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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 13 — Jul. 1, 2013
  • pp: 15595–15602
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Localized surface waves at the interface between linear dielectric and biased centrosymmetric photorefractive crystals

Weijun Chen, Keqing Lu, Juanli Hui, Tianrun Feng, Shuqin Liu, Pingjuan Niu, and Liyuan Yu  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 15595-15602 (2013)
http://dx.doi.org/10.1364/OE.21.015595


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Abstract

We study localized surface waves at the interface between linear dielectric and biased centrosymmetric photorefractive (CP) crystals. If the propagation constant b is fixed, the energy of localized surface waves increases with the order of localized surface waves. For low b values, the considerable part of the energy of localized surface waves is concentrated in the linear dielectric and decreases with an increase in b. For high b values, the part of the energy of localized surface waves concentrated in the nonlinear CP crystals is always higher than that in the linear dielectric and increases with b. The stability properties of these localized surface waves are also discussed in detail.

© 2013 OSA

1. Introduction

Optical spatial solitons in photorefractive media have attracted much attention due to the possibility of their observation at very low laser power levels and great potentials for applications in optical switching and routing. At present, many branches of photorefractive solitons are known: screening solitons [1

1. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994) [CrossRef] [PubMed] .

, 2

2. D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12(9), 1628–1633 (1995) [CrossRef] .

], photovoltaic solitons [3

3. M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14(7), 1772–1781 (1997) [CrossRef] .

, 4

4. H. Wang and W. She, “Incoherently coupled grey photovoltaic spatial soliton families,” Chin. Phys. Lett. 22(1), 128–131 (2005) [CrossRef] .

], screening-photovoltaic solitons [5

5. K. Lu, T. Tang, and Y. Zhang, “One-dimensional steady-state spatial solitons in photovoltaic photorefractive materials with an external applied field,” Phys. Rev. A 61(5), 053822 (2000) [CrossRef] .

, 6

6. E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004) [CrossRef] .

], and solitons in centrosymmetric photorefractive (CP) crystals [7

7. M. Segev and A. J. Agranat, “Spatial solitons in centrosymmetric photorefractive media,” Opt. Lett. 22(17), 1299–1301 (1997) [CrossRef] .

10

10. A. Ciattoni, A. Marini, C. Rizza, and E. DelRe, “Collision and fusion of counterpropagating micrometer-sized optical beams in periodically biased photorefractive crystals,” Opt. Lett. 34(7), 911–913 (2009) [CrossRef] [PubMed] .

], all of which form in bulk photorefractive materials. On the other hand, the interface of linear and photorefractive materials can support surface waves [11

11. Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, “Multipole vector solitons in nonlocal nonlinear media,” Opt. Lett. 31(10), 1483–1485 (2006) [CrossRef] [PubMed] .

22

22. V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, “Optical surface waves at the interface between a linear dielectric and a photorefractive crystal,” Quantum Electron. 30(10), 905–910 (2000) [CrossRef] .

]. Delocalized photorefractive surface waves at the interface between linear dielectric and biased photorefractive crystals [18

18. T. Zhang, X. Ren, B. Wang, C. Lou, Z. Hu, W. Shao, Y. Xu, H. Kang, J. Yang, D. Yang, L. Feng, and J. Xu, “Surface waves with photorefractive nonlinearity,” Phys. Rev. A 76(1), 013827 (2007) [CrossRef] .

] or unbiased photorefractive crystals [19

19. G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51(2), 1571–1577 (1995) [CrossRef] [PubMed] .

], which were predicted and observed [20

20. M. Cronin-Golomb, “Photorefractive surface waves,” Opt. Lett. 20(20), 2075–2077 (1995) [CrossRef] [PubMed] .

], have infinite energy due to the presence of the long slowly decaying oscillating tails going into the volume of the photorefractive crystals [20

20. M. Cronin-Golomb, “Photorefractive surface waves,” Opt. Lett. 20(20), 2075–2077 (1995) [CrossRef] [PubMed] .

]. Of particular interest are localized photorefractive surface waves, which have not oscillating tails in the volume of the photorefractive crystals. Such localized surface waves at the interface between linear dielectric and biased photorefractive crystals have been predicted [21

21. V. Aleshkevich, Y. Kartashov, A. Egorov, and V. Vysloukh, “Stability and formation of localized surface waves at the dielectric photorefractive crystal boundary,” Phys. Rev. E 64(5), 056610 (2001) [CrossRef] .

