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Frontiers in Optics

Coherence and polarization control by means of 90°-twist nematic liquid-crystal spatial light modulators (NLC-SLM)

Carolina Rickenstorff-Parrao, Elías Flores, Andrey S. Ostrovsky

Published Jan 1, 2011• 2 citations
Publisher

Abstract

The coherence and polarization degrees of an electromagnetic beam are modulated through two 90°-twist nematic liquid-crystal spatial light modulators placed at the opposite arms of a Mach-Zehnder interferometer. Statistical properties of the secondary source are modified applying random signals to the 90°-twist NLC-SLMs working in the phase mode. Experimental results are obtained using the commercial device LC2002 Holoeye.

DOI
10.1364/fio.2011.jwa16

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The coherence and polarization degrees of an electromagnetic beam are modulated through two 90°-twist nematic liquid-crystal spatial light modulators placed at the opposite arms of a Mach-Zehnder interferometer. Statistical properties of the secondary source are modified applying random signals to the 90°-twist NLC-SLMs working in the phase mode. Experimental results are obtained using the commercial device LC2002 Holoeye.
Abstract A Mach–Zehnder interferometer with an optical phase control by a twisted nematic (TN) liquid crystal (LC) device was studied. In a typical TN LC device, a change in the optical rotation state of π/2 can be obtained by applying a voltage of about 5 V with a cell thickness of several-micron. The TN cell is inserted into one optical path in the Mach–Zehnder interferometer. We obtained a pattern change when voltage was applied to the LC cell due to the change of the optical interference state. As a result, a change in the number of photons under weak light conditions is observed.
In our investigation into the effects of the degree of polarization in modulation of partially polarized light, we assume general settings of the interferometry of partially polarized light waves and perform theoretical analysis of the geometric phases: the Uhlmann phase and the interferometric phase. We introduce the relative Uhlmann phase determined by the Uhlmann holonomies of interfering beams and show that the interferometric phase generalized to the case of nonunitary evolution can, similar to the Uhlmann phase, be cast into the holonomy defined form. By using the technique based on a two-arm Mach-Zehnder interferometer, two different dynamical regimes of light modulation are experimentally studied: (a) modulation of the input light by the rotating quarter-wave plate (QWP), and (b) modulation of the testing beam by a birefringent plate with electrically controlled anisotropy represented by the deformed-helix ferroelectric liquid-crystal (DHFLC) cell. In the setup with the rotating QWP, the interferometric phase is found to be equal to the relative Uhlmann phase. Experimental and theoretical results being in excellent agreement show both that this phase is an oscillating function of the QWP angle and increases with the degree of polarization. For modulation by the DHFLC cell, the data derived from our electro-optic measurements are fitted using the theory of the orientational Kerr effect in FLCs. This theory in combination with the results of fitting is used to evaluate electric field dependencies of the interferometric and the Uhlmann phases.
Spatial light modulators (SLMs) are widely used to coherently control quantum states of light.When carrying out these experiments, some assumptions are made.For instance, it is supposed that the position-momentum correlations between twin photon pairs are not affected by the use of a liquid crystal display (LCD) as a SLM.Furthermore, it is assumed that the characterization of such devices performed with an intense laser source, is still valid in the single photon regime.In this work, we show that such assumptions are acceptable, within the experimental uncertainties, for a liquid crystal on silicon (LCoS) display.This is especially important when considering the use of this kind of displays for the coherent control of quantum states based on twin photon sources.
Liquid crystal displays (LCDs) are devices capable of manipulating properties of an incident light beam, such as amplitude, phase, and polarization, based on the voltage applied to their molecules. In this work, we will experimentally characterize the effect of an LCD on light polarization, aiming at its use as a programmable spatial light modulator (SLM) in optics and quantum information experiments. In the first part, we will determine the Mueller matrix of the device and, from it, its polarimetric properties. We will show that the LCD acts only approximately as an ideal retarder plate since it introduces depolarization to the incident light. In the second part, we investigate the behavior of the LCD through the formalism of quantum operations, treating its action as an operation on polarization qubit states. Through process tomography, we determine the matrix characterizing the device's operation and show that it is non-unitary. Next, we derive a general expression for the process matrix of an SLM, given by the combination of the LCD with wave plates. This expression will allow us to implement programmable operations on the polarization states of light based on the configuration of the wave plates and the voltage on the LCD. As an application, we will quantify the fidelity of the actual operation implemented by the SLM with an ideal unitary operation of interest in quantum information protocols.
Spatial light modulators are versatile devices employed in a vast range of applications to modify the transverse phase or amplitude profile of an incident light beam. Most experiments are designed to use a specific polarization which renders optimal sensitivity for phase or amplitude modulation. Here we take a different approach and apply the formalism of quantum information to characterize how a phase modulator affects a general polarization state. In this context, the spatial modulators can be exploited as a resource to couple the polarization and the transverse spatial degrees of freedom. Using a quasimonochromatic single-photon beam obtained from a pair of twin photons generated by spontaneous parametric down conversion, we performed quantum process tomography in order to obtain a general analytic model for a quantum channel that describes the action of the device on the polarization qubits. We illustrate the application of these concepts by demonstrating the implementation of a controllable phase flip channel. This scheme can be applied in a straightforward manner to characterize the resulting polarization states of different types of phase or amplitude modulators and motivates the combined use of polarization and spatial degrees of freedom in innovative applications.