Three-dimensional tomographic reconstruction using Voronoi weighting.

Three-dimensional tomographic reconstruction requires careful selection of the illumination angles, often under certain measurement constraints. When the angular distribution must be nonuniform, appropriate selection of the reconstruction weights is necessary. We show that Voronoi weighting can significantly improve the fidelity of optical diffraction tomography.

Laser: A two-domain photon-phonon laser.

The laser is one of the greatest inventions in history. Because of its ubiquitous applications and profound societal impact, the concept of the laser has been extended to other physical domains including phonon lasers and atom lasers. Quite often, a laser in one physical domain is pumped by energy in another.

Two-lens anisotropic image-inversion system for interferometric information processing.

Interferometric image processing systems based on image inversion normally use multiple paths with inversion mirrors. Since such systems must meet strict requirements of alignment and stability, a common-path implementation using polarization channels and six anisotropic optical elements was recently introduced. We demonstrate here the operation of a common-path polarization-based image-inversion interferometeric system using only two anisotropic lenses.

A common-path polarization-based image-inversion interferometer.

We present a collinear, common-path image-inversion interferometer using the polarization channels of a single optical beam. Each of the channels is an imaging system of unit magnification, one positive and the other negative (inverted). Image formation is realized by means of a set of anisotropic lenses, each offering refractive power in one polarization and none in the other.

Single-photon three-qubit quantum logic using spatial light modulators.

The information-carrying capacity of a single photon can be vastly expanded by exploiting its multiple degrees of freedom: spatial, temporal, and polarization. Although multiple qubits can be encoded per photon, to date only two-qubit single-photon quantum operations have been realized. Here, we report an experimental demonstration of three-qubit single-photon, linear, deterministic quantum gates that exploit photon polarization and the two-dimensional spatial-parity-symmetry of the transverse single-photon field.

Lattice topology dictates photon statistics.

Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues.

Orthogonal quasi-phase-matched superlattice for generation of hyperentangled photons.

A crystal superlattice structure featuring nonlinear layers with alternating orthogonal optic axes interleaved with orthogonal poling directions, is shown to generate high-quality hyperentangled photon pairs via orthogonal quasi-phase-matched spontaneous parametric downconversion. We demonstrate that orthogonal quasi-phase matching (QPM) processes in a single nonlinear domain structure correct phase and group-velocity mismatches concurrently. Compared with the conventional two-orthogonal-crystals source and the double-nonlinearity single-crystal source, the orthogonal QPM superlattice is shown to suppress the spatial and temporal distinguishability of the generated photon pairs by several orders of magnitude, depending on the number of layers.

Optical coherency matrix tomography.

The coherence of an optical beam having multiple degrees of freedom (DoFs) is described by a coherency matrix G spanning these DoFs. This optical coherency matrix has not been measured in its entirety to date--even in the simplest case of two binary DoFs where G is a 4 × 4 matrix. We establish a methodical yet versatile approach--optical coherency matrix tomography--for reconstructing G that exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science.

Two-point optical coherency matrix tomography.

The two-point coherence of an electromagnetic field is represented completely by a 4×4 coherency matrix G that encodes the joint polarization-spatial-field correlations. Here, we describe a systematic sequence of cascaded spatial and polarization projective measurements that are sufficient to tomographically reconstruct G--a task that, to the best of our knowledge, has not yet been realized. Our approach benefits from the correspondence between this reconstruction problem in classical optics and that of quantum state tomography for two-photon states in quantum optics.

Generalized optical interferometry for modal analysis in arbitrary degrees of freedom.

We generalize the traditional concept of temporal optical interferometry to any degree of freedom of a coherent optical field. By identifying the structure of a unitary optical transformation that we designate the generalized phase operator, we enable optical interferometry to be carried out in any modal basis describing a degree of freedom. The structure of the generalized phase operator is that of a fractional optical transform, thus establishing the connection between fractional transforms, optical interferometry, and modal analysis.

Angular and radial mode analyzer for optical beams.

We describe an approach to determining both the angular and the radial modal content of a scalar optical beam in terms of optical angular momentum modes. A modified Mach-Zehnder interferometer that incorporates a spatial rotator to determine the angular modes and an optical realization of the fractional Hankel transform (fHT) to determine the radial modes is analyzed. Varying the rotation angle and the order of the fHT produces a two-dimensional (2D) interferogram from which we extract the modal coefficients by simple 2D Fourier analysis.

Anderson localization in optical waveguide arrays with off-diagonal coupling disorder.

We report on the observation of Anderson wave localization in one-dimensional waveguide arrays with off-diagonal disorder. The waveguide elements are inscribed in silica glass, and a uniform random distribution of coupling parameters is achieved by a precise variation of the relative waveguide positions. In the absence of disorder we observe ballistic transport as expected from discrete diffraction in periodic arrays.

Modal and polarization qubits in Ti:LiNbO3 photonic circuits for a universal quantum logic gate.

Lithium niobate photonic circuits have the salutary property of permitting the generation, transmission, and processing of photons to be accommodated on a single chip. Compact photonic circuits such as these, with multiple components integrated on a single chip, are crucial for efficiently implementing quantum information processing schemes.We present a set of basic transformations that are useful for manipulating modal qubits in Ti:LiNbO(3) photonic quantum circuits.

Ultrabroadband coherence-domain imaging using parametric downconversion and superconducting single-photon detectors at 1064 nm.

