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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 23706–23715
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Self-accelerating optical beams in highly nonlocal nonlinear media

Rivka Bekenstein and Mordechai Segev  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 23706-23715 (2011)
http://dx.doi.org/10.1364/OE.19.023706


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Abstract

We find self-accelerating beams in highly nonlocal nonlinear optical media, and show that their propagation dynamics is strongly affected by boundary conditions. Specifically for the thermal optical nonlinearity, the boundary conditions have a strong impact on the beam trajectory: they can increase the acceleration during propagation, or even cause beam bending in a direction opposite to the initial trajectory. Under strong self-focusing, the accelerating beam decomposes into a localized self-trapped beam propagating on an oscillatory trajectory and a second beam which accelerates in a different direction. We augment this study by investigating the effects caused by a finite aperture and by a nonlinear range of a finite extent.

© 2011 OSA

1. Introduction

In this paper, we do just that: we present self-accelerating beams in nonlocal nonlinear optical media, focusing specifically on the highly nonlocal thermal optical nonlinearity. We show that the non-accelerating thermal boundary conditions have a strong impact on the beam trajectory: they can increase the acceleration during propagation, or even cause beam bending in a direction opposite to the initial trajectory. Under strong self-focusing, the accelerating beam decomposes into a localized self-trapped beam, and a second beam which accelerates in a different direction.

2. Accelerating self-trapped (propagation-invariant) solutions

The thermal nonlinear optical effect is caused due to absorption of light by the medium, which raises the local temperature. In such a medium, the temperature modifies the refractive index, according to Δn=βΔT,β=dn/dt [15], where β describes the temperature dependence of the refractive index, ΔT is the change in the temperature and Δn is the change in the refractive index. The temperature obeys the heat equation, which under steady-state conditions, yields an equation for the change in the refractive index [15]:
κβ2Δn=α|ψ|2
(1)
κis the thermal conductivity, α is the linear absorption coefficient of the material, and ψ is the slowly-varying amplitude of the electromagnetic field. The sign of β determines if the medium is of the self-focusing or self-defocusing type. In many relevant materials (e.g., lead glass), α is very small, such that absorption can be safely neglected for fairly large propagation distances, while the thermal nonlinearity is still very strong [15

15. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005). [CrossRef] [PubMed]

]. For simplicity, we henceforth analyze one-dimensional beams propagating in this nonlinear medium. The evolution of the slowly-varying envelope ψ(x,z) of such beams is described by the nonlinear paraxial equation:
iψz+12kψxx+kΔnn0ψ=0
(2)
where z is the optical axis, x is the transverse direction, k=2πn0/λ is the wavenumber, λ is the vacuum wavelength, n0 is the background refractive index of the medium, and Δn satisfies Eq. (1). As shown in [19

19. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett. 32(2), 154–156 (2007). [CrossRef] [PubMed]

], when the refractive index change Δn is not too large (~0.01 and smaller), the evolution is slow and adiabatic, such that the z-derivatives in Eq. (1) can be safely neglected. To find self-accelerating beams in such a medium, we use the same method used in [10

10. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011). [CrossRef] [PubMed]

] to find accelerating beams in media with local nonlinear response. We seek self-trapped self-accelerating solutions that satisfy |ψ(x,0)|=|ψ(xf(z),z)|, meaning that the beam is propagating along the curve x=f(z), while maintaining its exact intensity structure. Such a solution is a self-trapped solution in the accelerating frame of reference. We change variables x^=xf(z), transforming Eq. (2) to the accelerating frame, which yields

iψ^zif'(z)ψ^x^+12kψ^x^x^+kΔn^n0ψ^=0
(3)

