Publications

2011

Diffractive simultaneous bidirectional shearing interferometry using tailored spatially coherent light

Vanusch Nercissian, Irina Harder, Klaus Mantel, Andreas Berger, Gerd Leuchs, Norbert Lindlein, Johannes Schwider

APPLIED OPTICS 50 (4) 571-578 (2011) | Journal

Measurements of wavefront deformations can be carried out with the help of lateral shearing interferometers. Here the focus is on a setup providing two shears along orthogonal directions simultaneously to generate the data needed for a reconstruction. We describe a diffractive solution using Ronchi phase gratings with a suppressed zeroth order for both the doubling of the wavefront under test and the bidirectional shearing unit. A series arrangement of the gratings offers an on-axis geometry, which minimizes the systematic errors of the test. For illumination, an extended incoherent monochromatic light source is used. High-contrast fringes can be obtained by tailoring the degree of coherence via a periodic intensity distribution. (c) 2011 Optical Society of America

Interaction of highly focused vector beams with a metal knife-edge

P. Marchenko, S. Orlov, C. Huber, P. Banzer, S. Quabis, U. Peschel, G. Leuchs

OPTICS EXPRESS 19 (8) 7244-7261 (2011) | Journal

We investigate the interaction of highly focused linearly polarized optical beams with a metal knife-edge both theoretically and experimentally. A high numerical aperture objective focusses beams of various wavelengths onto samples of different sub-wavelength thicknesses made of several opaque and pure materials. The standard evaluation of the experimental data shows material and sample dependent spatial shifts of the reconstructed intensity distribution, where the orientation of the electric field with respect to the edge plays an important role. A deeper understanding of the interaction between the knife-edge and the incoming highly focused beam is gained in our theoretical model by considering eigenmodes of the metal-insulator-metal structure. We achieve good qualitative agreement of our numerical simulations with the experimental findings. (C) 2011 Optical Society of America

Adaptive frequency comb illumination for interferometry in the case of nested two-beam cavities

Irina Harder, Gerd Leuchs, Klaus Mantel, Johannes Schwider

APPLIED OPTICS 50 (25) 4942-4956 (2011) | Journal

The homogeneity test of glass plates in a Fizeau interferometer is hampered by the superposition of multiple interference signals coming from the surfaces of the glass plate as well as the empty Fizeau cavity. To evaluate interferograms resulting from such nested cavities, various approaches such as the use of broadband light sources have been applied. In this paper, we propose an adaptive frequency comb interferometer to accomplish the cavity selection. An adjustable Fabry-Perot resonator is used to generate a variable frequency comb that can be matched to the length of the desired cavity. Owing to its flexibility, the number of measurements needed for the homogeneity test can be reduced to four. Furthermore, compared to approaches using a two-beam interferometer as a filter for the broadband light source, the visibility of the fringe system is considerably higher if a Fabry-Perot filter is applied. (C) 2011 Optical Society of America

Multilevel Phase-Preserving Amplitude Regeneration Using a Single Nonlinear Amplifying Loop Mirror

Martin Hierold, Tobias Roethlingshoefer, Klaus Sponsel, Georgy Onishchukov, Bernhard Schmauss, Gerd Leuchs

IEEE PHOTONICS TECHNOLOGY LETTERS 23 (14) 1007-1009 (2011) | Journal

A possibility of multilevel phase-preserving amplitude regeneration using a nonlinear amplifying loop mirror (NALM) is presented for the optical star-8 quadrature amplitude modulation (QAM) transmission format as an example. Two significantly different state power ratios for the QAM signal, 1:3 and 1:7, were investigated. After the optimization of the coupler splitting ratio and the directional phase bias in the NALM, amplitude noise can be efficiently suppressed at both signal power levels simultaneously. Bit-error-ratio (BER) simulations have shown that in a system limited by nonlinear phase noise, the deployment of the NALM allows an increase of the fiber launch power by 1.9 and 2.2 dB at a BER of 10(-3) for a state power ratio of 1:3 and 1:7, respectively. The regeneration limits due to imperfections of the power transfer characteristic are also discussed.

