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Spatiotemporal dynamics of counterpropagating Airy beams.

Wiersma N, Marsal N, Sciamanna M, Wolfersberger D - Sci Rep (2015)

Bottom Line: We further identify the threshold above which the waveguide is no longer static but evolves dynamically either time-periodically or even chaotically.Above the stability threshold, each Airy-soliton moves erratically between privileged output positions that correspond to the spatial positions of the lobes of the counterpropagating Airy beam.These results suggest new ways of creating dynamically varying waveguides, optical logic gates and chaos-based computing.

View Article: PubMed Central - PubMed

Affiliation: Université de Lorraine, LMOPS/CentraleSupélec (EA 4423), Metz, 57070, France.

ABSTRACT
We analyse theoretically the spatiotemporal dynamics of two incoherent counterpropagating Airy beams interacting in a photorefractive crystal under focusing conditions. For a large enough nonlinearity strength the interaction between the two Airy beams leads to light-induced waveguiding. The stability of the waveguide is determined by the crystal length, the nonlinearity strength and the beam's intensities and is improved when comparing to the situation using Gaussian beams. We further identify the threshold above which the waveguide is no longer static but evolves dynamically either time-periodically or even chaotically. Above the stability threshold, each Airy-soliton moves erratically between privileged output positions that correspond to the spatial positions of the lobes of the counterpropagating Airy beam. These results suggest new ways of creating dynamically varying waveguides, optical logic gates and chaos-based computing.

No MeSH data available.


Spatiotemporal dynamics of two counterpropagating Airy beams in a long crystal L =  5.5Ld, with the normalized intensities. (a) Bifurcation diagram of the transverse output position of the forward off-shooting soliton at z = L, with the transverse normalized intensity profile of backward Airy beam at z = L. (b–g) Temporal evolution of the transverse output position of the forward off-shooting soliton at z = L: (b) steady-state (Γ = 9.3), (c) sinusoidal oscillations (Γ = 10.4), (d) second steady-state (Γ = 12.7), (e) first instabilities (Γ = 14), (f) periodical non-sinusoidal oscillations (Γ = 14.9) and (g) instabilities (Γ = 18). E.g. experimentally for CP Airy beams in a SBN:75 crystal (L*5mm*5mm) with x0 = 10μm: L = 28mm, Uext ∈ [500V, 900V].
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f3: Spatiotemporal dynamics of two counterpropagating Airy beams in a long crystal L =  5.5Ld, with the normalized intensities. (a) Bifurcation diagram of the transverse output position of the forward off-shooting soliton at z = L, with the transverse normalized intensity profile of backward Airy beam at z = L. (b–g) Temporal evolution of the transverse output position of the forward off-shooting soliton at z = L: (b) steady-state (Γ = 9.3), (c) sinusoidal oscillations (Γ = 10.4), (d) second steady-state (Γ = 12.7), (e) first instabilities (Γ = 14), (f) periodical non-sinusoidal oscillations (Γ = 14.9) and (g) instabilities (Γ = 18). E.g. experimentally for CP Airy beams in a SBN:75 crystal (L*5mm*5mm) with x0 = 10μm: L = 28mm, Uext ∈ [500V, 900V].

Mentions: For low Γ-values (Γ = 3), the nonlinearity Γ applied on the system is not high enough to create locally a large refractive index variation inside the crystal by the photorefractive effect and therefore to induce an off-shooting soliton. Still, the propagation of each Airy beam optically induces a curved waveguide along the deflecting Airy trajectory28. We call this region ‘static waveguide without off-shooting soliton’. For a larger nonlinearity strength, each CP Airy beam undergoes self-trapping and a part of the beam’s energy turns into an “off-shooting” soliton [Fig. 1(b)]. We define the existence of an off-shooting soliton, when at least of the input intensity exits at z = L and can be clearly distinguished from the linear output beam. Since almost half of the energy is stored in the first Airy lobe30, the nonlinearity of the system mostly influences the main lobes and the off-shooting solitons. The interaction of the two CP Airy beams then leads to various new static waveguide structures and we call this region ‘static waveguide with off-shooting soliton’. As presented in reference37, the photoinduced waveguide structure enables a Gaussian beam to exit the crystal at a single or at two output positions simultaneously. The parabolic trajectory of the CP Airy beams enables waveguiding structures even for transverse shifts of the interacting beams that by far exceed the beam waist. When we still increase the nonlinearity Γ, the waveguide is no longer steady in time but rather shows stable time-periodic dynamics: the off-shooting soliton evolves from a constant transverse output position to an output position that oscillates harmonically in time along the x-axis [Figs 1(c) and 3(c)]. We call this region ‘harmonic oscillations’. Similar to the case of CP Gaussian beams8, the critical nonlinearity strength that delimits the onset of time-periodic oscillations of the waveguide decreases with the increase of the crystal length L, see the line labelled ‘threshold static-dynamic’ in Fig. 2.