We seek propagation-invariant solutions for Eq. (3), namely, ψ^(x^,z)=u(x^)eiT(x^,z), where u is a real function. After setting to zero the coefficients of terms that diverge if u(x^) goes through zero, we obtain
12ku''+kΔn^n0uf''k(x^x1)u=0
(4)
with the condition f''k=const, which restricts f(z) to be parabolic. Other trajectories could be possible, if the additional terms of the form 1/u2,1/u4 are kept. However, to be physical, such solutions should not attain zero value anywhere. Keeping in mind that all accelerating beams in lossless media found thus far possess oscillations that go through zero [1

1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979). [CrossRef]

,21

21. E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011). [CrossRef] [PubMed]

], it seems unlikely that additional, non-parabolic, trajectories could exist for self-accelerating beams displaying propagation-invariant evolution. Hence, we focus here on beams propagating along parabolic trajectories only. We apply transformation of variables to Eqs. (1) and (4), finding x˜=A1/3(x^x1),u˜=2k2A2/3u,Δn˜=2k2A2/3n0Δn, where A=2k2f'' and c=βακn0, which yields

Δn˜''=c|u˜|2
(5)
u˜''+Δn˜u˜x˜u˜=0
(6)

The Green function of Eq. (5), for trivial boundary conditions, is G(x˜,x˜')=const|x˜x˜'|. Using this we rewrite Eq. (6):

u˜''c[LL|x˜x˜'||u(x˜')|2dx˜']u˜x˜u˜=0
(7)

To approximate the integral, we assume that the self-trapped solution has at least one decaying tail. Therefore, for some x0, (with x0>0, without loss of generality) every x˜>x0 satisfies |u(x˜)|20. We approximate the integral term for x˜>x0:

LL|x˜x'||u(x')|2dx˜'LL(x˜x')|u(x˜')|2dx'=x˜P+XCM
(8)

where P=LL|u˜(x')|2dx' and XCM=LLx'|u˜(x')|2dx'. This approximation is valid for any solution having at least one decaying tail. Under the condition cP<<1, which physically implies a weak nonlinearity, Eq. (7) is similar to the Airy equation u˜''x˜u˜=0, whose solutions are the Airy functions. This suggests that, for every such small cP, the refractive index change Δn˜(x) is approximately linear in x˜ for any x˜>x0. Hence, we expect the solution on the side of the decaying tail of u˜ to be similar to the Airy function, which is the eigen-function of a potential structured as a linear gradient.

We solve Eq. (5) and Eq. (6) numerically in the interval [a,a], and find the eigen-functions (the propagation-invariant solutions in the accelerated frame). As sketched in Fig. 1
Fig. 1 (a) Sketch of the physical system and the boundary conditions used to find the self-accelerating self-trapped solutions, with a typical beam shown at z = 0. To find these solutions, which are propagation-invariant in the accelerating frame, we assume that the boundaries of the nonlinear medium accelerate with the beam, such that the temperature at these boundaries is constant. (b-d) An example of a self-accelerating self-trapped solution in the thermal optical nonlinearity of the self-focusing type: (b) normalized refractive index change Δn˜(x˜) supporting the self-accelerating self-trapped beam, (c,d) normalized amplitude of such beam (red dotted) compared to the Airy function (blue dashed), far from main lobe (c) and at the vicinity of the main lobe (d).
, the boundary conditions for Δn˜ are Δn˜(x˜=a)=Δn˜(x˜=a)=0 (arising from T(x˜=±a)=T0, T0 being the temperature everywhere in the absence of light). The boundary conditions for the field amplitude, u˜(x˜=a) and u˜(x˜=a), can be any non-zero finite value. We choose this value to be such that does not make u˜ diverge. A typical solution is shown in Fig. 1.

Notice that the change in the refractive index, Δn˜, is approximately linear near the main lobe, as we expected. This implies that, near the main lobe, the solution is similar to the Airy function. As x˜a, the self-trapped solution differs from the Airy function, mainly due to the boundary conditions.

