Abstract

We show numerically and analytically that temporal reflections from a moving refractive-index boundary act as an analog of Lloyd’s mirror, allowing a single pulse to produce interference fringes in time as it propagates inside a dispersive medium. This interference can be viewed as the pulse interfering with a virtual pulse that is identical to the first, except for a π-phase shift. Furthermore, if a second moving refractive-index boundary is added to create the analog of an optical waveguide, a single pulse can be self-imaged or made to produce two or more pulses by adjusting the propagation length in a process similar to the Talbot effect.

© 2017 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (4)

M. F. Linder, R. Schützhold, and W. G. Unruh, “Derivation of Hawking radiation in dispersive dielectric media,” Phys. Rev. D 93, 104010 (2016).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Temporal waveguides for optical pulses,” J. Opt. Soc. Am. B 33, 1112–1119 (2016).
[Crossref]

Z. Deng, X. Fu, J. Liu, C. Zhao, and S. Wen, “Trapping and controlling the dispersive wave within a solitonic well,” Opt. Express 24, 10302–10312 (2016).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Spectral splitting of optical pulses inside a dispersive medium at a temporal boundary,” IEEE J. Quantum Electron. 52, 6100708 (2016).
[Crossref]

2015 (2)

M. Jacquet and F. König, “Quantum vacuum emission from a refractive-index front,” Phys. Rev. A 92, 023851 (2015).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “What is the temporal analog of reflection and refraction of optical beams?” Phys. Rev. Lett. 115, 183901 (2015).
[Crossref]

2013 (4)

S. Finazzi and I. Carusotto, “Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse,” Phys. Rev. A 87, 023803 (2013).
[Crossref]

R. Driben, A. V. Yulin, A. Efimov, and B. A. Malomed, “Trapping of light in solitonic cavities and its role in the supercontinuum generation,” Opt. Express 21, 19091–19096 (2013).
[Crossref]

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
[Crossref]

X. Li, Y. Shimizu, S. Ito, W. Gao, and L. Zeng, “Fabrication of diffraction gratings for surface encoders by using a Lloyd’s mirror interferometer with a 405  nm laser diode,” Proc. SPIE 8759, 87594Q (2013).
[Crossref]

2012 (6)

A. Choudhary and F. König, “Efficient frequency shifting of dispersive waves at solitons,” Opt. Express 20, 5538–5546 (2012).
[Crossref]

E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

L. Tartara, “Frequency shifting of femtosecond pulses by reflection at solitons,” IEEE J. Quantum Electron. 48, 1439–1442 (2012).
[Crossref]

S. Finazzi and R. Parentani, “Hawking radiation in dispersive theories, the two regimes,” Phys. Rev. D 85, 124027 (2012).
[Crossref]

D. Faccio, “Laser pulse analogues for gravity and analogue Hawking radiation,” Contemp. Phys. 53, 97–112 (2012).
[Crossref]

D. Faccio, T. Arane, M. Lamperti, and U. Leonhardt, “Optical black hole lasers,” Class. Quantum Grav. 29, 224009 (2012).
[Crossref]

2011 (2)

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

2010 (2)

S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

2009 (2)

N. N. Rozanov, “Transformation of electromagnetic radiation by rapidly moving inhomogeneities of a transparent medium,” J. Exp. Theor. Phys. 108, 140–148 (2009).
[Crossref]

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 17, 13588–13601 (2009).
[Crossref]

2008 (2)

N. N. Rosanov, “Transformation of electromagnetic radiation at moving inhomogeneities of a medium,” J. Exp. Theor. Phys. Lett. 88, 501–504 (2008).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. J. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

2007 (2)

A. V. Gorbach and D. V. Skryabin, “Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers,” Opt. Express 15, 14560–14565 (2007).
[Crossref]

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[Crossref]

2002 (1)

J. T. Mendonça and P. K. Shukla, “Time refraction and time reflection: two basic concepts,” Phys. Scripta 65, 160–163 (2002).
[Crossref]

1999 (3)

1996 (1)

E. B. Hochberg and N. L. Chrien, “Lloyd’s mirror for MTF testing of MISR CCD,” Proc. SPIE 2830, 274–285 (1996).
[Crossref]

1994 (1)

B. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[Crossref]

1989 (1)

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, and M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1989).
[Crossref]

1983 (1)

Agrawal, G. P.

