Inhomogeneous or gradient index media exhibit a refractive index varying with the position. This kind of media are very interesting because they can be found in both synthetic as well as real life optical devices such as the human lens. In this work we present the development of a computational tool for ray tracing in refractive optical systems. Particularly, the human eye is used as the optical system under study. An inhomogeneous medium with similar characteristics to the human lens is introduced and modeled by the so-called slices method. The useful of our proposal is illustrated by several graphical results.
Ametropies of the human eye, are refractive defects hampering the correct imaging on the retina. The most common ways to correct them is by means of spectacles, contact lenses, and modern methods as laser surgery. However, in any case it is very important to identify the ametropia grade for designing the optimum correction action. In the case of laser surgery, it is necessary to define a new shape of the cornea in order to obtain the wanted refractive correction. Therefore, a computational tool to calculate the focal length of the optical system of the eye versus variations on its geometrical parameters is required. Additionally, a clear and understandable visualization of the evaluation process is desirable. In this work, a model of the human eye based on geometrical optics principles is presented. Simulations of light rays coming from a punctual source at six meter from the cornea are shown. We perform a ray-tracing in three dimensions in order to visualize the focusing regions and estimate the power of the optical system. The common parameters of ametropies can be easily modified and analyzed in the simulation by an intuitive graphic user interface.
The optical characterization of nonlinear media through the Z-scan technique considers initially a thin
medium (with a thickness much less than the beam depth of focus). It has been observed that increasing the
thickness of the medium the transmittance increases, this means that n2 increases, for this reason we will
present a numerical model to determinate the minimum thin and the maximum thick medium limit. A thin
medium is considered as a thin lens with focal length F1 and a thick medium can be regarded as a set of such
thin lenses set with focal lengths F2, these lenses are contained in a medium whit a refraction index different
than air. This analysis is made through Matlab using the theory of Gaussian beams, ABCD matrices and the q
parameter, elementary theory in the development of this work, where the main feature of this model is that the
nonlinearity type of the medium is considered as an integer constant in its focal length3. We present the
graphs obtained from Z-scan for thick medium with both thermal and Kerr nonlinearities.
In this work we propose a method to characterize a laser beam based on the Gaussian beam propagation through a lens with
a simple experimental setup that can accurately measure the magnitude and location of the beam waist. The experimental
setup involves a lens and a chopper located on a mechanical mount separated by a distance equal to the focal length of the
lens. To characterize the laser the setup is moved away parallel to the axis of the beam beginning at a distance shorter than
the focal length. A photodetector behind the chopper measure the periodic transmitted intensity and an electrical circuit
generates a square wave whose pulse width is proportional to the beam width at the location of the chopper. The position of
the chopper where the beam width is minimum allow us to calculate the location of the waist, we just need to make a final
measurement of the beam width without the lens to find the magnitude of the waist. All the measurements are fast and only
few are needed to determine accurately the position and magnitude of the beam waist.
The transmission of an intense light beam through a thin nonlinear sample has been extensively studied, like in self
phase modulation experiment and Z-scan technique, with different approaches: the Gaussian decomposition method, the
Huygens-Fresnel principle, the diffraction theory, etc., The nonlocality in the response of the media in general leads to
solve more than one differential equation. In this work we present a simple model to calculate, in a numerical way, the
on axis far field intensity in a Z-scan experiment or the far field pattern in spatial self phase modulation experiment by
means of the diffraction theory and taking into account the locality of the thin nonlinear media. The obtained results
show that the peak-valley separation distance and the transmittance difference in a Z-scan experiment and the number of
rings, size and intensity distribution of the far field pattern in the spatial self phase modulation experiment are functions
of the locality in the nonlinear response of the media. The proposed model describes in good approximation
experimental results for samples, like absorbing liquids, liquid crystals, metal nanoparticles, etc., with different kind of
nonlinear response. This model is valid for any value of the nonlinear phase shift.
