Biomedical subjects
Publications and source records attributed to J P Woerdman.
We report a novel controllable source of spatial decoherence for twin photons, based upon commercially available wedge depolarizers. This allows us to convert the polarization-entangled singlet state into a tunable mixed state. A full characterization of this mixed state, by means of quantum tomography, shows that such a spatial decoherer can be used for synthesizing Werner-like states on demand.
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 the presence of uncontrolled experimental errors. We illustrate our method with the case of an unphysical measured Mueller matrix taken from the literature.
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) nonparaxial fields. For the first case the well-known paraxial results are fully recovered.
The singular nature of a noninteger spiral phase plate allows easy manipulation of spatial degrees of freedom of photon states. Using two such devices, we have observed very high-dimensional spatial entanglement of twin photons generated by spontaneous parametric down-conversion.
Experimental results on light depolarization due to multimode scattering are reported. By means of polarization tomography, we characterize the depolarizing power and the polarization entropy of a broad class of optically scattering media and confirm the recently predicted universal behavior of these two quantities [Phys. Rev. Lett. 94, 090406 (2005)].
Measurement of the point-spread function of metal nanohole arrays by using microscopic imaging reveals two contributions. The first of these is due to propagating resonant surface plasmons and the second to nonresonant transmission through the holes. We observe a Fano-type interference between these contributions.
Small-angle scattering due to mirror surface roughness is shown to couple the optical modes and deform the transmission spectra in a frequency-degenerate optical cavity. A simple model based on a random scattering matrix clearly visualizes the mixing and avoided crossings between multiple transverse modes. These effects are visible only in the frequency-domain spectra; cavity ringdown experiments are unaffected by changes in the spatial coherence, as they probe just the intracavity photon lifetime.
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 same scattering medium can be represented by different Mueller matrices. This result should serve as a warning for experimentalists.
We present a theoretical study of multimode scattering of light by optically random media, using the Mueller-Stokes formalism which permits us to encode all the polarization properties of the scattering medium in a real 4 x 4 matrix. From this matrix two relevant parameters can be extracted: the depolarizing power D(M) and the polarization entropy E(M) of the scattering medium. By studying the relation between E(M) and D(M), we find that all scattering media must satisfy some universal constraints. These constraints apply to both classical and quantum scattering processes. The results obtained here may be especially relevant for quantum communication applications, where depolarization is synonymous with decoherence.
We present a simple method to determine the cutting angle and thickness of birefringent crystals. Our method is based on chromatic polarization interferometry and allows for accuracies of typically 0.1 degrees in the cutting angle and 0.5% in the thickness.
We report polarization tomography experiments on metallic nanohole arrays with square and hexagonal symmetry. As a main result we find that a fully polarized input beam is partly depolarized after transmission through a nanohole array. This loss of polarization coherence is found to be anisotropic; i.e., it depends on the polarization state of the input beam. The depolarization is ascribed to a combination of two factors: (i) the nonlocal response of the array as a result of surface-plasmon propagation and (ii) the non-plane-wave nature of a practical input beam.
We develop a point-scattering approach to the plane-wave optical transmission of subwavelength metal hole arrays. We present a real-space description instead of the more conventional reciprocal-space description; this naturally produces interfering resonant features in the transmission spectra and makes explicit the tensorial properties of the transmission matrix. We give transmission spectra simulations for both square and hexagonal arrays; these can be evaluated at arbitrary angles and polarizations.
We propose a novel setup to investigate the entanglement of orbital angular momentum states living in a high-dimensional Hilbert space. We incorporate noninteger spiral phase plates in spatial analyzers, enabling us to use only two detectors. The two-photon states that are produced are not confined to a 2 x 2-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 that the Clauser-Horne-Shimony-Holt-Bell parameter S is larger than achievable for two qubits (S=2 sqrt[2]), namely, S=31 / 5.
We investigate the ray dynamics in an optical cavity when a ray-splitting mechanism is present. The cavity is a conventional two-mirror stable resonator, and the ray splitting is achieved by inserting an optical beam splitter perpendicular to the cavity axis. Using Hamiltonian optics, we show that such a simple device presents surprisingly rich chaotic ray dynamics.
We present a numerical investigation of the ray dynamics in a paraxial optical cavity when a ray-splitting mechanism is present. The cavity is a conventional two-mirror stable resonator and the ray splitting is achieved by inserting an optical beam splitter perpendicular to the cavity axis. We show that depending on the position of the beam splitter the optical resonator can become unstable and the ray dynamics displays a positive Lyapunov exponent.
We describe the fabrication and characterization of a high-quality spiral phase plate as a device to generate optical vortices of low (3-5) specified charge at visible wavelengths. The manufacturing process is based on a molding technique and allows for the production of high-precision, smooth spiral phase plates as well as for their replication. An attractive feature of this process is that it permits the fabrication of nominally identical spiral phase plates made from different materials and thus yielding different vortex charges. When such a plate is inserted in the waist of a fundamental Gaussian beam, the resultant far-field intensity profile shows a rich vortex structure, in excellent agreement with diffraction calculations based on ideal spiral phase plates. Using a simple optical test, we show that the reproducibility of the manufacturing process is excellent.
We study the effect of nonparaxiality in a folded resonator by accurate measurements of the Gouy phase as a function of the mode number for mode numbers up to 1500. Our experimental method is based on tuning the resonator close to a frequency-degenerate point. The Gouy phase shows a nonparaxial behavior that is much stronger in the folding plane than in the perpendicular plane. Agreement with ray-tracing simulations is established, and a link with aberration theory is made.
We investigate the orbital angular momentum (OAM) of paraxial beams containing off-axis phase dislocations and put forward a simple method to calculate the intrinsic orbital angular momentum of an arbitrary paraxial beam. Using this approach we find that the intrinsic OAM of a fundamental Gaussian beam with a vortex imprinted off axis has a Gaussian dependence on the vortex displacement, implying that the expectation value of the intrinsic OAM of a photon can take on a continuous range of values (i.e., integer and noninteger values in units of h). Finally, we investigate, both numerically and experimentally, the far-field profiles of beams carrying half-integer OAM per photon, these beams having been created by the method of imprinting off-axis vortices.