The Direct Writing of Plasmonic Gold Nanostructures by Electron-Beam-Induced Deposition

Katja Hoeflich, Ren Bin Yang, Andreas Berger, Gerd Leuchs, Silke Christiansen

SI 23 (22-23) 2657-+ (2011) | Journal

Various nanostructures are directly written by electron-beam-induced deposition using dimethyl-gold(III)-acetylacetonate as the precursor gas. After purification, their potential applications include plasmonic devices and metamaterials. Carbon contamination of the as-written structures can be completely removed by low-temperature ozone treatment, leaving polycrystalline pure gold structures (see figure). This treatment reduces the size of the nanostructures but does not substantially alter their functional shape.

Role of spatial coherence in Goos-Hanchen and Imbert-Fedorov shifts

Andrea Aiello, J. P. Woerdman

OPTICS LETTERS 36 (16) 3151-3153 (2011)

We present a theory for Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts for beams of light with arbitrary spatial coherence. By applying the well-known theory of partial spatial coherence, we can calculate explicitly spatial and angular GH and IF shifts for completely polarized beams of any shape and spatial coherence. For the specific case of a Gauss-Schell source, we find that only the angular part of GH and IF shifts is affected by the spatial coherence of the beam. A physical explanation of our results is given. (C) 2011 Optical Society of America

Spin Hall effect of light in metallic reflection

N. Hermosa, A. M. Nugrowati, Andrea Aiello, J. P. Woerdman

OPTICS LETTERS 36 (16) 3200-3202 (2011)

We report the first measurement of the spin Hall effect of light (SHEL) on an air-metal interface. The SHEL is a polarization-dependent out-of-plane shift on the reflected beam. For the case of metallic reflection with a linearly polarized incident light, both the spatial and angular variants of the shift are observed and are maximum for -45 degrees/45 degrees polarization, but zero for pure s and p polarization. For an incoming beam with circular polarization states however, only the spatial out-of-plane shift is present. (C) 2011 Optical Society of America

Direct generation of a multi-transverse mode non-classical state of light

Benoit Chalopin, Francesco Scazza, Claude Fabre, Nicolas Treps

OPTICS EXPRESS 19 (5) 4405-4410 (2011) | Journal

Quantum computation and communication protocols require quantum resources which are in the continuous variable regime squeezed and/or quadrature entangled optical modes. To perform more and more complex and robust protocols, one needs sources that can produce in a controlled way highly multimode quantum states of light. One possibility is to mix different single mode quantum resources. Another is to directly use a multimode device, either in the spatial or in the frequency domain. We present here the first experimental demonstration of a device capable of producing simultanuously several squeezed transverse modes of the same frequency and which is potentially scalable. We show that this device, which is an Optical Parametric Oscillator using a self-imaging cavity, produces a multimode quantum resource made of three squeezed transverse modes. (C) 2011 Optical Society of America

Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes

C. Gabriel, A. Aiello, W. Zhong, T. G. Euser, N. Y. Joly, P. Banzer, M. Foertsch, D. Elser, U. L. Andersen, et al.

PHYSICAL REVIEW LETTERS 106 (6) 060502 (2011) | Journal

Quantum systems such as, for example, photons, atoms, or Bose-Einstein condensates, prepared in complex states where entanglement between distinct degrees of freedom is present, may display several intriguing features. In this Letter we introduce the concept of such complex quantum states for intense beams of light by exploiting the properties of cylindrically polarized modes. We show that already in a classical picture the spatial and polarization field variables of these modes cannot be factorized. Theoretically it is proven that by quadrature squeezing cylindrically polarized modes one generates entanglement between these two different degrees of freedom. Experimentally we demonstrate amplitude squeezing of an azimuthally polarized mode by exploiting the nonlinear Kerr effect in a specially tailored photonic crystal fiber. These results display that such novel continuous-variable entangled systems can, in principle, be realized.

Birefringence and dispersion of cylindrically polarized modes in nanobore photonic crystal fiber

T. G. Euser, M. A. Schmidt, N. Y. Joly, C. Gabriel, C. Marquardt, L. Y. Zang, M. Foertsch, P. Banzer, A. Brenn, et al.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 28 (1) 193-198 (2011) | Journal

We demonstrate experimentally and theoretically that a nanoscale hollow channel placed centrally in the solid-glass core of a photonic crystal fiber strongly enhances the cylindrical birefringence (the modal index difference between radially and azimuthally polarized modes). Furthermore, it causes a large split in group velocity and group velocity dispersion. We show analytically that all three parameters can be varied over a wide range by tuning the diameters of the nanobore and the core. (C) 2010 Optical Society of America

