Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Limits to squeezing in the degenerate optical parametric oscillator

We develop a systematic theory of quantum fluctuations in the driven optical parametric oscillator, including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction in this nonequilibrium quantum phase transition. In particular, we compute the squeezing spectrum near threshold and calculate the optimum value. We find that the optimal noise reduction occurs at different driving fields, depending on the ratio of damping rates. The largest spectral noise reductions are predicted to occur with a very high-Q second-harmonic cavity. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory.

Positive-P and Wigner representations for quantum-optical systems with nonorthogonal modes

We generalize the basic concepts of the positive-P and Wigner representations to unstable quantum-optical systems that are based on nonorthogonal quasimodes. This lays the foundation for a quantum description of such systems, such as, for example an unstable cavity laser. We compare both representations by calculating the tunneling times for an unstable resonator optical parametric oscillator.

Separating the quantum sidebands of an optical field

In this paper we investigate the quantum optics of a double-ended optical cavity. We show that an impedance matched, far-detuned cavity can be used to separate the positive and negative sidebands of a field. The 'missing' sideband will be replaced by the equivalent sideband incident on the cavity from the other direction. This technique can be used to convert the quantum correlations between the sidebands of the incident fields into quantum correlations between the two spatially distinct output fields. We show that, under certain experimental conditions, the fields emerging from the cavity will display entanglement.

Optical barcoding of colloidal suspensions: applications in genomics, proteomics and drug discovery

The enormous amount of information generated through sequencing of the human genome has increased demands for more economical and flexible alternatives in genomics, proteomics and drug discovery. Many companies and institutions have recognised the potential of increasing the size and complexity of chemical libraries by producing large chemical libraries on colloidal support beads. Since colloid-based compounds in a suspension are randomly located, an encoding system such as optical barcoding is required to permit rapid elucidation of the compound structures. We describe in this article innovative methods for optical barcoding of colloids for use as support beads in both combinatorial and non-combinatorial libraries. We focus in particular on the difficult problem of barcoding extremely large libraries, which if solved, will transform the manner in which genomics, proteomics and drug discovery research is currently performed.

Absorption and dispersion by a multiple driven two-level atom

We investigate the absorption and dispersion properties of a two-level atom driven by a polychromatic field. The driving field is composed of a strong resonant (carrier) frequency component and a large number of symmetrically detuned sideband fields (modulators). A rapid increase in the absorption at the central frequency and the collapse of the response of the system from multiple frequencies to a single frequency are predicted to occur when the Rabi frequency of the modulating fields is equal to the Rabi frequency of the carrier field. These are manifestations of the undressing or a disentanglement of the atomic and driving field states, that leads to a collapse of the atom to its ground state. Our calculation permits consideration of the question of the undressing of the driven atom by a multiple-modulated field and the predicted spectra offer a method of observing undressing. Moreover, we find that the absorption and dispersion spectra split into multiplets whose structures depend on the Rabi frequency of the modulating fields. The spectral features can jump between different resonance frequencies by changing the Rabi frequency of the modulating fields or their initial phases, which can have potential applications as a quantum frequency filter.

Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays

We investigate the design of free-space optical interconnects (FSOIs) based on arrays of vertical-cavity surface-emitting lasers (VCSELs), microlenses, and photodetectors. We explain the effect of the modal structure of a multimodeVCSEL beam on the performance of a FSOI with microchannel architecture. A Gaussian-beam diffraction model is used in combination with the experimentally obtained spectrally resolved VCSEL beam profiles to determine the optical channel crosstalk and the signal-to-noise ratio (SNR) in the system. The dependence of the SNR on the feature parameters of a FSOI is investigated. We found that the presence of higher-order modes reduces the SNR and the maximum feasible interconnect distance. We also found that the positioning of a VCSEL array relative to the transmitter microlens has a significant impact on the SNR and the maximum feasible interconnect distance. Our analysis shows that the departure from the traditional confocal system yields several advantages including the extended interconnect distance and/or improved SNR. The results show that FSOIs based on multimode VCSELs can be efficiently utilized in both chip-level and board-level interconnects. (C) 2002 Optical Society of America.

The absorption and excretion of fluoride and arsenic in humans

The absorption and excretion of fluoride and arsenic were measured in a group of healthy volunteers given drinking water with naturally high concentration of fluoride (F 2.3 mg/l), or high concentration of arsenic (As 0.15 mg/l), or high concentrations of both fluoride and arsenic (F 2.25 mg/l, As 0.23 mg/l and F 4.05 mg/l, As 0.58 mg/l), respectively. The results indicated that, for arsenic, the absorption rate, the proportion of urinary excretion and the biological-half-life did not show statistically significant differences between drinking water containing high arsenic alone and drinking water containing different levels of high arsenic and fluoride. Excretion and retention of arsenic were positively correlated to the total arsenic intake. Similar results were observed for fluoride. This suggests that there are different metabolic processes for arsenic and fluoride in respect to absorption and excretion; and no joint action can be attributed by these two elements. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Mechanisms for the inhibition of amiloride-sensitive Na+ absorption by extracellular nucleotides in mouse trachea

Purinergic stimulation of airway epithelial cells induces Cl- secretion and modulates Na+ absorption by an unknown mechanism. To gain insight into this mechanism, we used a perfused micro-Ussing chamber to assess transepithelial voltage (V-te) and amiloride-sensitive short-circuit current (Isc-Amil) in mouse trachea. Exposure to apical ATP or UTP (each 100 mumol/l) caused a large initial increase in lumen negative V-te and I-sc corresponding to a transient Cl- secretion, while basolateral application of ATP/UTP induced only a small secretory response. Luminal, but not basolateral, application of nucleotides was followed by a sustained and reversible inhibition of Isc-Amil that was independent of extracellular Ca2+ or activation of protein kinase C and was not induced by carbachol (100 mumol/l) or the Ca2+ ionophore ionomycin (1 mumol/l). Removal of extracellular Cl- or exposure to 200 muM DIDS reduced UTP-mediated inhibition of Isc-Amil Substantially. The phospholipase inhibitor U73122 (10 mumol/l) and pertussis toxin (PTX 200 ng/ml) both attenuated UTP-induced Cl- secretion and inhibition of Isc-Amil. Taken together, these data imply a contribution of Cl- conductance and PTX-sensitive G proteins to nucleotide-dependent inhibition of the amiloride-sensitive Na+ current in the mouse trachea.

