Optical field-strength generalized polarization of multimode single photon states in integrated directional couplers

A quantum analysis of the generalized polarization properties of multimode single photon states is presented. It is based on the optical field-strength probability distributions in such a way that generalized polarization is understood as a significant confinement of the probability distribution along certain regions of the multidimensional optical field-strength space. The analysis is addressed to multimode integrated waveguiding devices, such as N?×?N integrated directional couplers, whose modes fulfil a spatial modal orthogonality relationship. For that purpose a definition of the quantum generalized polarization degree in a N-dimensional space, based on the concept of distance to an unpolarized N-dimensional Gaussian distribution, is proposed. The generalized polarization degree of pure and mixture multimode single photon states and also of some multi-photon states such as coherent and chaotic ones, is evaluated and analyzed.     

Optical field-strength generalized polarization of non-stationary quantum states in waveguiding photonic devices

A quantum analysis of the generalized polarization properties of multimode non-stationary states based on their optical field-strength probability distributions is presented. The quantum generalized polarization is understood as a significant confinement of the probability distribution along certain regions of a multidimensional optical field-strength space. The analysis is addressed to quantum states generated in multimode linear and nonlinear waveguiding (integrated) photonic devices, such as multimode waveguiding directional couplers and waveguiding parametric amplifiers, whose modes fulfill a spatial modal orthogonality. In particular, the generalized polarization degree of coherent, squeezed and Schrödinger’s cat states is analyzed.     

Design of polarization-independent optical couplers composed of three parallel slot waveguides

The characteristics of directional couplers and power splitters based on three-guide optical couplers in slot waveguide structures are analyzed in detail by a three-dimensional full-vectorial beam propagation method. The numerical results show the achievement of a compact three-guide directional coupler operating as polarization independent with a length of 58.0 microm and having almost evenly spaced propagation constants of the three lowest order modes for quasi-TE and quasi-TM modes. Thus, a high coupling efficiency from one outside waveguide to the other outside waveguide is demonstrated and is over 99.5% for both polarization states. For a three-guide power splitter, multiple sets of waveguide parameters for achieving polarization-independent operation are presented. Tolerances to operating wavelength and structural parameters are also analyzed, and the evolution of the injected field along the propagation distance through the proposed devices is demonstrated.     

Information Transfer with Two-state Two-particle Quantum Systems

Abstract

Any future quantum information machine will contain unitary operators and entangled particle states. The Hilbert space describing the action of the quantum information machine separates into a bosonic and a fermionic sector. Because the bosonic sector is of higher dimension, it is always possible to encode more information into a multiboson state than into a multifermion state, given the same complexity, that is unitary representation, of the quantum information machine. This is explicitly studied for the case of two particles defined in two modes. There the beam splitter is a generic representation of any U(2) matrix, and it has recently been shown that one can realize any N-dimensional unitary operator by successive application of such two-dimensional operators. The two-boson two-mode Hilbert space is of dimension three, and thus one can encode log₂3 = 1·57 bits of information into such an entangled state. Finally, some explicit schemes for creating and detecting the three possible, two-photon, two-mode states spanning the bosonic Bell basis are given.     

Novel approach for design of low index contrast multimode interference devices

Self-imaging theory is widely accepted as a good method in designing multimode interference (MMI) couplers, but it is also true that self-imaging theory is not suitable for low-contrast structures. An improved self-imaging theory is proposed in this paper for the optimal design of low-contrast 1 × N MMI couplers. The average effective width of the MMI waveguide and the average effective propagation constant of the MMI waveguide are used in the improved self-imaging theory. An approach is given to find the average effective width. We use this approach in the optimal design of a 1?×?4 silica MMI coupler, and the results show that the improved self-imaging theory is more accurate than conventional self-imaging theory for low-contrast structures.     

Coupling in Optical Fibres Determined by Improved Variational Approximation

Abstract

Analysis of optical fibre directional couplers is made much more accurate by the application of a new improved approximation. By adding another parameter to the modified Gaussian approximation, we are able to quantify optical fibre directional couplers covering the whole single-mode range in a simple and very accurate way.     

