Abstract

Photonic systems such as arrays of coupled waveguides are well suited to emulating quantum mechanics with periodic lattice potentials, allowing the investigation of many physical phenomena in a convenient experimental setting. Usually, photons will “hop” only between neighboring lattice sites at a rate given by a purely real coupling coefficient, thus limiting the rich physics enabled by long-range coupling with complex coupling coefficients. Here we suggest and experimentally realize a spectral photonic lattice that can be configured to realize a wide variety of complex-valued coupling parameters over arbitrary lattice separations. In this system, a weak signal propagates across discrete frequency channels, driven by nonlinear interaction from stronger pump lasers. Our approach allows the experimental investigation of new discrete lattice physics—as an example, we demonstrate two novel instances of the discrete Talbot effect.

© 2017 Optical Society of America

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References

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2017 (3)

C. Wolff, B. Stiller, B. J. Eggleton, M. J. Steel, and C. G. Poulton, New J. Phys. 19, 023021 (2017).
[Crossref]

Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, APL Photon. 2, 026102 (2017).
[Crossref]

K. Wang, Y. Shi, A. S. Solntsev, S. Fan, A. A. Sukhorukov, and D. N. Neshev, Opt. Lett. 42, 1990 (2017).
[Crossref]

2016 (4)

B. A. Bell, J. He, C. Xiong, and B. J. Eggleton, Opt. Express 24, 5235 (2016).
[Crossref]

Q. Li, M. Davanço, and K. Srinivasan, Nat. Photonics 10, 406 (2016).
[Crossref]

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, Phys. Rev. Lett. 117, 223601 (2016).
[Crossref]

L. Yuan, Y. Shi, and S. Fan, Opt. Lett. 41, 741 (2016).
[Crossref]

2015 (1)

S. Lefrancois, A. S. Clark, and B. J. Eggleton, Phys. Rev. A 91, 013837 (2015).
[Crossref]

2014 (1)

L. Lu, J. D. Joannopoulos, and M. Soljačić, Nat. Photonics 8, 821 (2014).
[Crossref]

2013 (2)

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

A. S. Clark, S. Shahnia, M. J. Collins, C. Xiong, and B. J. Eggleton, Opt. Lett. 38, 947 (2013).
[Crossref]

2012 (1)

2010 (1)

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, Phys. Rev. Lett. 105, 093604 (2010).
[Crossref]

2009 (3)

2008 (3)

2006 (1)

2005 (2)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, Opt. Express 13, 9131 (2005).
[Crossref]

1836 (1)

H. Talbot, Philos. Mag. Ser. 3 9, 401 (1836).
[Crossref]

Agha, I.

Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, APL Photon. 2, 026102 (2017).
[Crossref]

Bell, B. A.

Bersch, C.

Brenn, A.

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, Nat. Phys. 5, 276 (2009).
[Crossref]

Cerqueira, S. A.

Chavez Boggio, J. M.

Christodoulides, D. N.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Clark, A. S.

S. Lefrancois, A. S. Clark, and B. J. Eggleton, Phys. Rev. A 91, 013837 (2015).
[Crossref]

A. S. Clark, S. Shahnia, M. J. Collins, C. Xiong, and B. J. Eggleton, Opt. Lett. 38, 947 (2013).
[Crossref]

Clemmen, S.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, Phys. Rev. Lett. 117, 223601 (2016).
[Crossref]

Collins, M. J.

Davanço, M.

Q. Li, M. Davanço, and K. Srinivasan, Nat. Photonics 10, 406 (2016).
[Crossref]

Dreisow, F.

Eggleton, B. J.

C. Wolff, B. Stiller, B. J. Eggleton, M. J. Steel, and C. G. Poulton, New J. Phys. 19, 023021 (2017).
[Crossref]

B. A. Bell, J. He, C. Xiong, and B. J. Eggleton, Opt. Express 24, 5235 (2016).
[Crossref]

S. Lefrancois, A. S. Clark, and B. J. Eggleton, Phys. Rev. A 91, 013837 (2015).
[Crossref]

A. S. Clark, S. Shahnia, M. J. Collins, C. Xiong, and B. J. Eggleton, Opt. Lett. 38, 947 (2013).
[Crossref]

Fan, S.

