Polarization Aberration Effects Propagated in Optical Systems

Abstract

The propagation and imaging of polarized light through optical systems described by a polarization aberration expansion is treated by combining a scalar operator calculus with the Jones calculus. The martrix-operator framework provides a means for handling diffraction and propagation in optical systems containing polarization aberrations. An expansion for the polarization aberration function of an optical system, similar to the expansion of the wavefront aberration function into defocus, tilt, piston, and higher-order terms, is analysed. These polarization aberration terms introduce phase changes in the diffraction image proportional to the first and second derivatives of the non-polarization aberrated image structure.     

Jones matrix treatment for polarization fourier optics

Abstract

In this work we introduce the use of a Jones matrix method to evaluate the far-field diffraction produced by spatially variant polarization elements. We extend the scalar Fourier optics theory to a vectorial theory by the use of the Jones matrix formalism. With this method it is possible to analyse the diffraction pattern and the local state of polarization in the Fraunhofer approximation by means of the usual Jones matrix calculus.     

Conditions for the Physical Realizability of Polarization Matrices Characterizing Passive Systems

Abstract

We derive conditions for the physical realizability of polarization matrices characterizing passive systems or scattering media. By physically realizable, we mean that 0  g  1 where g ≡ (output intensity/input intensity). Using the singular-value decomposition of an arbitrary 2 × 2 complex-valued matrix, we prove that a Jones matrix T _J is physically realizable if 0  det T _J ⁺ T _J  1. Consequently singular Jones matrices (i.e. det T _J = 0) completely extinguish the output intensity irrespective of the input intensity because g ≡ 0. Corresponding results are obtained for Mueller-Jones matrices (the 4 × 4 real-valued matrices which are the four-dimensional representations of the two-dimensional 2 × 2 complex-valued Jones matrices). We also study the problem for general Mueller matrices; however because of their phenomenological character they do not admit of such criteria as do the Jones and Mueller-Jones matrices. This is because g now depends upon the matrix elements of the Mueller matrix and the input Stokes parameters; whereas for the Jones and Mueller-Jones matrices, g only depends upon the matrix elements. Finally we study the problem of relating the input and output mean randomness.     

The Interferometer as an Optical Network

Abstract

We consider a generic interferometric set-up as a device to record interference fringes. The system is characterized by two variable transmission beam-splitters. A coherent signal is measured and its noise properties are manipulated by mixing in a squeezed vacuum through the second input port. The performance is optimized either by minimizing the noise at the dark and the light fringes, or alternatively by keeping it below the standard quantum limit for all phase angles observed. The analysis is carried out using a quantum optical network formalism generalizing the classical Jones calculus. The results obtained are interpreted and explained using the Wigner function for the output signals.     

Spectral analysis of the device operators in polarization dynamics

Abstract

The spectral analysis of the device (instrument) operators, as an alternative approach to the dynamical polarization phenomena, is presented by means of an example of a classical time-varying optical device, the electrooptical modulator with longitudinal effect in crystals of KDP type. The polarization-spectral structure of the modulated light is analysed on this basis, both in terms of spectral Jones vectors and of spectral polarization matrices. Some experimental results are presented.     

White-light interferometry with depolarization of the radiation

It is shown that the precision of white-light interferometers with a single-mode fiber linking the sensing and processing interferometers can be enhanced by incorporating discrete or all-fiber “time-average” radiation depolarizers (Billings depolarizers). Relations are given to describe the dependence of the output signal and the “ zero” drift of white-light interferometers on the polarization characteristics of the optical channel. Relations are also presented for the elements of the Jones matrix of a Billings depolarizer. Pis’ma Zh. Tekh. Fiz. 23, 56–60 (July 26, 1997)     

Achromatic fan-out diffractive system for white-light free-space optical interconnects

Abstract

A simple and versatile white-light fan-out diffractive system based on the achromatization of the fractional Talbot effect is proposed. This achromatic configuration is able to interconnect a single polychromatic point source with a 2-D array of optoelectronic microdevices with low residual chromatic aberration even for white light. The whole broadband beamsplitter system is formed by two simple diffractive optical elements, a periodic diffractive lenslet array and a diffractive lens, that are made with a direct laser writing technique giving high light efficiency. The focal amplitude distribution corresponding to the lenslet array produces, by free-space propagation, self-replicas with different density of light points. These patterns, in conjunction with the achromatization process carried out by the additional diffractive lens, are, in short, the key to achieving a set of undistorted white-light spots at the output plane with high uniformity and variable separation between them. Experimental results are also shown.     

