In this work we apply an optical system with two cascaded liquid-crystal spatial light modulators (LC-SLMs) to produce multiple outputs with intensity and polarization control. We use a non-standard modulation configuration where the first LC-SLM operates as a phase-only modulator to encode a Fourier transform hologram multiplexing the desired multiple output beams, all with the same polarization. Next, the Fourier transform is optically formed onto the second LC-SLM, where each output beam is focused on different physical locations. The two SLMs have the LC director axis oriented horizontally. Thus, by rotating the linearly polarized output beams emerging from the first LC-SLM by 45 deg, we operate the second LC-SLM as a variable retarder. Then, by applying different phase-shifts at the different areas of the second LC-SLM, we can vary the polarization state of each output beam. Finally, the output is imaged onto a camera detector to demonstrate the polarization states. Experimental results demonstrate the capability for this approach to encode a variety of output beams with different states of polarization.
We introduce an approach for encoding a variety of independent outputs from a computer-generated diffractive optical element displayed on a spatial light modulator (SLM). In this approach, random binary 0-1 orthogonal patterns are multiplied to the different phase functions, effectively multiplexing the corresponding different outputs. We show experimental results with different examples of multiplexed phase functions. Additional functions can be multiplexed simply by adding more random binary patterns. We demonstrate the generation of up to eight different independent outputs. Although the technique was demonstrated years ago, nowadays it can be applied with high-resolution SLMs with a very large number of pixels, thus allowing for a larger number of multiplexed functions without significant degradation. Nevertheless, high-resolution SLMs are affected by pixel crosstalk caused by the fringing field effect. We show that the random patterns are quite sensitive to this effect, leading to a significant undesired DC order. Two alternative strategies to avoid this degradation and make the random multiplexing technique efficient are discussed.
In this work, we present a method to generate vector beams with a 4f polarization Fourier filtering system that combines a spatial light modulator (SLM) at the input plane and a polarization diffraction grating (PDG) at the output plane. In the Fourier plane, two quarter-wave plates are employed to transform the +1 and −1 diffraction orders onto circular right (RCP) and left (LCP) polarizations, respectively. The PDG at the output plane recombines the two beams producing the colinear superposition of RCP and LCP beams. The application of a random encoding technique to multiplex diffractive elements on the SLM allows the independent encoding of different patterns on the final beam, thus arbitrary vector beams can be generated at the output. Experimental results are included that demonstrate the capability for this approach to encode a variety of polarization vector beams with different topological charges.
In this work we present a new method to optically obtain the convolution / correlation between two functions. The technique is based on obtaining higher powers of a properly designed phase-only hologram. The approach combines some of the advantages of the classical 4f and the JFTC correlator systems. These higher powers of the hologram transmission function can be obtained easily using a spatial light modulator (SLM) with an extended phase modulation of various cycles of 2π radians. SLMs with such extended phase modulation present useful unusual diffraction properties that can be exploited to surpass some limits of SLM technology. In this case we exploit them to obtain higher order optical correlation terms. Computational simulations and experimental results agree with theory.
In standard phase spatial light modulators (SLM), showing a phase modulation of 2π radians, there is a limit to the shortest focal length of an encoded lens. This Nyquist focal length limit is caused by the aliasing originated by the SLM pixelated structure. In this work we show that SLMs with very large phase modulation (in our case about five cycles of 2π radians) can be used to surpass this effect and efficiently encode lenses with focal lengths much lower than the Nyquist limit. We include experimental results showing that this limit is reduced by a factor of about 1/10.
A holographic projection system based on the encoding of computer-generated holograms onto a spatial light modulator is discussed. We show how the size, location, and polarization state of the output can be controlled completely electronically, without physically moving any element in the system. It is finally shown that the system is capable to produce optical logical operations by superimposing two different images encoded onto orthogonal polarization states. We show how these images can be added or subtracted, giving a polarization-based logic system. Experimental results are included in all cases.
Commercial non-tunable q-plates have become popular optical elements to generate vector beams at the design wavelength where the device exhibits half-wave (HW) retardance. However, their use is restricted since both the topological charge and the operating wavelength are set in fabrication. In this work, we report how to make such commercial q-plates more versatile for generating vector beams of higher topological charge and in different wavelength ranges. First, we show how to add, subtract or change the sign of the charge, by combining q-plates with HW plates. Second, we perform a broadband spectral characterization of the q-plate retardance, and identify the wavelengths with retardance values relevant for vector beam generation π, ±π/2). The wavelength is then used as a tuning parameter to change the device performance from a HW q-plate to a QW q-plate. The vector beams expected at these QW wavelengths are obtained as a superposition of the input polarization state and the output state of a HW q-plate. Experimental results are shown using the red and blue lines of an Ar-Kr laser. For input linearly polarized light of 488 nm the device generates hybrid vector beams (where the ellipticity varies with the azimuthal angle), while for 647 nm pure radial vector beams with constant ellipticity are obtained. These results could extend the use of commercial q-plates for multicolor vector beam applications.
Vector beams where the polarization state is spatially dependent are being examined as new optical communication channels. We demonstrate a vector beam spectrum analyzer capable of simultaneously determining the topological charge and the state of polarization of an input vector beam. We encode a two-dimensional polarization diffraction grating that generates six different q-plate channels from -3 to +3 in the horizontal direction, and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincaré sphere. The horizontal q-plate grating is a optimized phase-only grating that produces harmonics of a given input q-plate having a charge of +1 all of which have equal strengths. The vertical polarization grating is specially designed to produce 6 orders where the amplitude and phase of each order can be independently controlled. Different gratings are required for the horizontal and vertical polarizations to create the desired polarization states in each diffracted order. Consequently, we generate 36 different channels in parallel. We demonstrate this polarization diffraction element using a single phase-only liquid-crystal spatial light modulator in a reflective optical architecture. Details are given regarding experimental details on this process. Finally, we demonstrate that this system can act as a vector beam polarization state spectrum analyzer allowing both the topological charge and the polarization state of the input vector beam to be simultaneously determined in a single experiment.
We present an experimental multichannel polarization imaging system based on a polarization diffraction grating (PDG). The PDG simultaneously creates six diffraction orders, each having a different polarization state. For this proof-of-concept experiment, we encoded the PDG onto a parallel-aligned liquid-crystal spatial light modulator (LCSLM), using a double-pass optical architecture. We use a birefringent object where the top is covered with a retardation film and the bottom is isotropic. We show experimental results, where we simultaneously produce six images of this birefringent object, each with a different polarization state. The proposed technique can produce a single-shot imaging polarimeter.
In this work we report on our achievements in generating switchable and arbitrary vector beams by means of q-plates. Two kind of q-plates are considered: i) a physical prototype from Citizen Co. and ii) a virtual device that is encoded onto a spatial light modulator (SLM). In both cases experimental and analytical results within the Jones formalism are shown. The performance of a segmented and tunable liquid crystal q-plate prototype is characterized at visible and telecommunications wavelengths, and the generation of first-order vector beams is probed. By using a reflective geometry and tuning the q-plate at half-wave or at quarter-wave retardance, it is shown how the device can operate either as a q-plate with double order. Finally, we show the generation of arbitrary programmable integer and fractional vector beams by encoding a q-plate onto a SLM based system. The system is based on a double-pass configuration that consecutively modulates the vertical and the horizontal polarization components of light using a transmissive LCoS display. Therefore, new and exotic q-plate designs can be analyzed prior to their fabrication.
