Positive Detuning Research Articles

Polarization Bistability in a 1550 nm Vertical-Cavity Surface-Emitting Laser Subject to Variable Polarization Optical Injection

The polarization bistability (PB) features in a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL) subject to variable polarization optical injection (VPOI) are experimentally investigated. We have investigated the influence of polarization angle $\theta _{p}$ of optical injection on PBs induced by scanning the power (power-induced PB) and the frequency of injected light (frequency-induced PB) along with different routes. The experimental results show that, for the fixed frequency of the injection laser and by scanning the injection power within a certain region, there exists a determined range of $\theta _{p}$ in which power-induced PB in the 1550 nm-VCSEL subject to VPOI can be observed. For VPOI with $\theta _{p}$ located within the determined range, the power-induced PB possesses larger hysteresis width, as compared with orthogonally polarized optical injection. The hysteresis width will be larger for a smaller value of $\theta _{p}$ . Under the condition of fixed injection power and continuously varying the frequency of the injection laser, two frequency-induced hysteresis cycles can be observed, of which one is located at negative frequency detuning, and the other is located at positive frequency detuning. The variations of the two hysteresis width with $\theta _{p}$ exhibit different trends. Also, when the bias current of the 1550 nm-VCSEL increases, the hysteresis width can be further broadened for the power-induced PB, and the broadening effect is relatively weak for the frequency-induced PB.

Modulation dynamic response of optical‐injection‐locked wavelength‐tunable semiconductor laser diodes

The effect of optical injection locking (OIL) on modulation dynamics of tunable laser diodes (TLDs) is investigated. The stable locking boundary map of OIL TLD which depends on the lasing wavelength was calculated and the TLD response in different injection states was investigated. Dramatic change in the emission spectra and the relaxation oscillation frequency (ROF) and huge improvement of these characteristics under OIL is demonstrated. Effect of the OIL parameters (frequency detuning and power ratio) on the TLD dynamics was studied for different tuning wavelengths. We show that forward optical injection and positive frequency detuning and blue-wavelength tuning are preferable regimes for enhanced modulation performance of OIL TLDs. Large increase of the ROF (>20GHz) and the modulation bandwidth (>25GHz) of the OIL TLD are demonstrated. The novel feature of the modulation response of the OIL TLD compared with usual single-mode lasers emitting at a fixed wavelength is the frequency dispersion of the differential gain in TLDs which increases with wavelength tuning. It is shown that the differential gain increase with wavelength tuning and the optical injection effect on the cavity resonance frequency shift contribute to a substantial enhancement of the modulation response of the OIL TLD.

A nonlinear model of cell interaction with an acoustic field

A theoretical and experimental nonlinear analysis of cellular response/displacement to ultrasound excitations is presented. Linear cell models can predict the resonant frequency (fR∼5MHz), but only a nonlinear analysis can reveal the amount of mechanical energy that couples into the cell and the bifurcation behavior of the cell when it is excited near resonance. The cell dynamics is described by the nonlinear viscoelastic constitutive behavior of the cytoplasm, nucleus and their respective membranes, in the presence of a fluid with an oscillating pressure field. The method of multiple scales is used to derive the amplitude of oscillation of the cytoplasm and nucleus as a function of frequency. A major finding is the existence of multiple solutions for a range of sub-resonant frequencies. At positive detuning (f>fR), the mechanical energy that couples into the cell is small, it is higher at resonance but significantly higher at sub-resonant frequencies in the multiplicity range. Experimentally it was shown when 3.5MHz is approached sub- and supra-resonance and 6.5MHz is approached sub-resonance, gene expression was statistically higher than that when stimulated directly. Thus, there exists an optimal range of frequencies for ultrasound treatment – in the region of multiplicity where deformation and thus mechanical energy coupling is maximized. The ultrasound protocol must be designed to operate at the solution associated with the higher mechanical energy – thus the start-up conditions should be in the domain of attraction of the high energy solution.

