Four-Wave Mixing And Phase Conjugation In Plasmas Using Ionization Nonlinearities

Polaron dephasing processes are investigated in InAs/GaAs dots using far-infrared transient four wave mixing (FWM) spectroscopy. We observe an oscillatory behaviour in the FWM signal shortly (< 5 ps) after resonant excitation of the lowest energy conduction band transition due to coherent acoustic phonon generation. The subsequent single exponential decay yields long intraband dephasing times of 90 ps. We find excellent agreement between our measured and calculated FWM dynamics, and show that both real and virtual acoustic phonon processes are necessary to explain the temperature dependence of the polarization decay. PACS numbers: 78.67.Hc, 78.47.+p, 42.50.Md, 71.38.-k The strong spatial confinement of carriers in semiconductor quantum dots (QDs) leads to striking differences in the carrier-phonon interaction compared with systems of higher dimensionality. In particular, the discrete energy level s tructure in QDs results in long exciton and electron dephasing times [1, 2, 3, 4], making these semiconductor nanostructures highly attractive for implementation in quantum information processing applications. The study of dephasing mechanisms in QDs is commonly carried out using transient four wave mixing (FWM) spectroscopy. Using resonant interband excitation, FWM measurements have revealed the absorption lineshape of single QDs to consist of a narrow zero phonon line (ZPL) and an acoustic phonon-related broadband centred at the same energy. The only intraband FWM study [5] involved resonant excitation of high energy transitions in th e valence band of p-doped QDs yielding dephasing times ∼ 15 ps. However it was not possible to determine the dephasing mechanisms in this case. Intraband studies of the well-resolved lowest energy conduction band electron transitions in InAs/GaAs QDs have provided deep insight into the electron-phonon interaction and carrier relaxation processes in n-doped samples. Clear evidence of strong coupling between electrons and phonons, resulting in polaron formation, has been demonstrated using magneto-transmission measurements [6]. Ultrafast studies [7, 8] of polaron decay have shown that the previously assumed ’phonon bottleneck’ picture is not valid. Compared with semiconductor quantum wells, the intraband population relaxation time in QDs is long (∼ 50 ps) suggesting relatively long dephasing times. However there have been no reports of direct dephasing measurements to date. In the present letter we present the first investigations of i ntraband dephasing in n-doped QDs using degenerate FWM. Our calculations of the absorption lineshape in this case sh ow marked differences in comparison with the interband absorption [9]. The intraband lineshape consists of peaked acoustic phonon sidebands separated by ∼ 1.5 meV from the ZPL, which corresponds to phonons with wavelength close to the dot size, and is reminiscent of the lineshape associated wit h impurity-bound electron transitions [10]. Using pulse durations short enough to excite both the ZPL and acoustic phonon sidebands we find damped oscillations in the FWM signal, indicative of coherent acoustic phonon generation, followed by a single exponential decay. In contrast with the interband case, where the origin of the strong temperature dependence of the excitonic linewidth is still subject to debate, the simple 3 -level structure of the lowest energy conduction band states in InAs QDs permits an accurate simulation of the temperature dependence of the FWM signal. The excellent agreement found between experiment and theory, shows that virtual transitions between the p-states is the dominant dephasing mechanism at high temperature. At low temperature, we have measured an intersublevel dephasing time of T2 ∼ 90 ps. It is also interesting to compare our results with previous intraband dephasing measurements in higher dimensional (quantum well) systems [11]. Here phonon-mediated processes are not significant with the intraband dephasing instead determined by electronelectron interactions, yielding typical dephasing times ∼ 0.3 ps which are approximately 2 orders of magnitude faster than for the QD samples studied here. The relatively long intraband dephasing time in QDs is key to the efficient operation of new types of mid-infrared QD-based devices, such as intersublevel polaron lasers [12] and may be relevant for potential device applications such as qubits for quantum information processors [13]. The investigated samples were grown on (100) GaAs substrates by molecular beam epitaxy in the Stranski-Krastranow mode. They comprise 80 layers of InAs self-assembled QDs separated by 50 nm wide GaAs barriers, thus preventing both structural and electronic coupling between QD layers. The polaron transitions were studied between s-like ground (s) and p-like first excited ( p) states within the conduction band. To populate the s state, the samples were delta-doped with Si 2 nm below each QD layer. The doping density was controlled in such a way that the average doping did not exceed 1 electron per dot (see Ref. [14] for more details). Absorp

