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