, 22

22. V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, “Optical surface waves at the interface between a linear dielectric and a photorefractive crystal,” Quantum Electron. 30(10), 905–910 (2000) [CrossRef] .

]. However, it is not clear whether localized surface waves at the interface between linear dielectric and biased CP crystals are also possible.

In this paper, we analyze localized surface waves at the interface between linear dielectric and biased CP crystals. The lowest energy of localized surface waves appears when the propagation constant b is equal to a certain threshold value. When b is less than such a certain threshold value, the considerable part of the energy of localized surface waves is concentrated in the linear dielectric and decreases with an increase in b. When b is greater than such a certain threshold value, the part of the energy of localized surface waves concentrated in the nonlinear CP crystals is always higher than that in the linear dielectric and increases with b. The stability properties of these localized surface waves have been investigated numerically and we have found that they are stable.

2. Theoretical model

Let us consider an optical beam that propagates near the interface between linear dielectric occupying the half-space x ≥ 0 and centrosymmetric photorefractive crystals occupying the half-space x < 0 along the z-axis and is allowed to diffract only along the x direction. Moreover, let us assume that the beam is linearly polarized along the x-axis and that the external bias electric field is applied in the same direction. For illustration purposes, let the centrosymmetric photorefractive crystal be potassium lithium tantalate niobate (KLTN) with its optical c-axis oriented along the x-axis. In this case, the propagation of the optical beam is described by the standard shortened wave equations for the complex amplitude A(x, z) of the light field:
iAz=12k02Ax2forx0,
(1a)
iAz=12k02Ax2k2k022k0Ak2k0nΔnAforx<0,
(1b)
where Δn=(1/2)n3geffε02(εr1)2Esc2 is the change in refractive index, n is the unperturbed refractive index of the CP crystal, geff is the effective quadratic electro-optic coefficient, ε0 and εr, respectively, are the vacuum and relative dielectric constants, Esc is the space-charge field inside the CP crystal, k = 2πn/λ is the wave number in the area of the CP crystal, λ is the free-space wavelength of the lightwave used, k0 = 2πn0/λ is the wave number in the area of the linear dielectric, n0 is the dielectric refractive index. For relatively broad beam configurations, the space-charge field can be obtained from the Kukhtarev-Vinetskii model and is approximately given by [2

2. D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12(9), 1628–1633 (1995) [CrossRef] .

]
Esc=E0IdI+Id+KBTexln(I+Id),
(2)
where I = |A|2 is the intensity of the light beam, KB is the Boltzmann constant, T is the absolute temperature, e is the electron charge, and Id is the dark irradiance of the crystal, E0 is the value of the space-charge field at x → ±∞. If the spatial extent of the optical wave is much less than the x-width l of the CP crystal, then under a constant voltage bias V, E0 is approximately given by ±V/l. Moreover, for simplicity, let us adopt the following dimensionless coordinates, i.e., let ξ=z/k0x02 and s = x/x0, where x0 is an arbitrary transverse scale. By employing these latter transformations and by substituting Eq. (2) into Eq. (1b), the complex amplitude of the light field is found to satisfy:
iAξ=122As2fors0,
(3a)
iAξ=122As2pA+βA(1+Id1|A|2)2+μ1A(1+Id1|A|2)2(Id1|A|2)s+μ2A(1+Id1|A|2)2[(Id1|A|2)s]2fors<0,
(3b)
where p=(k2k02)x02/2 is the guiding parameter describing the waveguiding properties of the boundary, β=x02k2(1/2)n2geffε02(εr1)2E02 is the relative contribution of the drift component of the nonlinear response, μ1=(KBT/e)x0k2n2geffε02(εr1)2E0 and μ2=(KBT/e)2k2(1/2)n2geffε02(εr1)2 are the relative contribution of the nonlocal diffusion component of the nonlinear response of first and second orders, respectively.

