Role of the input beam parameters on nematicon
excitation
Nazanin Karimi, Alessandro Alberucci, Matti Virkki, Martti Kauranen, and Gaetano Assanto
Department of PhysicsTampere University of Technology, Tampere, Finland
Optics & Photonics Days, May 18, 2016 Hotel Torni, Tampere, Finland
Contents
• Nematicons
• Reorientational self-focusing and trapping in nematic liquid crystals
• Nonlinear beam propagation in paraxial approximation
• Effect of input curvature and beam waist on nonlinear beam propagation
• ODE model for light self-trapping in NLC
• Beam propagation method (BPM) in a bidimensional structure
• Conclusions
2
Nematicons
y (μ
m)
z (mm)0 1.5y
(μm
)-250
250
250
-250
0
• Finite-size beams undergo a phase-front curvature due to diffraction
• In nonlinear optics, diffraction can be balanced out by light self-focusing, leading to the formation of spatial solitons
• Nematic liquid crystals (NLCs) are excellent platform for spatial solitons excited with low-power cw beams (Nematicons)
• The nonlinear response is linked to the electromagnetically-induced reorientation of the anisotropic NLC molecules
Optical self-focusing and trapping via reorientation in nematic liquid crystals
Molecular reorientation in the nematic phase
n
n||
n
^
Nematic phase
Soliton formation
z
y
EE
y
zΔnI
Linear diffraction
=
n̂
θ
n̂
k𝑛⏊<𝑛⎹⎹
Beam propagation in the paraxial approximation
0 Optical reorientationk
Sδ0
yz
INPUT BEAM θ0
0
𝟐 𝒊𝒌𝟎𝒏𝒆 (𝜽𝒎 ) (𝝏 𝑨𝝏𝒛 +𝒕𝒂𝒏𝜹𝟎𝝏 𝑨𝝏 𝒚 )+𝑫𝒚
𝝏𝟐 𝑨𝝏𝒚𝟐 +
𝝏𝟐𝑨𝝏 𝒙𝟐 +𝒌𝟎
𝟐∆𝒏𝒆𝟐 𝑨=𝟎
0
• Beam propagation is ruled by a NL Schrödinger-type eq:
NL index well
𝛾=𝜖0𝜖𝑎/ ( 4𝐾 )Effective NL strength
𝛿0=𝑎𝑟𝑐𝑡𝑎𝑛 [𝜖𝑎𝑠𝑖𝑛2 θ 0 /(𝜖𝑎+2𝑛⏊2+𝜖𝑎𝑐𝑜𝑠2θ 0)]Walk-off angle:
Optical anisotropy:
Planar cell filled with NLC
Lx = 100 μm
z0 = 0
2w0
z0 0
2w0𝛌=𝟏𝟎𝟔𝟒𝐧𝐦
Planar cell filled with NLC
Lx = 100 μm
z0
2w0
z0 0
2w0𝛌=𝟏𝟎𝟔𝟒𝐧𝐦
8
Role of the input curvature on nematicon propagation
9
• Self-confinement is more effective for • z0 = 0, • Larger input power• Larger waist
0.4 1.0 5.0 10.0 0.05
Input power (mW)
Width of the e-wave beam versus propagation distance
10
Semi-analytical model for light self-trapping in NLC
• Based on highly nonlocal approximation
• Describing the beam evolution with an ODE
11
Numerical beam propagation method (BPM) in a bidimensional structure
𝐳𝟎 =−𝟐𝟎𝟎𝛍𝐦
𝐳𝟎 =𝟎𝛍𝐦
𝐳𝟎 =𝟐𝟎𝟎𝛍𝐦
2 𝑖𝑘0𝑛𝑒 (𝜃𝑚 ) (𝜕 𝐴𝜕 𝑧 +𝑡𝑎𝑛𝛿 (𝜃𝑚 ) 𝜕 𝐴𝜕 𝑦 )+𝐷𝑦𝜕2 𝐴𝜕𝑦 2 +𝑘0
2∆𝑛𝑒2 𝐴=0
0
Conclusions
• The role of the phase-front curvature and waist on nematicon formation and propagation was discussed in detail
• Self-confined beams are harder to form when the focus is positioned inside or outside the sample, rather than at the entrance
• Beam trapping is favored for larger input waists
• Our findings improve the current understanding of solitary wave excitation for the precise design of waveguides in reorientational media
• Our analysis is an important step forward in the engineering of nonlinear optical lenses
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