PHOTONIC MATERIALS AND DEVICES Progress in relating rare-earth ion 4f and 5d energy levels to host bands in optical materials for hole burning,quantum information and phosphors

Rare-earth ions play an important role in modern technology as optically active elements in solid-state luminescent materials. In many of these materials, interactions between the electronic band states of the host crystal and the rare-earth ion's localized 4f ^N and 4f ^N?1 5d states influence the material's optical properties. The importance of these interactions is discussed for material applications in photon-gated hole burning, quantum information and phosphors. Material dependent trends in the relative binding energies of the 4f ^N states and the host bands have been observed and are summarized. An empirical model for the ion dependence of the 4f electron binding energies is formulated in terms of atomic number and compared with previous models. These models are extended to describe the 4f ^N?1 5d states with one additional parameter. Improved estimates for the free-ion ionization potentials used in the model are also presented and discussed.     

n-Fold Polarization Measures and Associated Thermodynamic Entropy of N Partially Coherent Pencils of Radiation

An n-fold (n=2,…,N) measure of the degree of polarization associated with an N×N coherency matrix characterizing N pencils of radiation is discussed. The measure is cast in terms of the N possible scalar invariants of the coherency matrix and automatically takes into account possible rank deficiency. When N = 2, the single polarization measure reduces to the usual expression for polarization as the fraction of the intensity contained in the polarized component. The N = 3 case is discussed as an illustrative example, with special reference to the rank deficiency of a plane wave arbitrarily oriented with respect to the given coordinate system. Finally, these results are used to redevelop von Laue's theory of the thermodynamic entropy of partially coherent pencils of radiation.     

d-Dimensional quantum secret sharing without entanglement

A d-dimensional quantum state secret sharing scheme without entanglement is proposed. In the proposed scheme, the dealer generates a single quantum state in d-dimensional Hilbert space, and performs the Pauli unitary operation on the quantum state according to the private keys of the participants. In the recovery phase, each participant performs the Pauli operation on the quantum state according to his private key, and the last participant will recover the original quantum state. Compared to the existing quantum secret sharing schemes, the main contribution of the proposed scheme is that the quantum state can be shared without the entanglement, so the sharing of the quantum state is more practical.     

Fabry-Perot method for the characterization of integrated optical directional couplers

A method to measure the loss and the power-transfer ratio of directional couplers is presented. It is based on the Fabry-Perot resonances from end-facet reflections. The dependence of the accuracy of the measurements on the facet tilts is described. For low facet misalignments, an uncertainty <0.3 dB in the loss measurements and power-transfer-ratio measurement errors <1% are obtained. For arbitrary facet tilts the errors depend on the extinction ratios. Experimental measurements are reported to verify the method, and its application to multimode interference couplers is shown.     

Higher-generation Schrödinger cat states in cavity QED

Abstract

Higher-generation Schrödinger cat states of the quantized electromagnetic field can be produced in a high-Q cavity, starting from a coherent state, through the passage of prepared Rydberg atoms interacting dispersively across it. These states are natural generalizations of the even and odd coherent states, the N ^th-generations corresponding to specific superpositions of 2 ^N states on a circle in phase space with well defined parity, and present very peculiar properties. Their photon statistics interchange between super- and sub-Poissonian behaviours and the nature of the photon bunching oscillates as the field intensity in the cavity is varied. For higher-generation even states, the minimum value of the Mandel factor almost reaches ?1.0 and the state represents the Fock state |2 ^N ). Squeezing properties and the Wigner function of these higher-generation Schrödinger cat states are also considered.     

Multimode Coherent States and HeNe Laser Light

Abstract

Among the quantum optical states of a tremolant optical cavity are multimode coherent states. Such states are also possible in open cavities where the cavity stabilization time is greater than the multimode beat time. In open cavity resonator lasers they reduce the power limiting effects of spectral hole burning and therefore tend to grow at the expense of single mode coherent states.     

Modal dynamics in multimode fibers

The dynamics of modes and their states of polarizations in multimode fibers as a function of time, space, and wavelength are experimentally and theoretically investigated. The results reveal that the states of polarizations are displaced in Poincaré sphere representation when varying the angular orientations of the polarization at the incident light. Such displacements, which complicate the interpretation of the results, are overcome by resorting to modified Poincaré sphere representation. With such modification it should be possible to predict the output modes and their state of polarization when the input mode and state of polarization are known.     