We present a modification to the classic Michelson interferometer that allows the interference of multiple beams with equal amplitude. The proposed architecture presents the same advantages and simplicity as those of a classic Michelson interferometer. The basic unit of the device consists of a beamsplitter and two mirrors arranged as in a Michelson interferometer. To increase the number of interfering beams, the mirrors are replaced by a basic unit. In order to demonstrate the type of interference patterns that can be obtained, we present interferograms corresponding to three to eight interfering beams. The system can be used to optically induce photonic lattices.
Nonlinear phase contrast microscopy is an optical technique that uses an intensity-dependent refractive index material to
produce high-contrasted images of transparent specimens. Earlier proposal of liquid crystals as phase filters for phase
contrast applications used optically addressed spatial light modulators fabricated with photoconductive film. Here, we
propose the use of a simpler planar nematic liquid crystal cell doped with 1% wt methyl red. Owing to their polarization
dependent enhancement factor a tunable phase filter can be photoinduced efficiently. Thus, images of different degree of
contrast (and even contrast reversal) can be obtained either by rotating the polarization vector. All optical real-time
imaging of dynamic events can be performed and image processing such as edge enhancement is demonstrated.
We present an analysis of the dynamics of conical waves partially obstructed by opaque objects. The analysis yields the incoming and outgoing conical waves that form the Bessel beams (or any other propagation-invariant beams) when opaque obstructions are set on and off axis. The results show that the invariance of Bessel beams with finite transverse extension is no longer maintained under the mentioned conditions.
We report on the first experimental observation of a large spatial lateral shift in the interaction of obliquely oriented spatial-dark soliton stripes. We demonstrate by numerical simulations that this new effect can be attributed to the specific features of optical media with nonlocal nonlinear response.
Dye-doped nematic liquid crystal samples where the vector director is not pre-aligned exhibits simultaneously positive
and negative nonlinear refractive index under cw illumination at room temperature, regardless the polarization state of
the illuminating beam. However, its relative contributions are polarization dependent. Experimental Z-scan curves for
100 μm thick methyl red doped 5CB nematic liquid crystals, demonstrate that negative nonlinearity is an order of
magnitude larger than the positive. The polarization state of the transmitted beam is change to elliptical carrying
information about the positive and negative nonlinearities.
Phase contrast microscopy, is a technique that can be used to produce high-contrast images of transparent objects. The
technique employs a phase mask, at the object Fourier transform plane, to create a synthetic reference wave that
interferes with the object wave at the image plane. However, the fabrication and alignment of these masks is an
expensive and delicate process. In this work, we present a nonlinear phase contrast microscope that can be implemented
with a conventional optical microscope using a low power CW coherent light source to illuminate the specimen. An
intensity dependent refractive index material is used to photoinduce the filter. Therefore, the aligning procedure is
greatly simplified. The nonlinear material is a thin cell of dye doped liquid crystal where it is possible to produce a
tunable phase delay depending on the incident light intensity, the light polarization, and the temperature. Due to these
characteristics the resulting setup is relatively inexpensive, easy to implement, and extremely robust.
Light beams and light pulses (in general any wave packet) tend, in a natural way, to broad as they propagate in a linear material. Optical solitons are beams that do not suffer broadening as they propagate in a nonlinear material. Spatial optical solitons are beams where the natural diffraction is compensated by a self induced refractive index change in the media, creating its own waveguide.
The importance of spatial solitons is their capacity to create its own waveguide (like optical fibers). The fact that a spatial soliton can creates a refractive index change in the media, following its intensity profile, allows that other beam can be confined inside it. As a result, light guiding light, allows thinking that spatial solitons can be used as active and passive elements of interconnection in all optical communication systems.
In this work we present a phenomenological, numerical and experimental study on the generation and properties of spatial solitons in different media, but that can be describe by the nonlinear Schroedinger equation. In particular we are going to focus in that solitons that can be generated using cw light beams; this means that the response time of the nonlinearity in the media is larger than milliseconds.
Flow visualization refers to a method used for qualitatively obtain information in the field of fluid mechanics. In this work, we show a simple single lens system using laser light illumination to observe flow dynamics using a setup similar to the schileren setup. As we will detail, it is based on a phase contrast technique in which the filter is made of a nonlinear optical material, therefore it is self-aligned and depends mainly on the illuminating intensity. Due to these characteristics, the resulting setup is extremely robust and builds up within a few milliseconds.