Farsi, A.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, Phys. Rev. Lett. 117, 223601 (2016).
[Crossref]

Fragnito, H. L.

Gaeta, A. L.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, Phys. Rev. Lett. 117, 223601 (2016).
[Crossref]

Harvey, J. D.

He, J.

Heinrich, M.

Hernandez-Figueroa, H. E.

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Joannopoulos, J. D.

L. Lu, J. D. Joannopoulos, and M. Soljačić, Nat. Photonics 8, 821 (2014).
[Crossref]

Kang, M. S.

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, Nat. Phys. 5, 276 (2009).
[Crossref]

Keil, R.

Knight, J. C.

Lederer, F.

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[Crossref]

Lefrancois, S.

S. Lefrancois, A. S. Clark, and B. J. Eggleton, Phys. Rev. A 91, 013837 (2015).
[Crossref]

Li, Q.

Q. Li, M. Davanço, and K. Srinivasan, Nat. Photonics 10, 406 (2016).
[Crossref]

Li, Y. H.

Lombardo, D.

Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, APL Photon. 2, 026102 (2017).
[Crossref]

Lu, L.

L. Lu, J. D. Joannopoulos, and M. Soljačić, Nat. Photonics 8, 821 (2014).
[Crossref]

Lumer, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

Mathews, J.

Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, APL Photon. 2, 026102 (2017).
[Crossref]

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

McGuinness, H. J.

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, Phys. Rev. Lett. 105, 093604 (2010).
[Crossref]

McKinstrie, C. J.

Min, Y.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Nazarkin, A.

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, Nat. Phys. 5, 276 (2009).
[Crossref]

Neshev, D. N.

Nolte, S.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

A. Szameit, R. Keil, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, and S. Tünnermann, Opt. Lett. 34, 2838 (2009).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Lett. 33, 2689 (2008).
[Crossref]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[Crossref]

Onishchukov, G.

Pertsch, T.

Peschel, U.

Plotnik, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

Podolsky, D.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

Poulton, C. G.

C. Wolff, B. Stiller, B. J. Eggleton, M. J. Steel, and C. G. Poulton, New J. Phys. 19, 023021 (2017).
[Crossref]

Radic, S.

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, Phys. Rev. Lett. 105, 093604 (2010).
[Crossref]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, Opt. Express 13, 9131 (2005).
[Crossref]

Ramelow, S.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, Phys. Rev. Lett. 117, 223601 (2016).
[Crossref]

Raymer, M. G.

Rechtsman, M. C.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

Rieznik, A. A.

Russell, P. St. J.

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, Nat. Phys. 5, 276 (2009).
[Crossref]

Segev, M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

Shahnia, S.

Shi, Y.

Sohler, W.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Soljacic, M.

L. Lu, J. D. Joannopoulos, and M. Soljačić, Nat. Photonics 8, 821 (2014).
[Crossref]

Solntsev, A. S.

Srinivasan, K.

Q. Li, M. Davanço, and K. Srinivasan, Nat. Photonics 10, 406 (2016).
[Crossref]

Steel, M. J.

C. Wolff, B. Stiller, B. J. Eggleton, M. J. Steel, and C. G. Poulton, New J. Phys. 19, 023021 (2017).
[Crossref]

Stegeman, G. I.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Stiller, B.

C. Wolff, B. Stiller, B. J. Eggleton, M. J. Steel, and C. G. Poulton, New J. Phys. 19, 023021 (2017).
[Crossref]

Sukhorukov, A. A.

Szameit, A.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

A. Szameit, R. Keil, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, and S. Tünnermann, Opt. Lett. 34, 2838 (2009).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Lett. 33, 2689 (2008).
[Crossref]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[Crossref]

Talbot, H.

H. Talbot, Philos. Mag. Ser. 3 9, 401 (1836).
[Crossref]

Tünnermann, A.