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Spectral splitting of optical pulses inside a dispersive medium at a temporal boundary,” IEEE J. Quantum Electron. 52, 6100708 (2016).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Temporal waveguides for optical pulses,” J. Opt. Soc. Am. B 33, 1112–1119 (2016).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “What is the temporal analog of reflection and refraction of optical beams?” Phys. Rev. Lett. 115, 183901 (2015).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Elsevier, 2013).

Amiranashvili, S.

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

Arane, T.

D. Faccio, T. Arane, M. Lamperti, and U. Leonhardt, “Optical black hole lasers,” Class. Quantum Grav. 29, 224009 (2012).
[Crossref]

Azaña, J.

Belgiorno, F.

E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Bolton, J. G.

J. G. Bolton, G. J. Stanley, and O. B. Slee, “Positions of three discrete sources of galactic radio-frequency radiation,” in Classics in Radio Astronomy (Springer, 1982), pp. 239–241.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 7th expanded ed. (Cambridge University, 1999).

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Cacciatori, S. L.

E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Carballar, A.

Carusotto, I.

S. Finazzi and I. Carusotto, “Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse,” Phys. Rev. A 87, 023803 (2013).
[Crossref]

Chen, L. R.

J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[Crossref]

Choudhary, A.

Chrien, N. L.

E. B. Hochberg and N. L. Chrien, “Lloyd’s mirror for MTF testing of MISR CCD,” Proc. SPIE 2830, 274–285 (1996).
[Crossref]

Clerici, M.

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Couairon, A.

E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

Dawson, J. M.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, and M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1989).
[Crossref]

Demircan, A.

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

Deng, Z.

Donaldson, W. R.

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Temporal waveguides for optical pulses,” J. Opt. Soc. Am. B 33, 1112–1119 (2016).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Spectral splitting of optical pulses inside a dispersive medium at a temporal boundary,” IEEE J. Quantum Electron. 52, 6100708 (2016).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “What is the temporal analog of reflection and refraction of optical beams?” Phys. Rev. Lett. 115, 183901 (2015).
[Crossref]

Driben, R.

Efimov, A.

Faccio, D.

E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

D. Faccio, “Laser pulse analogues for gravity and analogue Hawking radiation,” Contemp. Phys. 53, 97–112 (2012).
[Crossref]

D. Faccio, T. Arane, M. Lamperti, and U. Leonhardt, “Optical black hole lasers,” Class. Quantum Grav. 29, 224009 (2012).
[Crossref]

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Finazzi, S.

S. Finazzi and I. Carusotto, “Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse,” Phys. Rev. A 87, 023803 (2013).
[Crossref]

S. Finazzi and R. Parentani, “Hawking radiation in dispersive theories, the two regimes,” Phys. Rev. D 85, 124027 (2012).
[Crossref]

Fu, X.

Gao, W.

X. Li, Y. Shimizu, S. Ito, W. Gao, and L. Zeng, “Fabrication of diffraction gratings for surface encoders by using a Lloyd’s mirror interferometer with a 405  nm laser diode,” Proc. SPIE 8759, 87594Q (2013).
[Crossref]

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, “Bouncing of a dispersive pulse on an accelerating soliton and stepwise frequency conversion in optical fibers,” Opt. Express 15, 14560–14565 (2007).
[Crossref]

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[Crossref]

Gorini, V.

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

Hill, S.

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 17, 13588–13601 (2009).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. J. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Hochberg, E. B.

E. B. Hochberg and N. L. Chrien, “Lloyd’s mirror for MTF testing of MISR CCD,” Proc. SPIE 2830, 274–285 (1996).
[Crossref]

Ito, S.

X. Li, Y. Shimizu, S. Ito, W. Gao, and L. Zeng, “Fabrication of diffraction gratings for surface encoders by using a Lloyd’s mirror interferometer with a 405  nm laser diode,” Proc. SPIE 8759, 87594Q (2013).
[Crossref]

Jacquet, M.

M. Jacquet and F. König, “Quantum vacuum emission from a refractive-index front,” Phys. Rev. A 92, 023851 (2015).
[Crossref]

Jannson, T.

Jones, M. E.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, and M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1989).
[Crossref]

Katsouleas, T.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, and M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1989).
[Crossref]

Kolesik, M.

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

Kolner, B.

B. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[Crossref]

König, F.

M. Jacquet and F. König, “Quantum vacuum emission from a refractive-index front,” Phys. Rev. A 92, 023851 (2015).
[Crossref]

A. Choudhary and F. König, “Efficient frequency shifting of dispersive waves at solitons,” Opt. Express 20, 5538–5546 (2012).
[Crossref]

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 17, 13588–13601 (2009).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. J. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Kuklewicz, C.