3. Propagation dynamics of accelerating self-trapped beams

We tested the stability of the self-accelerating solution numerically under random noise in a magnitude of 10% of the amplitude of the main lobe. We find that the accelerating beams are virtually unaffected by the noise, for both the focusing and defocusing cases. This is in fact excepted from highly nonlocal nonlinearities, which always tend to suppress localized perturbations in the beam and/or the index change.

The results depicted in Fig. 2 show that varying the power of the beam changes the beam trajectory. Notice that the beam is no longer propagation-invariant in the accelerating frame of reference. The reason for this is the thermal boundary conditions. Namely, the boundary conditions are symmetric at z=0, however, as the beam is propagating, it undergoes spatial acceleration (beam bending), which inherently makes the boundaries to become non-symmetric with respect to the beam. As we know from [19

19. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett. 32(2), 154–156 (2007). [CrossRef] [PubMed]

], asymmetric boundary conditions exert forces on the beam, which affect the beam trajectory. The complex dynamics shown in Fig. 2 arises from this interplay between interference effects predesigned to support a particular accelerating trajectory and boundary forces exerted on the beam, in highly nonlocal nonlinear media. Clearly, these forces have a major impact on the beam trajectory, leading to accelerating trajectories that are very different from the parabolic trajectories found for the Airy beams propagating in linear media. For the self-focusing case, the acceleration decreases as the beam power is increased, and for strong self-focusing the trajectory becomes non-parabolic. This is a clear manifestation of the underlying nonlocal nonlinearity, because in nonlinearities where Δn has a local response, all trajectories are parabolic. Furthermore, all accelerating beams supported by linear interference effects must have convex trajectories [21

21. E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011). [CrossRef] [PubMed]

], in a sharp contrast to the “wiggly beam” of Fig. 2c, which exhibits a non-convex trajectory. Also, notice that under strong self-focusing the lobes of the accelerating beam become narrower as the beam is propagating. For the self-defocusing case (Fig. 2d), the acceleration increases as the beam power is increased, and for a strong defocusing nonlinearity all the lobes of the beam expand. Thus, controlling the power of the optical beam allows us to change the trajectory (spatial acceleration) of the beam, by virtue of boundary force effects arising from the long-range nonlocal nature of the thermal nonlinearity.

Another very interesting phenomenon occurs in the self-focusing case. For very strong nonlinearity, the original beam decomposes into two beams, as depicted in Fig. 3c: The original Airy-like beam that continues propagating on a different trajectory, until it loses all its power as a result of the finite aperture of the beam, and a second, new, localized beam that has taken its power from the original beam. Notice that this second beam lacks any oscillating tails characteristic of the Airy-like wavepackets, which accelerate due to their structure. Indeed, this second beam is self-trapped by virtue of the self-focusing nonlinearity: it is a spatial soliton [23

23. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999). [CrossRef] [PubMed]

]. For strong self-focusing, the nonlinear term in Eq. (6) becomes dominant, causing focusing of the beam that overcomes the tendency of the beam to accelerate. This new self-trapped beam first moves on an oscillatory trajectory while radiating power during propagation. Later on, after that beam has gained enough power, the trajectory oscillations decrease, and the beam stabilizes around a constant power, becoming a spatial soliton propagating at an approximately straight line trajectory in the z direction. Such oscillatory propagation dynamics of solitons in this highly nonlocal nonlinear medium is familiar from earlier work [19

19. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett. 32(2), 154–156 (2007). [CrossRef] [PubMed]

]: it appears when the soliton is launched off-center, such that the boundaries exert asymmetric forces on the beam. What we have shown here is a fascinating nonlinear phenomenon in which a localized soliton is created from a wide beam with very long tails, that are affected by far away boundary conditions through a highly nonlocal nonlinearity.

