Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display

Optimization for maximum modulation of a double-pass twisted nematic liquid crystal display

Spatial light modulators are widely used to perform modulations of different properties of the electromagnetic field. In this work, a simple optimization method for general double-pass setups was developed. It takes into account the involved polarizing elements and displays, and a numerical simulation based on an exhaustive search routine finds the optimal optical axis orientations of the polarizing elements for the desired modulation. By simultaneously considering both impingements, we are able to take full advantage of the modulation capabilities of the chosen spatial light modulators. In particular, different polarization modulations and complex amplitude modulations were studied for twisted nematic liquid crystal displays and passive linear optical elements. Examples of different optimization criteria are shown and compared with experimental results, supporting the feasibility of this approach. This method offers the possibility of independent modulation of two properties of the input light state, outperforming the use of a single screen.

Beyond the display: phase-only liquid crystal on Silicon devices and their applications in photonics [Invited]

Existing for almost four decades, liquid crystal on Silicon (LCOS) technology is rapidly growing into photonic applications. We review the basics of the technology, from the wafer to the driving solutions, the progress over the last decade and the future outlook. Furthermore we review the most exciting industrial and scientific applications of the LCOS technology.

Fiber-based lensless polarization holography for measuring Jones matrix parameters of polarization-sensitive materials

We report a fiber-based lensless holographic imaging system to realize a single-shot measurement of two dimensional (2-D) Jones matrix parameters of polarization-sensitive materials. In this system, a multi-source lensless off-axis Fresnel holographic recording geometry is adopted, and two optical fiber splitters are used to generate the multiple reference and illumination beams required for recording a four-channel angular-multiplexing polarization hologram (AMPH). Using this system and the method described in this paper, spatially resolved Jones matrix parameters of a polarization-sensitive material can be retrieved from one single-shot AMPH. We demonstrate the feasibility of the method by extracting a 2-D Jones matrix of a composite polarizer. Applications of the method to measure the Jones matrix maps of a stressed polymethyl methacrylate sample and a mica fragment are also presented. Benefit from the fiber-based and lensless off-axis holographic design, the system possesses a quite compact configuration, which provides a feasible approach for development of an integrated and portable system to measure Jones matrix parameters of polarization-sensitive materials.

Polarization state transformation using two quarter wave plates: application to Mueller polarimetry

We show that there are a number of ways to transform an arbitrary polarization state into another with just two quarter wave plates (QWPs). We have verified this geometrically using the trajectories of the initial and final polarization states corresponding to all the fast axis orientations of a QWP on the Poincaré sphere. The exact analytical expression for the locus of polarization states has also been given, and describes the trajectory. An analytical treatment of the equations obtained through matrix operations corresponding to the transformation supports the geometrical representation. This knowledge can be used to obtain the Mueller matrix by just using QWPs, which has been shown experimentally by exploiting projections of the output states on the input states.

Measuring the Mueller matrix of an arbitrary optical element with a universal SU(2) polarization gadget

We propose a new method for determining the Mueller matrix of an arbitrary optical element and verify it with three known optical elements. This method makes use of two universal SU(2) polarization gadgets to obtain the projection matrix directly from the experiment. It allows us to determine the Mueller matrix without precalibration of the setup, since the generated polarization states are fully determined by the azimuths of the wave plates. We calculate errors in determining the Mueller matrix and compare with other techniques.

Closed-loop adaptive optics with a single element for wavefront sensing and correction

We propose a closed-loop adaptive optical arrangement based on a single spatial light modulator that simultaneously works as a correction unit and as the key element of a wavefront sensor. This is possible by using a liquid crystal on silicon display whose active area is divided into two halves that are respectively programmed for sensing and correction. We analyze the performance of this architecture to implement an adaptive optical system. Results showing a closed-loop operation are reported, as well as a proof of concept for dealing with aberrations comparable to those typically found in human eyes.