T. G. Philbin, C. Kuklewicz, S. J. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
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D. Faccio, T. Arane, M. Lamperti, and U. Leonhardt, “Optical black hole lasers,” Class. Quantum Grav. 29, 224009 (2012).
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E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
[Crossref]

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 17, 13588–13601 (2009).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. J. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Li, X.

X. Li, Y. Shimizu, S. Ito, W. Gao, and L. Zeng, “Fabrication of diffraction gratings for surface encoders by using a Lloyd’s mirror interferometer with a 405  nm laser diode,” Proc. SPIE 8759, 87594Q (2013).
[Crossref]

Linder, M. F.

M. F. Linder, R. Schützhold, and W. G. Unruh, “Derivation of Hawking radiation in dispersive dielectric media,” Phys. Rev. D 93, 104010 (2016).
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Liu, J.

Lotti, A.

E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

Malomed, B. A.

Mendonça, J. T.

J. T. Mendonça and P. K. Shukla, “Time refraction and time reflection: two basic concepts,” Phys. Scripta 65, 160–163 (2002).
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J. T. Mendonça, Theory of Photon Acceleration, Plasma Physics Series (Institute of Physics, 2001).

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S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, and M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1989).
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Muriel, M. A.

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E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Parentani, R.

S. Finazzi and R. Parentani, “Hawking radiation in dispersive theories, the two regimes,” Phys. Rev. D 85, 124027 (2012).
[Crossref]

Philbin, T. G.

T. G. Philbin, C. Kuklewicz, S. J. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Plansinis, B. W.

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Spectral splitting of optical pulses inside a dispersive medium at a temporal boundary,” IEEE J. Quantum Electron. 52, 6100708 (2016).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Temporal waveguides for optical pulses,” J. Opt. Soc. Am. B 33, 1112–1119 (2016).
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B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “What is the temporal analog of reflection and refraction of optical beams?” Phys. Rev. Lett. 115, 183901 (2015).
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Rizzi, L.

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Robertson, S.

S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
[Crossref]

Robertson, S. J.

T. G. Philbin, C. Kuklewicz, S. J. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Rosanov, N. N.

N. N. Rosanov, “Transformation of electromagnetic radiation at moving inhomogeneities of a medium,” J. Exp. Theor. Phys. Lett. 88, 501–504 (2008).
[Crossref]

Rozanov, N. N.

N. N. Rozanov, “Transformation of electromagnetic radiation by rapidly moving inhomogeneities of a transparent medium,” J. Exp. Theor. Phys. 108, 140–148 (2009).
[Crossref]

Rubino, E.

E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Sala, V. G.

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Schützhold, R.

M. F. Linder, R. Schützhold, and W. G. Unruh, “Derivation of Hawking radiation in dispersive dielectric media,” Phys. Rev. D 93, 104010 (2016).
[Crossref]

Shimizu, Y.

X. Li, Y. Shimizu, S. Ito, W. Gao, and L. Zeng, “Fabrication of diffraction gratings for surface encoders by using a Lloyd’s mirror interferometer with a 405  nm laser diode,” Proc. SPIE 8759, 87594Q (2013).
[Crossref]

Shukla, P. K.

J. T. Mendonça and P. K. Shukla, “Time refraction and time reflection: two basic concepts,” Phys. Scripta 65, 160–163 (2002).
[Crossref]

Skryabin, D. V.

Slee, O. B.

J. G. Bolton, G. J. Stanley, and O. B. Slee, “Positions of three discrete sources of galactic radio-frequency radiation,” in Classics in Radio Astronomy (Springer, 1982), pp. 239–241.

Smith, P. W. E.

J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
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Stanley, G. J.

J. G. Bolton, G. J. Stanley, and O. B. Slee, “Positions of three discrete sources of galactic radio-frequency radiation,” in Classics in Radio Astronomy (Springer, 1982), pp. 239–241.

Steinmeyer, G.

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

Tartara, L.

L. Tartara, “Frequency shifting of femtosecond pulses by reflection at solitons,” IEEE J. Quantum Electron. 48, 1439–1442 (2012).
[Crossref]

Unruh, W. G.

M. F. Linder, R. Schützhold, and W. G. Unruh, “Derivation of Hawking radiation in dispersive dielectric media,” Phys. Rev. D 93, 104010 (2016).
[Crossref]

Wen, S.

Wilks, S. C.

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, and M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1989).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 7th expanded ed. (Cambridge University, 1999).

