Four-wave Mixing Intensity Research Articles

Ultrafast Nanoimaging of Electronic Coherence of Monolayer WSe2.

Transition-metal dichalcogenides (TMDs) have demonstrated a wide range of novel photonic, optoelectronic, and correlated electron phenomena for more than a decade. However, the coherent dynamics of their excitons, including possibly long dephasing times and their sensitivity to spatial heterogeneities, are still poorly understood. Here we implement adiabatic plasmonic nanofocused four-wave mixing (FWM) to image the coherent electron dynamics in monolayer WSe2. We observe nanoscale heterogeneities at room temperature with dephasing ranging from T2 ≲ 5 to T2 ≳ 60 fs on length scales of 50-100 nm. We further observe a counterintuitive anticorrelation between FWM intensity and T2, with the weakest FWM emission at locations of longest coherence. We interpret this behavior as a nonlocal nano-optical interplay between spatial coherence of the nonlinear polarization and disorder-induced scattering. The results highlight the challenges associated with heterogeneities in TMDs limiting their photophysical properties, yet also the potential of their novel nonlinear optical phenomena.

Rapid multiplex ultrafast nonlinear microscopy for material characterization.

We demonstrate rapid imaging based on four-wave mixing (FWM) by assessing the quality of advanced materials through measurement of their nonlinear response, exciton dephasing, and exciton lifetimes. We use a WSe2 monolayer grown by chemical vapor deposition as a canonical example to demonstrate these capabilities. By comparison, we show that extracting material parameters such as FWM intensity, dephasing times, excited state lifetimes, and distribution of dark/localized states allows for a more accurate assessment of the quality of a sample than current prevalent techniques, including white light microscopy and linear micro-reflectance spectroscopy. We further discuss future improvements of the ultrafast FWM techniques by modeling the robustness of exponential decay fits to different spacing of the sampling points. Employing ultrafast nonlinear imaging in real-time at room temperature bears the potential for rapid in-situ sample characterization of advanced materials and beyond.

Four-wave mixing involving Ξ−Vtype system: In view of dressed state picture

We theoretically investigate the four-wave mixing (FWM) characteristics in a Ξ−V type atomic system. The generated FWM is obtained by utilizing the density matrix formalism and solving the master equation. Interesting discrimination in the number of emerged peaks due to the chosen laser scanning schemes was pointed out. The dressed state picture is employed to elucidate the number of peaks emerged as well as the peak positions in the spectra. The dependence of the generated FWM signal accordingly to the change of parameters, such as Rabi frequencies and frequency detunings of the applied fields, are presented and well explained in the simplified dressed state picture. A prominent increase in FWM intensity is obtained when the Rabi frequencies of the coupling and driving field are approximately equal. The frequency detuning of the applied fields causes the shift in the peak positions, peak shape, and even brings about the FWM intensity enhancement.

Dynamically tunable vortex four-wave mixing in a six-level system.

We investigate the orbital angular momentum of vortex light in a six-level atomic system with a closed loop. We find that a vortex light field via four-wave mixing (FWM) is sensitive to the relative phase of the driving fields due to forming a closed loop configuration. Thus, it could periodically tune the phase and intensity of the vortex FWM field by adjusting the relative phase of the driving fields. Moreover, the spatial modulation of the vortex FWM phase and intensity also can be achieved by tuning the intensity of the microwave field and detuning of the driving fields.

Controllable four-wave mixing based on quantum dot-cavity coupling system

We theoretically study the four-wave mixing (FWM) response in a quantum dot-cavity coupling system, where a two-level quantum dot (QD) is placed in an optical cavity while the cavity mode is coupled to the nanomechanical resonator via radiation pressure. The influences of the QD-cavity coupling strength, the Rabi coupling strength of the QD, and the power of the pump light on the FWM intensity are mainly considered. The numerical results show that the FWM intensity in this hybrid system can be significantly enhanced by increasing the QD-cavity coupling strength. In addition, the FWM intensity can be effectively modulated by the Rabi coupling strength and the pump power. Furthermore, the effects of the cavity decay rate and the cavity-pump detuning on the FWM signal are also explored. The obtained results may have potential applications in the fields of quantum optics and quantum information science.

