Abstract

We study the nonlinear Raman–Nath diffraction (NRND) of femtosecond laser pulses in a 1D periodic nonlinear photonic structure. The calculated second-harmonic spectra represent frequency combs for different orders of transverse phase matching. These frequency combs are in close analogy with the well-known spectral Maker fringes observed in single crystals. The spectral intensity of the second harmonic experiences a redshift with a propagation angle, which is opposite the case of Čerenkov nonlinear diffraction. We analyze how NRND is affected by the group-velocity mismatch between fundamental and second-harmonic pulses and by the parameters of the structure. Our experimental results prove the theoretical predictions.

© 2014 Optical Society of America

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2013 (4)

2012 (3)

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, Appl. Phys. Lett. 101, 211114 (2012).
[CrossRef]

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, J. Phys. B 45, 055401 (2012).
[CrossRef]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, Opt. Lett. 37, 1832 (2012).
[CrossRef]

2011 (3)

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, Opt. Lett. 36, 3266 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, Appl. Phys. Lett. 98, 061104 (2011).
[CrossRef]

2010 (1)

2009 (2)

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Yu. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

2008 (4)

I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, Opt. Spectrosc. 105, 79 (2008).
[CrossRef]

K. A. Kuznetsov, G. Kh. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, JETP Lett. 87, 98 (2008).
[CrossRef]

P. Molina, M. Ramírez, and L. Bausá, Adv. Funct. Mater. 18, 709 (2008).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Yu. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef]

2007 (1)

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. V. Zamkov, and V. G. Arkhipkin, J. Opt. A 9, S334 (2007).
[CrossRef]

2006 (2)

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

V. Y. Shur, J. Mater. Sci. 41, 199 (2006).
[CrossRef]

1997 (1)

1968 (1)

I. Freund, Phys. Rev. Lett. 21, 1404 (1968).
[CrossRef]

Aleksandrovsky, A. S.

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, J. Opt. Soc. Am. B 30, 2014 (2013).
[CrossRef]

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, Appl. Phys. Lett. 101, 211114 (2012).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, Appl. Phys. Lett. 98, 061104 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. V. Zamkov, and V. G. Arkhipkin, J. Opt. A 9, S334 (2007).
[CrossRef]

An, N.

Arie, A.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, Opt. Lett. 36, 3266 (2011).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Yu. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Yu. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef]

Arkhipkin, V. G.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. V. Zamkov, and V. G. Arkhipkin, J. Opt. A 9, S334 (2007).
[CrossRef]

Ayoub, M.

Bang, O.

Bausá, L.

P. Molina, M. Ramírez, and L. Bausá, Adv. Funct. Mater. 18, 709 (2008).
[CrossRef]

Chen, X.

Chen, Y.

Chen, Z.

Chirkin, A. S.

I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, Opt. Spectrosc. 105, 79 (2008).
[CrossRef]

Dang, W.

Deng, X.

Denz, C.

Fischer, R.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Yu. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Freund, I.

I. Freund, Phys. Rev. Lett. 21, 1404 (1968).
[CrossRef]

Ikonnikov, A. A.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, Appl. Phys. Lett. 98, 061104 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
[CrossRef]

Imbrock, J.

Ivleva, L. I.

K. A. Kuznetsov, G. Kh. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, JETP Lett. 87, 98 (2008).
[CrossRef]

Jundt, D. H.

Kalinowski, K.

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, J. Phys. B 45, 055401 (2012).
[CrossRef]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, Opt. Lett. 37, 1832 (2012).
[CrossRef]

Kitaeva, G. Kh.

K. A. Kuznetsov, G. Kh. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, JETP Lett. 87, 98 (2008).
[CrossRef]

Kivshar, Y. S.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Kivshar, Yu. S.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Yu. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Yu. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Kong, Q.

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, J. Phys. B 45, 055401 (2012).
[CrossRef]

Koynov, K.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Krolikowski, W.

W. Wang, Y. Sheng, V. Roppo, Z. Chen, X. Niu, and W. Krolikowski, Opt. Express 21, 18671 (2013).
[CrossRef]

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, J. Phys. B 45, 055401 (2012).
[CrossRef]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, Opt. Lett. 37, 1832 (2012).
[CrossRef]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, Opt. Lett. 36, 3266 (2011).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Yu. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Yu. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Kuznetsov, K. A.

K. A. Kuznetsov, G. Kh. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, JETP Lett. 87, 98 (2008).
[CrossRef]

Lao, H.

Molina, P.

P. Molina, M. Ramírez, and L. Bausá, Adv. Funct. Mater. 18, 709 (2008).
[CrossRef]

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Yu. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Yu. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Niu, X.

Ozheredov, I. A.

I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, Opt. Spectrosc. 105, 79 (2008).
[CrossRef]

Pospelov, G. I.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, Appl. Phys. Lett. 98, 061104 (2011).
[CrossRef]

Ramírez, M.

P. Molina, M. Ramírez, and L. Bausá, Adv. Funct. Mater. 18, 709 (2008).
[CrossRef]

Ren, H.

Roedig, P.

Roppo, V.

Rovskii, V. E.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
[CrossRef]

Saltiel, S. M.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Yu. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Yu. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Sheng, Y.

