Noninterferometric characterization of partially coherent scalar wave fields and application to scattered light

We report on the application of a simple propagation-based phase-space tomographic technique to the determination of characteristic projections through the mutual optical intensity and the generalized radiance of a scalar, quasi-monochromatic partially coherent wave field. This method is applied to the reconstruction of the coherence functions of an initially spatially coherent optical wave field that has propagated through a suspension of polystyrene microspheres. As anticipated, we see that the field separates into a ballistic, or unscattered, component and a scattered component with a much shorter coherence length. Good agreement is obtained between experimental results and the results of a model based on a wave-transport equation.     

Power coupled between partially coherent vector fields in different states of coherence.

A procedure is described for calculating the power coupled between collimated, partially coherent vector fields that are in different states of coherence. This topic is of considerable importance in designing submillimeter-wave optical systems for astronomy. It is shown that if the incoming field S has coherence matrix A, and the outgoing field D has coherence matrix B, then the power coupled is simply Ps = Tr(ATBT), where the elements of T project the basis functions of B onto those of A. A similar technique can be used to calculate the power coupled from the background of S to D. The scheme is illustrated by calculating the power coupled between two scalar, Gaussian Schell-model beams. The procedure can be incorporated into optical design software.     

Phase retrieval of singular scalar light fields using a two-dimensional directional wavelet transform and a spatial carrier

We evaluate a method based on the two-dimensional directional wavelet transform and the introduction of a spatial carrier to retrieve optical phase distributions in singular scalar light fields. The performance of the proposed phase-retrieval method is compared with an approach based on Fourier transform. The advantages and limitations of the proposed method are discussed.     

Analyzing the power coupled between partially coherent waveguide fields in different states of coherence

A procedure is described for calculating the power coupled between partially coherent waveguide fields that are in different states of coherence. The method becomes important when it is necessary to calculate the power transferred from a distributed source S to a distributed load L through a length of multimode metallic, or dielectric, waveguide. It is shown that if the correlations between the transverse components of the electric and magnetic fields of S and L are described by coherence matrices M and M', respectively, then the normalized average power coupled between them is (eta) = Tr[MM']/Tr[M]Tr[M'], where Tr denotes the trace. When the modal impedances are equal, this expression for the coupled power reduces to an equation derived in a previous paper [J. Opt. Soc. Am. A 18, 3061 (2001)], by use of thermodynamic arguments, for the power coupled between partially coherent free-space beams.     

Mixture of two-mode unpolarized and pure quantum light states: quantum polarization and application in quantum communication

Quantum polarization is an important property that has been extensively used for quantum communication purposes. In this work, the mixture of an unpolarized two-mode state and a two-mode pure state is analysed. This mixture is controlled by a single parameter, namely the degree of purity. The quantum polarization of the two-mode mixed state is discussed using the quantum Stokes parameters and the quantum degree of polarization. A relation between the degree of purity and the quantum degree of polarization is established. The mixture is used to model coherent light amplified by an erbium-doped fibre amplifier, which focuses the loss of polarization due to the unpolarized light resulting from spontaneous emission. Finally, the use of such a mixed state in the quantum key distribution using multiphoton pulses is analysed.     

Reconstruction of spatial, phase, and coherence properties of light

Image reconstruction of partially coherent light is interpreted as quantum-state reconstruction. An efficient method based on the maximum-likelihood estimation is proposed for acquiring information from blurred intensity measurements affected by noise. Connections with incoherent-image restoration are pointed out. The feasibility of the method is demonstrated numerically. Spatial and correlation details significantly below the diffraction limit are revealed in the reconstructed pattern.     

Partial spatial coherence and partial polarization in random evanescent fields on lossless interfaces

We consider partial spatial coherence and partial polarization of purely evanescent optical fields generated in total internal reflection at an interface of two dielectric (lossless) media. Making use of the electromagnetic degree of coherence, we show that, in such fields, the coherence length can be notably shorter than the light's vacuum wavelength, especially at a high-index-contrast interface. Physical explanation for this behavior, analogous to the generation of incoherent light in a multimode laser, is provided. We also analyze the degree of polarization by using a recent three-dimensional formulation and show that the field may be partially polarized at a subwavelength distance from the surface even though it is fully polarized farther away. The degree of polarization can assume values unattainable by beamlike fields, indicating that electromagnetic evanescent waves generally are genuine three-dimensional fields. The results can find applications in near-field optics and nanophotonics.     

Measurements of spatial coherence of partially coherent light with and without orbital angular momentum

We study the spatial coherence of a partially coherent beam before and after being transmitted through a spiral phase plate that changes the overall orbital angular momentum of the field. The two-point coherence function is measured and directly visualized on a CCD through interference in a Mach-Zehnder interferometer equipped with an image rotator. We show, in particular, how the coherence singularities associated with Airy rings are strongly affected by the spiral phase plate.     