PT -symmetry-breaking-enhanced cavity optomechanical magnetometry

$\mathcal{PT}$-symmetry-breaking enhanced cavity optomechanical magnetometer is proposed, which is achieved by monitoring the change of intensity of a nonlinear four-wave mixing (FWM) process in a gain-cavity-assisted cavity optomechanical system (COMS). Compared with the traditional single loss COMS, the FWM intensity can be enhanced by two orders of magnitude when the gain-cavity-assisted COMS operates at the $\mathcal{PT}$-symmetry-breaking phase. Meanwhile, the sensitivity of magnetic field sensing can be increased from $10^{-9}$T to $10^{-11}$T. This originally comes from the fact that the effective detuning and decay of loss-cavity can be effectively modified in the $\mathcal{PT}$-symmetry-breaking phase. Our work shows that an ultrahigh-sensitivity magnetometer can be achieved in the $\mathcal{PT}$-symmetry-breaking COMS, which will have wide applications in the field of quantum sensing.

Controllable optical response in a quadratically coupled optomechanical system with mechanical driving

We study the response of the output field from a quadratically coupled optomechanical system, where the optical cavity is driven by a strong control field and a weak probe field. In addition, a weak coherent mechanical driving field is applied to excite the mechanical mode and modify the optical response of the system. Under different driving conditions, we show that the transmission spectrum of the probe field can exhibit the phenomena of optomechanically induced transparency, amplification, and Fano resonance. Within the narrow transparency and amplification windows, the four-wave mixing (FWM) intensity can be resonantly enhanced. Moreover, it is shown that the FWM intensity can be further enhanced or suppressed by tuning the amplitude and phase of the mechanical driving, and the physical origin is explained in terms of interference effect. Our results may find potential applications in optical switching and frequency conversion.

Four‐Wave Mixing Response via Hybrid Coulomb‐Coupled Cavity Optomechanics

AbstractThe generation and manipulation of the four‐wave mixing (FWM) phenomenon is reported in a hybrid electrostatically Coulomb‐coupled optomechanical system as a result of light–matter interaction. The cavity is driven by a strong coherent pump and a weak probe field simultaneously in the presence of nanomechanical resonators (NMRs), and the output field can produce a new frequency component called the FWM frequency. In a hybrid Coulomb‐coupled cavity scheme, the existence of optomechanical coupling due to radiation pressure gives rise to the FWM phenomenon, which is shown both analytically and numerically. A controllable enhancement of the FWM intensity is found by tuning the pump field strength and its spectrum disappears upon switching the strength off. A significant enhancement in the FWM spectrum with two peaks is also predicted due to the Coulomb coupling strength existing between two electrostatically coupled NMR1 and NMR2. A suppressive behavior of the FWM signal is also observed upon increasing the cavity decay rate and a substantial modulation in the signal by changing the probe‐pump field detuning. Finally, the FWM spectrum is very sensitive to both the effective resonance frequencies and effective masses of the NMRs.

Enhanced four-wave mixing in P T-symmetric optomechanical systems.

We investigate the enhanced four-wave mixing (FWM) process in a parity-time (P T)-symmetric optomechanical system, where an active cavity is coupled to a passive cavity supporting a mechanical mode. The passive cavity is optically driven by a strong control field and a weak probe field, and the mechanical mode is excited by a weak coherent driving field. By tuning the coupling strength between the two cavities with balanced gain and loss, we find that the FWM intensity can be significantly enhanced near the exceptional points (EPs) at low control power, which is about 12 orders of magnitude higher than that of the single-cavity case. Due to the interference effect induced by the optical and mechanical driving field, it is shown that the FWM intensity can be further enhanced or suppressed by tuning the amplitude and phase of the mechanical driving field. Moreover, the dependence of the FWM intensity on the frequency and power of the control field is also discussed. Our work provides a route to enhance the four-wave mixing process in a flexible way.

Optomechanically induced transparency and nonlinear responses based on graphene optomechanics system

Due to its unique properties of low mass density, high frequency, high quality-factor and intrinsically small size, graphene has received significant attention and is considered as an ideal material for fabricating nanomechanical systems. In this work, we demonstrate theoretically the coherent optical propagation under different detuning regimes in the graphene resonator-microwave cavity system. In the red detuning, optomechanically induced transparency induced the slow light effect is investigated and the maximum group delay can reach 0.4 ms. In the blue detuning, advancing microwave signal can reach 0.12 ms, and the parametric amplification process can behave as an optical transistor to amplify a weak microwave field via manipulating the pump field. Further, we research the nonlinear effects of four-wave mixing (FWM), and the FWM intensity can be efficiently controlled and modulated by the pump power, such as FWM spectrum can present the phenomenon of normal mode splitting with controlling the pump power. A straightforward optical means for determining the frequency of the resonator by the FWM spectrum is also presented. The graphene optomechanics may indicate applications in quantum information processing.