Yulin, A. V.

Zeng, L.

X. Li, Y. Shimizu, S. Ito, W. Gao, and L. Zeng, “Fabrication of diffraction gratings for surface encoders by using a Lloyd’s mirror interferometer with a 405  nm laser diode,” Proc. SPIE 8759, 87594Q (2013).
[Crossref]

Zhao, C.

Class. Quantum Grav. (1)

D. Faccio, T. Arane, M. Lamperti, and U. Leonhardt, “Optical black hole lasers,” Class. Quantum Grav. 29, 224009 (2012).
[Crossref]

Contemp. Phys. (1)

D. Faccio, “Laser pulse analogues for gravity and analogue Hawking radiation,” Contemp. Phys. 53, 97–112 (2012).
[Crossref]

Electron. Lett. (1)

J. Azaña, L. R. Chen, M. A. Muriel, and P. W. E. Smith, “Experimental demonstration of real-time Fourier transformation using linearly chirped fibre Bragg gratings,” Electron. Lett. 35, 2223–2224 (1999).
[Crossref]

IEEE J. Quantum Electron. (3)

B. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[Crossref]

L. Tartara, “Frequency shifting of femtosecond pulses by reflection at solitons,” IEEE J. Quantum Electron. 48, 1439–1442 (2012).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “Spectral splitting of optical pulses inside a dispersive medium at a temporal boundary,” IEEE J. Quantum Electron. 52, 6100708 (2016).
[Crossref]

J. Exp. Theor. Phys. (1)

N. N. Rozanov, “Transformation of electromagnetic radiation by rapidly moving inhomogeneities of a transparent medium,” J. Exp. Theor. Phys. 108, 140–148 (2009).
[Crossref]

J. Exp. Theor. Phys. Lett. (1)

N. N. Rosanov, “Transformation of electromagnetic radiation at moving inhomogeneities of a medium,” J. Exp. Theor. Phys. Lett. 88, 501–504 (2008).
[Crossref]

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

New J. Phys. (1)

E. Rubino, F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, M. Kolesik, and D. Faccio, “Experimental evidence of analogue hawking radiation from ultrashort laser pulse filaments,” New J. Phys. 13, 085005 (2011).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. A (4)

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[Crossref]

M. Jacquet and F. König, “Quantum vacuum emission from a refractive-index front,” Phys. Rev. A 92, 023851 (2015).
[Crossref]

S. Finazzi and I. Carusotto, “Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse,” Phys. Rev. A 87, 023803 (2013).
[Crossref]

S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81, 063835 (2010).
[Crossref]

Phys. Rev. D (2)

S. Finazzi and R. Parentani, “Hawking radiation in dispersive theories, the two regimes,” Phys. Rev. D 85, 124027 (2012).
[Crossref]

M. F. Linder, R. Schützhold, and W. G. Unruh, “Derivation of Hawking radiation in dispersive dielectric media,” Phys. Rev. D 93, 104010 (2016).
[Crossref]

Phys. Rev. Lett. (4)

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

B. W. Plansinis, W. R. Donaldson, and G. P. Agrawal, “What is the temporal analog of reflection and refraction of optical beams?” Phys. Rev. Lett. 115, 183901 (2015).
[Crossref]

S. C. Wilks, J. M. Dawson, W. B. Mori, T. Katsouleas, and M. E. Jones, “Photon accelerator,” Phys. Rev. Lett. 62, 2600–2603 (1989).
[Crossref]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

Phys. Scripta (1)

J. T. Mendonça and P. K. Shukla, “Time refraction and time reflection: two basic concepts,” Phys. Scripta 65, 160–163 (2002).
[Crossref]

Proc. SPIE (2)

X. Li, Y. Shimizu, S. Ito, W. Gao, and L. Zeng, “Fabrication of diffraction gratings for surface encoders by using a Lloyd’s mirror interferometer with a 405  nm laser diode,” Proc. SPIE 8759, 87594Q (2013).
[Crossref]

E. B. Hochberg and N. L. Chrien, “Lloyd’s mirror for MTF testing of MISR CCD,” Proc. SPIE 2830, 274–285 (1996).
[Crossref]

Sci. Rep. (1)

E. Rubino, A. Lotti, F. Belgiorno, S. L. Cacciatori, A. Couairon, U. Leonhardt, and D. Faccio, “Soliton-induced relativistic-scattering and amplification,” Sci. Rep. 2, 932 (2012).
[Crossref]

Science (1)

T. G. Philbin, C. Kuklewicz, S. J. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Other (6)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 7th expanded ed. (Cambridge University, 1999).