The first term in the right-hand side of Eq. (3b) describes the diffraction spreading of the beam, the second term characterizes the interaction of the beam with the interface between linear dielectric and CP crystals, the third term describes the beam self-focusing caused by the local drift component of nonlinear response, and the the fourth and fifth term describe the beam self-bending of first and second orders caused by the diffusion component of the nonlinear response of the CP crystal, respectively. In this study, we consider the following examples: Let E0 = 2×105V/m, λ = 0.5μm, and x0 = 9μm. The KLTN parameters [9

9. E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Pefaeli, and A. J. Agranat, “One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric potassium lithium tantalate niobate,” Opt. Lett. 23(6), 421–423 (1998) [CrossRef] .

] are taken to be n = 2.2, T = 21°C, and geff = 0.12m4C−2. For this set of values, β = 3.6, μ1 = 0.1, and μ2 = 0.00071.

3. Numerical results

For a solitary beam, the wave field amplitude A can be expressed as A=Idu(s)exp(ibξ), where b is the real propagation constant and the envelope u(s) is the real function. Substitution of this form of A into Eqs. (3a) and (3b) yields
d2uds2=2bufors0,
(4a)
d2uds2=2(bp)u+2βu(1+u2)2+4μ1u2(1+u2)2duds+8μ2u3(1+u2)2(duds)2fors<0,
(4b)
where both u and du/ds should match the continuity conditions at the boundary point s = 0. In the area of nonlinear CP medium, Eq. (4b) cannot be solved analytically and should be integrated numerically, for example, by the shooting method that reduces a two-point boundary problem to the Cauchy problem. The initial conditions are chosen by using the fact that in the area of linear dielectric the solutions of Eq. (4a) can be readily obtained and are given by u = mexp[−(2b)1/2s], where m is the free parameter describing the strength of the nonlinear effects. By varying parameters b and m, and integrating Eq. (4b), we obtained various profiles of surface waves at the interface between linear dielectric and biased CP crystals.

Now let us classify all possible types of solutions of Eq. (4b) by using quite general treatment based on the analogy of Eq. (4b) for the envelope of the surface wave with the equation describing the motion of a mechanical particle in a potential well with nonlinear dissipation, where the wave envelope u is equivalent to the particle position and the transverse coordinate s is equivalent to time. In the area of the nonlinear CP crystal (s < 0) Eq. (4b) can be readily written in the following form:
d(U+T)ds=4μ1u2(1+u2)2(duds)2+8μ2u3(1+u2)2(duds)3,
(5)
where U = (pb)u2 +β(1 + u2)−1β and T = (1/2)(du/ds)2 are the potential and kinetic energies of the particle with unit mass, respectively, and the right-hand side of Eq. (5) shows the nonlinear friction force. Figure 1 depicts typical profiles of the potential well U for different values of pb when β = 3.6. The potential well is symmetric with respect to the point u = 0. This figure shows only the right part of the potential well corresponding to positive values of u.

Fig. 1 Typical profiles of the potential well for pb = 5 (dashed curve), 0.8 (solid curve), and −2 (dash-dot curve) when β = 3.6.

For pb > β, the potential well has a single stable stationary point u = 0 (see dashed curve in Fig. 1). In this case, a mechanical particle with a nonzero initial energy U + T performs damped oscillations (as s varies from 0 to −∞), passing from the right wing of the potential well to the left wing and losing its energy because of the influence of nonlinear friction. When s → −∞, this particle asymptotically approaches the stable equilibrium position u = 0. This type of particle motion corresponds to the well-known delocalized surface waves [21

21. V. Aleshkevich, Y. Kartashov, A. Egorov, and V. Vysloukh, “Stability and formation of localized surface waves at the dielectric photorefractive crystal boundary,” Phys. Rev. E 64(5), 056610 (2001) [CrossRef] .