Spatiotemporal dynamics of counterpropagating Airy beams.

Wiersma N, Marsal N, Sciamanna M, Wolfersberger D - Sci Rep (2015)

Spatiotemporal dynamics of two counterpropagating Airy beams in a long crystal L =  5.5Ld, with the normalized intensities. (a) Bifurcation diagram of the transverse output position of the forward off-shooting soliton at z = L, with the transverse normalized intensity profile of backward Airy beam at z = L. (b–g) Temporal evolution of the transverse output position of the forward off-shooting soliton at z = L: (b) steady-state (Γ = 9.3), (c) sinusoidal oscillations (Γ = 10.4), (d) second steady-state (Γ = 12.7), (e) first instabilities (Γ = 14), (f) periodical non-sinusoidal oscillations (Γ = 14.9) and (g) instabilities (Γ = 18). E.g. experimentally for CP Airy beams in a SBN:75 crystal (L*5mm*5mm) with x0 = 10μm: L = 28mm, Uext ∈ [500V, 900V].
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4551959&req=5

f3: Spatiotemporal dynamics of two counterpropagating Airy beams in a long crystal L =  5.5Ld, with the normalized intensities. (a) Bifurcation diagram of the transverse output position of the forward off-shooting soliton at z = L, with the transverse normalized intensity profile of backward Airy beam at z = L. (b–g) Temporal evolution of the transverse output position of the forward off-shooting soliton at z = L: (b) steady-state (Γ = 9.3), (c) sinusoidal oscillations (Γ = 10.4), (d) second steady-state (Γ = 12.7), (e) first instabilities (Γ = 14), (f) periodical non-sinusoidal oscillations (Γ = 14.9) and (g) instabilities (Γ = 18). E.g. experimentally for CP Airy beams in a SBN:75 crystal (L*5mm*5mm) with x0 = 10μm: L = 28mm, Uext ∈ [500V, 900V].
Mentions: For low Γ-values (Γ = 3), the nonlinearity Γ applied on the system is not high enough to create locally a large refractive index variation inside the crystal by the photorefractive effect and therefore to induce an off-shooting soliton. Still, the propagation of each Airy beam optically induces a curved waveguide along the deflecting Airy trajectory28. We call this region ‘static waveguide without off-shooting soliton’. For a larger nonlinearity strength, each CP Airy beam undergoes self-trapping and a part of the beam’s energy turns into an “off-shooting” soliton [Fig. 1(b)]. We define the existence of an off-shooting soliton, when at least of the input intensity exits at z = L and can be clearly distinguished from the linear output beam. Since almost half of the energy is stored in the first Airy lobe30, the nonlinearity of the system mostly influences the main lobes and the off-shooting solitons. The interaction of the two CP Airy beams then leads to various new static waveguide structures and we call this region ‘static waveguide with off-shooting soliton’. As presented in reference37, the photoinduced waveguide structure enables a Gaussian beam to exit the crystal at a single or at two output positions simultaneously. The parabolic trajectory of the CP Airy beams enables waveguiding structures even for transverse shifts of the interacting beams that by far exceed the beam waist. When we still increase the nonlinearity Γ, the waveguide is no longer steady in time but rather shows stable time-periodic dynamics: the off-shooting soliton evolves from a constant transverse output position to an output position that oscillates harmonically in time along the x-axis [Figs 1(c) and 3(c)]. We call this region ‘harmonic oscillations’. Similar to the case of CP Gaussian beams8, the critical nonlinearity strength that delimits the onset of time-periodic oscillations of the waveguide decreases with the increase of the crystal length L, see the line labelled ‘threshold static-dynamic’ in Fig. 2.

Bottom Line: We further identify the threshold above which the waveguide is no longer static but evolves dynamically either time-periodically or even chaotically.Above the stability threshold, each Airy-soliton moves erratically between privileged output positions that correspond to the spatial positions of the lobes of the counterpropagating Airy beam.These results suggest new ways of creating dynamically varying waveguides, optical logic gates and chaos-based computing.

View Article: PubMed Central - PubMed

Affiliation: Université de Lorraine, LMOPS/CentraleSupélec (EA 4423), Metz, 57070, France.

ABSTRACT
We analyse theoretically the spatiotemporal dynamics of two incoherent counterpropagating Airy beams interacting in a photorefractive crystal under focusing conditions. For a large enough nonlinearity strength the interaction between the two Airy beams leads to light-induced waveguiding. The stability of the waveguide is determined by the crystal length, the nonlinearity strength and the beam's intensities and is improved when comparing to the situation using Gaussian beams. We further identify the threshold above which the waveguide is no longer static but evolves dynamically either time-periodically or even chaotically. Above the stability threshold, each Airy-soliton moves erratically between privileged output positions that correspond to the spatial positions of the lobes of the counterpropagating Airy beam. These results suggest new ways of creating dynamically varying waveguides, optical logic gates and chaos-based computing.

No MeSH data available.