Temperature induced nonlinearity in coupled microresonators

We present here, our most recent results from theoretical and experimental investigations of optical properties of coupled microresonators. While fused silica spherical microresonators with Q-factors of about 10⁷ to 10⁸ can be quite easily fabricated, the production of a number of equally sized spheres, which appears to be a necessary condition for effective light coupling, has proved challenging. In order to bypass this problem we focus our attention on the investigation of coupled disk microresonators made of fused silica. These may be fabricated in almost arbitrary two-dimensional configuration with nanometer precision. A Q-factor of 10⁵ can be routinely achieved, which relaxes the requirements on uniformity of the microdisks to within the range of fabrication accuracy. The achieved Q-factors are high enough to observe thermal nonlinear effects in the fabricated coupled disks. A detailed experimental analysis of the thermal nonlinear resonance behavior in a system of two coupled microdisks now follows. The results were found to be in good agreement with the respective calculations based on coupled mode theory including temperature induced nonlinear response.     

Optical third-harmonic generation in coupled microcavities based on porous silicon

The resonance features of the third-harmonic generation have been observed in 1D coupled microcavities consisting of three Bragg reflectors and two identical half-wave layers of mesoporous silicon. The third-harmonic intensity increases by a factor of about 10³ in the resonance of fundamental radiation with each of the modes of coupled microcavities. It has been shown that the resonance positions in the angular spectra of the third-harmonic intensity depend on the coupling between microcavities that is determined by the transmission of the intermediate Bragg reflector. In the framework of the transfer-matrix method with nonlinear sources, it has been shown that the basic mechanism of the enhancement of the third-harmonic generation in coupled microcavities based on porous silicon is the constructive interference of the partial third-harmonic waves that are generated by near-surface layers.     

Noise induced intercellular propagation of calcium waves

In this paper, we investigate the spatiotemporal dynamics of a bidirectional coupled chain of cells, in which a cell is subjected to an external noise. Noisy oscillations of calcium (Ca²⁺), that is, a bursting-like phenomenon induced by noise with fluctuations in the baseline values of calcium, are induced in the first cell and propagated along the chain with noise suppression. This phenomenon of noise suppression is further investigated by computing the normalized fluctuation of pulse durations. It is therefore found that the noise induced coherence resonance phenomenon occurs at the cellular level. Coherence biresonance behaviour appears in the transmission of noise induced oscillations at appropriate noise intensity or noise coupling (for low noise intensity) and the information flow in each cell can be simultaneously optimized at the optimal value of noise or coupling.     

Coupled whistler and ion-acoustic mode propagation in two-electron-temperature plasmas

The nonlinear coupling between whistler and ion-acoustic modes in a plasma having bi-Maxwellian distributed electrons is considered. For stationary propagation, the coupled waves lead to a novel nonlinear structure which has a triple-hump profile for the whistler field intensity. In the critical parameter regime (Δ = 3), only supersonic propagation of the coupled modes is allowed. In other regimes, three integrable cases of the coupled mode propagation have been identified.     

两个非平行波导间的能量转换

提出一种分析非平行波导间耦合的简明方法-耦合系数推广法.利用这种方法,导出一种新的非平行双波导的耦合方程,由此得到一组非平行波导耦合的完美的分析解,依据这些分析解可以优化非平行波导的传输距离、输入／输出端口波导间距和夹角.     

The analysis of stochastic resonance and bearing fault detection based on linear coupled bistable system under lévy noise

In this paper, the stochastic resonance (SR) phenomenon of the linear coupled bistable system induced by Lévy noise is analyzed. Meanwhile, the characteristics of Lévy noise is also analyzed according to its probability density functions (PDFs) of different stability index α, symmetry parameter β, scale parameter σ and location index μ. The mean of signal-noise ratio increase (MSNRI) is regarded as an index to measure the SR phenomenon. Then, the rules for MSNRI affected by noise intensity D are explored under different charastic indexes of Lévy noise, system parameters a, b, c and coupling coefficient r. The results are beneficial to the numerical simulation of single-frequency and multi-frequency weak signals detection based on single bistable system and linear coupled system respectively. It is found that the performance of the proposed system is better than single bistable system and results of bearing fault detection could also verify the conclusion.     

Design of two kinds of dual-core high birefringence and high coupling degree photonic crystal fibers

We propose two kinds of dual-core high birefringence and high coupling degree photonic crystal fibers (DHBHCD-PCFs) in this paper. The characteristics of birefringence and coupling are studied by multipole method. Numerical results show that the birefringence and the coupling length reach an order of 10^− 2 and 10^− 5 m at 1.55 μm, respectively. It is found that the birefringence and the coupling intensity increase with the increase of air-filling fraction, which is different from other dual-core fibers. The DHBHCD-PCFs with high degree of polarization-maintaining and high coupling degree are helpful for manufacturing minitype photonic apparatus.     