A Müller-Stokes Description of Polarization-mode Transformation in Uniformly Perturbed Optical Fibres

Abstract

On the basis of coupled-mode equations Müller matrices describing the polarization-mode transformation of twofold and fourfold degenerate LP-modes in the quasi-monochromatic case have been derived. Single-mode, two-mode and multimode regimes of operation have been studied. Improved polarization holding in W-type elliptical-core multimode optical fibres has been observed. It has been shown that the LP₁₁ mode cut-off wavelength λ_C can be determined by measuring the wavelength dependence of the relative cross-coupled power.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

Passive single-mode fiber depolarizer

We analyze and demonstrate a passive single-mode fiber depolarizer by using cascaded 2 x 2 couplers, recirculating delay lines, and a commercial laser diode. Design criteria and principles are discussed. We reduced the degree of polarization (DOP) to less than 20 dB by using ten cascaded couplers. The DOP can be reduced even further with more couplers. Experiments illustrate that this depolarizer is insensitive to the input polarization state and can eliminate polarization noise in a polarization-sensitive fiber-optic system.     

Subpixel Speckle Displacement Measurement Using a Digital Processing Technique

Abstract

This paper deals with the optical measurement of deformations and displacements of diffusing rough surfaces using changes in the speckle pattern obtained by laser illumination. A digitized speckle signal is obtained using a linear charge-coupled device photodetector that produces samples of one-dimensional signals of N pixels. A sequential numerical processing procedure is applied to detect the relative displacement of two speckle signals, corresponding to two different states of the surface; the accuracy is better than one micrometre. The principles of the method and the corresponding algorithms are described. Experimental results are given and these include an analysis of the deformation of video structure under directional traction.     

Polarization dependence of the coupling ratio in LiTaO3 directional couplers

The effect of design and fabrication parameters on the polarization dependence of the splitting ratio in directional couplers produced in LiTaO3 by Zn diffusion has been investigated experimentally at a wavelength of 1558 nm. The directional couplers featured various combinations of waveguide width, separation gaps between waveguides, bending angle, and diffusion conditions. In each case the coupling region was 3.5 mm long. Of particular interest was the identification of parameter sets for which the sum of power splitting ratios from TE and TM inputs equals unity at the output, as needed for electro-optic tunable filters with relaxed beam-splitter requirements.     

Space charge limited conduction and determination of density of localised states in semiconductor cobalt doped TiO2

Abstract

The space charge limited conduction (SCLC) mechanism in Co doped TiO₂ has been investigated at different temperatures. At lower electric fields, ohmic behaviour is observed while at higher electric fields nonohmic behaviour is observed. The results obtained confirm the presence of SCLC in Co doped TiO₂. The electronic parameters such as the position of the Fermi level above the valence band edge E _F, the density of states in valence band N _V and effective mass of holes m _h were found as 12·32 meV, 1·26 × 10¹⁵ m^?3 and 1·33 × 10^?7 m_e, respectively. The distribution of localised states in the forbidden band gap of the Co doped TiO₂ was characterised by current–voltage measurements and the density of localised states near the Fermi level N(E_F) was found to be 2·11 × 10¹⁷ eV^?1 m^?3.     

Toward Special-Relativity-on-a-Chip: analogue of Einstein velocity addition using optical add-drop filter (OADF)

We present an optical analogue of a central concept (not a specific relativistic effect) in Special Relativity (SR) that underlies many relativistic effects. This concept is the Einstein Velocity Addition (EVA) which plays a fundamental role in the development of SR. The photonic circuit analogue is between the EVA, and the complex electric field, through the output signal of the optical add-drop filter (OADF). The OADF is one of the key building blocks for wavelength filtering in photonic integrated circuits (PICs or photonic chip). This analogue strengthens the vision toward a Special-Relativity-on-a-Chip. The analogy is established by equating the two relativistic normalized velocities in EVA with the two transmission coupling coefficients of the two directional couplers in the OADF. Furthermore, the generating angle in the EVA is associated with the single-pass phase shift of the OADF. We analyze its magnitude and directional angle in detail. Lastly, other important consequences are also briefly discussed.