Nearly Degenerate Four-Wave Mixing in Single-Mode Fabry–Pérot Laser Diode Subject to Single Beam Optical Injection

In this paper, nearly degenerate four-wave mixing created by pump–probe structure with small frequency spacing and enough high power is demonstrated and discussed by introducing single optical beam into single-mode Fabry–Perot laser diode, in which the injected beam is called the probe wave, whose frequency detuning is controlled within ±50 GHz, and lasing resonance mode such as dominant mode or arbitrarily residual side mode is selected as the pump wave. In the case of dominant mode like the pump wave, conjugate signals around the pump–probe wave are easily observed for positive and negative probe detuning by judiciously tuning injected probe power. While external injection mode is moved towards the side mode selected as the pump wave, newly generated signals only occurred with small positive probe detuning. As the probe wave with positive frequency detuning is close to the pump wave, higher order conjugate signals are gradually grown. Under the condition of side mode as the pump wave, the strongly nonlinear mixing of the pump–probe wave also gives rise to new frequency signals on both sides of the dominant mode with enough high peak level. Against the change of correspondingly initial power and frequency detuning of the probe wave, outcome spectrum, output power, and conversion efficiency of conjugate signals are analyzed in detail, while dominant or one side mode is, respectively, selected as the pump wave.

Coherent and incoherent aspects of polariton dynamics in semiconductor microcavities

The interaction between coherent polaritons and incoherent excitons plays an important role in polariton physics. Using resonant pump-probe spectroscopy with selective excitation of single polariton branches, we investigate the different dephasing mechanisms responsible for generating a long-lived exciton reservoir. As expected, pumping the upper polariton results in a strong dephasing process that leads to the generation of a long lived reservoir. Unexpectedly, we observe an efficient reservoir creation while exciting only the lower polariton branch when the detuning is increased towards positive detuning. We propose a simple theoretical model, the polaritonic Bloch equations, to describe the dynamics of the system.

Ring modulator small-signal response analysis based on pole-zero representation

We present a closed-form expression for the small-signal response of a depletion-mode ring modulator and verify it by measurement results. Both electrical and optical behavior of micro-ring modulator as well as the loss variation due to the index modulation is considered in the derivation. This expression suggests that a ring modulator is a third-order system with one real pole, one zero and a pair of complex-conjugate poles. The exact positions of the poles/zero are given and shown to be dependent upon parameters such as electrical bandwidth, coupling condition, optical loss, and sign/value of laser detunings. We show that the location of zero is different for positive and negative detuning, and therefore, the ring modulator frequency response is asymmetric. We use the gain-bandwidth product as a figure of merit and calculate it for various pole/zero locations. We show that gain-bandwidth for the over-coupled ring modulator is superior compared to other coupling conditions. Also, we show that the gain-bandwidth product can be increased to a limit by increasing the electrical bandwidth.

Triad mode resonant interactions in suspended cables

A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equations for cable’s triad resonance are formulated by the multiple scale method. Dynamic conservative quantities, i.e., mode energy and Manley-Rowe relations, are then constructed. Equilibrium/dynamic solutions of the modulation equations are obtained, and full investigations into their stability and bifurcation characteristics are presented. Various bifurcation behaviors are detected in cable’s triad resonant responses, such as saddle-node, Hopf, pitchfork and period-doubling bifurcations. Nonlinear behaviors, like jump and saturation phenomena, are also found in cable’s responses. Based upon the bifurcation analysis, two interesting properties associated with activation of cable’s triad resonance are also proposed, i.e., energy barrier and directional dependence. The first gives the critical amplitude of high-frequency mode to activate cable’s triad resonance, and the second characterizes the degree of difficulty for activating cable’s triad resonance in two opposite directions, i.e., with positive or negative internal detuning parameter.

Chaotic Time-Delay Signature Suppression in a Semiconductor Laser With Frequency-Detuned Grating Feedback

Chaotic dynamics of a semiconductor laser subject to optical feedback from a frequency-detuned fiber Bragg grating (FBG) is investigated experimentally and numerically. Although the FBG is similar to a mirror in perturbing the laser into chaos, it is not the same as a mirror because it provides spatially distributed reflections. Such distributed reflections effectively suppress the undesirable time-delay signature (TDS) contained in the autocorrelation function of the chaotic intensity time-series. The investigation shows that the best suppression of TDS is attained when the FBG is positively detuned from the free-running laser frequency. The TDS suppression is due to dispersion at frequencies near an edge of the main lobe of the FBG reflectivity spectrum. The suppression prefers the FBG at a positive detuning frequency because the laser cavity is red-shifted by the antiguidance effect. Numerically, the dynamical behavior is mapped in the parameter space of detuning frequency and feedback strength, where wide regions of chaos are identified. Experimentally, the TDS suppression by FBG feedback is demonstrated for the first time. The positively detuned FBG suppresses the TDS by over ten times to below 0.04 in the experiments.