], which have long oscillating tails in the volume of the CP crystal. Figure 2 shows the profiles of such waves for two different values of m when β = 3.6, p = 6, b = 1, μ1 = 0.1, and μ2 = 0.00071.

Fig. 2 Profiles of the delocalized surface waves for β = 3.6, p = 6, b = 1, μ1 = 0.1, μ2 = 0.00071, and m = 4.5 and 2.

For 0 < pb < β, the potential well has two stable ( u=±β/(pb)1) and one unstable (u = 0) stationary points, as shown in Fig. 1. A particle with a nonzero initial energy U + T will be periodically transferred from the right wing of the potential well (corresponding to positive u) into the left wing of the well (corresponding to negative u) until it stops at one of the two stable stationary points u=±β/(pb)1 or at the unstable stationary point u = 0 because of the energy loss. The former case corresponds to the shock surface waves with an infinite energy [21

21. V. Aleshkevich, Y. Kartashov, A. Egorov, and V. Vysloukh, “Stability and formation of localized surface waves at the dielectric photorefractive crystal boundary,” Phys. Rev. E 64(5), 056610 (2001) [CrossRef] .

], which have a nonzero asymptotic form at s → −∞. Figure 3 depicts typical profiles of the shock surface waves of the first three orders. Note that the order of a wave is defined by the number of intersections of its envelope with the s-axis, including the point s = 0. When s → −∞, shock surface waves represent damped oscillations superimposed on the constant background where height is given by ±β/(pb)1, as shown in Fig. 3. On the other hand, shock surface waves in the diffusion medium are highly unstable since they have zero harmonic in the spatial spectrum and are affected by modulation instability.

Fig. 3 Profiles of the shock surface waves of the first three orders for β = 3.6, p = 1, b = 0.2, μ1 = 0.1, and μ2 = 0.00071.

Of particular interest is the case when a particle describing a surface wave stops at the unstable stationary point u = 0. This situation corresponds to the formation of localized surface waves without oscillating tails in the volume of the CP crystal. For low b values, Fig. 4(a) depicts the profiles of localized surface waves of the first three orders, whereas Fig. 4(b) depicts the profiles of the second order localized surface waves for three different values of b. The energy W=u2(s)ds conveyed by localized surface waves of first three orders versus the propagation constant is shown in Fig. 5. Figure 5 demonstrates that the lowest energy of localized surface waves appears when b is equal to a certain threshold value and the energy of localized surface waves increases with the order of localized surface waves when b is fixed. Moreover, Figs. 4(a) and 4(b) indicate that the considerable part of the energy of localized surface waves can be concentrated in the linear dielectric and decreases with an increase in b. For high b values, the profiles of localized surface waves of the first three orders are shown in Fig. 6(a), whereas the profiles of the third order localized surface waves for three different values of b are shown in Fig. 6(b). It is clearly seen from Figs. 6(a) and 6(b) that the part of the energy of localized surface waves concentrated in the nonlinear CP crystal is always higher than that in the linear dielectric and increases with b.

Fig. 4 (a) Profiles of the localized surface modes of the first three orders for b = 0.03; (b) profiles of the second order localized surface modes for b = 0.01, 0.03, and 0.06. In all cases β = 3.6, μ1 = 0.1, and μ2 = 0.00071.
Fig. 5 Dependence of the energy of localized surface waves of first three orders on the propagation constant for β = 3.6, p = 1.8, μ1 = 0.1, and μ2 = 0.00071.
Fig. 6 (a) Profiles of the localized surface modes of the first three orders for b = 1; (b) profiles of the third order localized surface modes for b = 0.06, 0.6, and 1. In all cases β = 3.6, μ1 = 0.1, and μ2 = 0.00071.