Anderson localization has been previously demonstrated both theoretically and experimentally for transmission of a Gaussian beam through long distances in an optical fiber consisting of a random array of smaller fibers, each having either a higher or lower refractive index. However, the computational times were extremely long. We show how to simulate these results using a fast Fresnel diffraction algorithm. In each iteration of this approach, the light passes through a phase mask, undergoes Fresnel diffraction over a small distance, and then passes through the same phase mask. We also show results where we use a binary amplitude mask at the input that selectively illuminates either the higher or the lower index fibers. Additionally, we examine imaging of various sized objects through these fibers. In all cases, our results are consistent with other computational methods and experimental results, but with a much reduced computational time.
In this paper, we review some of our recent advances in the generation and control of polarized light beams by means of liquid crystal light modulators. We use a reflective geometry where a single parallel-aligned spatial light modulator device is used to independently spatially modulate two orthogonal linear polarizations with two different phase profiles. In this way we are able to produce arbitrary polarization patterns, which can be combined to produce polarization diffractive elements. In this work we present two such new elements: 1) an anisotropic axicon capable to produce a line focus with axial arbitrary state of polarization, and 2) anisotropic diffraction gratings, capable to generate arbitrary orders of diffraction with different states of polarization designed at will. The anisotropic axicon generates a Bessel beam with polarization variation, which might be useful in micro-fabrication techniques. On the other hand, the anisotropic gratings are useful to produce snapshot polarimeters, capable to measure the Stokes parameters of a light beam in a single measurement. Finally, we will show that these elements can be combined with spiral phase patterns in order to convert them into cylindrically polarized light beams. Experimental results on the production of diffractive elements that generate light beams with these polarization features will be included.
We present the use of a q-plate device operating at the 1550 nm telecommunications wavelength. A prototype liquid-crystal device from Citizen Holdings Co. is demonstrated to be useful for the generation of vector beams and orbital angular momentum transfer at this important wavelength.
We describe the experimental implementation of a virtual optical beam propagator system. This virtual propagator system allows the experimental study of beam propagation without physically moving any element. The approach uses a Fresnel diffraction algorithm (usually called the angular spectrum method) and its implementation on a spatial light modulator. We discuss the limits of the technique and provide a detailed description of the experimental procedures. Experimental results are included where we design a hologram capable of producing two patterns at two different distances, and we can change the effective plane of observation by changing the encoded propagation instead of by moving any element on the experimental system.
In this paper the fast Fresnel diffraction algorithm is reviewed and applied to some novel applications. The algorithm (also named the convolution or angular spectrum method) is a very powerful numerical technique that has been employed in the calculation of diffraction patterns. It utilizes two Fourier transform operations, thus becoming computationally much faster than the conventional approach. We analyze the practical implementation with spatial light modulators (SLM). First, the ray matrix approach is applied to derive and reexamine this computational technique. This approach easily allows us to find explicit expressions for the maximum and minimum distances over which the algorithm is accurate. Then, we describe the practical implementation of this algorithm to encode Fresnel propagated masks onto a SLM. We discuss the limitations caused by the Nyquist limit. Finally, we apply the technique to create an experimental virtual optical beam propagator system. This system uses one SLM and allows the experimental study of the beam propagation without physically moving any element. This laboratory propagator system can be extremely useful to build compact optical architectures or to emulate beam propagation without misalignments caused by moving elements in the experimental system. As examples, we design holograms capable of producing different patterns at different distances, and we can change the effective plane of observation by changing the encoded propagation. The technique can find applications in many different contexts, including the analysis of propagation dynamics of nondiffracting beams, and Airy beams.
In this work we describe techniques for the generation of vortex beams, including vortex generating diffraction gratings
and diffractive lenses, as well as some possible applications in optical image processing. We then analyze the description
of radially polarized beams in terms of superposition of such vortex beams. We present some methods for the production
of radially polarized light, that include patterned linear polarizers, specially designed liquid crystal devices and spatial
light modulators (SLMs). We analyze the manipulation of this radial polarization by means of wave-plates, in order to
obtain other non-standard spatially variant polarized light beams. Theoretical analysis are presented based on the Jones
matrix theory, and experimental results are included for all cases.