Disentanglement in bipartite continuous-variable systems

F. A. S. Barbosa, A. J. de Faria, A. S. Coelho, K. N. Cassemiro, A. S. Villar, P. Nussenzveig, M. Martinelli

PHYSICAL REVIEW A 84 (5) 052330 (2011) | Journal

Entanglement in bipartite continuous-variable systems is investigated in the presence of partial losses such as those introduced by a realistic quantum communication channel, e. g., by propagation in an optical fiber. We find that entanglement can vanish completely for partial losses, in a situation reminiscent of so-called entanglement sudden death. Even states with extreme squeezing may become separable after propagation in lossy channels. Having in mind the potential applications of such entangled light beams to optical communications, we investigate the conditions under which entanglement can survive for all partial losses. Different loss scenarios are examined, and we derive criteria to test the robustness of entangled states. These criteria are necessary and sufficient for Gaussian states. Our study provides a framework to investigate the robustness of continuous-variable entanglement in more complex multipartite systems.

Photon Propagation in a Discrete Fiber Network: An Interplay of Coherence and Losses

Alois Regensburger, Christoph Bersch, Benjamin Hinrichs, Georgy Onishchukov, Andreas Schreiber, Christine Silberhorn, Ulf Peschel

PHYSICAL REVIEW LETTERS 107 (23) 233902 (2011) | Journal

We study light propagation in a photonic system that shows stepwise evolution in a discretized environment. It resembles a discrete-time version of photonic waveguide arrays or quantum walks. By introducing controlled photon losses to our experimental setup, we observe unexpected effects like subexponential energy decay and formation of complex fractal patterns. This demonstrates that the interplay of linear losses, discreteness and energy gradients leads to genuinely new coherent phenomena in classical and quantum optical experiments. Moreover, the influence of decoherence is investigated.

Accessing photon bunching with a photon number resolving multi-pixel detector

Dmitry A. Kalashnikov, Si Hui Tan, Maria V. Chekhova, Leonid A. Krivitsky

OPTICS EXPRESS 19 (10) 9352-9363 (2011) | Journal

In quantum optics and its applications, there is an urgent demand for photon-number resolving detectors. Recently, there appeared multi-pixel counters (MPPC) that are able to distinguish between 1,2,..10 photons. At the same time, strong coupling between different pixels (crosstalk) hinders their photon-number resolution. In this work, we suggest a method for 'filtering out' the crosstalk effect in the measurement of intensity correlation functions. The developed approach can be expanded to the analysis of higher-order intensity correlations by using just a single MPPC. (C) 2011 Optical Society of America

After-gate attack on a quantum cryptosystem

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, Ch Marquardt, V. Makarov, G. Leuchs

NEW JOURNAL OF PHYSICS 13 013043 (2011) | Journal

We present a method to control the detection events in quantum key distribution systems that use gated single-photon detectors. We employ bright pulses as faked states, timed to arrive at the avalanche photodiodes outside the activation time. The attack can remain unnoticed, since the faked states do not increase the error rate per se. This allows for an intercept-resend attack, where an eavesdropper transfers her detection events to the legitimate receiver without causing any errors. As a side effect, afterpulses, originating from accumulated charge carriers in the detectors, increase the error rate. We have experimentally tested detectors of the system id3110 (Clavis2) from ID Quantique. We identify the parameter regime in which the attack is feasible despite the side effect. Furthermore, we outline how simple modifications in the implementation can make the device immune to this attack.

Spectral and temporal Bloch oscillations in optical fibres

C. Bersch, G. Onishchukov, U. Peschel

SI 104 (3) 495-501 (2011) | Journal

Inspired by the space-time duality of paraxial beam diffraction and dispersive pulse spreading, the experimental implementation of a temporal equivalent of evanescently coupled waveguide arrays is demonstrated. Pulses interact with a time-periodic potential during their propagation through an optical fibre and the generic effect of discrete diffraction is observed in time. The presented system allows fast and high-resolving measurements of the complete signal evolution. To demonstrate the advanced capabilities, Bloch oscillations of an optical signal in both the time and frequency domains are realised.