4. Accelerating self-trapped beams carrying finite power

The self-accelerating beams discussed thus far in this article carry infinite power (truncated only by the boundaries of the sample). Physically, however, all beams must carry finite power. Accordingly, accelerating beams carrying finite power were analyzed theoretically in both the linear domain [2

2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

,3

3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef] [PubMed]

] and in local nonlinearities [10

10. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011). [CrossRef] [PubMed]

]. In this section, we study the propagation dynamic of accelerating beams carrying finite power in highly nonlocal nonlinear media. Specifically, we are interested to elucidate the influence of the width of the aperture (which is what makes the beam finite) on the propagation dynamic of the beam. We study numerically the propagation dynamic of such finite-power beams under self-focusing and self-defocusing, for varying power levels. It is important however to distinguish between the linear diffractive evolution associated with launching finite beams (namely, that the acceleration occurs only for a finite distance determined by the aperture [2

2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

,3

3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef] [PubMed]

,10

10. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011). [CrossRef] [PubMed]

]), and the effects caused by the nonlocal response of the nonlinearity. Consequently, we simulate finite beams whose initial width (aperture) is considerably narrower than the width of the nonlinear sample (2a in Fig. 1).

We find that, under self-focusing conditions, such self-accelerating finite beam exhibits all the phenomena described above with infinite beams, including the observation that, as the power of the beam is increased the acceleration decreases, and the intriguing effects occurring under strong self-focusing (Fig. 3). Likewise, under self-defocusing, as the beam power is increased the acceleration increases, similar to what happens with infinite beams.

The effects associated with the highly nonlocal nature of the nonlinearity do give rise to one important effect caused by the aperture: changing the aperture changes the distance of the beam from the boundaries. Hence, when the aperture is wider the boundary forces are more dominant and have a more significant influence on the acceleration of the beam. A typical example of the propagation dynamic of such a finite self-accelerating beam is displayed in Fig. 4
Fig. 4 (a) Normalized amplitude of a finite accelerating beam with an aperture of 1.8mm allowing 55 lobes (solid line), and the normalized change in the refractive index induced by such beam at z = 0 (dashed line). (b) Propagation dynamics occurring when the finite Airy-like beam of (a) is launched into a rectangular sample of 7.5mm, under self-focusing nonlinearity. The power is the same as the beam in Fig. 2a, however the maximum change in the refractive index is now much higher (5.4 ⋅ 10–3), and the finite launch beam decomposes into two separate beams, similar to the behavior of an infinite beam under strong self-focusing. (c) Normalized change in refractive index at z=0under nonlinearity with a range of nonlocality of 20μm. (d) Propagation dynamic occurring when this beam with a main lobe width of 50μm is launched into a rectangular sample of 7.5mm width, under nonlinearity with a finite range of nonlocality of 20μm. The power of the beam is the same as the beam in Fig. 2a. After propagation distance of 6.6cm the main lobe is shifted by 425μm in the x direction, which is more than in the infinite-range nonlocal case. In all plots x is normalized as described in the text, and the zunits are meters.
: a beam of wavelength λ=0.75μm, going through an aperture of 1.8mm, which allows 55 lobes with width varying from 50μm (main lobe) to 10μm (narrowest lobe). All the physical parameters of the beam and of the sample are exactly as for the beam in Fig. 2a. The beam enters a sample of 7.5mm width, the background refractive index is n0=1.5, and |c|=2105. The power is the same as of the beam in Fig. 2a. However, for this finite beam the same power gives rise to a change in the refractive index which at its peak is as large as 5.4103, one order of magnitude higher than that of the infinite beam. The reasoning is simple: the same power is now distributed over the finite aperture, which is narrower than the sample width, hence the higher nonlinear effects. Consequently, the main nonlinear effect caused by the finite width of an accelerating launch beam is that all the nonlinear effects are “scaled up”: they occur at power levels lower than those required to exhibit the same effects with infinite beams.