Circular and near-circular polarization states of evanescent monochromatic light fields in total internal reflection

Conditions for the production of near-circular polarization states of the evanescent field present in the rarer medium in total internal reflection of incident monochromatic p-polarized light at a dielectric-dielectric planar interface are determined. Such conditions are satisfied if high-index (>3.2) transparent prism materials (e.g., GaP and Ge) are used at angles of incidence well above the critical angle but sufficiently below grazing incidence. Furthermore, elliptical polarization of incident light with nonzero p and s components can be tailored to cause circular polarization of the resultant tangential electric field in the plane of the interface or circular polarization of the transverse electric field in a plane normal to the direction of propagation of the evanescent wave. Such polarization control of the evanescent field is significant, e.g., in the fluorescent excitation of molecules adsorbed at solid-liquid and solid-gas interfaces by total internal reflection.     

A law of interference of electromagnetic beams of any state of coherence and polarization and the Fresnel-Arago interference laws

A new general interference law is derived for the superposition of two random electromagnetic beams of any state of coherence and of any state of polarization when the beams are transmitted through polarizers and rotators. It includes, as special cases, a variety of interference laws that apply to particular situations. Some of them have a close bearing on the classic interference experiments of Fresnel and Arago that have played a basic role in elucidating the concept of polarization of light.     

Switching between generation of two quantum states in quantum-well laser diodes

The dynamics of emission spectra in semiconductor quantum-well lasers generating from two quantum states have been experimentally studied. In the case of electric pumping with 100-ns pulses, the lasing via transitions from the ground state is switched off and the emission from an excited state is switched on within 10–50 ns after laser turn-on. The switching is accompanied by a dip in the intensity of lasing, the duration of which depends on the pumping pulse amplitude. The observed phenomenon is explained in terms of gain clamping and redistribution of the carrier concentration between the ground and excited states.     

Hilbert-Schmidt distance and non-classicality of states in quantum optics

Abstract

The Hilbert—Schmidt distance between two arbitrary normalizable states is discussed as a measure of the similarity of the states. Unitary transformations of both states with the same unitary operator (e.g. the displacement of both states in the phase plane by the same displacement vector and squeezing of both states) do not change this distance. The nearest distance of a given state to the whole set of coherent states is proposed as a quantitative measure of non-classicality of the state which is identical when considering the coherent states as the most classical ones among pure states and the deviations from them as non-classicality. The connection to other definitions of the non-classicality of states is discussed. The notion of distance can also be used for the definition of a neighbourhood of considered states. Inequalities for the distance of states to Fock states are derived. For given neighbourhoods, they restrict common characteristics of the state as the dispersion of the number operator and the squared deviation of the mean values of the number operator for the considered state and the Fock state. Possible modifications in the definition of non-classicality for mixed states with dependence on the impurity parameter and by including the displaced thermal states as the most classical reference states are discussed.     

Normal state of short coherence length superconductors: Qualitative differences between spin and charge correlations

The temperature scaleT* at which the amplitude of the order parameter is formed is in general much higher than theT _c at which phase coherence is established in short coherence length superconductors. Using quantum Monte Carlo simulations for the attractive Hubbard model we show that for a degenerate 2D system the spin and charge responses show qualitatively different behavior in the normal state in the temperature rangeT _c <T<T*. We find that _s is stronglyT-dependent whiledn/d is independent ofT. A pseudo-gap develops in the one-particle density of states and leads to anomalous behavior of the NMR relaxation rate 1/T ₁ T _s (T) characteristic of spin gap behavior in the high-T _c materials.     

Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications

Giving a new physical interpretation to the principle of longitudinal coherence control, we propose an improved method for synthesizing a spatial coherence function along the longitudinal axis of light propagation. By controlling the irradiance of an extended quasi-monochromatic spatially incoherent source with a spatial light modulator, we generated a special optical field that exhibits high coherence selectively for a specific pair of points at specified locations along the axis of beam propagation. This function of longitudinal coherence control provides new possibilities for dispersion-free measurements in optical tomography and profilometry. A quantitative experimental proof of principle is presented.     

Information geometry in functional spaces of classical and quantum finite statistical systems

Statistical states and bounded random variables (observables) of finite physical systems can be represented in real Banach spaces L_s¹ and L_s^∞, respectively. Since both norms are Krein-weak, the solution of the estimation problem in these spaces is not necessarily unique. The latter property occurs on the Hilbert-Schmidt space L_s² which is connected with the Onicescu information energy and the method of least squares. The square information is only an approximation of the “true” logarithmic Shannon information which induces a “logarithmic” asymmetric geometry by means of the concept of relative information (gain of information). This geometry was known in the classical case as the asymmetric Pythagorean geometry (Chentsov [10]) and is approximated by the Riemannian geometry of Fisher's information (Kullback and Leibler [45]). This paper shows that a similar geometric construction is also possible in the quantum case. The fundamental formulae of the quantum case are given (they differ in some details from the classical ones), and possible physical applications are shortly sketched.     

The effects of temporal and longitudinal spatial coherence in a disbalanced-arm interferometer

During the interference of optical fields possessing broad frequency and angular spectra in an oscillating-mirror Michelson interferometer, the presence of a film introducing an additional optical path increment in one of the arms leads to a mutual shift (recession) of the signals of temporal and longitudinal spatial coherence. This phenomenon leads to breakage of the mutual coherence of the interfering fields. In the presence of two light sources, this effect can be used for the independent determination of the thickness and refractive index of the film.