High order harmonic generation: The role of the acceleration matrix elements and of the bound and continuum transitions

Abstract

The electromagnetic spectrum emitted by a one-dimensional atom driven by a strong laser field is obtained by use of the acceleration form and interpreted by means of few general properties of the matrix elements of the acceleration operator. We show that the emission occurs essentially in a region near the atomic core where the acceleration is significant and we investigate the role of the various emission channels arising from interference effects between transitions involving the bare atomic levels.     

Birefringence evaluation of helically wound optical fibres

Abstract

A simple, non-destructive method is presented for the characterization of the birefringence properties of a helically wound mono-mode optical fibre. It is shown that the Jones matrix model developed by J.N. Ross can be applied to describe them, if the polarization evolution of light is measured with respect to a local reference frame (Serret-Frenet frame). In this case the Ross model is equal to the matrix model developed by R.C. Jones for a twisted crystal. In order to use a fixed reference frame (laboratory reference frame) it is necessary to consider the rotation of the reference frame at the fibre input face produced by the fibre topology. The orientation of the helical fibre axes at the input is defined following the geometrical criteria proposed by Ross. The use of Poincaré's method and Mueller calculus to rewrite the Ross model simplifies the physical interpretation of the results. The method presented provides an easy way to measure the total linear retardation induced by the fibre curvature, and to separate the circular retardation associated with the photo-elastic response of the fibre, from the topological rotation of the reference frame defined only by the geometry of the helically wound fibre.     

Squeezing Properties and Photon Statistics in Multiphoton Processes with Radiative Damping of the Atomic Levels

Abstract

A model for the master equation of multiphoton processes with radiative damping of the atomic levels is proposed and a matrix method employed to solve exactly the rate equations for the matrix elements of the reduced density operator in the Fock representation. This model has been applied to the study of the low-noise properties of squeezed light in an all-optical transmission link formed from alternating sections of linear and nonlinear attenuating fibre and optical amplifiers. When the attenuators present radiative damping of the atomic levels (the lower atomic state is not the ground state) the signal-to-noise ratio is enhanced with respect to the case in which the lower atomic level is the ground state. The enhancement is improved when the input light is squeezed. The statistical properties of linear and two-photon amplification with an absorption process which exhibits radiative damping have also been analysed for coherent and squeezed inputs. The second-order fluctuations are reduced when radiative damping in the absorption process is considered except in the case of two-photon absorption for small values of the saturation parameter s_a . When the value of this parameter is increased the behaviour of the fluctuations changes and the noise is reduced. These results could be of interest in all-optical transmission links and are improved when the input light is squeezed.     

Anisotropic photoresponse investigation of chemical vapor transport (CVT) grown quaternary Cu2ZnSnS4 single crystals

The single crystals of quaternary transition metal chalcogenide Cu₂ZnSnS₄ (CZTS) are grown by a closed system chemical vapor transport technique. The high purity individual elemental precursors are employed in the growth of the crystals. These crystals are found to be single-phase by X-ray diffraction and Raman analysis. The near stoichiometry of the grown crystals is confirmed by spectroscopy analysis of the photoelectron generated by X-rays and analysis of the energy of the dispersive X-rays generated by electrons. The surface study by scanning electron microscopy showed the growth to happen by sheet spread mean and the electron diffraction showed fringe width match with (112) plane spacing. The study of the CZTS/Ag-paste/Cu-wire system for incident white light and three wavelengths of laser lights in two configuration modes of top-contact (II to the plane) and bottom-top-contact (⊥ to the plane) showed anisotropic behavior. The incident white light illumination intensity of 120 mW/cm² showed utmost photoresponse. The top-contact mode configuration showed maximum responsivity and detectivity of 0.72 mA/W and 0.33 × 10⁹ Jones, respectively, while bottom-top-contact showed 0.18 mA/W and 0.13 × 10⁹ Jones, respectively. The anisotropic photoresponse by the CZTS crystals insinuates the potential for future applications.

     

An analysis of the angular momentum of a light field in terms of angular harmonics

Abstract

This paper proposes an optical interpretation for the Lie algebra's symmetry operators of the paraxial wave equation. In particular, the angular momentum operator is used to derive a relation for the expression of the angular momentum of an arbitrary light field in terms of angular harmonics. Furthermore, experimental results are presented demonstrating a filter that extracts angular harmonics from different Gauss-Laguerre modes.     

