectrics,” Opt. Express 9, 519–532 (2001).
    [CrossRef] [PubMed]
  13. S. Glasgow, M. Meilstrup, J. Peatross, M. Ware, “Real-time recoverable and irrecoverable energy in dispersive-dissipative dielectrics,” Phys. Rev. E 75, 016616 (2007).
    [CrossRef]
  14. S. A. Glasgow, M. Ware, “Real-time dissipation of optical pulses in passive dielectrics,” Phys. Rev. A 80, 043817 (2009).
    [CrossRef]
  15. G. Gentili, “Free enthalpies, free energies and norms for dielectrics with fading memory,” Continuum Mech. Thermodyn. 8, 201–214 (1996).
    [CrossRef]
  16. V. Berti, G. Gentili, “The minimum free energy for isothermal dielectrics with memory,” J. Non-Equilib. Thermodyn. 24, 154–176 (1999).
  17. M. Fabrizio, A. Morro, “Dissipativity and irreversibility of electromagnetic systems,” Math. Models Methods Appl. Sci. 10, 217–246 (2000).
    [CrossRef]
  18. L. Deseri, G. Gentili, M. Golden, “An explicit formula for the minimum free energy in linear viscoelasticity,” J. Elasticity 54, 141–185 (1999).
    [CrossRef]
  19. J. M. Golden, “Consequences of non-uniqueness in the free energy of materials with memory,” Int. J. Eng. Sci. 39, 53–70 (2001).
    [CrossRef]
  20. J. M. Golden, “A proposal concerning the physical rate of dissipation in materials with memory,” Q. Appl. Math. 63, 117–155 (2005).

2009 (2)

R. W. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908–1915 (2009).
[CrossRef]

S. A. Glasgow, M. Ware, “Real-time dissipation of optical pulses in passive dielectrics,” Phys. Rev. A 80, 043817 (2009).
[CrossRef]

2007 (4)

F. Xia, L. Skaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

S. Glasgow, M. Meilstrup, J. Peatross, M. Ware, “Real-time recoverable and irrecoverable energy in dispersive-dissipative dielectrics,” Phys. Rev. E 75, 016616 (2007).
[CrossRef]

R. Camacho, M. Pack, J. Howell, R. Boyd, “Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor,” Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Z. Shi, R. W. Boyd, D. J. Gauthier, C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32, 915–917 (2007).
[CrossRef] [PubMed]

2006 (1)

V. S. Zapasskii, G. G. Kozlov, “A saturable absorber, coherent population oscillations, and slow light,” Opt. Spectrosc. 100, 419–424 (2006).
[CrossRef]

2005 (2)

J. M. Golden, “A proposal concerning the physical rate of dissipation in materials with memory,” Q. Appl. Math. 63, 117–155 (2005).

J. Sharping, Y. Okawachi, A. Gaeta, “Wide bandwidth slow light using a raman fiber amplifier,” Opt. Express 13, 6092–6098 (2005).
[CrossRef] [PubMed]

2004 (1)

S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
[CrossRef]

2001 (3)

2000 (2)

M. Fabrizio, A. Morro, “Dissipativity and irreversibility of electromagnetic systems,” Math. Models Methods Appl. Sci. 10, 217–246 (2000).
[CrossRef]

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

1999 (4)

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

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

L. Deseri, G. Gentili, M. Golden, “An explicit formula for the minimum free energy in linear viscoelasticity,” J. Elasticity 54, 141–185 (1999).
[CrossRef]

V. Berti, G. Gentili, “The minimum free energy for isothermal dielectrics with memory,” J. Non-Equilib. Thermodyn. 24, 154–176 (1999).

1996 (1)

G. Gentili, “Free enthalpies, free energies and norms for dielectrics with fading memory,” Continuum Mech. Thermodyn. 8, 201–214 (1996).
[CrossRef]

Behroozi, C. H.

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

Berti, V.

V. Berti, G. Gentili, “The minimum free energy for isothermal dielectrics with memory,” J. Non-Equilib. Thermodyn. 24, 154–176 (1999).

Boyd, R.

R. Camacho, M. Pack, J. Howell, R. Boyd, “Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor,” Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Boyd, R. W.

Camacho, R.

R. Camacho, M. Pack, J. Howell, R. Boyd, “Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor,” Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Chang, S.-W.

S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Chang-Hasnian, C. J.

S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Chuang, S.-L.

