Focused beam excitation of optical spatial solitons in nematic liquid crystals
1
N. Karimi*, A. Alberucci, M. Virkki, M. Kauranen and G. Assanto Optics Laboratory, Tampere University of Technology, FI-33101 Tampere, Finland * E-mail: [email protected] Focused beam excitation of optical spatial solitons in nematic liquid crystals Abstract Nematic liquid crystals (NLC) are soft matter systems exhibiting a macroscopic uniaxial optical response, even if the constituent molecules are randomly positioned. They are an excellent platform for the generation and control of optical spatial solitons (Nematicons) through the electromagnetically-induced rotation of the constitutive molecules. Despite the considerable number of studies in the last 15 years, to date important details of soliton excitation in actual NLC samples were not addressed. Here, we study the role of input beam parameters such as initial wavefront curvature and beam waist of the TEM 00 input beam on the formation and propagation of nematicons. The experimental results in planar cells are in excellent agreement with a semi-analytical model and numerical simulations. These findings can substantially aid characterization and generation of spatial solitons in liquid crystals and be readily generalized to other nonlocal nonlinear media and soft matter systems. References 1) G.Assanto and M.Peccianti, “Spatial solitons in nematic liquid crystals”, IEEE J. Quantum Electron. 39, pp. 13‐21, 2003 2) M.Peccianti and G.Assanto, “Nematicons”, Phys. Rep. 516, pp. 147-208, 2012 3) C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902, 2004 4) A. Alberucci, C.P. Jisha, and G. Assanto, “Breather solitons in highly nonlocal media”, arXiv:1602.01722 [physics.optics], 2016 5) M. Kwasny, A. Piccardi, A. Alberucci, M. Peccianti, M. Kaczmarek, M. A. Karpierz, and G. Assanto,“Nematicon–nematicon interactions in a medium with tunable nonlinearity and fixed nonlocality,” Opt. Lett. 36, pp. 2566–2568, 2011 A planar cell filled up with NLCs z y x input interface z x y beam 3 mm θ 0 beam 100 μm When the focal point is moved away from the cell entrance, self-trapping requires higher input powers due to the wave-front curvature. Moreover, soliton formation requires higher powers when the input beam waist w 0 is smaller, due to the larger diffraction. Width of the e-polarized beam versus propagation distance w 0 = 2 μm w 0 = 4 μm Input powers: 0.4 mW (red), 1.0 mW (yellow), 5.0 mW (violet), 10.0 mW (green). Dashed lines show the correspondent linear diffraction. In nematicon propagation, the net effect of optical losses is to reduce the beam power exponentially in propagation, i.e., P(z) = P 0 e −αz , α = 5 cm −1 . w 0 = 2 μm w 0 = 5 μm w 0 = 10 μm Semi-analytical model in the highly nonlocal limit w 0 = 2 μm w 0 = 5 μm w 0 = 10 μm Numerical simulations in (1+1)D z 0 = 0 μm z 0 = -200 μm z 0 = 200 μm S z 0 = 0 μm z 0 = 400 μm z 0 = -400 μm The e-polarized beam induces all- optical reorientation of the LC molecules leading to self-focusing through the formation of a refractive index well. For a fixed input power, the best self-confinement is achieved when the beam has a planar phase-front at the input. s k n 0 s : Poynting vector k : wave vector n : optic axis : walk-off angle Under the highly nonlocal approximation, the light-induced index well is a parabola. Then, the behavior of the beam width versus the propagation coordinate and the input power can be described by means of ODE. Extraordinary-polarized beams (λ = 1064 nm) propagating in the E7 NLC cell
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Transcript of Focused beam excitation of optical spatial solitons in nematic liquid crystals
N. Karimi*, A. Alberucci, M. Virkki, M. Kauranen and G. Assanto Optics Laboratory, Tampere University of Technology, FI-33101 Tampere, Finland
* E-mail: [email protected]
Focused beam excitation of optical spatial solitons in nematic
liquid crystals
Abstract
Nematic liquid crystals (NLC) are soft matter systems exhibiting a macroscopic uniaxial optical response, even if the
constituent molecules are randomly positioned. They are an excellent platform for the generation and control of optical spatial
solitons (Nematicons) through the electromagnetically-induced rotation of the constitutive molecules. Despite the considerable
number of studies in the last 15 years, to date important details of soliton excitation in actual NLC samples were not
addressed. Here, we study the role of input beam parameters such as initial wavefront curvature and beam waist of the TEM00
input beam on the formation and propagation of nematicons. The experimental results in planar cells are in excellent
agreement with a semi-analytical model and numerical simulations. These findings can substantially aid characterization and
generation of spatial solitons in liquid crystals and be readily generalized to other nonlocal nonlinear media and soft matter
systems.
References
1) G.Assanto and M.Peccianti, “Spatial solitons in nematic liquid crystals”,IEEE J. Quantum Electron. 39, pp. 13‐21, 2003
2) M.Peccianti and G.Assanto, “Nematicons”,Phys. Rep. 516, pp. 147-208, 2012
3) C. Conti, M. Peccianti, and G. Assanto,“Observationofopticalspatialsolitonsinahighlynonlocalmedium,”Phys.Rev.Lett.92, 113902,
2004
4) A. Alberucci, C.P. Jisha, and G. Assanto, “Breather solitons in highly nonlocal media”, arXiv:1602.01722 [physics.optics], 2016
5) M. Kwasny, A. Piccardi, A. Alberucci, M. Peccianti, M. Kaczmarek, M. A. Karpierz, and G. Assanto,“Nematicon–nematicon interactions in
amediumwithtunablenonlinearityandfixednonlocality,”Opt.Lett.36, pp. 2566–2568, 2011
A planar cell filled up with NLCs
z
y
x
input
interface
z
x
y
beam
3 mm
θ0
beam 100μm
When the focal point is moved away from the cell entrance, self-trapping
requires higher input powers due to the wave-front curvature.
Moreover, soliton formation requires higher powers when the input beam
waist w0 is smaller, due to the larger diffraction.
Width of the e-polarized beam versus propagation distance
w0 = 2 μm
w0 = 4 μm
Input powers: 0.4 mW (red), 1.0 mW (yellow), 5.0 mW (violet), 10.0 mW (green). Dashed lines show
the correspondent linear diffraction. In nematicon propagation, the net effect of optical losses is to reduce the beam power
exponentially in propagation, i.e., P(z) = P0e−αz , α = 5 cm−1.
w0 = 2 μm
w0 = 5 μm
w0 = 10 μm
Semi-analytical model in the highly nonlocal limit
w0 = 2 μm
w0 = 5 μm
w0 = 10 μm
Numerical simulations in (1+1)D
z0 = 0 μm
z0 = -200 μm
z0 = 200 μm
S
z0 = 0 μm
z0 = 400 μm
z0 = -400 μm
The e-polarized beam induces all-
optical reorientation of the LC
molecules leading to self-focusing
through the formation of a refractive
index well.
For a fixed input
power, the best self-confinement is
achieved when the beam has a planar
phase-front at the input.
s k
n
0
s : Poynting vector
k : wave vector
n : optic axis
: walk-off angle
Under the highly nonlocal approximation, the light-induced index well is a parabola. Then, the
behavior of the beam width versus the propagation coordinate and the input power can be
described by means of ODE.
Extraordinary-polarized beams (λ = 1064 nm) propagating in the E7 NLC cell
