Phase-Matched Third-Harmonic Generation in a Nematic Liquid Crystal Cell

Abstract

Liquid crystals (LCs) are known for their strong nonlinear optical properties. A large contribution to the nonlinearity originates from molecular reorientation, an effect that has been used to demonstrate many interesting optical phenomena, such as [1] wave mixing, self-phase modulation, self-focusing, optical bistability, and optical Freedericksz transitions. This nonlinear mechanism is effective even at relatively low optical powers, but is also relatively slow. Much faster is the electronic contribution to the nonlinearity of LCs, which leads to effects such as second and third harmonic generation. Second harmonic generation in most liquid crystals is only an interface effect because of symmetry requirements. Efficient third harmonic generation (THG) is difficult to achieve in the LC bulk because of phase mismatch. However, in cholesteric liquid crystals, phase matching can be achieved using the properties of the periodic medium [2]. In this paper, we present an observation of strong phase-matched THG from within a simple nematic LC cell which is one of the most widely used types of LCs. The nematic LC is composed of rodlike molecules with one molecular axis much longer than the other two. The long axis of the molecules tends to point along a common direction, the director, while they are free to move from one location to another. The phase-matched THG we present here resulted from the combination of two nonlinear processes of different origin. A tightly focused laser beam of femtosecond pulses is used, which slightly modifies the molecular orientation inside the LC cell, leading to the generation of phase-matched third harmonic from the focal point. The same laser beam that deforms the local molecular orientation is used to generate the third harmonic light. The experimental setup used to generate third harmonic light from a nematic LC is similar to the setup used in THG microscopy [3]. The laser source is a synchronously pumped optical parametric oscillator (SpectraPhysics Tzunami-Opal system) which provides 130 fs pulses at a wavelength of 1.5 mm with a repetition rate of 80 MHz. The laser beam was focused onto a LC cell at normal incidence, using 360, numerical aperture › 0.85 microscope objective, to a spot size of ,1 mm. The sample used for the experiment was a parallel-aligned E7 nematic LC with a thickness of 50 mm. The LC was held between two glass substrates. A rubbing material with a low pretilt angle was used (PI2555), to impose a high anchoring potential on the LC molecules at the cell surfaces. The depth of the focal point in the sample is controlled using a piezoelectric driven stage. The third-harmonic light at 0.5 mm is collected by a lens and measured by a photomultiplier after filtering out the fundamental wavelength. It was verified by spectral measurements that only third harmonic light was generated, while no second harmonics signal could be detected. The polarization of the input beam is controlled by a polarizer, ly4 and ly2 plates. The coordinate frame is chosen so that the top glass-LC interface is in the x-y plane while the director of the LC at this plane is pointed at the y axis. The electromagnetic field is therefore propagating along the positive z axis. Tightly focusing a Gaussian beam in a homogenous nonlinear medium usually results in no THG [4]. However, when the medium is not homogeneous or, more specifically, when there are variations of the nonlinear thirdorder susceptibility x s3d in the bulk, third harmonic light