S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Deseri, L.

L. Deseri, G. Gentili, M. Golden, “An explicit formula for the minimum free energy in linear viscoelasticity,” J. Elasticity 54, 141–185 (1999).
[CrossRef]

Dudley, C. C.

Dutton, Z.

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

Fabrizio, M.

M. Fabrizio, A. Morro, “Dissipativity and irreversibility of electromagnetic systems,” Math. Models Methods Appl. Sci. 10, 217–246 (2000).
[CrossRef]

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Gaeta, A.

Gauthier, D. J.

Gentili, G.

L. Deseri, G. Gentili, M. Golden, “An explicit formula for the minimum free energy in linear viscoelasticity,” J. Elasticity 54, 141–185 (1999).
[CrossRef]

V. Berti, G. Gentili, “The minimum free energy for isothermal dielectrics with memory,” J. Non-Equilib. Thermodyn. 24, 154–176 (1999).

G. Gentili, “Free enthalpies, free energies and norms for dielectrics with fading memory,” Continuum Mech. Thermodyn. 8, 201–214 (1996).
[CrossRef]

Glasgow, S.

Glasgow, S. A.

S. A. Glasgow, M. Ware, “Real-time dissipation of optical pulses in passive dielectrics,” Phys. Rev. A 80, 043817 (2009).
[CrossRef]

Golden, J. M.

J. M. Golden, “A proposal concerning the physical rate of dissipation in materials with memory,” Q. Appl. Math. 63, 117–155 (2005).

J. M. Golden, “Consequences of non-uniqueness in the free energy of materials with memory,” Int. J. Eng. Sci. 39, 53–70 (2001).
[CrossRef]

Golden, M.

L. Deseri, G. Gentili, M. Golden, “An explicit formula for the minimum free energy in linear viscoelasticity,” J. Elasticity 54, 141–185 (1999).
[CrossRef]

Görlitz, A.

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Gupta, S.

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Gustavson, T. L.

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Harris, S. E.

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

Hau, L. V.

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

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Howell, J.

R. Camacho, M. Pack, J. Howell, R. Boyd, “Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor,” Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Inouye, S.

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Ketterle, W.

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Kozlov, G. G.

V. S. Zapasskii, G. G. Kozlov, “A saturable absorber, coherent population oscillations, and slow light,” Opt. Spectrosc. 100, 419–424 (2006).
[CrossRef]

Ku, P.-C.

S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Löw, R. F.

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Lukin, M. D.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Meilstrup, M.

S. Glasgow, M. Meilstrup, J. Peatross, M. Ware, “Real-time recoverable and irrecoverable energy in dispersive-dissipative dielectrics,” Phys. Rev. E 75, 016616 (2007).
[CrossRef]

Morro, A.

M. Fabrizio, A. Morro, “Dissipativity and irreversibility of electromagnetic systems,” Math. Models Methods Appl. Sci. 10, 217–246 (2000).
[CrossRef]

Okawachi, Y.

Pack, M.

R. Camacho, M. Pack, J. Howell, R. Boyd, “Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor,” Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Palinginis, P.

S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Peatross, J.

Pfau, T.

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Pritchard, D. E.

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Sharping, J.

Shi, Z.

Skaric, L.

F. Xia, L. Skaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

Vlasov, Y.

F. Xia, L. Skaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

Wang, H.

S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Ware, M.

S. A. Glasgow, M. Ware, “Real-time dissipation of optical pulses in passive dielectrics,” Phys. Rev. A 80, 043817 (2009).
[CrossRef]

S. Glasgow, M. Meilstrup, J. Peatross, M. Ware, “Real-time recoverable and irrecoverable energy in dispersive-dissipative dielectrics,” Phys. Rev. E 75, 016616 (2007).
[CrossRef]

M. Ware, S. Glasgow, J. Peatross, “Energy transport in linear dielectrics,” Opt. Express 9, 519–532 (2001).
[CrossRef] [PubMed]

M. Ware, S. Glasgow, J. Peatross, “Role of group velocity in tracking field energy in linear dielectrics,” Opt. Express 9, 506–518 (2001).
[CrossRef] [PubMed]

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Xia, F.

F. Xia, L. Skaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

Zapasskii, V. S.

