Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude, and phase diffraction gratings
We analyze the performance of a ferroelectric liquid crystal on silicon display (FLCoS) as a binary polarization diffraction grating. We analyze the correspondence between the two polarization states emerging from the displayed grating and the polarization and intensity of the diffracted orders generated at the Fourier diffraction plane. This polarization-diffraction analysis leads, in a simple manner, to configurations yielding binary amplitude or binary phase modulation by incorporating an analyzer on the reflected beam. Based on this analysis, we present two useful variations of the polarization configuration. The first is a simplification using a single polarizer, which provides equival…
Achromatic linear retarder with tunable retardance
We present a universal design and proof-of-concept of a tunable linear retarder of uniform wavelength response in a broad spectral range. It consists of two half-wave retarders (HWR) between two quarter-wave retarders (QWRs), where the uniform retardance can be tuned continuously by simply rotating one of the HWRs. A proof-of-concept of this design is built by using commercially available Fresnel rhomb retarders that provide retardation with almost wavelength uniformity in the visible and near infrared from 450 to 1550 nm. The design is universal, since other achromatic QWRs and HWRs could also be employed. The system is experimentally demonstrated to control the state of polarization of a …
Using birefringence colors to evaluate a tunable liquid-crystal q-plate
Q-plates are geometrical phase elements that enable the realization of vector beams in simple and compact optical setups. In this work, we consider a tunable liquid-crystal commercial q-plate operative in the visible and near-IR range and study its spectral and color birefringence properties under broadband illumination. We first characterize the spectral retardance function of the device in a wide range from 400 to 1600 nm and determine how it changes upon applied voltage. Then we evaluate the color transmission characteristics when inserting the q-plate between crossed and parallel linear polarizers. These color properties agree with the trajectory in the CIExy chromaticity diagram as the…
Wavelength-compensated time-sequential multiplexed color joint transform correlator
We report a wavelength-compensated three-channel (RGB) joint transform correlator (JTC) for color pattern recognition using a ferroelectric liquid-crystal spatial light modulator (SLM) operating in binary pure phase modulation. We apply a previously reported time-multiplexing technique useful in creating wavelength-compensated diffraction patterns, based on the synchronization of properly scaled diffraction masks with the input wavelength selection obtained by applying a rotating RGB color-filter wheel to an Ar-Kr laser. The application of this technique to a JTC architecture permits real-time color object detection. In order to achieve a high light efficiency for the correlation process, w…
Optical System For Measuring The Spectral Retardance Function In An Extended Range
Optical retarders are key elements for the control of the state of polarization of light, and their wavelength dependance is of great importance in a number of applications. We apply a well-known technique for determinig the spectral retardance by measuring the transmission spectra between crossed or parallel polarizers. But we we develop an optical system to perform this measurement in a wide spectral range covering the visible (VIS) and near infrared (NIR) spectrum in the range from 400 to 1600 nm. As a result we can measure the spectral retardance of different retarders and easily identify the kind of reterder (multiple order, zero-order, achromatic). We show results with tunable liquid-…
Ray matrix analysis of anamorphic fractional Fourier systems
In this work we extend the application of the ray matrix approach to analyse anamorphic fractional Fourier systems, i.e., fractional Fourier optical systems where the fractional power is different for two orthogonal directions. The application of the ray matrix approach allows for easily obtaining the properties of the optical system, and it is therefore a powerful tool to design and simplify complicated systems. For simplicity we consider fractional Fourier systems with real orders and systems without apertures. We start by presenting the analysis of some previously reported anamorphic Fourier and fractional Fourier systems, and we end by proposing a simple optical system with tunable anam…
Generation of Bessel beam arrays through Dammann gratings.
In this work we apply the Dammann grating concept to generate an equal-intensity square array of Bessel quasi-free diffraction beams that diverge from a common center. We generate a binary phase mask that combines the axicon phase with the phase of a Dammann grating. The procedure can be extended to include vortex spiral phases that generate an array of optical pipes. Experimental results are provided by means of a twisted nematic liquid crystal display operating as a binary π phase spatial light modulator.
Vector modes generation using efficient on-axis system
Arbitrary polarized vector beam modes are efficiently generated. We use two flicker-free liquid-crystal on silicon (LCOS) spatial light modulators (SLM) in an on-axis common path architecture. Different superpositions of vector modes are obtained with high light efficiency.
Time-multiplexed chromatic-controlled axial diffractive optical elements
Programmable diffractive optical elements DOEs with axial response have many interesting applications, including diffractive lenses, axicons, and optical tweezers. In all these cases, it is essential to properly select the modulation configuration of the spatial light modulator SLM where the DOE is displayed, in order to avoid the undiffracted zero order component that appears on axis and overlaps the desired axial response. However, in general, the chromatic dispersion in liquid crystal SLMs prevents the cancellation of the zero order for a broadband light source, thus limiting the possibilities for polychromatic program- mable axial DOEs. We operate a ferroelectric liquid crystal on silic…
Fractional Fourier transforms, symmetrical lens systems, and their cardinal planes
We study the relation between optical lens systems that perform a fractional Fourier transform (FRFT) with the geometrical cardinal planes. We demonstrate that lens systems symmetrical with respect to the central plane provide an exact FRFT link between the input and output planes. Moreover, we show that the fractional order of the transform has real values between 0 and 2 when light propagation is produced between principal planes and antiprincipal planes, respectively. Finally, we use this new point of view to design an optical lens system that provides FRFTs with variable fractional order in the range (0,2) without moving the input and output planes.