Macroscopic Pure State of Light Free of Polarization Noise

Timur Sh. Iskhakov, Maria V. Chekhova, Georgy O. Rytikov, Gerd Leuchs

PHYSICAL REVIEW LETTERS 106 (11) 113602 (2011) | Journal

The preparation of completely nonpolarized light is seemingly easy; an everyday example is sunlight. The task is much more difficult if light has to be in a pure quantum state, as required by most quantum-technology applications. The pure quantum states of light obtained so far are either polarized or, in rare cases, manifest hidden polarization; even if their intensities are invariant to polarization transformations, higher-order moments are not. We experimentally demonstrate the preparation of the macroscopic singlet Bell state, which is pure, is completely nonpolarized, and has no polarization noise. Simultaneous fluctuation suppression in three Stokes observables below the shot-noise limit is demonstrated, opening perspectives for noiseless polarization measurements. The state is shown to be invariant to polarization transformations. This robust highly entangled isotropic state promises to fuel important applications in photonic quantum technologies.

Concentric ring metal grating for generating radially polarized light

Z. Ghadyani, I. Vartiainen, I. Harder, W. Iff, A. Berger, N. Lindlein, M. Kuittinen

APPLIED OPTICS 50 (16) 2451-2457 (2011) | Journal

A subwavelength concentric ring metal grating for visible light (lambda - 632.8 nm) is designed and fabricated by electron-beam lithography to transform circularly polarized light into radially polarized light. Experimental results are compared to theoretical predictions and the advantages and disadvantages of the element with alternative methods are discussed. (C) 2011 Optical Society of America

Modeling of Sloped Interfaces on a Yee Grid

Dzmitry M. Shyroki

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 59 (9) 3290-3295 (2011) | Journal

To represent material boundaries in the finite-difference time-domain or frequency-domain method, effective cell permittivity epsilon(eff) can be introduced for each grid cell crossed by material interface. In this paper we revisit the derivation of tensorial epsilon(eff) for a sloped interface, and describe possible interpolation schemes for coupling of different effective electric field and induction components near the interface. We put the resulting non-symmetric and symmetrized effective permittivity matrices to numerical tests in the frequency domain. For very-high-contrast interfaces the symmetrized schemes perform worse than simple staircasing while non-symmetrized interpolation retains the second-order convergence.

Rate analysis for a hybrid quantum repeater

Nadja K. Bernardes, Ludmila Praxmeyer, Peter van Loock

PHYSICAL REVIEW A 83 (1) 012323 (2011) | Journal

We present a detailed rate analysis for a hybrid quantum repeater assuming perfect memories and using optimal probabilistic entanglement generation and deterministic swapping routines. The hybrid quantum repeater protocol is based on atomic qubit-entanglement distribution through optical coherent-state communication. An exact, analytical formula for the rates of entanglement generation in quantum repeaters is derived, including a study on the impacts of entanglement purification and multiplexing strategies. More specifically, we consider scenarios with as little purification as possible and we show that for sufficiently low local losses, such purifications are still more powerful than multiplexing. In a possible experimental scenario, our hybrid system can create near-maximally entangled (F = 0.98) pairs over a distance of 1280 km at rates of the order of 100 Hz.

Perfect imaging of hypersurfaces via transformation optics

Klaus Mantel, Dustin Bachstein, Ulf Peschel

OPTICS LETTERS 36 (2) 199-201 (2011) | Journal

Conventional optical imaging systems suffer from the presence of many imperfections, such as spherical aberrations, astigmatism, or coma. If the imaging system is corrected for spherical aberrations and fulfills the Abbe sine condition, perfect imaging is guaranteed between two parallel planes but only in a small neighborhood of the optical axis. It is therefore worth asking for optical systems that would allow for perfect imaging between arbitrary smooth surfaces without restrictions in shape or extension. In this Letter, we describe the application of transformation optics to design refractive index distributions that allow perfect, aberration-free imaging for various imaging configurations in R(n). A special case is the imaging between two extended parallel lines in R(2), which leads to the well-known hyperbolic secant index distribution that is used for the fabrication of gradient index lenses. (C) 2011 Optical Society of America

Quadrant detector calibration for vortex beams

N. Hermosa, A. Aiello, J. P. Woerdman

OPTICS LETTERS 36 (3) 409-411 (2011) | Journal

This Letter reports an experimental and theoretical study of the response of a quadrant detector (QD) to an incident vortex beam, specifically a Laguerre-Gaussian (LG) beam. We have found that the LG beam response depends on the vorticity index l. We compare LG beams with hard-ringed beams and find that at higher l values, the QD response to LG beams can be approximated by its response to hard-ringed beams. Our findings are important in view of the increasing interest in optical vortex beams. (C) 2011 Optical Society of America