Improvement of the performance of the twisted-nematic liquid-crystal display as a phase modulator

A twisted-nematic liquid-crystal display (TN-LCD) placed between two linear polarizers (P) generally produces coupled intensity and phase modulations. For the purpose of phase-only modulation, quarter-wave plates (QWPs) are often used in front of or behind the LCD. In this paper, we demonstrate theoretically and experimentally the QWPs' effect on the modulation properties of the TN-LCD based on the general Jones matrix descriptions for all the devices, which circumvents the inconvenience of the traditional method on the basis of the TN-LCD's internal parameters. We prove that the phase modulation depth of the TN-LCD can be further increased in the configuration of P1-QWP1-LCD-QWP2-P2 with each component properly oriented, provided that the mean intensity transmission is decreased to a lower level. By observing the diffracted patterns of the Ronchi phase grating or blazed grating addressed onto the TN-LCD, we verify the validity of the proposed method. Improved reconstructed image quality from the kinoform loaded on the TN-LCD is obtained in this configuration. This approach is valuable when the TN-LCD is employed as a phase modulator, especially for the modern, thinner TN-LCD.

The minimum Euclidean distance principle applied to improve the modulation diffraction efficiency in digitally controlled spatial light modulators

Digital addressing of the electrical signal in spatial light modulators, as it is the case in present liquid crystal on silicon (LCoS) displays, may lead to temporal phase fluctuations in the optical beam. In diffractive optics applications a reduction in the modulation diffraction efficiency may be expected. Experimental work is done characterizing the fluctuations amplitude and phase depth for three different digital addressing sequences. We propose a diffractive model to evaluate the modulation diffraction efficiency of phase diffractive optical elements (DOEs) in the presence of phase fluctuations. Best results are obtained for the most stable electrical sequence even though its phase depth is as small as 280 degrees . The results show good agreement with the numerical calculation given by the model.

Direct calibration of a spatial light modulator by lateral shearing interferometry

A new interferometric technique is described to measure the complex modulation curve of a spatial light modulator. Based on a lateral shear imaging interferometer, it enables the amplitude and phase modulation for several modulation levels to be displayed simultaneously in a single interferogram. As an example of the power of this technique a heuristic optimization of input and output elliptical polarization states for a mostly-phase operation mode was obtained within a few minutes for a commercial twisted-nematic liquid crystal display.

Influence of the incident angle in the performance of liquid crystal on silicon displays

In this paper we experimentally analyze the performance of a twisted nematic liquid crystal on silicon (LCoS) display as a function of the angle of incidence of the incoming beam. These are reflective displays that can be configured to produce amplitude or phase modulation by properly aligning external polarization elements. But we demonstrate that the incident angle plays an important role in the selection of the polarization configuration. We performed a Mueller matrix polarimetric analysis of the display that demonstrates that the recently reported depolarization effect observed in this type of displays is also dependant on the incident angle.

Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics

In this paper we provide evidence of the temporal fluctuations of the phase modulation property of a liquid crystal on silicon (LCoS) display, and we analyze its effect when the device is used for displaying a diffractive optical element. We use a commercial twisted nematic LCoS display configured to produce a phase-only modulation, and we provide time resolved measurements of the diffraction efficiency that show rapid fluctuations of the phase modulation, in the millisecond order. We analyze how these fluctuations have to be considered in two typical methods for the characterization of the phase modulation: two beam interference and diffraction from a binary grating. We finally provide experimental results on the use of this device for displaying a computer generated hologram. A reduction of the modulation diffraction efficiency results from the phase modulation fluctuation.

Time-resolved Mueller matrix analysis of a liquid crystal on silicon display

We present a full polarimetric characterization of a liquid crystal on silicon (LCoS) display, with time resolution measurements below the frame period of the device. This time-resolved analysis shows evidence of temporal fluctuations in the millisecond range in the state of polarization of the beam reflected by the display. We demonstrate that light reflected by the display is maintained fully polarized, but these temporal fluctuations result in an effective depolarization effect when detectors with long time integration intervals are used in the characterization of the display.