We present a simple method to check the exact realization of a radially polarized light beam by means of a vortex-sensing diffraction grating. The use of this grating easily allows the determination of the topological charges included in each of the two circular polarization components of the incident beam. Therefore a pure radially polarized beam can be easily distinguished from a pseudo-radially polarized beam. Experimental results are presented with radial beams generated with two different devices: a patterned radial polarizer and a specially designed liquid crystal device.
We used patterned radial polarizers to easily generate and detect radially polarized beams. We then showed how to spatially manipulate the two-dimensional polarization mapping provided by a radial polarizer using different waveplate systems to obtain new two-dimensional polarization states. One system is particularly useful, since it converts the radial polarized beam into the azimuthally polarized beam. The transformed beams were analyzed using linear, circular, and radial polarizers. The Jones matrix formalism was applied for the theoretical analysis.
KEYWORDS: Interferometers, Refractive index, Radio propagation, Dispersion, Photonic crystals, Terahertz radiation, Signal attenuation, Mach-Zehnder interferometers, Signal processing, Signal generators
In this work, we demonstrate the existence of abnormal pulse propagation regimes in linear and passive multiple-beam
interferometers, where the group velocity can be tuned from subluminal to superluminal values by simply changing the
length of one of the interferometer's arms. Experiments are performed in the radiofrequency range by using coaxial
transmission lines. The interferometers group delay is characterized both in the frequency and in the time domain. Group
velocities of 2c and tunnelling with negative group velocity of -0.11c were measured for electromagnetic wave packets
of 2 μs width travelling through a Mach-Zehnder interferometer. In a 4-beam interferometer, the group velocity of a 5 μs
wide pulse was reduced to only 0.3c (compared to the usual value of 0.67c). The system is scalable to other frequency
ranges and its implementation for narrowband optical pulses could be feasible by means of micromachining
technologies. A scaling approach for advancing/delaying optical pulses at 1.55 μm is discussed. These systems are
proposed as an alternative for controlling the group velocity without the need of using photonic crystals or periodically
microstructuring, doping or using non-linear media.
It is present a unique compact optical circular-polarization-splitting common-path interferometer, described based on a
zero-twist liquid crystal display (LCD) [1]. A blazed diffraction grating is encoded onto the LCD. The optical train
produces two beams, a reference beam with a sense of circular polarized light and a diffracted one with the opposite
sense of circular polarized light. Using a linear polarizer, these two beams form an interferogram that can be used to
analyze optically active media. The detail of the light behaviour through the optical train is present using Jones
matrix's.
We review the three types of laser beams - Hermite-Gaussian (HG), Laguerre-Gaussian (LG) and the newly discovered Ince-Gaussian (IG) beams. We discuss the helical forms of the LG and IG beams that consist of linear combinations of the even and odd solutions and form a number of vortices that are useful for optical trapping applications. We discuss how to generate these beams by encoding the desired amplitude and phase onto a single parallel-aligned liquid crystal display (LCD). We introduce a novel interference technique where we generate both the object and reference beams using a single LCD and show the vortex interference patterns.
We explore the analogies between a system of coaxial cables with periodicity in the impedance, and a system of dielectric stacks with periodicity in the index of refraction. The latter is a photonic crystal with wave propagation control in the optical range, while the former can be regarded as a "coaxial" photonic crystal for radiofrequency control. We reproduce electrical analogs of widely used thin-film optical devices, such as Bragg reflectors, Fabry-Perot resonators and harmonic transmission filters. Coaxial crystals represent an inexpensive way of teaching multilayer optical coatings. We show also that a simple phasor analysis provides an intuitive technique to describe the transmission properties of optical multilayers.
