Retrieving the phase of diffraction orders generated with tailored gratings.

A technique is performed to quantitatively evaluate the intensity and phase of the diffraction orders generated by tailored phase gratings displayed onto a liquid-crystal spatial light modulator (LC-SLM). The SLM displays the grating together with a lens to obtain the Fourier transform. The setup is converted into a polarization common-path interferometer by simply rotating a polarizer. This configuration allows a phase-shifting interferometry algorithm to be applied to retrieve the phase of the diffraction orders. The quadratic phase arising in the system, which must be subtracted, is calibrated using triplicator gratings of varying periods. Various tailored designs with controlled phase shift between diffraction orders are experimentally tested to prove the advantage and simplicity of the technique.

Measuring the spatial deformation of a liquid-crystal on silicon display with a self-interference effect.

We present a simple technique to characterize the spatial non-uniformity of a liquid-crystal on silicon (LCOS) spatial light modulator (SLM). It is based on illuminating the display with a wavelength out of the operation range, so there is a significant reflection at the output surface. As a consequence, a Gires-Tournois interferometer is directly created, without any alignment requirement and insensitive to vibrations. The beam reflected at the output surface is the reference beam, while the beam reflected at the silicon backplane is modulated with the addressed gray level in order to quantitatively derive its deformation. We provide an experimental demonstration using a LCOS-SLM designed to operate in the near-infrared range but illuminated with visible light.

Programmable color tuning of a multiline laser by means of a twisted nematic liquid crystal display.

An optical system useful to tune in a controlled way the color of a triline argon krypton (Ar-Kr) laser by means of a twisted nematic liquid crystal display (TNLCD) is presented. The optical setup employs a 4f system and two blazed gratings to first separate and then recombine the spectrum of the light beam. The TNLCD is included in the intermediate focal plane operating in the amplitude modulation mode to control the relative transmission of each spectral line. The resulting color is accurately predicted by using a previously developed physical model of the spectral and voltage dependence of the TNLCD birefringence. By simply changing the gray level image addressed to the display, the Ar-Kr laser is color modulated at a video rate, thus becoming an interesting, reconfigurable, coherent light source for applications such as multicolor holography or color inspection.

Customized depolarization spatial patterns with dynamic retardance functions.

In this work we demonstrate customized depolarization spatial patterns by imaging a dynamical time-dependent pixelated retarder. A proof-of-concept of the proposed method is presented, where a liquid-crystal spatial light modulator is used as a spatial retarder that emulates a controlled spatially variant depolarizing sample by addressing a time-dependent phase pattern. We apply an imaging Mueller polarimetric system based on a polarization camera to verify the effective depolarization effect. Experimental validation is provided by temporal integration on the detection system. The effective depolarizance results are fully described within a simple graphical approach which agrees with standard Mueller matrix decomposition methods. The potential of the method is discussed by means of three practical cases, which include non-reported depolarization spatial patterns, including exotic structures as a spirally shaped depolarization pattern.

Resonant frequencies of Fabry-Perot interferometers with ultrathin mirror spacings.

Fabry-Perot interferometers (FPIs) with multilayer dielectric mirrors and mirror spacings as low as 0.7% of the operating wavelength are studied. It is shown how these low-order FPIs are affected by the phase dispersion characteristics of multilayer dielectric mirrors. Because experimental results in the optical regime are extremely difficult to obtain, radio frequency experiments are performed with coaxial cable FPI structures. Experimental results show excellent agreement with theory. These phase effects in FPIs with ultrathin mirror spacings are of great interest in the design of tunable microcavities with possible applications in optical communications.

Fourier analysis of harmonic frequency transmission dielectric structures.

We use an analytical calculation based on the Fourier-transform method to study the transmission spectra of multilayer dielectric optical structures as a function of the relative widths of the layers that constitute the unit cell. We can select which harmonics of the fundamental design frequency are transmitted. The results of this Fourier-transform approach are compared with the exact transmission calculated by means of the transfer matrix method and provide a more intuitive understanding of the transmission spectrum. A simple phasor diagram is derived from this Fourier-transform analysis for this purpose. Inasmuch as it is difficult for us to perform experiments in the optical region, we fabricate rf analogs of these structures, using coaxial cables that have different impedances. Experimental results agree with theory.