Sabino Chávez-Cerda

Parabolic nondiffracting optical wave fields

We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.

Observation of parabolic nondiffracting optical fields

We report the first experimental observation of parabolic non-diffracting beams, the fourth fundamental family of propagation-invariant optical fields of the Helmholtz equation. We generate the even and odd stationary parabolic beam and with them we are able to produce traveling parabolic beams. It is observed that these fields exhibit a number of unitary in-line vortices that do not interact on propagation. The experimental transverse patterns show an inherent parabolic structure in good agreement with the theoretical predictions. Our results exhibit a transverse energy flow of traveling beams never observed before.

Bessel–Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis

A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.

Experimental observation of interfering Bessel beams.

We experimentally verified the interference resulting of the superposition of two Bessel beams propagating in free space and showed for first time the self imaging effect using nondiffracting beams. Our results are supported by numerical simulations and possible applications are discussed.

Experimental demonstration of novel effects on the far-field diffraction patterns of a Gaussian beam in a Kerr medium

We report on the experimental observation of the effects on the far-field patterns obtained when a divergent or convergent beam interacts with a thin self-defocusing material. The measurements were performed using a CW laser beam propagated through a cell containing a colloidal system that presents a very large nonlinear refractive index. The high nonlinearity of the colloid allowed for the observation of patterns never investigated before, revealing a quite different behaviour on the far field from a convergent or a divergent beam due to the opposite interaction with the negative Kerr nonlinearity of the medium. An unpredicted relation between the number of generated rings and the nonlinear phase-shift is obtained in the case of a convergent beam. Our results are in good agreement with a model for thin nonlinear media.

Self-healing property of a caustic optical beam

It is well known that Bessel beams and the other families of propagation-invariant optical fields have the property of self-healing when obstructed by an opaque object. Here it is shown that there exists another kind of field distribution that can have an analog property. In particular, we demonstrate that a class of caustic wave fields, whose transverse intensity patterns change on propagation, when perturbed by an opaque object can reappear at a further plane as if they had not been obstructed. The physics of the phenomenon is fully explained and shown to be related to that of self-healing propagation invariant optical fields.

Conical dynamics of Bessel beams

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.

Theory of the unstable Bessel resonator

A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The Huygens-Fresnel self-consistency equation is solved to extract the first eigenmodes and eigenvalues of the cavity, taking into account the finite apertures of the mirrors. Attention was directed to the dependence of the output transverse profiles; the losses; and the modal-frequency changes on the curvature of the output coupler, the cavity length, and the angle of the axicon. Our analysis revealed that while the stable Bessel resonator retains a Gaussian radial modulation on the Bessel rings, the unstable configuration exhibits a more uniform amplitude modulation that produces output profiles more similar to ideal Bessel beams. The unstable cavity also possesses higher-mode discrimination in favor of the fundamental mode than does the stable configuration.

Z-scan and spatial self-phase modulation of a Gaussian beam in a thin nonlocal nonlinear media

Considering that the nonlinear photoinduced phase shift to a Gaussian beam in a thin sample of nonlocal nonlinear media can be modeled as a Gaussian function to some real power the far-field can be calculated using the Fraunhofer integral. In this paper we calculate numerically this integral to obtain the on-axis intensity in a Z-scan experiment or the intensity pattern in a self-phase modulation experiment. Experimental results of samples under cw illumination are fitted using the model with a good correspondence between experimental and numerical results. The model presented is adequate to describe samples with any magnitude of the maximum nonlinear photoinduced phase shift of purely refractive local or nonlocal nonlinear thin media.

Exact nonparaxial beams of the scalar Helmholtz equation

It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For what is believed to be the first time, their beam behavior is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by a hyperbola, we formally establish the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams. These results are also helpful for investigating exact vector nonparaxial beams.