Field coupling-induced synchronization via a capacitor and inductor

Resistor-based voltage coupling is often used to realize complete synchronization between identical nonlinear circuits while phase synchronization is investigated between non-identical nonlinear circuits (periodic or chaotic oscillation). Indeed, the coupling resistor used to consume certain Joule heat and energy before reaching the synchronization target when continuous current passed across the coupling device. In this paper, capacitor and inductor is paralleled with one coupling resistor, respectively, and the coupling devices are used bridge connection between two LC hyperchaotic circuits for investigating synchronization problems. As a result, the coupling channel can be activated to propagate energy and balance the outputs voltage from the two circuits. The dimensionless dynamical equations are obtained by applying scale transformation on the circuit equations when field coupling is switched on. It is found that the threshold of coupling intensity for reaching synchronization and the power consumption of controller can be decreased when the coupling resistor is paralleled with on capacitor or inductor. The mechanism could be that involvement of coupling capacitor(or inductor) can trigger time-varying electric field (or magnetic field), and the energy flow of field coupling via coupling capacitor (or inductor) can contribute the exchange of energy in the coupled nonlinear circuits. It can give insights to investigate synchronization on chaotic systems, neural circuits and neural networks including synapse coupling and field coupling. Finally, the experimental results on circuits are also supplied for further verification.     

Single-shot reflection <Emphasis Type="Italic">Z</Emphasis>-scan for measurements of the nonlinear refraction of nontransparent materials

Extremely large optical Kerr non-linearities (n₂) and (n₄) were measured in two closed degenerate two-level transitions in the caesium D₂ line when a probe and a coupling laser simultaneously probed and coupled the hyperfine structure in an atomic beam. The magnitude of the measured non-linearities in both transitions were found to be a function of the coupling laser intensity and of the probe detuning from the two-photon resonance. In a figure of merit, the ratio between the non-unitarian part of the refractive index and the absorption coefficient measured in conditions of electromagnetically induced transparency showed a maximum value for a probe detuning of 160 kHz from the two-photon resonance and resulted in being 10⁵ times larger than in the absence of the coupling laser field. PACS 32.70.Jz; 42.50.Gy; 42.65-k     

A complicated Duffing oscillator in the surface-electrode ion trap

The oscillation coupling and different nonlinear effects are observed in a single trapped ⁴⁰Ca⁺ ion confined in our home-built surface-electrode trap (SET). The coupling and the nonlinearity are originated from the high-order multipole potentials, such as hexapole and octopole potentials, due to different layouts and the fabrication asymmetry of the SET. We solve a complicated Duffing equation with coupled oscillation terms by the multiple-scale method, which fits the experimental values very well. Our investigation in the SET helps for exploring multi-dimensional nonlinearity using currently available techniques and for suppressing instability of qubits in quantum information processing with trapped ions.     

Nonlinear optical characteristics of a pseudoisocyanine solution

The saturated nonlinear absorption and Kerr nonlinearities of an aqueous pseudoisocyanine solution are investigated at the wavelengths of 532 and 529 nm with the use of pulsed laser radiation of different duration (8 ns and 475 fs). The measured values of the nonlinear refractive indices amount to ?6×10^?12 (t=8 ns) and ?8×10^?14 cm²W^?1 (t=475 fs). The change in self-action effects in pseudoisocyanine from self-defocusing to self-focusing revealed in the case of increasing intensity of femtosecond laser pulses is attributed to the effect of a fifth-order nonlinear optical process. The nonlinear refractive index responsible for this process amounts to 4×10^?24 cm⁴ W^?2. The imaginary part of the third-order nonlinear susceptibility, responsible for the induced transparency of the pseudoisocyanine solution, is Imχ ⁽³⁾=?2×10^?12 esu. Temporal changes in the shape of nanosecond laser pulses due to the nonlinear refraction induced by a thermal process are analyzed.     

Nonlinear Refractive Index of Er3+-Doped Fiber and Its Application to Nonlinear Fiber Coupler

A large change in the refractive index originating in the transition absorption of erbium ions is induced in an Er³⁺-doped fiber. It is shown that the Er³⁺-doped fiber exhibits the nonlinear refractive index of n₂=7.4 × 10⁻¹⁵ m²/W, which is 10⁵−10⁶ times larger than that caused by the optical Kerr effect in a usual silica fiber at the pumping, wavelength of 514.5 nm. The large nonlinear refractive index occurred in a fiber directional coupler fabricated with the Er³⁺-doped fiber optically changes the coupling condition. The coupling ratio changes up to 0.16 by increasing the pumping power up to 0.7 mW.     

Beam Delivery of the Vanderbilt Free Electron Laser with Hollow Wave Guides: Effect on Temporal and Spatial Pulse Propagation

Hollow Wave Guides were evaluated as a beam delivery system for the Free Electron Laser (FEL) at Vanderbilt in preparation of surgical applications. They can transmit the mid-infrared wavelength range (2µm - 9µm) and tolerate the high peak intensity (&gt;10¹⁴ W/m²) in the micropulse of the FEL. Changes in the temporal and spatial beam characteristics induced by the transmission through 1.5 meter Hollow Wave Guides with bore radii of 250 µm and 530 µm were investigated. Temporal broadening of the micro pulses was studied using intensity autocorrelation measurements and beam profile measurements were performed with a pyroelectric camera. Results demonstrate significant pulse broadening and development of higher order modes induced by sub-optimal coupling of the beam into the Hollow Wave Guide. Bending of the Hollow Wave Guide induced additional losses and reduced propagation of higher modes responsible for broadening the pulse. Calculations with a geometrical ray model support the findings on pulse broadening. Optimal coupling conditions are extremely critical for maximal transmission performance of the Hollow Wave Guide. Design consequences for a FEL delivery system are discussed.     