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Lett. 33, 2689 (2008).
[Crossref]

Tünnermann, S.

Wang, K.

Wang, L. J.

Wolff, C.

C. Wolff, B. Stiller, B. J. Eggleton, M. J. Steel, and C. G. Poulton, New J. Phys. 19, 023021 (2017).
[Crossref]

Xiong, C.

Yuan, L.

Zeuner, J. M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

Zhao, Y.

Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, APL Photon. 2, 026102 (2017).
[Crossref]

Zhao, Y. Y.

APL Photon. (1)

Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, APL Photon. 2, 026102 (2017).
[Crossref]

Nat. Photonics (2)

L. Lu, J. D. Joannopoulos, and M. Soljačić, Nat. Photonics 8, 821 (2014).
[Crossref]

Q. Li, M. Davanço, and K. Srinivasan, Nat. Photonics 10, 406 (2016).
[Crossref]

Nat. Phys. (1)

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, Nat. Phys. 5, 276 (2009).
[Crossref]

Nature (1)

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[Crossref]

New J. Phys. (1)

C. Wolff, B. Stiller, B. J. Eggleton, M. J. Steel, and C. G. Poulton, New J. Phys. 19, 023021 (2017).
[Crossref]

Opt. Express (4)

Opt. Lett. (7)

Philos. Mag. Ser. 3 (1)

H. Talbot, Philos. Mag. Ser. 3 9, 401 (1836).
[Crossref]

Phys. Rev. A (2)

S. Lefrancois, A. S. Clark, and B. J. Eggleton, Phys. Rev. A 91, 013837 (2015).
[Crossref]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. A 77, 043804 (2008).
[Crossref]

Phys. Rev. Lett. (3)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

H. J. McGuinness, M. G. Raymer, C. J. McKinstrie, and S. Radic, Phys. Rev. Lett. 105, 093604 (2010).
[Crossref]

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, Phys. Rev. Lett. 117, 223601 (2016).
[Crossref]

Supplementary Material (1)

NameDescription
» Supplement 1       Additional derivations and simulation results

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Figures (5)

Fig. 1.
Fig. 1. (a) FWM-BS in a χ(3) waveguide. A pair of pumps can up- or down-shift the signal in frequency. (b) With multiple pumps present (left), the evolution of the signal (right) is governed by multiple hopping coefficients across the lattice, depending on the amplitudes of pairs of pumps.
Fig. 2.
Fig. 2. (a) Experimental setup. MLL, mode-locked laser; SPS, spectral pulse shaper; EDFA, erbium-doped fiber amplifier; Att., variable attenuator; DL, tunable delay line; HNLF, highly nonlinear fiber; OSA, optical spectrum analyzer. (b) Measurement result with only two pumps. The dynamics of the evolution are apparent as the total average pump power P is varied. (c) Calculated band structure.
Fig. 3.
Fig. 3. Measurement results with the addition of a third pump, A4, creating second- and third-order hopping |c3||c2|0.15|c1|. The phase of the new pump is set to (a) 0, (b) π/2, (c) π, or (d) 3π/2. Insets to the bottom right show calculated band structures.
Fig. 4.
Fig. 4. Experimental demonstration of spectral discrete Talbot effect, for input signals with periodicity (a) N=2, (b) N=3, and (c) N=4. Horizontal solid (dashed) lines mark the positions of real (displaced) images of the input. The band structures to the right of each measurement are marked with the positions of the non-zero k components in each case (orange dots).
Fig. 5.
Fig. 5. (a) Talbot effect combined with image shift for N=3. A π/2 phase shift between the pumps creates an asymmetric propagation in which regular displaced images appear. (b) Talbot effect for N=5, which required first- and second-order couplings realized with three pump frequencies.

Equations (4)

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

dandz=ij=1+[cjan+j+cj*anj],
β(k)=j=1+[cjeijk+cj*eijk]=2γmlAm(0)Al*(0)ei(ml)k.
βiβ0βjβ0=pipj,
βm=(β0/4){1,1,4,1,1},

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