Polarization insensitive linear intensity modulation in a Sagnac fiber-optic loop with an electro-optic cell and optoelectronic feedback

We present a modulation scheme consisting of a fiber-optic Sagnac interferometer, which has an electro-optic modulator (Pockels cell) in the loop of the interferometer. In order to diminish the nonlinearity of the Sagnac interferometer transmittance function, we monitor a very small part of the output light intensity by means of a photodiode and then amplify this signal by a constant factor ξ. This amplified signal is added to the electrical modulating signal that is being applied to the electro-optical modulator. The consequence of introducing this feedback loop is that by properly choosing the amplifying factor ξ, we can increase the linearity of the modulation. The device is insensitive to the polarization state of the input light, so it should be used for intensity modulation of nonpolarized light with up to 100% modulation depth. The theoretical and experimental examination of the device is presented.     

‘Best-case’ noise performance of feedback interferometers, potential for micromachine applications

We present a theoretical analysis of the noise performance of phase measuring feedback interferometers. We first analyse the operation of this kind of instrument and note that under certain circumstances bistability can occur. The bistable region should be avoided if possible when using feedback interferometry for high-accuracy measurement with low-input powers, as it can give rise to very high-noise levels. We then go on to investigate the effects of shot noise (on the interferometer output signal) and thermal noise (in the feedback loop), and relate these to the phase measurement accuracy of the interferometer. A ‘best-case’ calculation indicates that phase noise of about 0.005λ is possible at input powers in the nanowatt region. In practice, we expect that noise levels will be higher than predicted (particularly at high-input powers) due to the effects of vibration and air turbulence.     

Active Phase-Shifting Interferometer Using Current Modulation of a Laser Diode

An active phase-shifting interferometer using current modulation of a laser diode is proposed. Fringe movement in the instrument is detected by a spatial filtering detector whose output is fed back to the injection current of the laser diode to lock the fringes and shift them correctly for phase shifting analysis. Frequency modulation characteristics of the laser diode and frequency response of the feedback system are first investigated. We constructed a portable interferometer head set apart from a mirror under test then measured the shape of a spherical mirror 130 mm in diameter, which was placed on a wooden table subject to vibration. Measurement repeatability of λ/35 was achieved.     

Frequency, field, and temperature dependence of the AC penetration depth of a GdBa2Cu3O7−δ film in the mixed state

We report on a systematic mutual induction measurement of the complex AC penetration depth λ of a sputtered high-quality GdBa₂Cu₃O_7−δ film in the mixed state by a very small coil system arranged near the sample surface. The complex penetration depth λ(B, T, ω) for DC inductions B 0.65 T (perpendicular to the film), for temperatures 36 K T 81 K, and for frequencies 1 kHz ω/2π 500 kHz was determined from the measured signal by a novel inversion scheme. The results are consistent with theoretical predictions based upon single vortex pinning. The Labusch parameter , the flux creep relaxation time τ, as well as the effective activation energy U are simulateneously determined.     

Determination of the optical constants of metals and semiconductors by combining ellipsometry with electron spectroscopy microscopy and X-ray specular reflection analysis

The optical constants n(λ) and k(λ) of metals and semiconductors can be determined by spectroellipsometry, however, their apparent values are considerably affected by the roughness and oxide overlayer thickness dof the sample. Aluminium thin film samples of high perfection and very low roughness (<1 nm) have been studied by cross-disciplinary experimental methods: X-ray specular reflection analysis for determining the structure and thickness of the natural (hydrated) oxide overlayer and roughness of the substrate; plasmon electron energy loss spectroscopy supplied d. For calibration of the d measurements a special thin film multilayer system was developed, suitable for preparing cross-sectional samples for resolution transmission electron microscopy. Knowing the roughness and d-data, the optical constants n(λ) and k(λ) of aluminium were determined by spectroellipsometry in the spectral range λ=365–633 nm. Experimental results and a nomogram are presented for evaluating n(λ) and k(λ). The dependence of the ellipsometric optical constants on roughness and d is discussed. Very good agreement of the optical constants with the corrected ellipsometric results of Blanco and the synchrotron spectroscopy data of Hagemann was found. The cross-disciplinary methods can be applied to metals and semiconductors covered with an overlayer.     

Upper bound on all products of R-parity violating couplings λ′ and λ″ from proton decay

We prove that any product of R-parity violating couplings λ′ (L-violating) and λ″ (B-violating) can be strongly restricted by proton decay data. For any pair λ′ and λ″ the decay exists at least at one loop level. For squark masses below 1 TeV we find the conservative bounds |λ′ · λ″| < 10⁻⁹ in absence of squark flavor mixing, and |λ′ · λ″| < 10⁻¹¹ when this mixing is taken into account. We study the dependence of the bounds on the flavor basis in which R-parity breaking couplings are determined.     