J. T. Mendonça, Theory of Photon Acceleration, Plasma Physics Series (Institute of Physics, 2001).

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

J. G. Bolton, G. J. Stanley, and O. B. Slee, “Positions of three discrete sources of galactic radio-frequency radiation,” in Classics in Radio Astronomy (Springer, 1982), pp. 239–241.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Elsevier, 2013).

R. W. Boyd, Nonlinear Optics (Academic, 2003).

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Figures (5)

Fig. 1.
Fig. 1.

(a)–(c) Output pulse shapes for two hyperbolic-secant pulses propagating in a dispersive medium with initial pulse separations of (a)  T s = 2.5    ps , (b)  T s = 5    ps , and (c)  T s = 5    ps . The initial pulses in (c) have a π -phase offset. The predicted fringe locations are marked with dashed black lines. (d)–(f) Evolution of pulse shape for the same pulses demonstrating the fan-like interference fringes similar to those from a double slit.

Fig. 2.
Fig. 2.

(a) Fringe pattern after propagating 100 m for a single sech-shaped pulse with T 0 = 0.3    ps (solid blue curve). The pulse is offset initially by 2.5 ps from a co-propagating refractive-index boundary. The two-pulse fringe pattern seen in Fig. 1(c) is represented by the dotted red curve. Evolution of the (b) shape and (c) spectrum of the single sech-shaped pulse propagating with the moving refractive-index boundary. (d) Dispersion curves for t < 0 (solid blue curve) and t > 0 (dashed red curve). The dashed black curve shows the minimum initial momentum needed to cross the boundary.

Fig. 3.
Fig. 3.

(a) Total internal reflection (TIR) phase shift plotted as a function of frequency. (b) Output pulse shapes in the cases of a single pulse (solid blue curve) and two pulses (dotted red curve). The two fringe patterns match when the frequency-dependent phase shift, ϕ r , is applied to the second pulse.

Fig. 4.
Fig. 4.

Evolution of a train of sech-shaped pulses ( T 0 = 0.2    ps ) with an initial separation of 5 ps. Adjacent pulses differ in phase by π .

Fig. 5.
Fig. 5.

Evolution of the (a) shape and (b) spectrum of a sech-shaped pulse ( T 0 = 0.3    ps ) confined to a 5 ps window through two temporal boundaries.

Equations (18)

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β ( ω ) = β 0 + β 1 ( ω ω 0 ) + β 2 2 ( ω ω 0 ) 2 ,
β ( ω ) = β 0 + β 2 2 ( ω ω 0 ) 2 .
A z + i β 2 2 2 A t 2 = 0 ,
A ( z , t ) = A ˜ ( 0 , ω ) exp [ i β 2 z 2 ( ω ω 0 ) 2 i ω t ] d ω ,
A ( z , t ) = A ˜ ( 0 , Ω = t β 2 z ) exp ( i t 2 2 β 2 z ) .
A ( 0 , t ) = A 0 ( t T s / 2 ) + A 0 ( t + T s / 2 ) ,
A ˜ ( 0 , ω ) = 2 A ˜ 0 ( ω ) cos ( ω T s / 2 ) ,
| A ( z , t ) | 2 = 4 | A ˜ 0 | 2 cos 2 ( T s t 2 β 2 z ) .
A ( 0 , t ) = sech ( t T s / 2 T 0 ) + sech ( t + T s / 2 T 0 ) exp ( i ϕ ) ,
| A ( z , t ) | 2 = 4 | A ˜ 0 | 2 sin 2 ( T s t 2 β 2 z ) .
A z + i β 2 2 2 A t 2 = i β B ( t ) A ,
β ( ω ) = β 0 + β 2 2 ( ω ω 0 ) 2 + β B 0 ,
Δ ω r = Δ ω i , Δ ω t = Δ ω i 1 2 β B β 2 ( Δ ω i ) 2 ,
E ( t ) = { A i e i ( β z Δ ω i t ) + A r e i ( β z Δ ω r t ) t < 0 , A t e i ( β z Δ ω t t ) t > 0 ,
A i + A r = A t , Δ ω i A i + Δ ω r A r = Δ ω t A t .
r = Δ ω t Δ ω i Δ ω r Δ ω t .
r = 1 i Q 1 1 + i Q 1 , Q = 2 β B β 2 ( Δ ω i ) 2 ,
ϕ r = 2 tan 1 ( Q 1 ) .