The possibility to perform broad wavelength generation and conversion is of great interest in classical and quantum optics. With the introduction of integrated nonlinear silicon photonics, these tasks have been made even more viable thanks to the combination of the high nonlinear refractive index of silicon with the high confinement provided by the photonic waveguides. Exploiting this platform, several solutions for wavelength conversion have been investigated, for both optical processing [1] and applications in the Mid Infrared (MIR) [2]. The possibility to perform broad and controllable wavelength generation can be exploited also for creating integrated sources of quantum states of light based on single photons [3] or correlated photon pairs [4]. Both the generation and conversion can be accomplished by means of Four Wave Mixing (FWM). FWM is a nonlinear optical process in which two pump photons at frequency are converted into signal and idler photons at frequencies and ω/ respectively (with ω I /ω S ). In the particular case of wavelength conversion, FWM is stimulated by a seed wave at the same wavelength of the signal (idler) that will be converted to the wavelength of the idler (signal). FWM has to satisfy the energy conservation, according to which the relation ω P + ω P = ω S + ω I holds, and its efficiency is ruled by the phase matching condition. This latter condition is related to the phase mismatch among the waves involved in the FWM process, that is evaluated as Δk = k p + k p −k S −k I , where k P , k S , k I are the wavevectors for the pump, the signal and the idler, respectively. When Δk = 0, the phase matching condition is fulfilled and the efficiency of FWM is maximized. What is important for wavelength generation and conversion is the spectral position of the phase matching condition, which determines the wavelength at which the maximum efficiency of the conversion or generation process is achieved. Because of this, techniques for the control of the phase matching condition have been developed, focusing on the possibility to tailor the Group Velocity Dispersion (GVD) through a proper engineering of the waveguide geometry [5]. While these techniques consider only the first order waveguide mode, here we propose to exploit the higher order modes propagating inside a multimode waveguide. The dispersion of the higher order modes can be used to tune the spectral position of the phase matching condition for the FWM process, achieving controllable and large spectral translation in both Stimulated Four Wave Mixing (sFWM) and Spontaneous Four Wave Mixing (SFWM).