Optical bistability and four-wave mixing in a hybrid optomechanical system

We explore theoretically the optical bistability and four-wave mixing (FWM) in a hybrid optomechanical system, where the mechanical resonator is simultaneously coupled to a cavity field and a two-level system (qubit). We can use a strong control field driving the cavity to control the bistable behavior of the steady-state photon number, phonon number, and the population inversion. The impact of qubit-resonator coupling strength on the bistable behavior is discussed. Furthermore, the two-level system can significantly modify the output fields of the cavity, leading to double optomechanically induced transparency (OMIT) and the enhancement of the FWM intensity. We find that the distance between the two peaks in the FWM spectrum can be controlled by the qubit-resonator coupling strength, and the peak value of the FWM intensity can be adjusted by the Rabi frequency of the control field.

Microwave Frequency Graphene Optomechanics. Coherent Propagation Properties and Nonlinear Responses

We demonstrate theoretically the slow and fast light effects based on the coupled graphene nanomechanical resonator–microwave cavity system. The numerical results show that the maximum group delay and advancing microwave signals can reach 0.4 and 0.12 ms, respectively, in the graphene resonator–microwave cavity system. In addition, the system can also behave as an optical transistor to amplify a weak microwave field through manipulating the pump field. Further we investigate the nonlinear effects of four-wave mixing (FWM) and show that the FWM intensity can be efficiently controlled and modulated by the pump power. The graphene optomechanics provides a good medium for controlling microwave photons at different frequencies and may indicate applications in quantum information processing.

Controllable four-wave mixing based on mechanical vibration in two-mode optomechanical systems

We theoretically investigate the four-wave mixing (FWM) process in a two-mode cavity optomechanical system, where two cavity modes are coupled to a common mechanical resonator. The left cavity is driven by a strong pump laser beam and a weak probe laser beam simultaneously, but the right cavity is only driven by a strong pump laser beam. It is shown that when both cavities are driven at their respective red sidebands, optomechanically induced transparency (OMIT) appears and FWM is resonantly enhanced with reduced linear absorption. However, when the left cavity is driven at its red sideband but the right cavity is driven at its blue sideband, robust photon entanglement can be realized (Tian L., Phys. Rev. Lett., 110 (2013) 233602). In this case, the FWM intensity can be increased by three orders of magnitude at lower pump power.

Imaging Gold Nanorods by Plasmon-Resonance-Enhanced Four Wave Mixing

The current work investigates the four-wave mixing (FWM) signal from gold nanorods (NRs) using two synchronized lasers and its potential applications in bioimaging. Using the lightning rod model, we show that the strongest FWM occurs when the pump laser wavelength is tuned to be resonant with the longitudinal plasmon resonance wavelength of NR. The calculation is experimentally demonstrated by comparing the intensities of FWM from NRs with different plasmon resonance wavelengths. The FWM signal is further found to be enhanced by aggregation of NRs and is strongly dependent on pulse width. The FWM intensity from NRs is ∼39 times stronger than the coherent anti-Stokes Raman scattering intensity from melamine beads. This plasmon-resonance-enhanced FWM signal enables NRs to be used as a nonlinear optical (NLO) imaging probe.

Characteristics of nondegenerate four-wave mixing in electroabsorption modulator

The characteristics of nondegenerate four-wave mixing (FWM) in an electroabsorption modulator are reported. The input power dependence of FWM intensity agrees well with theoretical results based on third-order nonlinearity over a wide input power range of 16dB. The detuning characteristics of FWM have a −6dB∕octave response based on the carrier-density pulsation effect. The experimental results show that a higher reverse voltage brings about a faster carrier recombination. The asymmetricity of positive and negative detuning is the reverse of that of the semiconductor optical amplifier and is explained through a rate equation simulation.