Modeling diffraction in free-space optical interconnects by the mode expansion method

Free-space optical interconnects (FSOIs), made up of dense arrays of vertical-cavity surface-emitting lasers, photodetectors and microlenses can be used for implementing high-speed and high-density communication links, and hence replace the inferior electrical interconnects. A major concern in the design of FSOIs is minimization of the optical channel cross talk arising from laser beam diffraction. In this article we introduce modifications to the mode expansion method of Tanaka et al. [IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972)] to make it an efficient tool for modelling and design of FSOIs in the presence of diffraction. We demonstrate that our modified mode expansion method has accuracy similar to the exact solution of the Huygens-Kirchhoff diffraction integral in cases of both weak and strong beam clipping, and that it is much more accurate than the existing approximations. The strength of the method is twofold: first, it is applicable in the region of pronounced diffraction (strong beam clipping) where all other approximations fail and, second, unlike the exact-solution method, it can be efficiently used for modelling diffraction on multiple apertures. These features make the mode expansion method useful for design and optimization of free-space architectures containing multiple optical elements inclusive of optical interconnects and optical clock distribution systems. (C) 2003 Optical Society of America.

Bovine-serum-albumin-containing receptor phase better predicts transdermal absorption parameters for lipophilic compounds

Based on the hypothesis that limited receptor solubility of lipophilic compounds may result in lower observed permeability parameters, the aim of this study was to determine the in vitro human epidermal permeability coefficients and membrane retention of a series of aliphatic alcohols (C1-C10, log p -0.72 to 4.06) using two different receptor solutions (water and 4% bovine serum albumin in phosphate-buffered saline). Aqueous solutions of radiolabeled alcohols were dosed into the stratum corneum side of membranes mounted in side-by-side glass diffusion cells. Appearance of alcohol in the receptor compartment filled with either of the two solutions was monitored over a 7 h period when both stratum corneum (assessed by tape stripping) and the remaining epidermis levels of radioactivity were determined. In a separate study the degree of binding of alcohols to 4% bovine serum albumin was determined. The data showed increased receptor phase solubility in the bovine serum albumin solution and higher permeability coefficients for the more lipophilic alcohols in the series. No changes were seen in the partitioning of the alcohols from the vehicle into either the stratum corneum or tape-stripped epidermis with the two receptor phases; however, a decrease in the amount of the more lipophilic alcohols partitioning into the water receptor phase from the tape-stripped epidermis was observed. We conclude that bovine serum albumin receptor phase allows better estimation of real permeability parameters for lipophilic compounds due to its increased solubility capacity and we question whether permeability parameters for lipophilic solutes from older data sets based on aqueous receptor phases are completely reliable.

Ultrasonic absorption in polymer gel dosimeters

Ultrasonic absorption in polymer gel dosimeters was investigated. An ultrasonic interferometer was used to study the frequency (f) dependence of the absorption coefficient (alpha) in a polyacrylamide gel dosimeter (PAG) in the frequency range 5-20 MHz. The frequency dependence of ultrasonic absorption deviated from that of an ideal viscous fluid. The presence of relaxation mechanisms was evidenced by the frequency dependence of alpha/f(2) and the dispersion in ultrasonic velocity. It was concluded that absorption in polymer gel dosimeters is due to a number of relaxation processes which may include polymer-solvent interactions as well as relaxation due to motion of polymer side groups. The dependence of ultrasonic absorption on absorbed dose and formulation was also investigated in polymer gel dosimeters as a function of pH and chemical composition. Changes in dosimeter pH and chemical composition resulted in a variation in ultrasonic dose response curves. The observed dependence on pH was considered to be due to pH induced modifications in the radiation yield while changes in chemical composition resulted in differences in polymerisation kinetics. (C) 2003 Elsevier B.V. All rights reserved.

Optical experiments beyond the quantum limit: Squeezing entanglement and teleportation

Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.

Anomalous water absorption in porous materials

The absorption of fluid by unsaturated, rigid porous materials may be characterized by the sorptivity. This is a simple parameter to determine and is increasingly being used as a measure of a material's resistance to exposure to fluids (especially moisture and reactive solutes) in aggressive environments. The complete isothermal absorption process is described by a nonlinear diffusion equation, with the hydraulic diffusivity being a strongly nonlinear function of the degree of saturation of the material. This diffusivity can be estimated from the sorptivity test. In a typical test the cumulative absorption is proportional to the square root of time. However, a number of researchers have observed deviation from this behaviour when the infiltrating fluid is water and there is some potential for chemo-mechanical interaction with the material. In that case the current interpretation of the test and estimation of the hydraulic diffusivity is no longer appropriate. Kuntz and Lavallee (2001) discuss the anomalous behaviour and propose a non-Darcian model as a more appropriate physical description. We present an alternative Darcian explanation and theory that retrieves the earlier advantages of the simple sorptivity test in providing parametric information about the material's hydraulic properties and allowing simple predictive formulae for the wetting profile to be generated.