[Paper Review] Nematicons in liquid crystals with negative dielectric anisotropy

Jing Wang, Jun-zhu Chen+7 more|arXiv (Cornell University)|Mar 10, 2014

Liquid Crystal Research Advancements3 citations

TL;DR

This study experimentally demonstrates bright nematicon formation in a planar nematic liquid crystal cell with negative dielectric anisotropy under an external voltage, where molecular reorientation induces a nonlocal nonlinearity that balances linear diffraction. The key contribution is the observation of stable, self-trapped optical solitons in a system with a negative Kerr coefficient and oscillatory response, validated by a simplified model linking to quadratic solitons and confirmed via numerical and experimental results.

ABSTRACT

We report a theoretical and experimental work on the nematicon in the planar cell containing the nematic liquid crystal with negative dielectric anisotropy, aligned homeotropically in the presence of an externally applied voltage. The formation of the soliton is resulted from the balance between the linear difrraction and the nonlocal nonlinearity due to molecular reorientation.

Motivation & Objective

• To investigate nematicon formation in nematic liquid crystals (NLCs) with negative dielectric anisotropy, which exhibit unique molecular reorientation under low-frequency electric fields.
• To establish a theoretical model that accounts for the nonlocal nonlinearity arising from molecular reorientation in NLCs with negative dielectric anisotropy.
• To experimentally demonstrate the existence of bright nematicons in a planar cell with homeotropic alignment and externally applied voltage.
• To derive a simplified model with a negative Kerr coefficient and oscillatory response function that supports bright nematicon solutions.
• To connect the observed nematicon dynamics to quadratic soliton theory through a dimensionless system derived from the governing equations.

Proposed method

• Modeling the system using coupled equations (2) and (3) that describe the evolution of the optical beam envelope $ A $ and the molecular tilt angle $ heta $, incorporating the effects of external RF field and optical intensity.
• Applying a low-frequency electric field to pretilt the NLC molecules, enabling the formation of a nonlocal nonlinear response due to reorientation, with the response function determined by the applied voltage and material parameters.
• Deriving a dimensionless system (10)–(11) via normalization, which decouples the optical beam evolution from the nonlocal response, enabling numerical simulation of soliton formation.
• Using a Green's function approach to solve the nonlocal response equation (11), revealing that the response function $ R $ exhibits exponential decay or sine-oscillatory behavior depending on the cell thickness relative to $ /pi $.
• Performing numerical simulations with Gaussian beam profiles to predict soliton formation and stability under varying voltage and pretilt angle conditions.
• Conducting experiments using a Verdi laser, 10X objective, and CCD imaging to observe beam propagation and diffraction in a 80-μm thick KY19-008 NLC cell with negative dielectric anisotropy ($ ho^{rf}_a = -5.3 $), comparing results with and without applied voltage.

Experimental results

Research questions

• RQ1 Can bright nematicons be formed in a nematic liquid crystal with negative dielectric anisotropy under an externally applied voltage?
• RQ2 How does the nonlocal nonlinearity arising from molecular reorientation in NLCs with negative dielectric anisotropy support soliton formation?
• RQ3 What is the role of the pretilt angle $ heta_0 $, induced by the applied RF field, in determining the soliton width and critical power?
• RQ4 How does the response function of the nonlocal nonlinearity (oscillatory vs. decaying) depend on the cell geometry and applied voltage?
• RQ5 To what extent can the nematicon dynamics in this system be described by a simplified model analogous to quadratic solitons?

Key findings

• Bright nematicons were experimentally observed in a planar NLC cell with negative dielectric anisotropy (KY19-008, $ ho^{rf}_a = -5.3 $) when the applied voltage exceeded the Fréedericksz threshold ($ V_{fr} hinspace ext{approx} hinspace 1.45 ext{V} $), with stable self-trapping observed at 3.4 V.
• The soliton formation was confirmed by comparing experimental images (Fig. 2c) and numerical simulations (Fig. 2d), showing suppression of diffraction and beam self-confinement under voltage bias.
• The characteristic soliton width $ w_m $ and the effective negative Kerr coefficient $ n_2 $ were found to vary nonmonotonically with the pretilt angle $ heta_0 $, reaching a minimum at intermediate values.
• The critical power for soliton formation was numerically determined and found to depend monotonically on $ heta_0 $, with a minimum value observed at $ heta_0 hinspace ext{approx} hinspace rac{ heta_{ ext{max}}}{2} $, indicating optimal conditions for soliton stability.
• The nonlocal response function $ R $ was shown to transition from exponential decay to sine-oscillatory behavior depending on the cell thickness: oscillatory when $ l > rac{ heta_{ ext{max}}}{ heta_{ ext{min}}} $, consistent with the analytical solution of the Green's function.
• Numerical solutions of the dimensionless system (10)–(11) revealed that soliton profiles and tilt angle distributions depend strongly on the sample size $ l_x, l_y $ and propagation constant $ eta $, with oscillatory tilt profiles observed when $ l_x > heta_{ ext{max}} $.