Biexcitonic Bound and Continuum States of Homogeneously and Inhomogeneously Broadened Exciton Resonances

In this paper by Wolfgang Langbein and Jørn M. Hvam [1], selected as Editor's Choice in the present issue of phys. stat. sol. (a), the localization of biexcitonic and excitonic states in GaAs quantum wells is investigated by spectrally resolved four-wave mixing (FWM) experiments. The cover picture is a contour plot of the FWM intensity as a function of temporal pulse separation τ12 for cross-linear and co-polarization, scaled with the exciton binding energy R*y. Data are shown for three single and multi quantum well structures with different thicknesses, causing varying homogeneous and inhomogeneous broadening of the excitonic transitions (for details see [1]). The paper is an invited presentation and part of the Proceedings of the International Workshop on “Physics of Light–Matter Coupling in Nitrides (PLMCN-1)” held in Rome, Italy, September 26–29, 2001.

Line by‐line imaging of laser‐produced plasmas using one‐dimensional coherent four‐wave mixing

An experimental technique based on coherent one-dimensional four-wave mixing (FWM) with hyper-Raman resonances was developed for line-by-line imaging of the atomic distribution of excited atoms in a low-temperature plasma of optical breakdown. Comparison of the measured time dependences of FWM intensity and plasma transmission with the results of numerical simulations of plasma expansion allows the assessment of the influence of phase mismatch and one-photon absorption on FWM in a laser-produced plasma and demonstrates that FWM images of atomic spatial distributions free of distortions due to phase mismatch and absorption can be obtained for certain stages of plasma expansion. Copyright © 2000 John Wiley & Sons, Ltd.

Mixed biexcitons in single quantum wells

Biexcitonic complexes in a ZnSe single quantum well are investigated by spectrally resolved four-wave mixing (FWM). The formation of heavy-heavy-hole ${\mathrm{XX}}_{h}$ and of mixed heavy-light-hole ${\mathrm{XX}}_{m}$ biexcitons showing binding energies of ${\ensuremath{\Delta}}_{h}=4.8\mathrm{meV}$ and ${\ensuremath{\Delta}}_{m}=2.8\mathrm{meV}$ is identified by polarization selection rules. The coherent dynamics of the FWM response and the observed FWM intensity ratio between the ${\mathrm{XX}}_{h}$ and ${\mathrm{XX}}_{m}$ biexciton-induced nonlinear signals are in agreement with the solution of an extended optical Bloch equation.

Theory of the effect of odd-photon destructive interference on optical shifts in resonantly enhanced multiphoton excitation and ionization

We present a theory for two- and three-photon excitation, optical shifting, and four-wave mixing when a first laser is tuned onto, or near, a two-photon resonance and a second much more intense laser is tuned near or on resonance between the two-photon resonance and a second excited state. When the second excited state has a dipole-allowed transition back to the ground state and the concentration is sufficiently high, a destructive interference is produced between three-photon coupling of the ground state and the second excited state and one-photon coupling between the same states by the internally generated four-wave mixing field. This interference leads to several striking effects. For instance, as the onset of the interference occurs, the optical shifts in the two-photon resonance excitation line shape become smaller in copropagating geometry so that the line shapes for multiphoton ionization enhanced by the two-photon resonance eventually become unaffected by the second laser. In the same range of concentrations the four-wave mixing field evolves to a concentration-independent intensity. With counterpropagating laser beams the line shape exhibits normal optical shifts like those observed for both copropagating and counterpropagating laser beams at very low concentrations. The theoretical work presented here extends our earlier works by more » including the effect of laser bandwidth and by removing the restriction of having the second laser be tuned far from three-photon resonance. In this way we have now included, as a special case, the effect of both laser bandwidth and interference on laser-induced transparency. Unlike other effects related to odd-photon destructive interference, the effect of a broad bandwidth is to bring about the predicted effects at much lower concentrations. Studies in rubidium show good agreement between theory and experiment for both ionization line shapes and four-wave mixing intensity as a function of concentration. {copyright} {ital 1998} {ital The American Physical Society} « less

Application of coherent four-wave mixing for two-dimensional mapping of the spatial distribution of excited atoms in a laser-produced plasma

An experimental technique for the two-dimensional mapping of the relative populations of excited states of atoms and ions in a low-temperature plasma of optical breakdown is developed on the basis of coherent four-wave mixing (FWM) with hyper-Raman resonances. The possibility to extract information concerning the spatial distribution of the populations of excited atomic and ionic states from two-dimensional maps of the FWM intensity allowing for phase mismatch and one-photon absorption is considered. Conditions when FWM in a plasma occurs in the phase-matched regime and is not subject to a considerable influence of one-photon absorption are experimentally determined.