W. Wang, Y. Sheng, V. Roppo, Z. Chen, X. Niu, and W. Krolikowski, Opt. Express 21, 18671 (2013).
[CrossRef]

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, J. Phys. B 45, 055401 (2012).
[CrossRef]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, Opt. Lett. 37, 1832 (2012).
[CrossRef]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, Opt. Lett. 36, 3266 (2011).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Shevlyuga, A. V.

K. A. Kuznetsov, G. Kh. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, JETP Lett. 87, 98 (2008).
[CrossRef]

Shiloh, R.

Shumitski, A. V.

I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, Opt. Spectrosc. 105, 79 (2008).
[CrossRef]

Shur, V. Y.

V. Y. Shur, J. Mater. Sci. 41, 199 (2006).
[CrossRef]

Shutov, I. V.

I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, Opt. Spectrosc. 105, 79 (2008).
[CrossRef]

Slabko, V. V.

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, J. Opt. Soc. Am. B 30, 2014 (2013).
[CrossRef]

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, Appl. Phys. Lett. 101, 211114 (2012).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
[CrossRef]

Volk, T. R.

K. A. Kuznetsov, G. Kh. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, JETP Lett. 87, 98 (2008).
[CrossRef]

Voloch-Bloch, N.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Vyunishev, A. M.

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, J. Opt. Soc. Am. B 30, 2014 (2013).
[CrossRef]

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, Appl. Phys. Lett. 101, 211114 (2012).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, Appl. Phys. Lett. 98, 061104 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. V. Zamkov, and V. G. Arkhipkin, J. Opt. A 9, S334 (2007).
[CrossRef]

Wang, W.

Zaitsev, A. I.

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, J. Opt. Soc. Am. B 30, 2014 (2013).
[CrossRef]

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, Appl. Phys. Lett. 101, 211114 (2012).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, Appl. Phys. Lett. 98, 061104 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
[CrossRef]

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. V. Zamkov, and V. G. Arkhipkin, J. Opt. A 9, S334 (2007).
[CrossRef]

Zamkov, A. V.

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. V. Zamkov, and V. G. Arkhipkin, J. Opt. A 9, S334 (2007).
[CrossRef]

Zheng, Y.

Adv. Funct. Mater. (1)

P. Molina, M. Ramírez, and L. Bausá, Adv. Funct. Mater. 18, 709 (2008).
[CrossRef]

Appl. Phys. Lett. (3)

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, and G. I. Pospelov, Appl. Phys. Lett. 98, 061104 (2011).
[CrossRef]

A. M. Vyunishev, A. S. Aleksandrovsky, A. I. Zaitsev, and V. V. Slabko, Appl. Phys. Lett. 101, 211114 (2012).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

J. Mater. Sci. (1)

V. Y. Shur, J. Mater. Sci. 41, 199 (2006).
[CrossRef]

J. Opt. A (1)

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. V. Zamkov, and V. G. Arkhipkin, J. Opt. A 9, S334 (2007).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, J. Phys. B 45, 055401 (2012).
[CrossRef]

JETP Lett. (1)

K. A. Kuznetsov, G. Kh. Kitaeva, A. V. Shevlyuga, L. I. Ivleva, and T. R. Volk, JETP Lett. 87, 98 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Opt. Spectrosc. (1)

I. V. Shutov, I. A. Ozheredov, A. V. Shumitski, and A. S. Chirkin, Opt. Spectrosc. 105, 79 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

I. Freund, Phys. Rev. Lett. 21, 1404 (1968).
[CrossRef]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Yu. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef]

Quantum Electron. (1)

A. S. Aleksandrovsky, A. M. Vyunishev, A. I. Zaitsev, A. A. Ikonnikov, G. I. Pospelov, V. E. Rovskii, and V. V. Slabko, Quantum Electron. 41, 748 (2011).
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Figures (4)

Fig. 1.
Fig. 1.

(a) Experimental scheme. (b) Part of etched polar surface of the sample. (c) SH pattern on the screen (inset: expanded view of NRND). Peripheral and central SH spots correspond to CND and NRND, respectively.

Fig. 2.
Fig. 2.

(a) Calculated angular distribution of SH spectral intensity for the parameters: w=40μm, L=400μm, D=0.75 (top scale corresponds to NRND order). (b) SH spectra averaged over the angle for NRND (m=±3, blue) and CND (m=±21, pink). (c) and (d) Local angular plots of SH spectral intensity for NRND of the third order (m=±3) and CND (m=±21), respectively. The vertical scale corresponds to the propagation angle.

Fig. 3.
Fig. 3.

Measured (blue) and calculated (red) angular dependences of SH intensity integrated over the spectrum. Inset: SH beam profile (m=+2).

Fig. 4.
Fig. 4.

(a) Calculated (green), averaged (black), and measured (blue) SH spectra for NRND order m=+2. Measured squared fundamental (red) and SH spectra (blue) for NRND order (b) m=0 and for (c) m=+2.

Tables (1)

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Table 1. Comparison between Predicted and Measured NRND Order Parameters

Equations (2)

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S(Ω,K,y)=(|αy|)2exp(τ2Ω24)×sinc(y2[Δk+νΩK22k2])2R(K),
R(K)=(mgmexp[a2(mG0+K)2/8])2

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