Solc filters in a reflective geometry
We present the realization of a bulk optics birefringent Solc filter in a reflective geometry. This geometry reduces by half the number of required retarders, ensures the same spectral retardance function in pairs of retarders, and helps to make more compact filters. The key element is a quarter-wave Fresnel rhomb located in between the set of retarders and a mirror. Two cases are considered: the first Solc filter uses multiple-order quartz retarders, and the second one uses two liquid-crystal retarders. The latter has the advantage of being tunable via an applied voltage. Experimental results show how to filter the spectral content of a supercontinuum laser.
Liquid crystal spatial light modulator with very large phase modulation operating in high harmonic orders.
Unusually large phase modulation in a commercial liquid crystal spatial light modulator (LCSLM) is reported. Such a situation is obtained by illuminating with visible light a device designed to operate in the infrared range. The phase modulation range reaches 6π radians in the red region of the visible spectrum and 10π radians in the blue region. Excellent diffraction efficiency in high harmonic orders is demonstrated despite a concomitant and non-negligible Fabry–Perot interference effect. This type of SLM opens the possibility to implement diffractive elements with reduced chromatic dispersion or chromatic control.
Analysis of multiple internal reflections in a parallel aligned liquid crystal on silicon SLM
Multiple internal reflection effects on the optical modulation of a commercial reflective parallel-aligned liquid-crystal on silicon (PAL-LCoS) spatial light modulator (SLM) are analyzed. The display is illuminated with different wavelengths and different angles of incidence. Non-negligible Fabry-Perot (FP) effect is observed due to the sandwiched LC layer structure. A simplified physical model that quantitatively accounts for the observed phenomena is proposed. It is shown how the expected pure phase modulation response is substantially modified in the following aspects: 1) a coupled amplitude modulation, 2) a non-linear behavior of the phase modulation, 3) some amount of unmodulated light…
Optical retarder system with programmable spectral retardance.
An optical system that works as a retarder waveplate with programmable spectral retardance is proposed. The system is based on a pixelated liquid crystal on silicon (LCoS) spatial light modulator (SLM). The input light beam is spectrally dispersed and different spectral components are projected onto different pixels of the LCoS-SLM. A different retardance is then addressed for each pixel, adapted to the incoming wavelength. Light reflected from the SLM is then recombined by the same setup. In this way a programmable polarization spectrum can be encoded. We illustrate the broadband characterization that is required for proper use of the system. Then several examples are shown, including spec…
Teaching Fourier optics through ray matrices
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics prov…
Efficient on-axis SLM engineering of optical vector modes
Abstract This work presents a method for the efficient experimental generation of arbitrary polarized vector beam modes. The optical system employs two liquid-crystal on silicon (LCOS) spatial light modulators (SLM) in a common path architecture, avoiding the use of beam-splitters. Each SLM displays a different phase-only mask, each one encoding a different pattern onto two orthogonal linear polarization components of the input beam. These phase-only masks are designed using a recently proposed random technique to encode complex amplitude values. This encoding technique reconstructs the complex function on-axis, thus avoiding incorporating carrier phases. By addressing such properly designe…
Programmable Supercontinuum Laser Spectrum Generator Based on a Liquid-Crystal on Silicon Spatial Light Modulator
Supercontinuum (SC) lasers combine a broadband light spectrum with the unique properties of single-mode lasers. In this work we present an optical system to spectrally filter a SC laser source using liquid-crystal on silicon (LCoS) spatial light modulators (SLM). The proposed optical system disperses the input laser and the spectrally separated components are projected onto the LCoS-SLM, where the state of polarization of each wavelength is separately modulated. Finally, recombining the modulated spectral components results in an output laser source where the spectrum can be controlled dynamically from a computer. The system incorporates two branches to independently control the visible (VI…
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–K…
Accurate color predictability based on a spectral retardance model of a twisted-nematic liquid-crystal display
Abstract In this work we present the application of a simple physical model to accurately predict the broadband spectral transmittance and colorimetric properties of a twisted-nematic liquid crystal display (TNLCD). We spectroscopically calibrate the retardance parameters to evaluate the spectrum of the light transmitted by a TNLCD sandwiched between two linear polarizers. When the TNLCD is illuminated with a broadband light source, the full spectrum can be predicted as a function of the addressed gray level for any arbitrary orientation of the polarizers. Thus, the color of the transmitted light can be also be estimated with very good accuracy. As an example, a polarizers' configuration is…