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis describes an experimental and theoretical study on modal dispersal of information and wave mixing in photorefractive crystals for vector phase conjugation and real-time information processing. Photorefractive crystals with short drift lengths (BaTiO3 and [...]) and long drift ones (Bi12SiO20 and semi-insulating GaAs) are particularly used in this thesis. In the first part, the photorefractive effect in electrooptic crystals is described in terms of Kukhtarev's band transport model. The explicit solution of the space-charge electric field for the case of one photorefractive species and one type of charge carrier is extended to the case of two photorefractive species and two types of charge carriers. The enhancement of the space-charge electric field is also described. In particular an approximate solution to Stepanov and Petrov's enhancement method of using AC external electric field is extended to a general case that describes the transient behavior for AC external electric field of arbitrary waveform. The anisotropic refractive index change due to the space-charge field formation is then described in terms of tensorial forms of the nonlinear susceptibility. In the second part, anisotropic beam coupling in photorefractive crystals is presented and a general set of coupled-wave equations that describes beam coupling in amplitude, phase, and polarization is derived by using the nonlinear and tensorial susceptibility. The polarization properties of the interacting waves are particularly stressed. Two limiting cases, i.e., one for scalar beam coupling and the other for cross-polarization beam coupling, are obtained from the general expression and solved. Experimental results of beam coupling in semi-insulating GaAs are presented, and the signs of dominant charge carriers and the density of photorefractive species are estimated from beam-coupling gain. The enhancement of beam-coupling gain and its temperature dependence are also discussed. In the third part, four-wave mixing for scalar and vector phase conjugation is described. Self-pumped phase-conjugate mirrors using photorefractive crystals are presented and one of the most interesting properties of these mirrors, i.e., the response to phase changes of inputs, is emphasized both theoretically and experimentally. In the fourth part, two-wave and four-wave mixing in photorefractive crystals are applied to moving object detection, mathematical operation on images, and one-way image transmission through phase-distorting media. In these applications, polarization properties of interacting waves are particularly utilized. In the fifth part, a novel method of vector phase conjugation by modal dispersal and scalar phase conjugation is discussed. The propagation characteristics of conjugate waves in strongly scattering media (e.g., mode-scrambling multimode fibers) are described theoretically, followed by the experimental demonstration of vector phase conjugation. In the theory the unitarity and time-reversal symmetry of the scattering matrix are incorporated into the analysis of the coherency matrix of the conjugate field. This theory which describes the physical process of the generation of vector phase conjugation can successfully explain the experimental results of its fidelity. In the last part, we describe experiments in which the new concept of modal dispersal of information and scalar phase conjugation is used for several novel applications that include nonreciprocal polarization-distortion correction, amplitude-distortion correction, and phase-conjugate multimode fiber-optic sensors. Experiments as well as proposals for these applications are presented.

Brillouin enhanced four-wave mixing and phase conjugation of electromagnetic waves in weakly collisional fully ionized plasmas are considered. It is found that the nonlinearity associated with the nonlocal electron heat transport may dominate over the ponderomotive force and consequently there might appear an enhanced degenerate four-wave mixing and phase conjugation reflectivity.

Recently rocket observations on spikelets of lower‐hybrid waves along with strong density cavities and transversely heated ions were reported. The observed thin filamentary cavities oriented along the magnetic field in the auroral plasma have density depletions up to several tens of percent. These observations have been interpreted in terms of a theory for lower‐hybrid wave condensation and collapse. The modulational instability leading to the wave condensation of the lower‐hybrid waves yields only weak density perturbations, which cannot explain the above strong density depletions. The wave collapse theory is based on the nonlinear pondermotive force in a homogeneous ambient plasma and the density depletion is determined by the balance between the wave pressure (pondermotive force) and the plasma pressure. In the auroral plasma, the balance is achieved in a time τwc ≤1 ms. It is shown here that the mirror force, acting on the transversely heated ions at a relatively long time scale, is an effective mechanism for creating the strong plasma cavities. We suggest that the process of wave condensation, through the pondermotive force causing generation of short wavelength waves from relatively long wavelength waves, is a dominant process until the former waves evolve and become effective in the transverse heating of ions. As soon as this happens, mirror force on ions becomes an important factor in the creation of the density cavities, which may further trap and enhance the waves. Results from a model of cavity formation by transverse ion heating show that the observed depletions in the density cavities can be produced by the heating rates determined by the observed wave amplitudes near the lower‐hybrid frequency. It is found that the creation of a strong density cavity takes a few minutes.

This paper investigates bidirectional transmission using four wave mixing (FWM) for wavelength division multiplex passive optical network (WDM-PON) applications. A semiconductor optical amplifier (SOA) is considered to generate FWM. A use of FWM makes it possible to convert a downstream data wavelength to a different wavelength, which is used for upstream transmission. The wavelength generated by FWM can realize bidirectional transmission with a single fiber. We assume intensity modulation (IM) for both up- and down-transmission. Both an injection locked Fabry-Perot laser diode (FP-LD) transmitter and a transmitter with an external modulator are considered for upstream transmission. In both cases, an extinction ratio (Ex) of downstream signal light is very important for both sending and receiving properties and the Ex influences the bit error rate (BER) property. This paper clarifies the relationship between the Ex of FWM and the power penalty ΔP. This paper also clarify the Ex value of FWM as a function of input signal Ex using a model SOA theoretically. Fundamental transmission experiments, 10 Gbit/s downstream and 2.5 Gbit/ s upstream, using both types of transmitters confirmed the possibilities of the bidirectional transmission using FWM.