Frustrated quantum phase diffusion and increased coherence of solitons due to nonlocality

Sascha Batz, Ulf Peschel

PHYSICAL REVIEW A 83 (3) 033826 (2011) | Journal

We investigate the quantum properties of solitons with nonlocal self-interaction. We find significant changes when compared to the local interaction. Quantum phase diffusion of nonlocal solitons is always reduced with respect to the local interaction and vanishes in the strongly nonlocal limit. Thus, coherence is increased in the nonlocal case. Furthermore, we compare the intrinsic quantum wave packet spreading to the recently discussed classical Gordon-Haus effect for nonlocal solitons [V. Folli and C. Conti, Phys. Rev. Lett. 104, 193901 (2010)].

Experimental cross-polarization detection of coupling far-field light to highly confined plasmonic gap modes via nanoantennas

J. Wen, P. Banzer, A. Kriesch, D. Ploss, B. Schmauss, U. Peschel

APPLIED PHYSICS LETTERS 98 (10) 101109 (2011) | Journal

We experimentally demonstrate the coupling of far-field light to highly confined plasmonic gap modes via connected nanoantennas. The excitation of plasmonic gap modes is shown to depend on the polarization, position, and wavelength of the incident beam. Far-field measurements performed in crossed polarization allow for the detection of extremely weak signals re-emitted from gap waveguides and can increase the signal-to-noise ratio dramatically. (C) 2011 American Institute of Physics. [doi:10.1063/1.3564904]

Goos-Hanchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam

Andrea Aiello, J. P. Woerdman

OPTICS LETTERS 36 (4) 543-545 (2011) | Journal

Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts are diffractive corrections to geometric optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question of how the GH and IF shifts behave for a "nondiffracting" Bessel beam. (C) 2011 Optical Society of America

Generation of bright squeezed vacuum in the Karassiov states

M. V. Chekhova, T. Sh. Iskhakov, G. Leuchs, G. O. Rytikov

OPTICS AND SPECTROSCOPY 111 (4) 565-569 (2011) | Journal

We suggest an experimental procedure allowing one to prepare squeezed vacuum in a special type of generalized Bell states, first introduced by V.P. Karassiov. We present the first results on the experimental generation of such states and observation of their polarization properties.

Superlinear threshold detectors in quantum cryptography

Lars Lydersen, Nitin Jain, Christoffer Wittmann, Oystein Maroy, Johannes Skaar, Christoph Marquardt, Vadim Makarov, Gerd Leuchs

PHYSICAL REVIEW A 84 (3) 032320 (2011) | Journal

We introduce the concept of a superlinear threshold detector, a detector that has a higher probability to detect multiple photons if it receives them simultaneously rather than at separate times. Highly superlinear threshold detectors in quantum key distribution systems allow eavesdropping the full secret key without being revealed. Here, we generalize the detector control attack, and analyze how it performs against quantum key distribution systems with moderately superlinear detectors. We quantify the superlinearity in superconducting single-photon detectors based on earlier published data, and gated avalanche photodiode detectors based on our own measurements. The analysis shows that quantum key distribution systems using detector(s) of either type can be vulnerable to eavesdropping. The avalanche photodiode detector becomes superlinear toward the end of the gate. For systems expecting substantial loss, or for systems not monitoring loss, this would allow eavesdropping using trigger pulses containing less than 120 photons per pulse. Such an attack would be virtually impossible to catch with an optical power meter at the receiver entrance.

Discontinuous space variant sub-wavelength structures for generating radially polarized light in visible region

Z. Ghadyani, S. Dmitriev, N. Lindlein, G. Leuchs, O. Rusina, I. Harder

JOURNAL OF THE EUROPEAN OPTICAL SOCIETY-RAPID PUBLICATIONS 6 11041 (2011) | Journal

A discontinuous space variant sub-wavelength dielectric grating is designed and fabricated for generating radially polarized light in visible region (lambda = 632.8 nm). The design is based on sub-wavelength silicon nitride structures introducing a retardation of pi/2 by form birefringence, with space variant orientation of the optical axis. The pattern is divided into concentric ring segments with constant structural parameters, therefore reducing electron-beam writing time significantly. The design avoids the technological challenges encountered in the generation of a continuous space variant grating while maintaining good quality of the resulting polarization mode. [DOI: http://dx.doi.org/10.2971/jeos.2011.11041]

