We present a simple technique for the calibration, prediction, and optimization of the optical modulation properties of a liquid-crystal display (LCD). The method is useful when there is no information about the internal fabrication parameters of the device (the orientation of liquid-crystal molecules, the twist angle, or the birefringence of the material). A complete determination of the LCD Jones matrix is accomplished by means of seven irradiance measurements for a single wavelength. This technique only requires two linear polarizers and one quarter-wave plate. Once the Jones matrix has been calibrated, the amplitude, phase, and polarization modulation response can be predicted. Therefore, it can be optimized through the control of the polarization configuration. The validity of the proposed method is experimentally probed. Finally, we present a particular application to produce phase-only modulation.

We generate programmable vector beams with arbitrary q-plates encoded using a spatial light modulator system. Consequently, we can analyze new and exotic q-plate designs without the difficulty of fabricating individual plates. We show experimental results for positive and negative integer and new fractional vector beam values.

In this work we study a prototype q-plate segmented tunable liquid crystal retarder device. It shows a large modulation range (5π rad for a wavelength of 633 nm and near 2π for 1550 nm) and a large clear aperture of one inch diameter. We analyze the operation of the q-plate in terms of Jones matrices and provide different matrix decompositions useful for its analysis, including the polarization transformations, the effect of the tunable phase shift, and the effect of quantization levels (the device is segmented in 12 angular sectors). We also show a very simple and robust optical system capable of generating all polarization states on the first-order Poincaré sphere. An optical polarization rotator and a linear retarder are used in a geometry that allows the generation of all states in the zero-order Poincaré sphere simply by tuning two retardance parameters. We then use this system with the q-plate device to directly map an input arbitrary state of polarization to a corresponding first-order vectorial beam. This optical system would be more practical for high speed and programmable generation of vector beams than other systems reported so far. Experimental results are presented.

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We discuss a simple method for fabricating interference birefringent filters using common cellophane tape layers. Cellophane tape layers can be superimposed with different orientations to generate different spectral responses. We demonstrate this behavior with a portable spectrophotometer. This technique is a simple and inexpensive way of investigating the optical properties of birefringent filters.

We demonstrate superluminal and negative group velocity regimes in a linear passive Mach–Zehnder interferometer. This phenomenon occurs in a narrow frequency region around the interferometer’s transmission minima. Experiments are performed in the radio frequency range by using coaxial cables and 1×2 wave splitters. Group velocities of 2c and tunneling with a maximum fractional advancement of 0.12 were measured for electromagnetic sinusoidal wave packets of 2 μs width. These results agree with theoretical predictions using the interferometer’s transmission phase function. This system is proposed as a simpler alternative to photonic crystals and active or microstructured multiple-beam interferometers for sustaining anomalous group velocities.

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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 provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics.