A straight effective method to produce partially coherent beams with controllable time-dependent coherence is demonstrated. We theoretically deduce that a time-dependent partially coherent beam can be generated by imposing dynamic random phase on a coherent laser beam. The degree of coherence of the beam is determined by an amplitude control parameter of the dynamic random phase. We experimentally corroborate that after a completely coherent laser beam reflected from a spatial light modulator, loaded with a particular dynamic random phase, this beam is transformed into a partially coherent beam with time-dependent coherence.
We analyze and demonstrate, numerically and experimentally, the self-healing effect in scaled propagation invariant beams, subject to opaque obstructions. The effect is quantitatively evaluated employing the Root Mean Square deviation and the similarity function.
This article [Opt. Eng.. 52, (8 ), 081605 (2013)] was originally published on 21 February 2013 with Figs. 4 and 5 reversed, although the captions were correct. The corrected figures and captions are reprinted below.
The segmented large millimeter telescope (LMT/GTM) is the largest spatial light modulator capable of producing vortex beams of integer topological charge. This observing mode could be applied for direct exoplanet searches in the millimeter or submillimeter regimes. The stability of the vortex structure against aberrations and diffraction effects inherent to the size and segmented nature of the collector mirror was studied. In the presence of low-order aberrations, the focal distribution of the system remains stable. Results show that these effects depend on the topological charge of the vortex and the relative orientation of the aberration with respect to the antenna axis. Coma and defocus show no large effects in the image at the focal plane; however, the system is very sensitive to astigmatism. Heat turbulence, simulated by random aberrations, shows that the system behaves in a similar way as astigmatism dissociating the vortices. The segmented vortex telescope is proposed as a novel approach for the detection of giant planets outside circumstellar disks around nearby stars. Since results are applicable to other facilities with segmented surfaces, it is suggested that this idea should be considered as a regular observation mode complementary to interferometric methods.
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.
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.
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.
Spatial self-phase modulation was observed when a CW laser beam propagated along a cell containing castor oil. The minimum power needed to excite this effect decreases when the sample length is increased, as well as when the laser wavelength approaches to the absorption band of the medium. The same phenomenon was also observed when a laser beam interacts with a colloidal solution of gold nanoparticles in castor oil. For this system the self-phase modulation
minimum power decreased dramatically, which indicates that the nonlinear refractive index for this system is enhanced due to the gold nanoparticles. Moreover, for laser wavelength near to the plasmon resonance of the gold nanoparticles, this enhancement factor is even higher. Although the large value of those media nonlinearity, its temporal response is slow. This fact suggests that this phenomenon is due to thermal effects mainly.
The development of technology of small dimensions requires a different treatment of electromagnetic beams with transverse dimensions of the order of the wavelength. These are the nonparaxial beams either in two or three spatial dimensions. Based on the Helmholtz equation, a theory of nonparaxial beam propagation in two and three dimensions is developed by the use of the Mathieu and oblate spheroidal wave functions, respectively. Mathieu wave functions are the solutions of the Helmholtz equation in planar elliptic coordinates that is a special case of the prolate spheroidal geometry. So we may simply refer to the solutions, either in two or three dimensions, as spheroidal wave functions. Besides the order mode, the spheroidal wave functions are characterized by a parameter that will be referred to as the spheroidal parameter. Divergence of the beam is characterized by choosing the numeric value of this spheroidal parameter, having a perfect control on the nonparaxial properties of the beam under study. When the spheroidal parameter is above a given threshold, the well known paraxial Laguerre-Gauss and Hermite-Gauss beams are recovered, in their respective dimensions. In other words, the spheroidal wave functions represent a unified theory that can describe electromagnetic beams in the nonparaxial regime as well as in the paraxial one.
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.
In the area of ophthalmic refractive surgery research, the Zernike expansion of the Wavefront aberrations has been the key factor in the measurement, representation and evaluation of the human eye aberrations in many different clinical situations. The Wavefront Aberrations described by the Zernike expansion can be translated as the polynomial expansion of the exit pupil of an optical system that represents the total Wavefront aberrations (corneal + internal elements) of the eye. In this direction, we can use this exit pupil to calculate both the incoherent Point Spread Function (PSF) and the Optical Transfer Function (OTF) of this system. With either of these two functions (PSF or OTF), we can easily calculate the output image of a certain object. This information can be used to evaluate the visual performance of the eyes with a set of pre-determined objects and their corresponding images. We apply these results to characterize the behavior of the aberrations of human eyes that in principle do not need any type of refractive compensation or correction, in order to have a reference which may be ethnical-dependent. We are interested in describing the set of aberration characterizing the Normal Mexican Eye (NME). To achieve our goal, we start our study with a group of Mexican Males with an Uncorrected Visual Acuity (UCVA) of 20/20, 20/30, and 20/40. We present the preliminary results of our characterization.
We present a detailed study of the unstable Bessel resonator. The cavity of this laser consists of a reflective axicon and a convex spherical output coupler. A matrix method analysis for the bare resonator is employed to extract the eigenmodes and eigenvalues of the cavity, which allows us to obtain the fundamental and higher-order modes. Diffractive losses and relative phase shift behavior, in terms of both the varying radius of curvature of the output coupler and the cavity length, are studied with the matrix method and the Fox-Li algorithm. Direct comparison of the transverse mode profiles with a similar resonator employing a concave output coupler is performed, showing excellent agreement for large values of the radius of curvature. We also considered the effects of varying the aperture of the output coupler and the wedge angle of the axicon on the transverse mode profiles and diffractive losses.
Propagation of light beams with apparent nondiffracting properties have intrigued the scientific community since they were introduced. In this talk we will introduce the fundamentals of nondiffracting beams and discuss the dynamics of optical vortices embedded in the new two families of nondiffracting beams we have recently discovered, Mathieu and parabolic beams.
The fiber Raman amplifier employs the intrinsic properties of silica fiber to obtain the amplification, thus they use the transmission fiber as the amplification medium, where the gain is created along the transmission line. The amplification is realized by Stmulated Raman Scattering (SRS). This nonlinear process occurs when a sufficiently powerful pump is within the same fiber as the signal. In this paper, we showed experimental and numerical analysis of SRS in optical fibers. We obtain a continuous spectral when we plot the energy content in each Stokes sublines with the wavelength, which are self-pump between them. The numerical results are in agreement with the experimental results, just as the waveform in the time of optical fiber end and the energy is transferred from the signal pump to the Stokes sublines. With the simulations, we can obtain several parameters of this optical amplifier like the optical fiber effective length to obtain the amplification.
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.
Recently, a new class of nondiffracting beams has been demonstrated theoretically. Namely, Parabolic nondiffracting optical wavefields constitute the last member of the family of fundamental nondiffracting wavefields. Additionally, the existence of a new class of parabolic traveling waves associated to these wavefields has been demonstrated along the same lines. We have succeeded in demonstrating experimentally the fundamental odd and even parabolic wavefields in the laboratory. In this work, we present and discuss the experimental generation of higher-order parabolic nondiffracting wavefields. Because these fields show a complex structure, their generation relies in the successful construction of the field.
A novel experimental arrangement to produce high-order Bessel beams is proposed. The system is based on the decomposition of the even and odd spatial components of the Bessel beam. The reconstruction is made with a Mach-Zender interferometer. The original annular squeme of Durnin is used to generate each component of the Bessel beam. The main advantage of our setup is that the annular transmittances have only discrete changes of phase.
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.
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.
Optical guiding of micron-sized particles is shown using both Gaussian and zeroth-order Bessel light beams. Axial and transverse forces for guiding in both beams are calculated. Experiments show that the Bessel beam allows for extended guiding distances compared to a Gaussian beam, at the expense of guiding velocity.
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.
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 present a geometrical optics analysis of a novel laser cavity with conical mirrors (reflective axicons). A further two dimensional study of the cavity is carried out through formal diffraction theory. We will show that the profile of the modes of such resonator are approximately Bessel-Gauss beams. The design also supports higher order modes, however these turn out to be unstable when perubations are present, they eventually decay to the lowest order mode. An explanation for the Bessel structure is due to the conical nature of the wave-front induced by the axicons, while the bell-shaped profile arises from the finite extent of the cavity.
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 discuss the theory, the experiment and applications to the interference resulting of the superposition of two or more Bessel beams propagating in free space and showed for first time a self imaging effect using nondiffracting beams.