Multidimensional coherent spectroscopy of a semiconductor microcavity

Rephasing and non-rephasing two-dimensional coherent spectra map the anti-crossing associated with normal-mode splitting in a semiconductor microcavity. For a 12-meV detuning range near zero detuning, it is observed that there are two diagonal features related to the intra-action of exciton-polariton branches and two off-diagonal features related to coherent interaction between the polaritons. At negative detuning, the lineshape properties of the diagonal intra-action features are distinguishable and can be associated with cavity-like and exciton-like modes. A biexcitonic companion feature is observed, shifted from the exciton feature by the biexciton binding energy. Closer to zero detuning, all features are enhanced and the diagonal intra-action features become nearly equal in amplitude and linewidth. At positive detuning the exciton- and cavity-like characteristics return to the diagonal intra-action features. Off-diagonal interaction features exhibit asymmetry in their amplitudes throughout the detuning range. The amplitudes are strongly modulated (and invert) at small positive detuning, as the lower polariton branch crosses the bound biexciton energy determined from negative detuning spectra.

Impact of the phase-mismatch in the SHG crystal and consequential self-action of the fundamental wave by cascaded second-order effects on the THG efficiency of a Q-switched 1342 nm Nd:YVO₄ laser.

We report on the influence of self-focusing and self-defocusing in the phase-mismatched frequency doubling crystal on the third harmonic generation (THG) efficiency in a two crystal frequency tripling scheme. By detuning the temperature of the doubling crystal, the impact of a phase-mismatch in second harmonic generation (SHG) on the subsequent sum frequency mixing process was investigated. It was found that adjusting the temperature not only affected the power ratio of the second harmonic to the fundamental but also the beam diameter of the fundamental beam in the THG crystal, which was caused by self-focusing and self-defocusing of the fundamental beam, respectively. This self-action was induced by a cascaded χ(2) : χ(2) process in the phase-mismatched SHG crystal. Self-defocusing was observable for positive detuning and self-focusing for negative detuning of the phase-matching temperature. Hence, the THG efficiency was not symmetric with respect to the point of optimum phase-matching. Optimum THG was obtained for positive detuning and the resulting self-defocusing in combination with the focusing lens in front of the THG stage was also beneficial for the beam quality of the third harmonic.

Magnetic-field induced bistability in a quasi-one-dimensional semiconductor microcavity

We theoretically study the magnetic-field induced bistability in a quasi-one-dimensional semiconductor microcavity. A critical magnetic field is obtained, and the bistability appears if a magnetic field is greater than the critical value. For a positive energy detuning of the pump from the bare exciton polaritons, one bistability loop first emerges, then it divides into two loops, and finally one of them vanishes with the increasing magnetic field. This phenomenon originates from the magnetic-field modulated interactions for opposite spins. In the variational process, there are two important effects: one is a logic gate with a small variation of the excitation laser, and the other is a spin texture like skyrmion and this texture is periodic if the energy detuning varies periodically in real space, which is useful for designing the spin-dependent optoelectronic devices.

Continuous and discontinuous dark solitons in polariton condensates

Bose-Einstein condensates of exciton-polaritons are described by a Schr\"odinger system of two equations. Nonlinearity due to exciton interactions gives rise to a frequency band of dark soliton solutions, which are found analytically for the lossless zero-velocity case. The soliton's far-field value varies from zero to infinity as the operating frequency varies across the band. For positive detuning (photon frequency higher than exciton frequency), the exciton wavefunction becomes discontinuous when the operating frequency exceeds the exciton frequency. This phenomenon lies outside the parameter regime of validity of the Gross-Pitaevskii (GP) model. Within its regime of validity, we give a derivation of a single-mode GP model from the initial Schr\"odinger system and compare the continuous polariton solitons and GP solitons using the healing length notion.