We review the operation of both twisted and parallel-aligned nematic liquid-crystal displays (LCD's) for applications in optical computing, image processing, pattern recognition and diffractive optical elements. For these applications, three spatial modulation characteristics are of interest: phase-only, amplitude-only, and combined full amplitude and phase. We review how to achieve these three operating conditions. We begin with a discussion of the Jones matrix model for the twisted-nematic LCD displays. We examine optical configurations for achieving amplitude-only modulation and polarization eigenvectors for achieving phase-only modulation. Then we review an extremely successful technique for obtaining combined full amplitude and phase modulation with a single LCD by spatially modulating the maximum phase depth. Finally we discuss new advances in achieving 2D polarization modulation.
In this work, we present an analysis of harmonic frequency transmission filters based on one-dimensional photonic crystals using a Fourier transform approach. This approach relates the photonic crystal transmittance with the Fourier transform of the logarithmic derivate of their refraction index profile. We compare this Fourier approach with the exact transmission calculated by means of the transfer matrix method. We study the accuracy of different functions proposed in the literature that relate the Fourier transform of the index profile with the transmittance. This Fourier approach provides a more intuitive understanding of the transmission properties of one-dimensional photonic crystals. We experimentally demonstrate these properties by using coaxial cables of different impedances. This kind of electrical system is easier to perform experimentally and reproduces, in the radiofrequency range, the properties of one-dimensional photonic crystals.
We study experimentally and by numerical simulation the Fresnel diffraction on the recently introduced fractal zone plates (ZPs) associated with Cantor sets. The focusing properties of these ZPs and the evolution of the intensity patterns at the plane transversal to the propagation direction are discussed. As it follows from numerical simulation the series of conventional and doughnut-like secondary focuses are observed around the principal focus. The position, depth and the size of these focuses depends on the type of Cantor set and the level of the fractal, which are directly related to the number of the corresponding Fresnel zones. The results obtained by numerical simulations are verified in the experiments. The fractal Cantor ZPs of different levels are implemented with a liquid crystal display and with the diapositives. The experimental results obtained by both types of the dispositives are in good agreement with the theory and numerical simulations.
We present the use of ray-matrix optics to study lens systems that perform optical Fourier transforms. The analysis is based on the interpretation of a ray in terms of a plane wave, and it avoids the necessity of using diffraction integrals. We also extend the analysis to fractional Fourier transform systems. This formulation represents a compact derivation of Fourier optics, useful for teaching the topic to engineers and physicists.
In this work we review the application of twisted nematic liquid crystal displays (TN-LCD's) for image processing, pattern recognition and diffractive optical elements. For these applications, three kinds of spatial modulations are of interest: phase-only, amplitude-only and combined full amplitude and phase modulation. However TN-LCD's generally provide coupled phase and amplitude modulation. We review how to achieve these three desired operating conditions. We begin with a discussion of different Jones matrix models for TN-LCD displays. We examine optical configurations for achieving amplitude-only modulation and polarization eigenvectors for achieving phase-only modulation. Then we review an extremely successful technique for obtaining combined full amplitude and phase modulation by spatially modulating the maximum phase depth.
In this paper we will revise the application of twisted nematic liquid crystal displays (TN-LCD) as spatial light modulators (SLM) for image processing and diffractive optics. In general two kind of responses are desired for the mentioned applications: amplitude-only and phase-only modulation. In general the users of commercially available LCDs do not know the optical properties of the used material. Thus, a reverse-engineering approach is needed to optimize the LCD response. First, we show a simplified model, that we recently proposed, for the orientation of the LC molecules. The model allows the determination of the physical parameters of the LCD by means of simple intensity measurements. Second, we demonstrate the capability of the model to provide very accurate predictions of the optical transmission. Therefore, we can perform computer searches for the optimum orientation of the added polarizing elements to obtain the required optical transmission. We demonstrate the need to insert wave plates in front and behind the LCD to obtain either amplitude-only or phase-only regimes with the LCD. Finally, we show the application of the optimized LCD to display images and filters in optical image processing, as well as we show the design of diffractive optical elements and apodizers.
