Abstract

We consider propagation of an electromagnetic (EM) wave through a dynamic optical medium whose refractive index varies with time. Specifically, we focus on the reflection and transmission of EM waves from a temporal boundary and clarify the two different physical processes that contribute to them. One process is related to impedance mismatch, while the other results from temporal scaling related to a sudden change in the speed of light at the temporal boundary. Our results show that temporal scaling of the electric field must be considered for light propagation in dynamic media. Numerical solutions of Maxwell’s equations are in full agreement with our theory.

© 2014 Optical Society of America

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  1. F. R. Morgenthaler, IRE Trans. Microwave Theory Tech. 6, 167 (1958).
    [CrossRef]
  2. C.-L. Jiang, IEEE Trans. Antennas Propag. 23, 83 (1975).
    [CrossRef]
  3. T. Ruiz, C. Wright, and J. Smith, IEEE Trans. Antennas Propag. 26, 358 (1978).
    [CrossRef]
  4. J. C. AuYeung, Opt. Lett. 8, 148 (1983).
    [CrossRef]
  5. D. K. Kalluri and V. R. Goteti, J. Appl. Phys. 72, 4575 (1992).
    [CrossRef]
  6. M. Cirone, K. Rzaz-dotewski, and J. Mostowski, Phys. Rev. A 55, 62 (1997).
    [CrossRef]
  7. J. T. Mendonca and P. K. Shukla, Phys. Scr. 65, 160 (2002).
    [CrossRef]
  8. D. K. Kalluri and C. Jinming, IEEE Trans. Antennas Propag. 57, 2698 (2009).
    [CrossRef]
  9. S. C. Wilks, J. M. Dawson, and W. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
    [CrossRef]
  10. N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
    [CrossRef]
  11. A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
    [CrossRef]
  12. M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
    [CrossRef]
  13. M. F. Yanik and S. Fan, Phys. Rev. Lett. 93, 173903 (2004).
    [CrossRef]
  14. M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803(R) (2006).
    [CrossRef]
  15. S. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
    [CrossRef]
  16. T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
    [CrossRef]
  17. J. T. Mendonca, Theory of Photon Acceleration (Taylor & Francis, 2000).
  18. F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
    [CrossRef]
  19. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), p. 302.
  20. Y. Xiao, G. P. Agrawal, and D. N. Maywar, Opt. Lett. 36, 505 (2011).
    [CrossRef]
  21. Y. Xiao, D. N. Maywar, and G. P. Agrawal, Opt. Lett. 37, 1271 (2012).
    [CrossRef]

2012 (2)

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

Y. Xiao, D. N. Maywar, and G. P. Agrawal, Opt. Lett. 37, 1271 (2012).
[CrossRef]

2011 (1)

2010 (1)

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
[CrossRef]

2009 (1)

D. K. Kalluri and C. Jinming, IEEE Trans. Antennas Propag. 57, 2698 (2009).
[CrossRef]

2007 (2)

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

S. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

2006 (1)

M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803(R) (2006).
[CrossRef]

2004 (2)

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 93, 173903 (2004).
[CrossRef]

2002 (2)

J. T. Mendonca and P. K. Shukla, Phys. Scr. 65, 160 (2002).
[CrossRef]

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

1997 (1)

M. Cirone, K. Rzaz-dotewski, and J. Mostowski, Phys. Rev. A 55, 62 (1997).
[CrossRef]

1992 (1)

D. K. Kalluri and V. R. Goteti, J. Appl. Phys. 72, 4575 (1992).
[CrossRef]

1988 (1)

S. C. Wilks, J. M. Dawson, and W. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef]

1983 (1)

1978 (1)

T. Ruiz, C. Wright, and J. Smith, IEEE Trans. Antennas Propag. 26, 358 (1978).
[CrossRef]

1975 (1)

C.-L. Jiang, IEEE Trans. Antennas Propag. 23, 83 (1975).
[CrossRef]

1958 (1)

F. R. Morgenthaler, IRE Trans. Microwave Theory Tech. 6, 167 (1958).
[CrossRef]

Agrawal, G. P.

Amann, A.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

AuYeung, J. C.

Beggs, D. M.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Biancalana, F.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Cirone, M.

M. Cirone, K. Rzaz-dotewski, and J. Mostowski, Phys. Rev. A 55, 62 (1997).
[CrossRef]

Dawson, J. M.

S. C. Wilks, J. M. Dawson, and W. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef]

Fan, S.

M. F. Yanik and S. Fan, Phys. Rev. Lett. 93, 173903 (2004).
[CrossRef]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef]

Gao, H.

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

Goteti, V. R.

D. K. Kalluri and V. R. Goteti, J. Appl. Phys. 72, 4575 (1992).
[CrossRef]

Higashiguchi, T.

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

Ito, H.

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), p. 302.

Jiang, C.-L.

C.-L. Jiang, IEEE Trans. Antennas Propag. 23, 83 (1975).
[CrossRef]

Jinming, C.

D. K. Kalluri and C. Jinming, IEEE Trans. Antennas Propag. 57, 2698 (2009).
[CrossRef]

Kalluri, D. K.

D. K. Kalluri and C. Jinming, IEEE Trans. Antennas Propag. 57, 2698 (2009).
[CrossRef]

D. K. Kalluri and V. R. Goteti, J. Appl. Phys. 72, 4575 (1992).
[CrossRef]

Kampfrath, T.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Kodama, R.

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

Krauss, T. F.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Kuipers, L.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Lipson, M.

S. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Maywar, D. N.

Melloni, A.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Mendonca, J. T.

J. T. Mendonca and P. K. Shukla, Phys. Scr. 65, 160 (2002).
[CrossRef]

J. T. Mendonca, Theory of Photon Acceleration (Taylor & Francis, 2000).

Mitsugi, S.