A Study about Single-Photon Transport Controlled by Dipole-Dipole Interaction in a One-Dimensional Coupled Waveguide Cavity

In this paper, by regulating the dipole-dipole interaction between atoms, we can successfully control the behavior of single-photon transport in one-dimensional waveguide cavity. Our findings indicate that the dipole-dipole interaction is equivalent to the positive detuning. Furthermore, we also found that there is a competition between dipole-dipole interaction and the atom-cavity coupling. In addition, we also studied the influences of dipole-dipole interaction on transport spectrum under extreme conditions of high and low energy.

Power-induced polarization switching and bistability characteristics in 1550-nm VCSELs subjected to orthogonal optical injection**Project supported by the National Natural Science Foundation of China (Grant Nos. 61178011, 61275116, and 61475127) and the Natural Science Foundation of Chongqing City, China (Grant No. 2012jjB40011).

The polarization switching (PS) and polarization bistability (PB) characteristics of a 1550-nm vertical-cavity surface-emitting laser (VCSEL) subjected to orthogonal optical injection are systematically investigated. The simulated results show that the PS and polarization-resolved nonlinear dynamical states of the VCSEL are critically dependent on the changing paths of the injected power. The polarization dynamics for different scanning directions of the injected power is presented to explain the polarization evolution during the formation of PS. In the case of forward scanning injected power, with the increase of frequency detuning level between the VCSEL and the injected light, the injected power required for PS gradually increases for negative frequency detuning but exhibits fluctuations for positive frequency detuning. In the case of reversely scanning injected power, the injected power required for PS displays fluctuant changes within the whole frequency detuning range. Specifically, PS may disappear under certain negative frequency detuning and large bias current. Furthermore, the hysteresis width as a function of the frequency detuning is calculated, and the regions for the appearance and disappearance of PB have been determined in the parameter space of the bias current and frequency detuning.

First-order optimal linear and nonlinear detuning of centrifugal pendulum vibration absorbers

Centrifugal pendulum vibration absorbers are used to attenuate steady-state torsional vibrations in rotating and reciprocating machines. In most practical implementations, a set of multiple absorbers is symmetrically arranged on a rotor. Typically, each absorber mass is bifilar suspended, which allows the absorber mass to be moved along a prescribed path. Previous studies have considered how to determine absorber paths in order to obtain absorbers with amplitude-independent frequency known as tautochronic absorbers. It is known that a tautochronic absorber is highly desirable if only one absorber is installed on the rotor. However, in most applications multiple interacting absorbers are installed and as a result symmetry-induced nonlinear instabilities or localization caused by relative imperfections among the absorbers may occur. An effective strategy to avoid such situations is to perturb the tautochronic tuning which has been confirmed in practice and by previous theoretical investigations.This paper presents an approach for detuning a recently developed general tautochronic absorber design. The general design makes it possible to consider a wide class of tautochronic absorbers, e.g. absorbers without bifilar suspensions. The intent of this paper is to extend the existing tautochronic design guideline to non-tautochronic designs. As a result, different absorber designs can be addressed by one uniform theoretical approach, and existing absorber designs are included as special cases. Former studies on detuning of bifilar tautochronic absorbers use a one-parameter family of curves on which the absorber mass rides. Here, however, the detuning is not restricted to a one-parameter family of curves, which makes it possible to either optimize system performance or to avoid asynchronous absorber responses. In the case of synchronously responding equal absorbers, a necessary condition for optimal performance is derived analytically. Further, it is shown that asynchronous responses can be avoided by applying positive detuning.

Remote control of turn-on latency time in a semiconductor diode laser

Turn-on latency time is numerically investigated in a system of unidirectionally coupled semiconductor diode lasers. The optical output of a diode laser (master) is unidirectionally injected into another diode laser (slave). The slave’s turn-on latency time is found to have a logarithmic dependence on master’s transmission coefficient. This dependency is studied at different bias levels of the lasers. The frequency detuning between the lasers is found to influence the turn-on latency time, and is found that the turn-on latency time is relatively larger for positive detuning than that of negative detuning. Thus, we present a possibility of a remote control of the turn-on latency time of a diode laser (slave) by controlling the operating parameters of another (master) diode laser.