The stability properties of these localized surface waves will be discussed. In particular, their stability is investigated here using a beam propagation method. Localized surface waves given by Eqs. (4a) and (4b) have been used as the input beam profiles. As an example, consider the second order localized surface modes for b = 0.01 and 0.03 in Fig. 4(b). Figures 7(a) and 7(b) depict the evolution of the second order localized surface modes for b = 0.01 and 0.03 in Fig. 4(b) when their input amplitude have been perturbed by 20%. Moreover, consider the third order localized surface modes for b = 0.06 and 1 in Fig. 6(b). Figures 7(c) and 7(d) show the evolution of the third order localized surface modes for b = 0.06 and 1 in Fig. 6(b) when their input amplitude have been perturbed by 20%. The solitary behavior of these localized surface modes is evident in these figures since they propagate unchanged. Similarly, a stability study of other localized surface modes in Figs. 4(b) and 6(b) shows that they are also stable.

Fig. 7 Stable propagation of the second order localized surface modes for (a) b = 0.01 and (b) b = 0.03 and the third order localized surface modes for (c) b = 0.06 and (d) b = 1 when their amplitudes are perturbed by 20% at the input.

Finally, for pb < 0, the potential well has a single unstable stationary point u = 0 (see dash-dot curve in Fig. 1). In this case, the finite motion of a particle with a nonzero energy U + T is not possible and it is useless to speak about surface waves.

4. Conclusion

In conclusion, we have studied localized surface waves at the interface between linear dielectric and biased CP crystals. We have shown that when b is fixed, the energy of localized surface waves increases with the order of localized surface waves. We have found that for low b values the considerable part of the energy of localized surface waves is concentrated in the dielectric and decreases with an increase in b and that for high b values the part of the energy of localized surface waves concentrated in the nonlinear CP crystals is always higher than that in the linear dielectric and increases with b. The stability of these localized surface waves have been investigated numerically and it has been found that they are stable.

Acknowledgment

The work was supported by the Natural Science Foundation of Chinese Tianjin (No. 13JCY-BJC16400) and by the National Natural Science Foundation of China (Nos. 10674176 and 10474136).

References and links

1.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994) [CrossRef] [PubMed] .

2.

D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12(9), 1628–1633 (1995) [CrossRef] .

3.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B 14(7), 1772–1781 (1997) [CrossRef] .

4.

H. Wang and W. She, “Incoherently coupled grey photovoltaic spatial soliton families,” Chin. Phys. Lett. 22(1), 128–131 (2005) [CrossRef] .

5.

K. Lu, T. Tang, and Y. Zhang, “One-dimensional steady-state spatial solitons in photovoltaic photorefractive materials with an external applied field,” Phys. Rev. A 61(5), 053822 (2000) [CrossRef] .

6.

E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett. 85(12), 2193–2195 (2004) [CrossRef] .

7.

M. Segev and A. J. Agranat, “Spatial solitons in centrosymmetric photorefractive media,” Opt. Lett. 22(17), 1299–1301 (1997) [CrossRef] .

8.

K. Zhan, C. Hou, and S. Pu, “Temporal behavior of spatial solitons in centrosymmetric photorefractive crystals,” Optics & Laser Technology 43(7), 1274–1278 (2011) [CrossRef] .

9.

E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Pefaeli, and A. J. Agranat, “One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric potassium lithium tantalate niobate,” Opt. Lett. 23(6), 421–423 (1998) [CrossRef] .

10.

A. Ciattoni, A. Marini, C. Rizza, and E. DelRe, “Collision and fusion of counterpropagating micrometer-sized optical beams in periodically biased photorefractive crystals,” Opt. Lett. 34(7), 911–913 (2009) [CrossRef] [PubMed] .

11.

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, “Multipole vector solitons in nonlocal nonlinear media,” Opt. Lett. 31(10), 1483–1485 (2006) [CrossRef] [PubMed] .

12.

W. Chen, Y. He, and H. Wang, “Surface defect superlattice solitons,” J. Opt. Soc. Am. B 24(10), 2584–2588 (2007) [CrossRef] .

13.

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, “Surface lattice solitons,” Opt. Lett. 31(18), 2774–2776 (2006) [CrossRef] [PubMed] .

14.

W. Q. Chen, X. Yang, S. Y. Zhong, Z. Yan, T. H. Zhang, J. G. Tian, and J. J. Xu, “Surface dark screening solitons,” Opt. Lett. 36(19), 3801–3803 (2011) [CrossRef] [PubMed] .