V. S. Zapasskii, G. G. Kozlov, “A saturable absorber, coherent population oscillations, and slow light,” Opt. Spectrosc. 100, 419–424 (2006).
[CrossRef]

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Continuum Mech. Thermodyn. (1)

G. Gentili, “Free enthalpies, free energies and norms for dielectrics with fading memory,” Continuum Mech. Thermodyn. 8, 201–214 (1996).
[CrossRef]

Int. J. Eng. Sci. (1)

J. M. Golden, “Consequences of non-uniqueness in the free energy of materials with memory,” Int. J. Eng. Sci. 39, 53–70 (2001).
[CrossRef]

J. Elasticity (1)

L. Deseri, G. Gentili, M. Golden, “An explicit formula for the minimum free energy in linear viscoelasticity,” J. Elasticity 54, 141–185 (1999).
[CrossRef]

J. Mod. Opt. (1)

R. W. Boyd, “Slow and fast light: fundamentals and applications,” J. Mod. Opt. 56, 1908–1915 (2009).
[CrossRef]

J. Non-Equilib. Thermodyn. (1)

V. Berti, G. Gentili, “The minimum free energy for isothermal dielectrics with memory,” J. Non-Equilib. Thermodyn. 24, 154–176 (1999).

Math. Models Methods Appl. Sci. (1)

M. Fabrizio, A. Morro, “Dissipativity and irreversibility of electromagnetic systems,” Math. Models Methods Appl. Sci. 10, 217–246 (2000).
[CrossRef]

Nat. Photonics (1)

F. Xia, L. Skaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

Nature (1)

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

Opt. Express (3)

Opt. Lett. (1)

Opt. Spectrosc. (1)

V. S. Zapasskii, G. G. Kozlov, “A saturable absorber, coherent population oscillations, and slow light,” Opt. Spectrosc. 100, 419–424 (2006).
[CrossRef]

Phys. Rev. A (1)

S. A. Glasgow, M. Ware, “Real-time dissipation of optical pulses in passive dielectrics,” Phys. Rev. A 80, 043817 (2009).
[CrossRef]

Phys. Rev. B (1)

S.-W. Chang, S.-L. Chuang, P.-C. Ku, C. J. Chang-Hasnian, P. Palinginis, H. Wang, “Slow light using excitonic population oscillation,” Phys. Rev. B 70, 235333 (2004).
[CrossRef]

Phys. Rev. E (1)

S. Glasgow, M. Meilstrup, J. Peatross, M. Ware, “Real-time recoverable and irrecoverable energy in dispersive-dissipative dielectrics,” Phys. Rev. E 75, 016616 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

R. Camacho, M. Pack, J. Howell, R. Boyd, “Wide-bandwidth, tunable, multiple-pulse-width optical delays using slow light in cesium vapor,” Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

S. Inouye, R. F. Löw, S. Gupta, T. Pfau, A. Görlitz, T. L. Gustavson, D. E. Pritchard, W. Ketterle, “Amplification of light and atoms in a bose-einstein condensate,” Phys. Rev. Lett. 85, 4225–4228 (2000).
[CrossRef] [PubMed]

Q. Appl. Math. (1)

J. M. Golden, “A proposal concerning the physical rate of dissipation in materials with memory,” Q. Appl. Math. 63, 117–155 (2005).

Supplementary Material (2)

» Media 1: MOV (3052 KB)     
» Media 2: MOV (2754 KB)     

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Figures (6)

Fig. 1
Fig. 1

The real (a) and imaginary (b) parts of the the index of refraction for the parameters in Eq. (44). (c) The group delay function for this medium. (d) The power spectrum of the pulse, which has been arbitrarily normalized to have a maximum value of one. This pulse-medium combination should exhibit moderately slow propagation delays, around 900 times slower than c.

Fig. 2
Fig. 2

An animation of the spatial distribution of energy densities as the pulse defined in Eq. (45) traverses the medium defined in Eq. (44) ( Media 1). (a) The propagation in vacuum before and after the medium, represented by the vertical line at z = 0. The solid line plots the field energy distribution with the medium present and the dotted line plots the field energy distribution would have been if the medium were not present for comparison. (b) The distribution of ufield in the medium. (c) The distribution of uint in the medium. All plots have been locally time-averaged to remove the rapid fluctuations at the carrier frequency.

Fig. 3
Fig. 3

The total energy stored in the medium Uint compared with the real-time loss Uloss of energy for the pulse-medium combination illustrated in Fig. 2.