5. Accelerating self-trapped beams in nonlinear media with a finite range of nonlocality

6. Conclusion

We have found self-accelerating self-trapped beams supported by the highly nonlocal thermal nonlinearity. We demonstrated the complex dynamic of an accelerating beam propagating under non-accelerating boundary conditions that exert forces on the beam. We showed that changing the nonlinearity strength allows control over the trajectories of the beam, to the extent that it gives rise even to trajectories that are completely different from those of the linear self-accelerating Airy beam. Moreover, we found a new surprising phenomenon created by the presence of high focusing nonlinearity: a very broad (“infinite”) launch beam decomposes into two beams, one of which becoming a localized spatial soliton, whose trajectory oscillates around a straight line, while the other beam is shedding power and eventually dies out. This picturesque phenomenon brings about a variety of intriguing questions: can the interaction between nonlinear accelerating beams produce spatial solitons? What would be their trajectories? Can they be pre-designed? We leave these ideas for future research.

Acknowledgments

The authors are grateful to Ido Kaminer for introducing his method for finding the self-accelerating nonlinear beams, and for his helpful support. This project was support by the Binational USA – Israel Science Foundation, the Israel Science Foundation, and by an Advanced Grant from the European Research Council.

References and links

1.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979). [CrossRef]

2.

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007). [CrossRef] [PubMed]

3.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007). [CrossRef] [PubMed]

4.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optical mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008). [CrossRef]

5.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009). [CrossRef] [PubMed]

6.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010). [CrossRef]

7.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010). [CrossRef] [PubMed]

8.

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett. 35(23), 3952–3954 (2010). [CrossRef] [PubMed]

9.

R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82, 043832 (2010).

10.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011). [CrossRef] [PubMed]

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J. A. Giannini and R. I. Joseph, “The role of the second Painleve transcendent in nonlinear optics,” Phys. Lett. A 141(8-9), 417–419 (1989). [CrossRef]

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Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express 19(18), 17298–17307 (2011). [CrossRef] [PubMed]

13.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011). [CrossRef]

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F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. 13(8), 284–286 (1968). [CrossRef]

15.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005). [CrossRef] [PubMed]

16.

E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A 48(1), 611–622 (1993). [CrossRef] [PubMed]

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C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91(7), 073901 (2003). [CrossRef] [PubMed]

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E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, “Stable spatial solitons in semiconductor optical amplifiers,” Opt. Lett. 28(4), 251–253 (2003). [CrossRef] [PubMed]

19.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett. 32(2), 154–156 (2007). [CrossRef] [PubMed]

20.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. 2(11), 769–774 (2006). [CrossRef]

21.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011). [CrossRef] [PubMed]

22.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. 98(21), 213901 (2007). [CrossRef] [PubMed]

23.

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999). [CrossRef] [PubMed]

24.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68(7), 923–926 (1992). [CrossRef] [PubMed]

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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]

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W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998). [CrossRef]

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J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066615 (2002). [CrossRef] [PubMed]

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 9, 2011
Revised Manuscript: October 23, 2011
Manuscript Accepted: October 24, 2011
Published: November 7, 2011

Citation
Rivka Bekenstein and Mordechai Segev, "Self-accelerating optical beams in highly nonlocal nonlinear media," Opt. Express 19, 23706-23715 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23706


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References

  1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979). [CrossRef]
  2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32(8), 979–981 (2007). [CrossRef] [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007). [CrossRef] [PubMed]
  4. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optical mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008). [CrossRef]
  5. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009). [CrossRef] [PubMed]
  6. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4(2), 103–106 (2010). [CrossRef]
  7. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett.105(25), 253901 (2010). [CrossRef] [PubMed]
  8. Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett.35(23), 3952–3954 (2010). [CrossRef] [PubMed]
  9. R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A82, 043832 (2010).
  10. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106(21), 213903 (2011). [CrossRef] [PubMed]
  11. J. A. Giannini and R. I. Joseph, “The role of the second Painleve transcendent in nonlinear optics,” Phys. Lett. A141(8-9), 417–419 (1989). [CrossRef]
  12. Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express19(18), 17298–17307 (2011). [CrossRef] [PubMed]
  13. A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011). [CrossRef]
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