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J. P. Woerdman

Publications and source records attributed to J. P. Woerdman.

At least 37 records · Page 2Linked to original sources
arXiv2009

Brewster cross-polarization

We theoretically derive the polarization-resolved intensity distribution of a $TM$-polarized fundamental Gaussian beam reflected by an air-glass plane interface at Brewster incidence. The reflected beam has both a dominant ($TM$) and a cross-polarized ($TE$) component, carried by a $\text{TEM}_{10}$ and a $\text{TEM}_{01}$ Hermite-Gaussian spatial mode, respectively. Remarkably, we find that the $TE$-mode power scales quadratically with the angular spread of the incident beam and it is comparable to the $TM$-mode power. Experimental confirmations of the theoretical results are also presented.

physics.optics↗
arXiv2008

Shannon dimensionality of quantum channels and its application to photon entanglement

We introduce the concept of Shannon dimensionality D as a new way to quantify bipartite entanglement as measured in an experiment. This is applied to orbital-angular-momentum entanglement of two photons, using two state analyzers composed of a rotatable angular-sector phase plate that is lens-coupled to a single-mode fiber. We can deduce the value of D directly from the observed two-photon coincidence fringe. In our experiment, D varies between 2 and 6, depending on the experimental conditions. We predict how the Shannon dimensionality evolves when the number of angular sectors imprinted in the phase plate is increased and anticipate that D = 50 is experimentally within reach.

quant-ph↗
arXiv2008

Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts

We derive the polarization-dependent displacements parallel and perpendicular to the plane of incidence, for a Gaussian light beam reflected from a planar interface, taking into account the propagation of the beam. Using a classical-optics formalism we show that beam propagation may greatly affect both Goos-Hänchen and Imbert-Fedorov shifts when the incident beam is focussed.

physics.optics↗
arXiv2007

Observation of Goos-Hänchen shifts in metallic reflection

We report the first observation of the Goos-H$\rm \ddot{\textbf{a}}$nchen shift of a light beam incident on a metal surface. This phenomenon is particularly interesting because the Goos-H$\rm \ddot{\textbf{a}}$nchen shift for $p$ polarized light in metals is negative and much bigger than the positive shift for $s$ polarized light. The experimental result for the measured shifts as a function of the angle of incidence is in excellent agreement with theoretical predictions. In an energy-flux interpretation, our measurement shows the existence of a backward energy flow at the bare metal surface when this is excited by a $p$ polarized beam of light.

physics.optics↗
arXiv2007

Maximally Entangled Mixed-State Generation via Local Operations

We present a general theoretical method to generate maximally entangled mixed states of a pair of photons initially prepared in the singlet polarization state. This method requires only local operations upon a single photon of the pair and exploits spatial degrees of freedom to induce decoherence. We report also experimental confirmation of these theoretical results.

quant-ph↗
arXiv2006

Entangled mixed-state generation by twin-photon scattering

We report experimental results on mixed-state generation by multiple scattering of polarization-entangled photon pairs created from parametric down-conversion. By using a large variety of scattering optical systems we have experimentally obtained entangled mixed states that lie upon and below the Werner curve in the linear entropy-tangle plane. We have also introduced a simple phenomenological model built on the analogy between classical polarization optics and quantum maps. Theoretical predictions from such model are in full agreement with our experimental findings.

quant-ph↗
arXiv2006

Linear optics and quantum maps

We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.

quant-ph↗
arXiv2006

Maximally entangled mixed states made easy

We show that it is possible to achieve maximally entangled mixed states of two qubits from the singlet state via the action of local non-trace-preserving quantum channels. Moreover, we present a simple, feasible linear optical implementation of one of such channels.

quant-ph↗
arXiv2006

Linear Algebra for Mueller Calculus

We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the Mueller-Stokes formalism and derive some useful mathematical relation between physical quantities. Finally a useful decomposition theorem is reviewed.

math-ph↗
arXiv2006

Angular spectrum of quantized light beams

We introduce a generalized angular spectrum representation for quantized light beams. By using our formalism, we are able to derive simple expressions for the electromagnetic vector potential operator in the case of: {a)} time-independent paraxial fields, {b)} time-dependent paraxial fields, and {c)} non-paraxial fields. For the first case, the well known paraxial results are fully recovered.

quant-ph↗
arXiv2005

Maximum-likelihood estimation prevents unphysical Mueller matrices

We show that the method of maximum-likelihood estimation, recently introduced in the context of quantum process tomography, can be applied to the determination of Mueller matrices characterizing the polarization properties of classical optical systems. Contrary to linear reconstruction algorithms, the proposed method yields physically acceptable Mueller matrices even in presence of uncontrolled experimental errors. We illustrate the method on the case of an unphysical measured Mueller matrix taken from the literature.

physics.optics↗
arXiv2005

Unravelling Two-Photon High-Dimensional Entanglement

We propose an interferometric method to investigate the non-locality of high-dimensional two-photon orbital angular momentum states generated by spontaneous parametric down conversion. We incorporate two half-integer spiral phase plates and a variable-reflectivity output beam splitter into a Mach-Zehnder interferometer to build an orbital angular momentum analyzer. This setup enables testing the non-locality of high-dimensional two-photon states by repeated use of the Clauser-Horne inequality.

quant-ph↗
arXiv2005

Notes on Polarization Measurements

We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller matrices, which are well known in classical polarization-measurement theory.

quant-ph↗
arXiv2005

Exact Paraxial Quantization

A non-perturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. The theoretical formalism yields a seamless transition between the paraxial- and the Maxwell-equation solutions. This obviates the need to introduce either "ad hoc" or perturbatively-defined field operators. In the limit of narrow beam-like fields, the theory is in agreement with approximated quantization schemes provided by other authors.

quant-ph↗
arXiv2005

Role of spatial coherence in polarization tomography

We analyze an experimental setup in which a quasi-monochromatic spatially coherent beam of light is used to probe a paraxial optical scatterer. We discuss the effect of the spatial coherence of the probe beam on the Mueller matrix representing the scatterer. We show that according to the degree of spatial coherence of the beam, the \emph{same} scattering system can be represented by \emph{different} Mueller matrices. This result should serve as a warning for experimentalists.

physics.optics↗
arXiv2004

Depolarizing power and polarization entropy of light scattering media: experiment and theory

We experimentally investigate the depolarizing power and the polarization entropy of a broad class of scattering optical media. By means of polarization tomography, these quantities are derived from an effective Mueller matrix, which is introduced through a formal description of the multi-mode detection scheme we use, as recently proposed by Aiello and Woerdman (arXiv:quant-ph/0407234). This proposal emphasized an intriguing universality in the polarization aspects of classical as well as quantum light scattering; in this contribution we demonstrate experimentally that this universality is obeyed by a surprisingly wide class of depolarizing media. This, in turn, provides the experimentalist with a useful characterization of the polarization properties of any scattering media, as well as a universal criterion for the validity of the measured data.

physics.optics↗
arXiv2004

Violation of local realism in a high-dimensional two-photon setup with non-integer spiral phase plates

We propose a novel setup to investigate the quantum non-locality of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate non-integer spiral phase plates in spatial analyzers, enabling us to use only two detectors. The resulting setup is somewhat reminiscent of that used to measure polarization entanglement. However, the two-photon states that are produced, are not confined to a 2X2-dimensional Hilbert space, and the setup allows the probing of correlations in a high-dimensional space. For the special case of half-integer spiral phase plates, we predict a violation of the Clauser-Horne-Shimony-Holt version of the Bell inequality (S<=2), that is even stronger than achievable for two qubits (S=2*(2^1/2)), namely S=16/5

quant-ph↗