Flow visualization refers to a method used for qualitatively obtain information in the field of fluid mechanics. In this work, we show a simple single lens system using laser light illumination to observe flow dynamics using a setup similar to the schileren setup. As we will detail, it is based on a phase contrast technique in which the filter is made of a nonlinear optical material, therefore it is self-aligned and depends mainly on the illuminating intensity. Due to these characteristics, the resulting setup is extremely robust and builds up within a few milliseconds.
In this paper we present different intensity distributions produced by an axicon when is illuminated with a particular field. The incident plane beam was modified using masks, cylindrical lens or tilting the axicon. The distributions obtained were analyzed to different distances using a CCD camera.
The nonlinear common path interferometer is a simple and robust single lens optical processor using an intensity dependent medium placed on its geometrical focal plane to observe deformed wavefronts. It is described either as a nonlinear inteferometer or as an image processor. We demonstrate that this system requires excess surrounding illumination beyond the geometrical boundaries of the disturbance to operate. We discuss recent progress on this setup. In particular, the effect of large phase changes in the filter and the dynamics of the filter formation.
We study the property of propagation beams disturbed by an opaque obstacle. The fronts of the Hankel waves are disturbed and beyond the obstacle they are reconstructed. We report the observation of two shadow produced by the obstacle, and the fact that the Bessel beam is formed of ingoing and outgoing conical waves. We numerically solve the Helmholtz equation to show the evolution and the reconstruction of the Bessel beam and we demonstrate the correspondence of these results with the experimental part.
In this work, we show a simple single lens system using laser light illumination to observe flow dynamics. It is based on a phase contrast technique in which the filter is made of a nonlinear optical material, therefore it is self-aligned and depends mainly on the illuminating intensity. Due to these characteristics, the resulting setup is extremely robust and builds up within a few milliseconds.
We report on the observation of a normal streak effect on hollow micron sized spheres when illuminated by a focused Gaussian beam in a conventional optical tweezers setup. The hollow microspheres suspended in water can be optically trapped at the center of the illuminating beam. When the microsphere is illuminated off center, an emerging beam approximately perpendicular respect to the incoming beam is generated. This effect due to total internal reflections has been observed in microspheres with different external diameters, ranging from 5-20 microns. The generated normal beam is used to either pull or push other particles or objects around the microsphere or to remove particles stuck to the sphere due to radiation pressure.
An analysis of the image fill factor effect on Zernike-type phase contrast filtering is presented. We define image fill factor as the ratio of the object support area over the illuminating area. Numerical simulations are presented for binary phase objects where the contrast of the output image is evaluated as a function of the image fill factor and image phase variations. The results obtained show that the image fill factor can significantly modify the contrast of the output image.
In this paper we show numerically and experimentally the generation of ring dark spatial solitons using a phase disk and an opaque ring. In the first case one dark ring is generated and in the second a pair. The propagation and stability of this solitons is analyzed.
The interest in propagation invariant optical fields (PIOF's) is due to the fact that, under optimal conditions, they propagate long distances without significant change of their transverse intensity distribution. These kind of wavefields were first identified and described in terms of Bessel function. Based on the separability of the Helmholtz equation in elliptic cylindrical coordinates we have demonstrated that there exist another class of PIOF's. The lowest order mode may have a highly localised distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other. Higher order modes are composed of elliptical vortices and the corresponding intensity profiles are formed by propagation-invariant confocal elliptical rings. These fields are described by the Mathieu-Hankel functions which are exact solutions of Helmholtz equation and for this reason we have called them Mathieu beams. We demonstrate that Bessel beams are a particular case of Mathieu beams, which have a broader fan of interesting features. Since the Mathieu functions form a whole set of exact travelling wave solutions of the Helmholtz wave equation they can be used to describe a class of PIOF's. The McCutchen theorem provides the relation between the general class of PIOF's and these new beams.