15.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface lattice solitons in diffusive nonlinear media,” Opt. Lett. 33(8), 773–775 (2008) [CrossRef] [PubMed] .

16.

J. Safioui, E. Fazio, F. Devaux, and M. Chauvet, “Surface-wave pyroelectric photorefractive soliton,” Opt. Lett. 35(8), 1254–1256 (2010) [CrossRef] [PubMed] .

17.

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Observation of discrete quadratic surface solitons,” Opt. Express. 14(12), 5508–5516 (2006) [CrossRef] [PubMed] .

18.

T. Zhang, X. Ren, B. Wang, C. Lou, Z. Hu, W. Shao, Y. Xu, H. Kang, J. Yang, D. Yang, L. Feng, and J. Xu, “Surface waves with photorefractive nonlinearity,” Phys. Rev. A 76(1), 013827 (2007) [CrossRef] .

19.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51(2), 1571–1577 (1995) [CrossRef] [PubMed] .

20.

M. Cronin-Golomb, “Photorefractive surface waves,” Opt. Lett. 20(20), 2075–2077 (1995) [CrossRef] [PubMed] .

21.

V. Aleshkevich, Y. Kartashov, A. Egorov, and V. Vysloukh, “Stability and formation of localized surface waves at the dielectric photorefractive crystal boundary,” Phys. Rev. E 64(5), 056610 (2001) [CrossRef] .

22.

V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, “Optical surface waves at the interface between a linear dielectric and a photorefractive crystal,” Quantum Electron. 30(10), 905–910 (2000) [CrossRef] .

OCIS Codes
(190.4350) Nonlinear optics : Nonlinear optics at surfaces
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 25, 2013
Revised Manuscript: May 21, 2013
Manuscript Accepted: May 27, 2013
Published: June 21, 2013

Citation
Weijun Chen, Keqing Lu, Juanli Hui, Tianrun Feng, Shuqin Liu, Pingjuan Niu, and Liyuan Yu, "Localized surface waves at the interface between linear dielectric and biased centrosymmetric photorefractive crystals," Opt. Express 21, 15595-15602 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15595


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References

  1. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett.73(24), 3211–3214 (1994). [CrossRef] [PubMed]
  2. D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B12(9), 1628–1633 (1995). [CrossRef]
  3. M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, “Photovoltaic spatial solitons,” J. Opt. Soc. Am. B14(7), 1772–1781 (1997). [CrossRef]
  4. H. Wang and W. She, “Incoherently coupled grey photovoltaic spatial soliton families,” Chin. Phys. Lett.22(1), 128–131 (2005). [CrossRef]
  5. K. Lu, T. Tang, and Y. Zhang, “One-dimensional steady-state spatial solitons in photovoltaic photorefractive materials with an external applied field,” Phys. Rev. A61(5), 053822 (2000). [CrossRef]
  6. E. Fazio, F. Renzi, R. Rinaldi, M. Bertolotti, M. Chauvet, W. Ramadan, A. Petris, and V. I. Vlad, “Screening-photovoltaic bright solitons in lithium niobate and associated single-mode waveguides,” Appl. Phys. Lett.85(12), 2193–2195 (2004). [CrossRef]
  7. M. Segev and A. J. Agranat, “Spatial solitons in centrosymmetric photorefractive media,” Opt. Lett.22(17), 1299–1301 (1997). [CrossRef]
  8. K. Zhan, C. Hou, and S. Pu, “Temporal behavior of spatial solitons in centrosymmetric photorefractive crystals,” Optics & Laser Technology43(7), 1274–1278 (2011). [CrossRef]
  9. E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Pefaeli, and A. J. Agranat, “One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric potassium lithium tantalate niobate,” Opt. Lett.23(6), 421–423 (1998). [CrossRef]
  10. A. Ciattoni, A. Marini, C. Rizza, and E. DelRe, “Collision and fusion of counterpropagating micrometer-sized optical beams in periodically biased photorefractive crystals,” Opt. Lett.34(7), 911–913 (2009). [CrossRef] [PubMed]
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