Device Calibration Impacts Security of Quantum Key Distribution

Nitin Jain, Christoffer Wittmann, Lars Lydersen, Carlos Wiechers, Dominique Elser, Christoph Marquardt, Vadim Makarov, Gerd Leuchs

PHYSICAL REVIEW LETTERS 107 (11) 110501 (2011) | Journal

Characterizing the physical channel and calibrating the cryptosystem hardware are prerequisites for establishing a quantum channel for quantum key distribution (QKD). Moreover, an inappropriately implemented calibration routine can open a fatal security loophole. We propose and experimentally demonstrate a method to induce a large temporal detector efficiency mismatch in a commercial QKD system by deceiving a channel length calibration routine. We then devise an optimal and realistic strategy using faked states to break the security of the cryptosystem. A fix for this loophole is also suggested.

Quick root searching method for resonances of dielectric optical microcavities with the boundary element method

Chang-Ling Zou, Harald G. L. Schwefel, Fang-Wen Sun, Zheng-Fu Han, Guang-Can Guo

OPTICS EXPRESS 19 (17) 15669-15678 (2011) | Journal

In this paper, we developed an efficient method for searching the resonant eigenfrequency of dielectric optical microcavities by the boundary element method. By transforming the boundary integral equation to a general eigenvalue problem for arbitrary, symmetric, and multi-domain shaped optical microcavities, we analyzed the regular motion of the eigenvalues against the frequency. The new strategy can predict multiple resonances, increase the speed of convergence, and avoid non-physical spurious solutions. These advantages greatly reduce the computation time in the search process of the resonances. Moreover, this method is not only valuable for dielectric microcavities, but is also suitable for other photonic systems with dissipations, whose resonant eigenfrequencies are complex numbers. (C) 2011 Optical Society of America

Quantum Light from a Whispering-Gallery-Mode Disk Resonator

J. U. Fuerst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch Marquardt, G. Leuchs

PHYSICAL REVIEW LETTERS 106 (11) 113901 (2011) | Journal

Optical parametric down-conversion has proven to be a valuable source of nonclassical light. The process is inherently able to produce twin-beam correlations along with individual intensity squeezing of either parametric beam, when pumped far above threshold. Here, we present for the first time the direct observation of intensity squeezing of -1.2 dB of each of the individual parametric beams in parametric down-conversion by use of a high quality whispering-gallery-mode disk resonator. In addition, we observed twin-beam quantum correlations of -2.7 dB with this cavity. Such resonators feature strong optical confinement and offer tunable coupling to an external optical field. This work exemplifies the potential of crystalline whispering-gallery-mode resonators for the generation of quantum light. The simplicity of this device makes the application of quantum light in various fields highly feasible.

Theory of anisotropic whispering-gallery-mode resonators

Marco Ornigotti, Andrea Aiello

PHYSICAL REVIEW A 84 (1) 013828 (2011) | Journal

An analytic solution for a uniaxial spherical resonator is presented using the method of Debye potentials. This serves as a starting point for the calculation of whispering gallery modes (WGMs) in such a resonator. Suitable approximations for the radial functions are discussed in order to best characterize WGMs. The characteristic equation and its asymptotic expansion for the anisotropic case is also discussed, and an analytic formula with a precision of the order O[nu(-1)] is also given. Our careful treatment of both boundary conditions and asymptotic expansions makes the present work a particularly suitable platform for a quantum theory of whispering gallery resonators.

Polarization properties of macroscopic Bell states

Timur Sh. Iskhakov, Ivan N. Agafonov, Maria V. Chekhova, Georgy O. Rytikov, Gerd Leuchs

PHYSICAL REVIEW A 84 (4) 045804 (2011) | Journal

The four two-photon polarization Bell states are one of the main instruments in the toolbox of quantum optics and quantum information. In our experiment we produce their multiphoton counterparts, macroscopic Bell states. These are relevant to applications in quantum technologies because they provide efficient interactions with material quantum objects and with each other via nonlinear interactions. Furthermore, we study the polarization properties of these states using the concept of second-order degree of polarization and its higher-order generalization.