Fig. 4
Fig. 4

(a) The temporal profile of a the Gaussian pulse Eq. (43) with the parameters in Eq. (45). (b) The first half of the pulse is the same as (a), but the second half is the optimum future recovery field for the medium described in Eq. (44).

Fig. 5
Fig. 5

An animation of the spatial distribution of energy densities as the pulse defined in Eq. (45) traverses the medium defined in Eq. (44) ( Media 2). (a) The propagation in vacuum before and after the medium, represented by the vertical line at z = 0. The solid line plots the field energy distribution with the medium present and the dotted line plots the field energy distribution would have been if the medium were not present for comparison. (b) The distribution of ufield in the medium. (c) The distribution of uint in the medium. All plots have been locally time-averaged to remove the rapid fluctuations at the carrier frequency.

Fig. 6
Fig. 6

The solid lines plot the total energy stored in the medium Uint and the real-time loss Uloss of energy for the pulse-medium combination illustrated in Fig. 5. Dashed lines plot the same quantities from Fig. 3 for comparison.

Equations (45)

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E ( z , t ) = E ( z , t ) j , P ( z , t ) = P ( z , t ) j , H ( z , t ) = H ( z , t ) i
P ^ ( z , ω ) = χ ( ω ) ( θ + ( z ) θ + ( z L ) ) E ^ ( z , ω ) ,
F ^ ( z , ω ) = 1 2 π + d t F ( z , t ) e + i ω t F ( z , t ) = 1 2 π + d ω F ^ ( z , ω ) e i ω t .
H ^ ( z , ω ) = c i ω E ^ ( z , ω )
E ^ ( z , ω ) = ω 2 c 2 ( 1 + χ ( ω ) [ θ + ( z ) θ + ( z L ) ] ) E ^ ( z , ω )
E ^ ( z , ω ) = { E ^ i ( ω ) e i k 0 ( ω ) z + E ^ r ( ω ) e i k 0 ( ω ) z z 0 E ^ f ( ω ) e i k ( ω ) z + E ^ b ( ω ) e i k ( ω ) z 0 z L E ^ t ( ω ) e i k 0 ( ω ) ( z L ) z L
𝒩 ( ω ) = 1 + χ ( ω ) = ε ( ω ) = n ( ω ) + i κ ( ω ) .
E ^ t ( ω ) = t ( ω ) E ^ i ( ω ) E ^ r ( ω ) = r ( ω ) E ^ i ( ω ) E ^ f ( ω ) = f ( ω ) E ^ i ( ω ) e i k ( ω ) L E ^ b ( ω ) = b ( ω ) E ^ i ( ω ) e i k ( ω ) L
t ( ω ) = 4 𝒩 ( ω ) ( 1 + 𝒩 ( ω ) ) 2 e i k ( ω ) L ( 1 𝒩 ( ω ) ) 2 e i k ( ω ) L r ( ω ) = 2 i sin ( k ( ω ) L ) 𝒩 ( ω ) + 1 𝒩 ( ω ) 1 e i k ( ω ) L 𝒩 ( ω ) 1 𝒩 ( ω ) + 1 e i k ( ω ) L f ( ω ) = 2 ( 𝒩 ( ω + 1 ) ) ( 1 + 𝒩 ( ω ) ) 2 e i k ( ω ) L ( 1 𝒩 ( ω ) ) 2 e i k ( ω ) L b ( ω ) = 2 ( 𝒩 ( ω ) 1 ) ( 1 + 𝒩 ( ω ) ) 2 e i k ( ω ) L ( 1 𝒩 ( ω ) ) 2 e i k ( ω ) L
u ˙ ( z , t ) + c S ( z , t ) = 0 ,
u ( z , t ) = u field ( z , t ) + u int ( z , t )
u field ( z , t ) = 1 2 H ( z , t ) H ( z , t ) + 1 2 E ( z , t ) E ( z , t )