State dependent fluctuations: A case study with properties both of “internal” and “external” kind

The model under study both from a theoretical and an experimental point of view consists of a slow oscillator interacting with an ideal thermal source at the temperature T₁ and, via a nonlinear coupling, with a fast one which, in turn, is coupled with an ideal thermal source at the temperature T₂. It is shown that the slow oscillator exhibits a variety of properties ranging from those typical of the hamiltonian models to the phenomena of “noise induced phase transitions”. The results of an analog experiment are shown to be in satisfactory agreement with the theoretical predictions.     

The third order nonlinear optical characteristics of amorphous vanadium oxide thin film

We studied the nonlinear absorptive characteristics (saturation intensity threshold and effective nonlinear absorption coefficients) and nonlinear refraction in a 50-nm-thick VO _x thin amorphous film prepared by pulsed DC magnetron reactive sputtering. The absorptive and refractive nonlinearities were investigated by pump–probe and Z-scan techniques. The closed-aperture Z-scan results reveal self-defocussing characteristics of the amorphous VO _x thin film for both nanosecond and picosecond pulse durations. Experimental results show that a phase transition does not occur in the range of intensities used for the experiments and the investigated sample can be treated as an amorphous semiconductor structure. The open-aperture Z-scan curves with nanosecond pulses exhibit saturable absorption for all input intensities. On the other hand, the open-aperture Z-scan curves with picosecond pulses exhibit nonlinear absorption/saturable absorption for low/high input intensities, respectively. Saturation intensity thresholds were found to be 15.3 MW/cm² for 4-ns pulse duration and 586 MW/cm² for 65-ps pulse duration.     

Study of the maximum conversion efficiency of the four-wave mixing process based on the Hamiltonian approach

In the four-wave mixing process, since the intensity of the generated coherence field is related closely to the third-order nonlinear susceptibility. With the help of a Hamiltonian approach, we obtain the expression of third-order nonlinear susceptibility χ⁽³⁾, and the special relation between χ⁽³⁾ and the nonlinear conversion coefficient. They are very useful to analyze the phase mismatch due to the Kerr effect and linear refraction contributions, which affect the maximum conversion efficiency under the condition taking account into pump field depletion. The investigative results show that energy conversion efficiency from the weak idler field to the generated field may exceed 100% when the phase mismatch induced by linear refraction is compensated, though the phase mismatch contribution from the Kerr effect can not be compensated simultaneously. Moreover, the conversion efficiency of the photon numbers fast reaches a plateau value.     

Thermally induced optical bistability in a new polymeric blend at room temperature

The transition from the transmission to the reflection regime for an Ar⁺-laser beam propagating in the new polymeric blend PMMA-EVA at a nonlinear interface has been observed. A comparison between the experimental data and a calculation of the input optical intensity at which this transition should occur (1.45×10⁷ W m^–2) is presented using Kaplan's theory. The results suggest the presence of thermally induced optical bistability in PMMA-EVA.     

On Algebraic Integrability of the Deformed Elliptic Calogero-Moser Problem

Abstract

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? ⁴ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.     

The adsorption of CO on evaporated iridium films,studied with infrared reflection-absorption spectroscopy

The adsorption of ^12CO on Ir films evaporated under ultrahigh vacuum (UHV) conditions was studied using infrared reflection-absorption spectroscopy (IRAS). Only a single absorption band was observed at 300 K, shifting continuously from the “singleton” value ~2010 cm^?1 at very low coverages to 2093 cm^?1 at saturation coverage. This band is attributed to CO adsorbed on top of the surface atoms. Synchronously with this shift the bandwidth at half maximum intensity $\text{Δv}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ decreases from ~30 to 8 cm^?1. The integrated peak area increases linearly with coverage up to a relative coverage (θ_r) of approximately 0.4, then the increase levels off and a maximum is observed. Upon continuing adsorption the intensity decreases slightly. In addition results are presented on adsorption at 300 K of ¹²CO?¹³CO isotopic mixtures. The coverage induced frequency shift is discussed in terms of a dipole-dipole coupling mechanism and it is concluded that intermolecular coupling can explain the shift (~83 cm^?1) observed. The decrease in intensity at coverages > 0.4 is attributed to the formation of a compressed overlayer with part of the CO molecules adsorbed in a multicentre position with different spectral properties. No infrared bands of nitrogen adsorbed at 78 K could be detected at pressures up to 6.7 kPa (1 Pa = 0.0075 Torr, 1 Torr = 133.32 Pa).