Systematic analysis of signal-to-noise ratio in bipartite ghost imaging with classical and quantum light

G. Brida, M. V. Chekhova, G. A. Fornaro, M. Genovese, E. D. Lopaeva, I. Ruo Berchera

PHYSICAL REVIEW A 83 (6) 063807 (2011) | Journal

We present a complete and exhaustive theory of signal-to-noiseratio in bipartite ghost imaging with classical (thermal) and quantum (twin beams) light. The theory is compared with experiment for both twin beams and thermal light in a certain regime of interest.

Artificial boundary conditions for certain evolution PDEs with cubic nonlinearity for non-compactly supported initial data

V. Vaibhav

JOURNAL OF COMPUTATIONAL PHYSICS 230 (8) 3205-3229 (2011) | Journal

The paper addresses the problem of constructing non-reflecting boundary conditions for two types of one dimensional evolution equations, namely, the cubic nonlinear Schrodinger (NLS) equation, partial derivative(t)u + Lu - i chi vertical bar u vertical bar(2)u = 0 with L -i partial derivative(2)(x), and the equation obtained by letting L partial derivative(3)(x). The usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain. We adapt the pseudo-differential approach developed by Antoine et al. (2006) [5] for the NLS equation to the second type of evolution equation, and further, extend the scheme to the aforementioned class of initial data for both of the equations. In addition, we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness. (C) 2011 Elsevier Inc. All rights reserved.

COMPARATIVE TEST OF TWO METHODS OF QUANTUM EFFICIENCY ABSOLUTE MEASUREMENT BASED ON SQUEEZED VACUUM DIRECT DETECTION

I. N. Agafonov, M. V. Chekhova, A. N. Penin, G. O. Rytikov, O. A. Shumilkina, T. Sh Iskhakov

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION 9 251-262 (2011) | Journal

We realize and test in experiment a method recently proposed for measuring absolute quantum efficiency of analog photodetectors. Similar to the traditional (Klyshko) method of absolute calibration, the new one is based on the direct detection of two-mode squeezed vacuum at the output of a traveling wave OPA. However, in the new method, one measures the difference-photocurrent variance rather than the correlation function of photocurrents (number of coincidences), which makes the technique applicable for high-gain OPA. In this work we test the new method versus the traditional one for the case of photon-counting detectors where both techniques are valid.

Bell-inequality tests with macroscopic entangled states of light

M. Stobinska, P. Sekatski, A. Buraczewski, N. Gisin, G. Leuchs

PHYSICAL REVIEW A 84 (3) 034104 (2011) | Journal

Quantum correlations may violate the Bell inequalities. Most experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiments which simultaneously close this loophole and the locality loophole are highly desirable and remain challenging. An approach to loophole-free Bell tests is based on amplification of the entangled photons (i.e., on macroscopic entanglement), for which an optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of the possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell tests and quantum protocols are the subject of an intensive study in the field nowadays.

Generation of Kerr non-Gaussian motional states of trapped ions

M. Stobinska, A. S. Villar, G. Leuchs

EPL 94 (5) 54002 (2011) | Journal

Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally present in this kind of system. We perform detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits generation of all other complex non-Gaussian states with negative Wigner functions resulting from Kerr nonlinear interaction. Especially, superpositions of several coherent states are achieved at a fraction of the time necessary to produce the cat state. Copyright (C) EPLA, 2011

Intensity correlations of thermal light

T. Iskhakov, A. Allevi, D. A. Kalashnikov, V. G. Sala, M. Takeuchi, M. Bondani, M. Chekhova

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 199 (1) 127-138 (2011) | Journal

We demonstrate measurement of normalized Glauber's intensity correlation functions of different orders using an array photodetector. As the light source, we use a laser beam scattered by a rotating ground-glass disc, which has statistics close to that of thermal light. We compare the measurements of the normalized correlation functions to that of the difference-intensity variance and show that they are in a certain sense complementary. The independence of the variance measurement on the number of temporal modes has been demonstrated for the first time. Different versions of high-order ghost imaging are also realized and characterized quantitatively.