Energetic, temporal and spectral characteristics of the phase conjugation (PC) process at intracavity degenerate four wave mixing (DFWM) of frequency selective pulsed ebeam controlled discharge (EBCD) CO laser radiation are studied both experimentally and theoretically. Laser gas mixture CO:N2:He=1:4:5, gas density 0.3 Amagat, gas temperature 120-140 K, interaction angle ~10 mrad at DFWM without optical delay between probe wave E3 and co-propagating pumping one E1, active medium length 1.2 m, laser resonator length 17.7 m. PC reflectivity (PCR) on energy was ~1%, being independent of specific input energy. The dependencies of PCR on pressure had quite different behavior for different selected spectral lines. An influence of the neighboring vibrational band lasing on PCR for the spectral line under the investigation is demonstrated (Tab.l), PCR decreasing at switching on neighboring line lasing.

Optimizing experimental parameters on OPC in PMMA polymer doped azo dye

The phase-conjugate field fidelity in backward-going four-wave mixing, based on the diffraction model solvable analytically, is investigated. The method assumes interaction of the non-depleted infinite plane pump waves with the spatially limited probe and signal waves inside the nonlinear medium. Solutions are obtained applying the Fourier transformation and the Green function technique under various boundary conditions for coupled wave equations. The probe and its phase-conjugate waves are defined by using a complex phase formulation including both the phase variation and amplitude modulation. It is shown that the analysed approach can involve assumptions leading to the ideal or distorted phase conjugation.

The resonant third-order nonlinear optical properties of hemicyanine, 3-methyl-2-(6-morpholino-1,3,5-hexatrienyl)-benzoxazolium iodide (HC) doped polymethylmethacrylate (PMMA) thin films were measured by degenerate four- wave mixing (DFWM) at 580nm with 4ps pulses. It was found that the temporal profile of DFWM signal in 0.01M HC doped PMMA film was much different from that in dilute dimethylsulfoxide solution of HC. The decay of DFWM signal in the thin film consisted of the faster component (∼10ps) in addition to the slower one (>100ps). The phase conjugate reflectivity was not proportional to the square of pump intensity and saturated even in the weak pump intensity. The effective X (3) xxxx value of the thin film was relatively large (2.8∼10−9esu) at weak pump intensity (0.03μJ/pulse).

The optical nonlinear effects can provide different advanced electromagnetic functionalities, such as wave mixing and phase conjugation, which can be applied in a variety of new applications. However, these effects usually suffer from extremely weak nature and require high input intensity values in order to be excited. Interestingly, the large third order nonlinearity of graphene, along with the strong field confinement stemming from its plasmonic behavior, can be utilized to enhance several relative weak nonlinear effects at infrared (IR) and terahertz (THz) frequencies. Towards this goal, various nonlinear graphene metasurfaces are presented in this work to effectively increase the efficiency of different optical nonlinear effects and, as a result, decrease the required input intensity needed to be excited. In particular, we will show that the efficiency of four-wave mixing (FWM) can be improved by several orders of magnitude by using a nonlinear metasurface composed of patterned graphene ribbons, a dielectric interlayer, and a metallic reflector acting as substrate. We also demonstrate that the self-phase modulation (SPM) nonlinear process can be enhanced by using an alternative graphene nonlinear metasurface, operating as coherent perfect absorber, leading to a pronounced shift in the resonant frequency of the coherent perfect absorption (CPA) effect of this structure as the input intensity of the impinging incident waves is increased. This property will provide a robust mechanism to dynamically tune and switch the CPA process. Furthermore, it will be presented that strong negative reflection and refraction can be achieved by a single graphene monolayer film due to the enhancement of another nonlinear process, known as phase conjugation. This nonlinear process is envisioned to be used in the construction of a perfect imaging device with subwavelength resolution.