A practical depth distribution function for angle-resolved Auger/photoelectron spectroscopy

It is shown that, to a good approximation, over the range of energies (single scattering albedo, ω 0.5) and angles (take-off angle >30°) used in angle-resolved AES and XPS spectroscopy, the depth distribution function (DDF) is approximately exponential with decay length Λ = λ_i(1 + λ_i/λ_tr)^−1/2, for inelastic mean free path (IMFP) λ_i, and transport mean free path λ_tr.

As Λ is also the length measured for the attenuation length experimentally (with either the overlayer technique or from backscatter spectra, equivalent to λ_i, using an interpretation which neglects elastic effects), the CDP may be obtained by straightforward Laplace inversion using experimentally determined attenuation lengths. That is, the correct composition depth profile may be obtained from systematically ignoring elastic scattering.     

Transitive and quasitransitive actions of affine groups preserving a generalized Lorentz-structure

Let Aⁿ be the n-dimensional affine space over and A (n) its groups of motions. The map λ:A (n) → GL_n( ) associates to an affine motion its linear part. In the first part of the paper we prove that any subgroup Й A (n) which acts discontinously with compact quotient on Aⁿ and which has the property that λ(Й) is contained in a Lie group of rank 1 is polycyclic by finite. The second part of the paper classifies such groups which satisfy λ(Й) 0 (n - 1, 1) up to commensurability.     

Study of in fiber Mach–Zehnder interferometer based on two spaced 3-dB long period gratings surrounded by a refractive index higher than that of silica

The paper deals with the response of a Mach–Zehnder interferometer composed by two 3-dB long period gratings (LPG) with different external refractive indices higher than that of silica (leaky configuration). A rough analysis of the cladding propagation arising in leaky configuration has allowed us to establish a model that is sufficient to describe the interferometer couplings evolution at the resonance. In particular, we have shown that the interferometer sensitivity depends strongly on its phase-shift Δ and is optimized for Δ equal to π [2π] or 3π/4 [2π]. An experimental study was undertaken and allowed us to validate our model. Finally, a comparison with a single LPG demonstrated an increased sensitivity to the external index, suggesting the conception of a new fiber sensor operating with external refractive indices higher than that of silica.     

Vortex penetration depth of κ-(ET)2Cu[N(CN)2]Br

The magnetic field dependence of the in-plane penetration depth λ_|(H) for single crystal κ-(ET)₂Cu[N(CN)₂]Br has been measured at 3, 9.6, and 36 MHz. Over a limited range, λ_| scales with a characteristic field H^*(T) that coincides with a shoulder in the λ_| vs. H curves. Above that field, λ_| increases sharply toward a second inflection point at H^**(T) that coincides with is close to the irreversibility line measured by magnetization. For fields larger than H^** the penetration depth diverges, suggesting that the vortex lattice has melted. The field dependence at one frequency agrees qualitatively with a model of pinned vortices at low fields giving way to flux flow at higher fields. However, the observed frequency dependence deviates significantly from the predictions of this model, suggesting that collective effects play a major role. Our technique also yields a new measurement for the interplane penetration depth λ 300 μm, implying an anisotropy λ/λ_| > 200.     

Determination of optical properties of aluminium including electron reradiation in the Lorentz-Drude model

The effect of electron reradiation was included in the Lorentz-Drude (LD) model and by applying the least-squares fitting method the values of the characteristic parameters (ω_p, Г, τ) of electrons in aluminium were determined. The values of these parameters allowed the determination of optical properties of aluminium for light of wavelengths λ[43.5 nm, 200 μm]. By including the reradiation of electrons the precision of the LD model has been increased in the infra-red region of wavelengths λ[1 μm, 200 μm]. In addition, the reradiation of electrons gives the square frequency dependence for damping frequency [Г′(ω) = Г +τω²], enabling the suitable application of the LD model in the broad range of wavelengths λ[43.5 nm, 200 μm]. It was estimated that the short wave limit at which the LD model can be used for aluminium occurs at about λ_min = 43.5 nm.     

Polarization instability in lasers with weakly anisotropic cavities

A theoretical study is made of the influence of the active medium and the cavity parameters, as well as that of an external magnetic field, on the properties of spontaneous pulsation regimes of lasers with weakly anisotropic cavities. Our results provide a physical interpretation of recently reported experimental data for spontaneous intensity pulsations of orthogonal components of the electromagnetic field generated by a single-mode, Fabry-Perot, HeNe gas laser at λ = 3.3922 μm and by a HeXe laser at λ = 3.51 μm.     

The temperature dependence of the short wavelength transmittance limit of vacuum ultraviolet window materials—I. Experiment

The short wavelength transmittance limit or cut-off wavelength, λ_co, of LiF, MgF₂, CaF₂, LaF₃, BaF₂, sapphire, synthetic crystal quartz and fused quartz has been measured from about 100°C to about 10°K. λ_co is not a well denned quantity, so for the purpose of this experiment it has been arbitrarily taken as the wavelength where transmittance could just be measured, usually 0.1-0.5 per cent. With one exception λ_co shifted to shorter wavelengths as the sample was cooled; the shift varied from about 40 to 80 Å over the temperature range from 100°C to 10°K, depending on the material, with the largest shift occurring in BaF₂;. The exception was LaF₃ which showed no measurable change in λ_co wth temperature. Over the temperature range from 20° to 100°C the slope of λ_co, with temperature for all materials was fairly constant, but below 20°C it decreased, approaching zero as the temperature approached 20°-10°K. In the case of synthetic crystal quartz, for example, the slope changed from about 0.28 Å/°K at room temperature to about 0.055 Å/°K at 80°K.     

