Carmen Bao

Timing jitter smoothing by Talbot effect. I. Variance

A study of the stochastic description of the Talbot effect in the temporal domain under random timing jitter is presented. The relevant statistical quantity is the variance. The variance of a train of pulses, each one affected by random timing jitter, shows peaks in the edges of the pulses. When this train is Talbot-imaged, the variance becomes flattened along the unit interval corresponding to each pulse as a result of the dispersion of the individual pulses of the train. Fractional Talbot devices are also analyzed. In particular, it is shown that this smoothing effect also occurs in Talbot devices leading to N× repetition rates of the original train.

Description of gradient-index crystalline lens by a first-order optical system

This paper uses the correspondence between the canonical integral transform and the ray-transfer matrix of a first-order optical system to analyse paraxial properties of the crystalline lens of the human eye regarded as a gradient-index (GRIN) medium limited by curved surfaces. Matrix factorization is provided to evaluate cardinal elements and refractive powers of the crystalline lens.

PLANAR-SURFACE-WAVEGUIDE EVANESCENT-WAVE CHEMICAL SENSORS

Abstract It is shown that planar-surface waveguides have several attractive features for evanescent-wave sensing. We present expressions, in terms of normalized waveguide parameters, for the penetration depth of the evanescent wave in the sensing medium, the absorption coefficient due to the latter, and the fluorescence collection efficiency from the sources present in this medium, which acts as the cover of the multimode waveguide. A comparison with optical-fibre sensors shows that planar guides not only offer reasonable performance in terms of absorption and fluorescence collection efficiency, but their asymmetry allows control of the penetration depth, which can be made relatively independent of the guided mode. Finally, we demonstrate that single-mode planar guides can also have comparable performance in situations where evanescent-wave chemical sensing using single-mode fibres can be quite challenging.

Timing jitter smoothing by Talbot effect. II. Intensity spectrum

The power spectral density of the intensity of jittery trains after an integer temporal Talbot dispersive line is computed in the small-signal approximation. The influence in the spectrum of the optical linewidth and chirp of the Gaussian pulses of the train and also of different pulse-to-pulse timing jitter correlations is addressed. Before entering the Talbot dispersive line, timing jitter produces noise sidebands around the harmonics of the train. The temporal Talbot effect adds a multiplicative factor to the noise spectral density that depends on the characteristics of both the pulses and the dispersive line but not on the pulse-to-pulse correlation or the value of the timing jitters standard deviation. The structure of this multiplicative term is peaked, resulting in narrowband noise patterns in specific locations of the spectrum and, in particular, around the harmonics of the train. Thus the temporal Talbot effect provides a dispersive mechanism for noise filtering. The bandwidth of the dispersion-induced noise peaks is ∼1 order of magnitude below the repetition-rate frequency.

Fractional Talbot effect in a Selfoc gradient-index lens

The fractional Talbot effect is demonstrated inside a standard 0.25-pitch Selfoc gradient-index lens under uniform illumination. Comparisons with theoretical expressions of positions and magnification of fractional Talbot images are given.

Talbot effect in a tapered gradient-index medium for nonuniform and uniform illumination

A generalization of the Talbot effect to the case of a tapered gradient-index medium for nonuniform and uniform illumination is considered. Self-image positions are changed by a function depending on the taper profile, the illumination, and the periodic object. An analogy with the conventional lens-imaging formula for both types of illumination is presented.

Gradient parameter and axial and field rays in the gradient-index crystalline lens model

Gradient-index models of the human lens have received wide attention in optometry and vision sciences for considering how changes in the refractive index profile with age and accommodation may affect refractive power. This paper uses the continuous asymmetric bi-elliptical model to determine gradient parameter and axial and field rays of the human lens in order to study the paraxial propagation of light through the crystalline lens of the eye.

Fractional Talbot effect in a tapered gradient- index medium: unit cell

A generalization of the fractional Talbot effect to the case of a tapered gradient-index medium for uniform illumination is considered. A unit cell of the fractional Talbot image contains the superposition of unit cell images of the periodic object.

Coupling of planar waveguides with hyperbolic secant refractive-index profiles by butt joining: beam-size controller design

An analysis of the butt-joining coupling between two inhomogeneous planar optical waveguides with hyperbolic secant refractive-index profiles is made from the point of view of geometrical optics. Furthermore, the design of a new device to contract or expand a collimated beam is presented, and a relationship between sizes of the input and output beams is obtained.

Temporal zone plate.

This paper extends the investigation of zone plates to the temporal case. By exploiting the space-time duality between the paraxial diffraction of beams in space and the linear dispersion of optical pulses, we present the time-domain analog of a multiple imaging system. The temporal system is created by using a digital chirp signal generator together with two dispersive delay lines. The key motivation is the potential application of the temporal zone plate to multiple compressions of pulses in dispersive lines.