Pedro Andrés

Designing the properties of dispersion-flattened photonic crystal fibers.

We present a systematic study of group-velocity-dispersion properties in photonic crystal fibers (PCFs). This analysis includes a thorough description of the dependence of the fiber geometrical dispersion on the structural parameters of a PCF. The interplay between material dispersion and geometrical dispersion allows us to established a well-defined procedure to design specific predetermined dispersion profiles. We focus on flattened, or even ultraflattened, dispersion behaviors both in the telecommunication window (around 1.55 microm) and in the Ti-Za laser wavelength range (around 0.8 microm}. We show the different possibilities of obtaining normal, anomalous, and zero dispersion curves in the above frequency domains and discuss the limits for the existence of the above dispersion profiles.

Nearly zero ultraflattened dispersion in photonic crystal fibers

We present a procedure for achieving photonic crystal fibers with nearly zero ultraflattened group-velocity dispersion. Systematic knowledge of the special guiding properties of these fibers permits the achievement of qualitatively novel dispersion curves. Unlike the behavior of conventional fibers, this new type of dispersion behavior permits remarkably improved suppression of third-order dispersion, particularly in the low-dispersion domain.

Full-vector analysis of a realistic photonic crystal fiber

We analyze the guiding problem in a realistic photonic crystal fiber, using a novel full-vector modal technique. This is a biorthogonal modal method based on the non-self-adjoint character of the electromagnetic propagation in a fiber. Dispersion curves of guided modes for different fiber structural paremeters are calculated, along with the two-dimensional transverse intensity distribution of the fundamental mode. Our results match those achieved in recent experiments in which the feasibility of this type of fiber was shown.

Vector description of higher-order modes in photonic crystal fibers

We extensively study the propagation features of higher-order modes in a photonic crystal fiber (PCF). Our analysis is based on a full-vector modal technique specially adapted to accurately describe light propagation in PCFs. Unlike conventional fibers, PCFs exhibit a somewhat unusual mechanism for the generation of higher-order modes. Accordingly, PCFs are characterized by the constancy of the number of modes below a wavelength threshold. An explicit verification of this property is given through a complete analysis of the dispersion relations of higher-order modes in terms of the structural parameters of this kind of fiber. The transverse irradiance distributions for some of these higher-order modes are also presented, showing an excellent agreement with recent experimental measurements. In the same way, the full-vector nature of our approach allows us to analyze the rich polarization structure of the PCF mode spectrum.

Three-dimensional superresolution by annular binary filters

We present a new family of annular binary filters for improving the three-dimensional resolving power of optical systems. The filters, whose most important feature is their simplicity, permit to achieve a significant reduction, both in the transverse and in the axial direction, of the central lobe width of the irradiance point spread function of the system. The filters can be used for applications such as optical data storage or confocal scanning microscopy.

Biorthonormal-basis method for the vector description of optical-fiber modes

This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.

Tunable axial superresolution by annular binary filters. Application to confocal microscopy

We present a set of annular binary pupil filters for increasing the axial resolving capacity of imaging systems. The filters consist of two transparent annuli of the same area. It is shown that by changing the area of the transparent regions it is possible to obtain a tunable reduction of the width of the central lobe of the axial point spread function of the imaging system. However, this reduction is accompanied by a severe increase of the strength of secondary lobes, what can make these filters not very useful when used in conventional imaging systems. That is why we propose to use these filters for apodizing confocal microscopy systems. It is shown that in this case an important reduction is achieved in the volume of the central lobe of the three-dimensional point spread function.

Compressive holography with a single-pixel detector

This Letter develops a framework for digital holography at optical wavelengths by merging phase-shifting interferometry with single-pixel optical imaging based on compressive sensing. The field diffracted by an input object is sampled by Hadamard patterns with a liquid crystal spatial light modulator. The concept of a single-pixel camera is then adapted to perform interferometric imaging of the sampled diffraction pattern by using a Mach-Zehnder interferometer. Phase-shifting techniques together with the application of a backward light propagation algorithm allow the complex amplitude of the object under scrutiny to be resolved. A proof-of-concept experiment evaluating the phase distribution of an ophthalmic lens with compressive phase-shifting holography is provided.

Single-shot digital holography by use of the fractional Talbot effect

We present a method for recording in-line single-shot digital holograms based on the fractional Talbot effect. In our system, an image sensor records the interference between the light field scattered by the object and a properly codified parallel reference beam. A simple binary two-dimensional periodic grating is used to codify the reference beam generating a periodic three-step phase distribution over the sensor plane by fractional Talbot effect. This provides a method to perform single-shot phase-shifting interferometry at frame rates only limited by the sensor capabilities. Our technique is well adapted for dynamic wavefront sensing applications. Images of the object are digitally reconstructed from the digital hologram. Both computer simulations and experimental results are presented.

Image transmission through dynamic scattering media by single-pixel photodetection

Smart control of light propagation through highly scattering media is a much desired goal with major technological implications. Since interaction of light with highly scattering media results in partial or complete depletion of ballistic photons, it is in principle impossible to transmit images through distances longer than the extinction length. Nevertheless, different methods for image transmission, focusing, and imaging through scattering media by means of wavefront control have been published over the past few years. In this paper we show that single-pixel optical systems, based on compressive detection, can also overcome the fundamental limitation imposed by multiple scattering to successfully transmit information. But, in contrast with the recently introduced schemes that use the transmission matrix technique, our approach does not require any a-priori calibration process that ultimately makes the present method suitable to use with dynamic scattering media. This represents an advantage over previous methods that rely on optical feedback wavefront control, especially for short speckle decorrelation times.