Outer curvature and conformal geometry of an imbedding

The differential geometry of an imbedded (e.g. string or membrane world sheet) surface in a higher-dimensional background is shown to be conveniently describable (except in the null limit case) in terms of what are designated as its first, second, and third fundamental tensors, which will have the respective symmetry properties η_μν = η_(μν) as a trivial algebraic identity, K_μν^ρ = K_(μν)^ρ as the “generalised Weingarten identity”, which is the (Frobenius type) integrability condition for the imbedding, and Ξ_λμν^ρ = Ξ_(λμν)^ρ as a “generalised Codazzi equation”, which depends on the background geometry being flat or of constant curvature, needing replacement by a more complicated expression for a generic value of the background curvature B_κλ^μ_ν. The “generalised Gauss equation” expressing the dependence on this background curvature of the internal curvature tensor R_κλ^μ_ν of the imbedded surface is converted into terms of the first and second fundamental tensors, and it is thereby demonstrated that the vanishing of the (conformally invariant) “conformation tensor”, i.e. the trace free part C_μν^ρ of the second fundamental tensor K_μv^ρ, is a sufficient condition for conformal flatness of the imbedded surface (and thus in particular for the vanishing of its (Weyl type) conformal curvature tensor C_κλ^μ_ν) provided the background is itself conformally flat. In a trio of which the first two members are the generalised Gauss and Codazzi equations, the “third” member is shown to give an expression in terms of C_μν^ρ for the (trace free, conformally invariant) “outer curvature” tensor Ω_κλ^μ_ν whose vanishing is the condition for feasibility of the natural generalisation of the Walker frame transportation ansatz. The vanishing of C_μν^ρ is shown to be sufficient in a conformally flat background for the vanishing also of Ω_κλ^μ_ν.     

Distortion of optical feedback signals in microchip Nd:YAG lasers subjected to external multi-beam interference feedback

This paper proposes a theoretical analysis for the characteristics of an external cavity Nd:YAG laser with feedback of multiple-beam interference, which is induced by the multi-reentrance of the light from the external Fabry--Perot cavity. The theoretical model considers the multiple beam interference of the external Fabry--Perot cavity. It is found that the optical feedback signals are distorted to pulse waveforms instead of the sinusoidal ones in conventional feedback. The experimental results are in good agreement with the theoretical analysis. The obtained theoretical and experimental results can advance the development of a laser feedback interferometer.     

Spontaneous breaking of scale invariance in a supersymmetric model

The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ₀=λ_c=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ₀ leaves these Goldstone particles massless.     

Electronic structure of quantum spheres and quantum wires

The electronic structures of quantum spheres and quantum wires are studied in the framework of the effective-mass theory. The spin-orbital coupling (SOC) effect is taken into account. On the basis of the zero SOC limit and strong SOC limit the hole quantum energy levels as functions of SOC parameter λ are obtained. There is a fan region in which the ground and low-lying excited states approach those in the strong SOC limit as λ increases. Besides, some theoretical results on the corrugated superlattices (CSL) are given.     

Estimation of cut-off wavelength of rare earth doped single-mode fibers

A new empirical relation is proposed describing spectral variation of mode-field radius (MFR) as inferred from measurements in the far-field of the fiber. It is shown that using this relation, it is possible to estimate the cut-off wavelength (λ_c) of the fiber. The proposed technique is successfully tested through measurements made on two standard step index single-mode fibers, as well as on an erbium doped fiber (EDF) having λ_c falling within its strong absorption band around 980 nm. This empirical formula is more accurate than the widely used Marcuse's formula to describe spectral dependence of MFR determined through measurements made in the fiber's far-field. The proposed technique is especially suited for estimation of λ_c of doped fibers in which λ_c falls within an absorption band.     

Optimizing the bandwidth and noise performance of distributed multi-pump Raman amplifiers

Based on hybrid genetic algorithm (HGA), the signal bandwidth of the distributed multi-pump Raman amplifiers is optimized, and the corresponding noise figure is obtained. The results show that: (1) the optimal signal bandwidth Δλ decreases with the increase of the span length L, e.g., Δλ is 79.6 nm for L=50 km and 41.5 nm for L=100 km under our simulated conditions; (2) the relationship between Δλ and L is approximately linear; (3) the equivalent noise figure can be negative and increases with the extension of L; (4) there are one or several global maximum signal bandwidth on the determinate conditions; (5) to realize the fixed Δλ, several candidates can be obtained by means of HGA, as has important applications on the design of distributed multi-pump Raman amplifiers in practice.