Absolute calibration of photodetectors: photocurrent multiplication versus photocurrent subtraction

I. N. Agafonov, M. V. Chekhova, T. S. Iskhakov, A. N. Penin, G. O. Rytikov, O. A. Shcherbina

OPTICS LETTERS 36 (8) 1329-1331 (2011)

We report testing of the new absolute method of photodetector calibration based on the difference-signal measurement for two-mode squeezed vacuum by comparison with the traditional absolute method based on coincidence counting. Using low-gain parametric downconversion, we have measured the quantum efficiency of a counting detector by both methods. The difference-signal method was adapted for the counting detectors by taking into account the dead-time effect. (c) 2011 Optical Society of America

Classical and quantum properties of cylindrically polarized states of light

Annemarie Holleczek, Andrea Aiello, Christian Gabriel, Christoph Marquardt, Gerd Leuchs

OPTICS EXPRESS 19 (10) 9714-9736 (2011) | Journal

We investigate theoretical properties of beams of light with non-uniform polarization patterns. Specifically, we determine all possible configurations of cylindrically polarized modes (CPMs) of the electromagnetic field, calculate their total angular momentum and highlight the subtleties of their structure. Furthermore, a hybrid spatio-polarization description for such modes is introduced and developed. In particular, two independent Poincare spheres have been introduced to represent simultaneously the polarization and spatial degree of freedom of CPMs. Possible mode-to-mode transformations accomplishable with the help of Bconventional polarization and spatial phase retarders are shown within this representation. Moreover, the importance of these CPMs in the quantum optics domain due to their classical features is highlighted. (C) 2011 Optical Society of America

Phase noise suppression in a DPSK transmission system by the use of an attenuation-imbalanced NOLM

C. Stephan, K. Sponsel, G. Onishchukov, B. Schmauss, G. Leuchs

OPTICS COMMUNICATIONS 284 (12) 3079-3083 (2011) | Journal

A nonlinear optical loop mirror (NOLM) imbalanced by attenuation has been used for the suppression of nonlinear phase noise in a DPSK transmission system. It has been experimentally shown that such a passive, NOLM-based regenerator can significantly improve the performance of a phase-encoded transmission when it is limited by nonlinear phase noise. A brief overview over the advantages und limitations of different NOLM-based phase-preserving amplitude regenerators is also given. (C) 2011 Elsevier B.V. All rights reserved.

Geometric Spin Hall Effect of Light at polarizing interfaces

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, G. Leuchs

APPLIED PHYSICS B-LASERS AND OPTICS 102 (3) 427-432 (2011) | Journal

The geometric Spin Hall Effect of Light (geometric SHEL) amounts to a polarization-dependent positional shift when a light beam is observed from a reference frame tilted with respect to its direction of propagation. Motivated by this intriguing phenomenon, the energy density of the light beam is decomposed into its Cartesian components in the tilted reference frame. This illustrates the occurrence of the characteristic shift and the significance of the effective response function of the detector. We introduce the concept of a tilted polarizing interface and provide a scheme for its experimental implementation. A light beam passing through such an interface undergoes a shift resembling the original geometric SHEL in a tilted reference frame. This displacement is generated at the polarizer and its occurrence does not depend on the properties of the detection system. We give explicit results for this novel type of geometric SHEL and show that at grazing incidence this effect amounts to a displacement of multiple wavelengths, a shift larger than the one introduced by Goos-Hanchen and Imbert-Fedorov effects.

Parallel two-step phase-shifting digital holograph microscopy based on a grating pair

Peng Gao, Baoli Yao, Irina Harder, Junwei Min, Rongli Guo, Juanjuan Zheng, Tong Ye

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 28 (3) 434-440 (2011) | Journal

An optical configuration for parallel two-step phase-shifting digital holographic microscopy (DHM) based on a grating pair is proposed for the purpose of real-time phase microscopy. Orthogonally circularly polarized object and reference waves are diffracted twice by a pair of gratings, and two parallel copies for each beams come into being. Combined with polarization elements, parallel two-step phase-shifting holograms are obtained. Based on the proposed configuration, two schemes of DHM, i.e., slightly off-axis and on-axis DHM, have been implemented. The slightly off-axis DHM suppresses the dc term by subtracting the two phase-shifting holograms from each other, thus the requirement on the off-axis angle and sampling power of the CCD camera is reduced greatly. The on-axis DHM has the least requirement on the resolving power of the CCD camera, while it requires that the reference wave is premeasured and its intensity is no less than 2 times the maximal intensity of the object wave. (C) 2011 Optical Society of America

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