Phase conjugation (PC) that is due to degenerate forward four-wave mixing is studied both theoretically and experimentally. Similarly to backward four-wave mixing, the limiting efficiency of this process corresponds to the total energy transfer from each pump wave into the signal and conjugate waves, although in this case the Yariv oscillations do not occur. The numerical solution of the nonstationary problem is presented, revealing the transient oscillations of the PC-beam intensity with maxima many times exceeding the saturation value. PC of Q-switched and free-oscillating solid-state laser radiation is obtained by using the thermal nonlinearity of absorbing solutions. PC of cw laser radiation is obtained in a LiNbO3 crystal, the PC-beam intensity being six times larger than the initial intensity of the signal beam. The self-compensation of nonlinear phase distortions of the recording medium is demonstrated.

Earlier studies on coronal mass ejections (CMEs), using remote sensing and in situ observations, have attempted to determine some internal properties of CMEs, which were limited to a certain position or a certain time. To understand the evolution of the internal thermodynamic state of CMEs during their heliospheric propagation, we improve the self-similar flux-rope internal state model, which is constrained by the measured propagation and expansion speed profiles of a CME. We implement the model in a CME that erupted on 2008 December 12 and probe the internal state of the CME. It is found that the polytropic index of the CME plasma decreased continuously from 1.8 to 1.35 as the CME moved away from the Sun, implying that the CME released heat before it reached an adiabatic state and then absorbed heat. We further estimate the entropy changing and heating rate of the CME. We also find that the thermal force inside the CME is the internal driver of CME expansion while the Lorentz force prevented the CME from expanding. It is noted that the centrifugal force due to poloidal motion decreased at the fastest rate, and the Lorentz force decreased slightly faster than the thermal pressure force as the CME moved away from the Sun. We also discuss the limitations of the model and approximations made in the study.

Study of optical nonlinearity of functionalized multi-wall carbon nanotubes by using degenerate four wave mixing and Z-scan techniques

Degenerate four wave mixing (DFWM) in supersonically cooled pyrazine was investigated using different polarization combinations of the three input beams. A common feature of these spectra was the strong Q branch, stronger than the corresponding spectra for a single photon process. The ratios for all the rotational branches demonstrated strong dependence on the polarization combination. The YYXX combination showed similar intensities for the P and R branches, while the YXYX combination had a much stronger R branch. The Q branch, relative to the P branch, was the strongest for the YYYY combination. All experiments probed for the same electronic transition with the same Hönl–London factor; therefore the variation in the rotational branching ratios was solely an effect of the polarization combinations. This polarization dependence of DFWM can be traced back to the selectivity in the magnetic quantum number for this multiphoton process. Based on the theoretical framework by Williams et al. [J. Chem. Phys. 101, 1072 (1994)], these spectra were simulated successfully. The calculations and analysis of the experimental conditions revealed that among the twelve gratings included in the original theory, only three of them had observable contributions to the experimental spectra, i.e., the gratings formed through the ground-state molecules via the two forward beams. The other nine gratings either were washed out or decayed in the collision free environment (supersonic expansion) under an excitation pulse of 7 ns. This argument was further confirmed by another experiment using a time delay between the backward probe beam and the two forward beams. The spectra recorded with a 15 ns delay in the probe beam (longer than the pulse duration of each input beam) were similar to those without delays. These results implied that (1) the backward beam did not participate in the grating formation process even when it arrived at the interaction region simultaneously with the two forward beams. (2) Relaxation from any of the three contributing gratings was not observable. (3) The fast intersystem crossing, known to exist in pyrazine, had no effect on the grating formation and relaxation processes. Although complex in nature, degenerate four wave mixing offers versatility in experimental arrangements, providing both dynamics and spectroscopy information.