u int ( z , t ) = t d τ E ( z , τ ) P ˙ ( z , τ ) .
U tot : = + d z u ( z , t ) .
U tot = U ( , 0 ] ( t ) + U [ 0 , L ] ( t ) + U [ L , ) ( t )
U [ 0 , L ] ( t ) = U [ 0 , L ] , field ( t ) + U int ( t )
U int ( t ) = U irrec ( t ) + U rec ( t ) ,
U int ( t ) = U loss ( t ) + U trans ( t ) ,
U loss ( ) = c + d ω | E ^ r ( 0 , ω ) | 2 + + d ω 0 L d z ρ ( ω ) | E ^ ( z , ω ) | 2
U loss ( ) = L γ ω p 2 d ω m ( ω ) | ω χ ( ω ) E ^ i ( 0 , ω ) | 2
m ( ω ) = ω p 2 γ ( L / c ) M ( ω ) | i ω χ ( ω ) | 2 ,
M ( ω ) = | r ( ω ) | 2 + ρ ( ω ) 0 L / c d τ | f ( ω ) e i ω 𝒩 ( ω ) τ + b ( ω ) e i ω 𝒩 ( ω ) τ | 2 .
γ = lim ω ω Im χ ( ω ) Re χ ( ω ) ,
ω p 2 = lim ω ω 2 χ ( ω ) .
0 τ L : = L / c d τ | f ( ω ) e i ω 𝒩 ( ω ) τ + b ( ω ) e + i ω 𝒩 ( ω ) τ | 2 = ( | f ( ω ) | 2 e τ L ω κ ( ω ) + | b ( ω ) | 2 e τ L ω κ ( ω ) ) sinh ( τ L ω κ ( ω ) ) ω κ ( ω ) + ( f ( ω ) b * ( ω ) e i τ L ω n ( ω ) + b ( ω ) f * ( ω ) e + i τ L ω n ( ω ) ) sin ( τ L ω n ( ω ) ) ω n ( ω ) .
lim ω 0 m ( ω ) = ω p 2 γ ( L / c ) ( ( L / c ) 2 4 + Im [ χ ( 0 ) ] χ 2 ( 0 ) ( L / c ) ) ,
m ( ω ) = m + ( ω ) m + ( ω )
m + ( ω ) = ( exp F θ 0 + F 1 log ) m ( ω )
U loss ( ) = L γ ω p 2 + d ω | P ˙ ^ eff ( ω ) | 2 .
U loss ( ) = L γ ω p 2 + d τ P ˙ eff 2 ( τ ) ,
P ˙ eff ( τ ) : = F 1 [ P ˙ ^ eff ( ω ) ]
( E i ) t ( τ ) = { E i ( τ ) , τ t , 0 , τ > t , ( E i ) t + ( τ ) : = { 0 , τ t E i ( τ ) , τ > t .
U loss [ E i ] ( ) = L γ ω p 2 t d τ P ˙ eff 2 [ ( E i ) t + ( E i ) t + ] ( τ ) + L γ ω p 2 t + d τ P ˙ eff 2 [ ( E i ) t + ( E i ) t + ] ( τ ) .
U loss [ E i ] ( ) = L γ ω p 2 t d τ P ˙ eff 2 [ ( E i ) t ] ( τ ) + L γ ω p 2 t + d τ P ˙ eff 2 [ ( E i ) t + ( E i ) t + ] ( τ ) .
L γ ω p 2 t + d τ | P ˙ eff [ ( E i ) t + ( E i ) t , opt + ] ( τ ) | 2 0 , τ > t .
P ˙ eff [ ( E i ) t + ( E i ) t , opt + ] ( τ ) 0 , ( τ > t ) .
( E i ) t , opt + = ( F 1 e i ω t M + 1 F θ 0 + F 1 M + e i ω t F ) ( E i ) t ,
M + ( ω ) : = i ω m + ( ω ) χ ( ω ) .
M + 1 ( ω ) : = 1 M + ( ω ) = 1 i ω m + ( ω ) χ ( ω )
U loss ( t ) = L γ ω p 2 t d τ P ˙ eff 2 [ ( E i ) t ] ( τ ) .
M irrec ( ω ) = ρ ( ω ) 0 L / c d τ | f ( ω ) e i ω 𝒩 ( ω ) τ + b ( ω ) e i ω 𝒩 ( ω ) τ | 2 ,
χ ( ω ) = j = 1 N χ j ( ω ) = j = 1 N f j ω p j 2 ω j 2 i γ j ω ω 2 .
E i ( t ) = E 0 e t 2 / τ 2 cos ( ω ¯ t + ϕ )
γ 1 = 0.1 γ 2 ω 1 = ω 2 = 100 γ 2 f 1 ω p 1 2 = 9.95 γ 2 2 f 2 ω p 2 = 100 γ 2 2 L = c / γ 2
τ = 1000 γ 2 1 ω ¯ = 100 γ 2 ϕ = 0 .

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