M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803(R) (2006).
[CrossRef]

Morgenthaler, F. R.

F. R. Morgenthaler, IRE Trans. Microwave Theory Tech. 6, 167 (1958).
[CrossRef]

Mori, W. B.

S. C. Wilks, J. M. Dawson, and W. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef]

Mostowski, J.

M. Cirone, K. Rzaz-dotewski, and J. Mostowski, Phys. Rev. A 55, 62 (1997).
[CrossRef]

Nakata, M.

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

Niiyama, T.

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

Nishida, A.

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

Nishida, Y.

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

Notomi, M.

M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803(R) (2006).
[CrossRef]

O’Reilly, E. P.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Otsuka, T.

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

Preble, S.

S. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Ruiz, T.

T. Ruiz, C. Wright, and J. Smith, IEEE Trans. Antennas Propag. 26, 358 (1978).
[CrossRef]

Rzaz-dotewski, K.

M. Cirone, K. Rzaz-dotewski, and J. Mostowski, Phys. Rev. A 55, 62 (1997).
[CrossRef]

Sasaki, S.

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

Sentoku, Y.

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

Shukla, P. K.

J. T. Mendonca and P. K. Shukla, Phys. Scr. 65, 160 (2002).
[CrossRef]

Smith, J.

T. Ruiz, C. Wright, and J. Smith, IEEE Trans. Antennas Propag. 26, 358 (1978).
[CrossRef]

Suzuki, F.

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

Uskov, A. V.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

White, T. P.

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
[CrossRef]

Wilks, S. C.

S. C. Wilks, J. M. Dawson, and W. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef]

Wright, C.

T. Ruiz, C. Wright, and J. Smith, IEEE Trans. Antennas Propag. 26, 358 (1978).
[CrossRef]

Xiao, Y.

Xu, Q.

S. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Yanik, M. F.

M. F. Yanik and S. Fan, Phys. Rev. Lett. 93, 173903 (2004).
[CrossRef]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef]

Yugami, N.

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

A. Nishida, N. Yugami, T. Higashiguchi, T. Otsuka, F. Suzuki, M. Nakata, Y. Sentoku, and R. Kodama, Appl. Phys. Lett. 101, 161118 (2012).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

D. K. Kalluri and C. Jinming, IEEE Trans. Antennas Propag. 57, 2698 (2009).
[CrossRef]

C.-L. Jiang, IEEE Trans. Antennas Propag. 23, 83 (1975).
[CrossRef]

T. Ruiz, C. Wright, and J. Smith, IEEE Trans. Antennas Propag. 26, 358 (1978).
[CrossRef]

IRE Trans. Microwave Theory Tech. (1)

F. R. Morgenthaler, IRE Trans. Microwave Theory Tech. 6, 167 (1958).
[CrossRef]

J. Appl. Phys. (1)

D. K. Kalluri and V. R. Goteti, J. Appl. Phys. 72, 4575 (1992).
[CrossRef]

Nat. Photonics (1)

S. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (3)

T. Kampfrath, D. M. Beggs, T. P. White, A. Melloni, T. F. Krauss, and L. Kuipers, Phys. Rev. A 81, 043837 (2010).
[CrossRef]

M. Cirone, K. Rzaz-dotewski, and J. Mostowski, Phys. Rev. A 55, 62 (1997).
[CrossRef]

M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803(R) (2006).
[CrossRef]

Phys. Rev. E (2)

N. Yugami, T. Niiyama, T. Higashiguchi, H. Gao, S. Sasaki, H. Ito, and Y. Nishida, Phys. Rev. E 65, 036505 (2002).
[CrossRef]

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 93, 173903 (2004).
[CrossRef]

S. C. Wilks, J. M. Dawson, and W. B. Mori, Phys. Rev. Lett. 61, 337 (1988).
[CrossRef]

Phys. Scr. (1)

J. T. Mendonca and P. K. Shukla, Phys. Scr. 65, 160 (2002).
[CrossRef]

Other (2)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), p. 302.

J. T. Mendonca, Theory of Photon Acceleration (Taylor & Francis, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic illustration of reflection and transmission of an EM fields at a temporal boundary where the refractive index changes from n1 (left panel) to its final value n2 (right panel) at t=t0.

Fig. 2.
Fig. 2.

Electric field of a four-cycle pulse after propagation across a temporal boundary. Reflected wave is generated because of impedance mismatch. The amplitudes of the reflected and transmitted fields agree with Eqs. (4) and (5).

Fig. 3.
Fig. 3.

Electric field of a four-cycle pulse after propagation across a temporal boundary with impedance matching. No electric field is reflected back. The amplitudes of the reflected and transmitted fields agree with Eqs. (4) and (5).

Fig. 4.
Fig. 4.

Comparison of transmitted electric fields in cases 1 (red curve, impedance changes) and 2 (green curve, impedance matched). Dotted black curve shows the analytic prediction based on Eq. (10). The input electric field is shown for comparison with a purple curve. FDTD simulations confirm our prediction and agree fully with our time transformation theory.

Equations (10)

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

×E=Bt,×H=Dt,
·D=0,·B=0,
D(t=t0)=D(t=t0+),B(t=t0)=B(t=t0+).
rDBErEin=12(ε1ε2μ1ε1μ2ε2),
tDBEtEin=12(ε1ε2+μ1ε1μ2ε2).
E(t=t0)=E(t=t0+),H(t=t0)=H(t=t0+).
rEHErEin=12(1μ2ε1μ1ε2),
tEHEtEin=12(1+μ2ε1μ1ε2).
rDB=n1n2rEH,tDB=n1n2tEH,
Et(t)=sEin(stsTd),

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