Effects of dipole-dipole interaction on the transmitted spectrum of two-level atoms trapped in an optical cavity

The transmission spectrum of two dipole-dipole coupled atoms interacting with a single-mode optical cavity in strong coupling regime is investigated theoretically for the lower and higher excitation cases, respectively. The dressed states containing the dipole-dipole interaction (DDI) are obtained by transforming the two-atom system into an effective single-atom one. We found that the DDI can enhance the effects resulting from the positive atom-cavity detunings but weaken them for the negative detunings cases for lower excitation, which can promote the spectrum exhibiting two asymmetric peaks and shift the heights and the positions of them. For the higher excitation cases, DDI can augment the atomic saturation and lead to the deforming of the spectrum. Furthermore, the large DDI can make the atom and the cavity decouple, making a singlet of the normal-mode spectrum.

Dynamical Instability of a Bose-Einstein Condensate in an Optical Ring Resonator

We experimentally investigate the dynamical instability of a Bose-Einstein condensate in an optical ring resonator for various cavity detuning and pump powers. The resulting stability diagram is asymmetric with respect to the cavity detuning and can be described by the coupling of two atomic modes with one optical mode. We compare the experimental data to a numerical simulation and to an analytic expression of the phase boundary. For positive and negative pump cavity detuning, different coupling mechanisms are identified explaining the asymmetry of the stability diagram. We present a physical interpretation and discuss the connection to the Dicke quantum phase transition.

Lasing and high-temperature phase transitions in atomic systems with dressed-state polaritons

We consider the fundamental problem of high temperature phase transitions in the system of high density two-level atoms off-resonantly interacting with a pump field in the presence of optical collisions (OCs) and placed in the cavity. OCs are considered in the framework of thermalization of atomic dressed state (DS) population. For the case of a strong atom-field coupling condition we analyze the problem of thermodynamically equilibrium superradiant phase transition for the order parameter representing a real amplitude of cavity mode and taking place as a result of atomic DSs thermalization process. Such transition is also connected with condensed (coherent) properties of low branch (LB) DS-polaritons occurring in the cavity. For describing non-equilibrium phase transitions we derive Maxwell-Bloch like equations which account for cavity decay rate, collisional decay rate and spontaneous emission. Various aspects of transitions to laser field formation by using atomic DS levels for both positive and negative detuning of a pump field from atomic transition frequency are studied in detail. It is revealed, that for positive atom-light detuning DS lasing can be obtained in the presence of quasi-equilibrium DS population that corresponds to a true two-level atomic system with the inversion in nonresonant limit.

Effects of excitation frequency on high-order terahertz sideband generation in semiconductors

We theoretically investigate the effects of the excitation frequency on the plateau of high-order terahertz sideband generation (HSG) in semiconductors driven by intense terahertz (THz) fields. We find that the plateau of the sideband spectrum strongly depends on the detuning between the near-infrared laser field and the band gap. We use the quantum trajectory theory (three-step model) to understand the HSG. In the three-step model, an electron–hole pair is first excited by a weak laser, then driven by the strong THz field, and finally recombined to emit a photon with energy gain. When the laser is tuned below the band gap (negative detuning), the electron–hole generation is a virtual process that requires quantum tunneling to occur. When the energy gained by the electron–hole pair from the THz field is less than 3.17 times the ponderomotive energy (Up), the electron and the hole can be driven to the same position and recombined without quantum tunneling, so that the HSG will have large probability amplitude. This leads to a plateau feature of the HSG spectrum with a high-frequency cutoff at about 3.17Up above the band gap. Such a plateau feature is similar to the case of high-order harmonics generation in atoms where electrons have to overcome the binding energy to escape the atomic core. A particularly interesting excitation condition in HSG is that the laser can be tuned above the band gap (positive detuning), corresponding to the unphysical ‘negative’ binding energy in atoms for high-order harmonic generation. Now the electron–hole pair is generated by real excitation, but the recombination process can be real or virtual depending on the energy gained from the THz field, which determines the plateau feature in HSG. Both the numerical calculation and the quantum trajectory analysis reveal that for positive detuning, the HSG plateau cutoff depends on the frequency of the excitation laser. In particular, when the laser is tuned more than 3.17Up above the band gap, the HSG spectrum presents no plateau feature but instead sharp peaks near the band edge and near the excitation frequency.