We show numerically and experimentally that ring dark spatial solitons can be generated using a phase disk mask or an opaque ring. In the first case one ring is produced and in the second a pair. Rings generated by phase disk are very stable when they are perturbed with one-dimensional dark solitons. The stability of rings generated by opaque rings depends on the size of the perturbation and symmetry of the initial condition. The propagation and stability of these solitons is analyzed numerically and experimentally.
In this paper we report the observation of nonlinear behavior of Kerr type of developed and bleached photographic film using cw laser sources. The nonlinear characterization is made using the Z-scan technique with Argon and He-Nel lasers beams. The results show that depending on the intensity, wavelength and exposition time the refractive index changes can be reversed or permanent giving new application to this material.
In this paper we demonstrate a novel phase contrast system that employs a BR film. Since the filter is optically induced by the Fourier transform of the phase object, no alignment is necessary at the filter plane making it extremely robust. Due to the optical properties of BR films the phase filter can be induced with low light intensity levels. The material response allows operation at video frame rates, processing of high spatial resolution objects, and the use of relatively inexpensive laser sources. Such characteristics and the fact that BR films can be produced at a low cost makes the system simple to implement, relatively inexpensive and extremely robust. The effects of varying the illuminating area beyond the phase object area and filter saturation are also analyzed.
In this work we propose a convolution kernel capable of realizing phase visualization when operated with a phase function. The proposed convolution kernel is a binary complex function. We present numerical simulations of its performance on one and two-dimensional binary phase functions. We also briefly discuss its implementation in a joint transform architecture and the requirements imposed by the detector at the system's Fourier plane. Finally, we analyze the effect of quantizing the Fourier data on the contrasted output images.
The objective of this work is to study, numerically and experimentally the waveguide properties of dark spatial soliton arrays generated in photorefractive media. Experimentally we produced the dark solitons using a He-Ne laser beam and a photorefractive BTO crystal under external electric field to excite the drift nonlinearly. The beam to be guided was obtained from a semiconductor laser at a wavelength where the photorefractive effect was lower. This probe beam was focused in different regions and at different angels with respect to the array. The result obtained shown that the guiding ability of the array depends on the period, the external field and the probe beam angle. Numerical simulations solving the nonlinear Schrodinger equations are in correspondence with the experimental observations.
We present a new class of invariant optical fields that we named Mathieu beams because they are described by radial and angular Mathieu functions. The angular spectrum of these beams when mapped on the McCutchen sphere gives the clue to create them in the laboratory. The corresponding experimental setup is described and the results obtained corroborated our theoretical predictions. The experimental parameters can be easily adjusted to obtain a variety of transverse intensity patterns that range from cosine to Bessel. There are two main families of higher order Mathieu beams, one of them are confocal elliptically ringed and can present phase rotating characteristics that are interesting for creating elliptical rotating waves. The other family of these high order beams have bowtie shapes. Mathieu beams are a variant of superposition of uniform conical waves, i.e. Bessel beams, and for these reason they have also the capability of self-reconstruction after finite obstructions.
We present a new material with potential application in holography. We have used a film of mixing ammonium dichromate with rosin resin diluted in isopropyl alcohol. This material can be easily elaborate in the laboratory. A phase grating in this material was recording using Argon-Ion laser at (lambda) equals 457 nm, showing good diffraction efficiency. This material is capable of high resolution when we record some diffraction gratings, observing 2,000 l/mm (grooves). A characteristic of the developed process is their simplicity, takes approximately 25 seconds.
We present a numerical study of the reflection of 1D spatial solitons at non-linear interface between a photorefractive medium and a linear medium. In this work, we have considered that non-linear medium is governed by both; drift and diffusion mechanisms. Our study places emphasis on determining the physical conditions under which the beam reflected is still a spatial soliton. The beam is deflected into the interface using the self-bending effect.
We present a theoretical and experimental analysis of the Z-scan technique in thick media with thermal nonlinearity in steady-state regime. The theoretical model considers the thick medium as a stack of thin thermal lenses. Numerical solution for the Z-scan technique is obtained. Experimental results for the technique using a sample of methylene blue in a solvent under cw illumination from a 10 mW He-Ne laser beam are obtained. Comparison of the experimental and theoretical results is made. Good agreement between theory and experiment is obtained.
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