Coherence-domain imaging systems can be operated in a single-photon-counting mode, offering low detector noise; this in turn leads to increased sensitivity for weak light sources and weakly reflecting samples. We have demonstrated that excellent axial resolution can be obtained in a photon-counting coherence-domain imaging (CDI) system that uses light generated via spontaneous parametric downconversion (SPDC) in a chirped periodically poled stoichiometric lithium tantalate (chirped-PPSLT) structure, in conjunction with a niobium nitride superconducting single-photon detector (SSPD). The bandwidth of the light generated via SPDC, as well as the bandwidth over which the SSPD is sensitive, can extend over a wavelength region that stretches from 700 to 1500 nm.

Odd- and even-order dispersion cancellation in quantum interferometry.

We describe a novel effect involving odd-order dispersion cancellation. We demonstrate that odd- and even-order dispersion cancellation may be obtained in different regions of a single quantum interferogram using frequency-anticorrelated entangled photons and a new type of quantum interferometer. This offers new opportunities for quantum communication and metrology in dispersive media.

Even-order aberration cancellation in quantum interferometry.

We report the first experimental demonstration of even-order aberration cancellation in quantum interferometry. The effect is a spatial counterpart of the spectral group velocity dispersion cancellation, which is associated with spectral entanglement. It is manifested in temporal interferometry by virtue of the multiparameter spatial-spectral entanglement.

Spatial coherence effects on second- and fourth-order temporal interference.

We report the results of two experiments performed with two-photon light, produced via collinear degenerate optical spontaneous parametric downconversion (SPDC), in which both second-order (one-photon) and fourth-order (two-photon) interferograms are recorded in a Mach-Zehnder interferometer (MZI). In the first experiment, high-visibility fringes are obtained for both the second- and fourth-order interferograms. In the second experiment, the MZI is modified by the removal of a mirror from one of its arms; this leaves the fourth-order interferogram unchanged, but extinguishes the second-order interferogram.

Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion.

We generate ultrabroadband biphotons via the process of spontaneous parametric down-conversion (SPDC) in quasi-phase-matched nonlinear gratings that have a linearly chirped wave vector. By using these ultrabroadband biphotons (300-nm bandwidth), we measure the narrowest Hong-Ou-Mandel dip to date, having a full width at half maximum of 7.1 fs.

Maximum-likelihood image estimation using photon-correlated beams.

A theory is presented addressing the fundamental limits of image estimation in a setup that uses two photon-correlated beams. These beams have the property that their photon arrivals, as a point process, are ideally synchronized in time and space. The true image represents the spatial distribution of the optical transmittance (or reflectance) of an object.

Synthesis and analysis of entangled photonic qubits in spatial-parity space.

We present the novel embodiment of a photonic qubit that makes use of one continuous spatial degree of freedom of a single photon and relies on the parity of the photon's transverse spatial distribution. Using optical spontaneous parametric down-conversion to produce photon pairs, we demonstrate the controlled generation of entangled-photon states in this new space. Specifically, two Bell states, and a continuum of their superpositions, are generated by simple manipulation of a classical parameter, the optical-pump spatial parity, and not by manipulation of the entangled photons themselves.

Experimental violation of Bell's inequality in spatial-parity space.

We report the first experimental violation of Bell's inequality in the spatial domain using the Einstein-Podolsky-Rosen state. Two-photon states generated via optical spontaneous parametric down-conversion are shown to be entangled in the parity of their one-dimensional transverse spatial profile. Superpositions of Bell states are prepared by manipulation of the optical pump's transverse spatial parity-a classical parameter.

Non-collinear and non-degenerate polarization-entangled photon generation via concurrent type-I parametric downconversion in PPLN.

A periodically poled lithium niobate (PPLN) crystal has been used as an efficient source of non-collinearly generated polarization-entangled photon pairs at 810 and 1550 nm. The PPLN crystal was endowed with a specially designed poling pattern and the entangled photons were generated via the nonlinear optical process of spontaneous parametric down conversion (SPDC). A novel design based on overlapping two concurrent type-I quasi-phase-matching structures in a single PPLN crystals produced correlated pairs of alternatively polarized photons in largely separated spectral regions.

Selective functionalization of 3-D polymer microstructures.

We demonstrate the selective functionalization of 3-D polymer microstructures that were created using multiphoton absorption polymerization. By fabricating different portions of the structures with acrylic and methacrylic polymers, we are able to take advantage of the differential reactivities of these materials to perform functionalization chemistry on a single polymeric component. We demonstrate the selective deposition of metal to create structures, such as a functional microinductor.

Broadband light generation by noncollinear parametric downconversion.

Broadband light generation is demonstrated by noncollinear spontaneous parametric downconversion with a cw pump laser. By use of a suitable noncollinear phase-matching geometry and a tightly focused pump beam, downconverted signals that feature a bell-shaped spectral distribution with a bandwidth approaching 200 nm are obtained. As an application of the generated broadband light, submicrometer axial resolution in an optical coherence tomography scheme is demonstrated; a free-space resolution down to 0.

Wolf equations for two-photon light.

The spatiotemporal two-photon probability amplitude that describes light in a two-photon entangled state obeys equations identical to the Wolf equations, which are satisfied by the mutual coherence function for light in any quantum state. Both functions therefore propagate similarly through optical systems. A generalized van Cittert-Zernike theorem explains the predicted enhancement in resolution for entangled-photon microscopy and quantum lithography.