We show the feasibility of two new programmable diffractive optical elements (DOE). On one hand, we demonstrate the realization of programmable apodizers. With the term apodizer we refer to non-uniform amplitude filters used to modify the point-spread function (PSF) of an optical system. On the other hand, we show the simultaneous realization of a Fresnel lens and an amplitude filter in a single DOE: the programmable amplitude apodized Fresnel lens (PAAFL). Two different modulation regimes are required to generate these DOEs: amplitude-only regime for the programmable apodizer and phase-only regime for the PAAFL. We show that a twisted-nematic liquid crystal spatial light modulator (TN-LCSLM) inserted between two wave plates and two polarizers is able to provide both modulation regimes. Different types of amplitude filters, such as axial hyperresolving, transverse apodizing and transverse hyperresolving have been implemented both as programmable apodizers and as PAAFLs. We provide experimental results for the performance of the two new DOEs. The agreement with the numerical results is excellent, thus demonstrating the feasibility of our proposal.
In this paper we show a technique to simultaneously encode a Fresnel lens and an amplitude filter in a single diffractive optical element (DOE) displayed on a spatial light modulator (SLM). IN particular we have displayed this new DOE, which we call amplitude apodized Fresnel lens (AAFL), on a twisted nematic liquid-crystal working in the phase-only regime. The programmability of the AAFL permits to change dynamically its focal length and its action on the point-spread function of an optical system. We provide a method to encode the complex amplitude information of the AAFL on a phase-only function. We also demonstrate how to compensate for the inherent equivalent apodizing effect due to the pixelated structure of SLMs. Different types of AAFLs, such as transverse apodizing AAFL and transverse hyper resolving AAFL are implemented. The excellent quantitative agreement between experimental and numerical results shows the feasibility of AAFLs on a phase-only SLM.
In this contribution we present a method for the determination of the twist angle of an arbitrary twisted nematic liquid crystal spatial light modulator.
The phase-only filter is of great interest for optical pattern recognition applications because of its sensitivity and because it can easily be programmed onto spatial light modulators. In evaluating the suitability of this filter for a correlator, it is useful to understand the impulse response function that is actually being correlated with the input function. In this research, we derive an analytic expression for the impales response function for the phase-only filter corresponding to a one-dimensional rectangle function. We show that this impulse response function represents a bipolar edge-enhanced version of the input function. This can be easily generalized to a two-dimensional box function. Experimental results verify the analysis.
The output from diffraction gratings is formed using a Fourier transform lens. Because optical detectors are sensitive to intensity, information about the phase of the diffracted beams is lost. The relative phase shift between different diffracted orders can be measured using a multiplexed lens consisting of two offset lenses This lens forms two separate copies of the diffraction pattern. If a diffracted order from one copy overlaps a different order from the second copy, the resulting interference allows analysis of the relative phase between the different diffracted orders. Experimental results are presented using multiplexed lenses written onto a magneto-optic spatial light modulator.
The output from a Dammann grating can be modified by forming the Fourier transform lens onto a programmable spatial light modulator. We show how the positions and numbers of the outputs can be varied. In addition, the technique allows analysis of the phase of the diffracted beams.
We discuss the encoding of new types of binary optical elements onto programmable spatial light modulators (SLMs). After introducing the technique and limitations, some past work will be reviewed and new ideas presented.
Diffractive optical elements can be easily made and tested using programmable spatial light modulators (SLM's). We discuss limitations imposed by using SLM's for such purposes and present experimental results showing a variety of applications.
We discuss a number of anomalies that can result in the output of a joint Fourier transform correlator. Some of these are caused by the writing of the joint power spectrum onto a spatial light modulator having a grid structure. Others result from the binary recording of the joint power spectrum. These effects can cause spurious output cross-correlation peaks
and can affect the strengths of the desired cross correlation peaks.
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