Fiber-based polarization-sensitive Mueller matrix optical coherence tomography with continuous source polarization modulation

We report on a new configuration of fiber-based polarization-sensitive Mueller matrix optical coherence tomography that permits the acquisition of the round-trip Jones matrix of a biological sample using only one light source and a single depth scan. In this new configuration, a polarization modulator is used in the source arm to continuously modulate the incident polarization state for both the reference and the sample arms. The Jones matrix of the sample can be calculated from the two frequency terms in the two detection channels. The first term is modulated by the carrier frequency, which is determined by the longitudinal scanning mechanism, whereas the other term is modulated by the beat frequency between the carrier frequency and the second harmonic of the modulation frequency of the polarization modulator. One important feature of this system is that, for the first time to our knowledge, the Jones matrix of the sample can be calculated with a single detection channel and a single measurement when diattenuation is negligible. The system was successfully tested by imaging both standard polarization elements and biological samples.     

Optical Measurement Accuracy in the Case of Non-classical Light

Abstract

The influence of optical elements on the statistical properties of the input radiation is analysed by quantum-theoretical means for a representative optical arrangement consisting of beam splitters as well as for various types of grating spectrometers. In particular non-classical light states are studied. Optimum conditions for the maintenance of the signal-to-noise ratio of sub-Poissonian input radiation are derived.     

Calvert Richard Jones the earlier wark

Abstract

For almost a century after his death in 1877, Calvert Jones's work was neglected and his photographs commonly attributed to Henry Fox Talbot. Only in the past few years has it become evident that Jones was responsible for some of the most visually exciting images of early photography and that his pictures represent a coherent and notably well-directed body of work. It is now clear that Jones possessed a remarkable and original artistic vision; he was also one of the most irresistible personalities of photography's beginning.     

Time Evolution for a Three-level Atom in Interaction with Two Modes

Abstract

The problem of a three-level atom and two modes is treated quantum mechanically and constants of motion are obtained. The evolution operator is calculated for the case of exact two-photon resonance. The probability distribution functions are calculated for the atom in one of its states. Some statistical quantities of the fields and the atomic systems are given. The interaction with squeezed light is investigated.     

A brain-based system for adaptive automation

Adaptive automation refers to technology that can change its mode of operation dynamically. Further, both the technology and the operator can initiate changes in the level or mode of automation. One of the important issues surrounding this technology concerns the method for initiating changes in the state of automation. The present paper considers the potential of using brain activity to drive an adaptive automation system. Relevant research on EEG is presented followed by a review of several experiments in which EEG is used to trigger changes among system modes in an adaptive automation system. The system moderates operator task load based upon an index derived from a ratio of EEG power bands. The research shows that it may be feasible to build an adaptive automation system and use this index of brain activity to drive the system. The paper concludes with a discussion of several issues that still need to be addressed before this approach can move beyond the laboratory.     

Time Reversal for the Polarization State in Optical Systems

Abstract

The time-reversal operator for the polarization state can be successfully implemented in any optical system where a beam retraces its path. A Faraday rotator followed by a mirror realizes a device whose representative matrix is similar to the quantum mechanics time-reversal operator for the spin. Any effect of the medium birefringence is cancelled and, for linear polarization, the beam always returns opposite polarized with respect to the entrance state. Analogies with the operation of a phase-conjugation mirror are pointed out and suggested consequences of the novel optical configuration are given.     

Radon transform and pattern functions in quantum tomography

Abstract

The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the latter is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite polynomials which is appropriate for practical calculations. The structure of the pattern functions as first derivatives of the products of normalizable and non-normalizable eigenfunctions to the number operator is considered from the point of view of this new representation.     

On the algebraic characterization of a Mueller matrix in polarization optics. II. Necessary and sufficient conditions for Jones-derived Mueller matrices

Abstract

We show that every Mueller matrix, that is a real 4 × 4 matrix M which transforms Stokes vectors into Stokes vectors, may be factored as M = L ₂ KL ₁ where L ₁ and L ₂ are orthochronous proper Lorentz matrices and K is a canonical Mueller matrix having only two different forms, namely a diagonal form for type-I Mueller matrices and a non-diagonal form (with only one non-zero off-diagonal element) for type-II Mueller matrices. Using the general forms of Mueller matrices so derived, we then obtain the necessary and sufficient conditions for a Mueller matrix M to be Jones derived. These conditions for Jones derivability, unlike the Cloude conditions which are expressed in terms of the eigenvalues of the Hermitian coherency matrix T associated with M, characterize a Jones-derived matrix M through the G eigenvalues and G eigenvectors of the real symmetric N matrix N = [Mtilde]GM associated with M. Appending the passivity conditions for a Mueller matrix onto these Jones-derivability conditions, we then arrive at an algebraic identification of the physically important class of passive Jones-derived Mueller matrices.