Four-wave Mixing Scheme Research Articles

Ultrafast Four‐Wave Mixing Phase‐Matched by Transient Nonlinear Phase Modulation in a MAPbBr3 Single Crystal

AbstractA degenerated four‐wave‐mixing (FWM) process in single‐crystal (CH3NH3)PbBr3 (MAPbBr3) is reported, where 150‐fs laser pulses at 1.33 µm are employed as the pump. Two pump photons interact with a single crystal, producing another two photons with higher and lower energies, respectively. One of the FWM‐generation sidebands is tuned from ∼1.23 to 1.21 µm and the other from ∼1.43 to 1.48 µm for the center wavelength, as the pump fluence is increased from 2.6 to 11.69 mJ cm−2. The self‐phase modulation induced by the strong pump pulses through the optical Kerr effect is responsible for the tuning dynamics. Transient spectroscopy not only verifies the FWM scheme for the interacting waves but also reveals the interference dynamics between the FWM‐generated sidebands and the probe pulse. In particular, the angular dependence of the FWM generation supplies direct evidence for the phase‐matching geometry. Using experimental data, a nonlinear refractive index coefficient of 1.19 × 10−14 cm2 W−1 at 1.33 µm for single‐crystal MAPbBr3 is determined.

Ultrafast temporal phase-resolved nonlinear optical spectroscopy in the molecular frame

In an ultrafast nonlinear optical interaction, the electric field of the emitted nonlinear signal provides direct access to the induced nonlinear transient polarization or transient currents and thus carries signatures of ultrafast dynamics in a medium. Measurement of the electric field of such signals offers sensitive observables to track ultrafast electron dynamics in various systems. In this work, we resolve the real-time phase of the electric field of a femtosecond third-order nonlinear optical signal in the molecular frame. The electric field emitted from impulsively pre-aligned gas-phase molecules at room temperature, in a degenerate four-wave mixing scheme, is measured using a spectral interferometry technique. The nonlinear signal is measured around a rotational revival to extract its molecular-frame angle dependence from pump-probe time-delay scans. By comparing these measurements for two linear molecules, carbon dioxide and nitrogen, we show that the measured second-order phase parameter (temporal chirp) of the signal is sensitive to the valence electronic symmetry of the molecules, whereas the amplitude of the signal does not show such sensitivity. We compare measurements to theoretical calculations of the chirp observable in the molecular frame. This work is an important step towards using electric field measurements in nonlinear optical spectroscopy to study ultrafast dynamics of electronically excited molecules in the molecular frame.

Two-dimensional nonlinear spectroscopy in the extreme ultraviolet to study dynamics of atomic and molecular gases

We present a two-dimensional (2D) nonlinear four-wave mixing scheme in the extreme ultraviolet (XUV) to investigate ultrafast electronic wave-packets dynamics of multi-electron states in the above-threshold ionization region, using atomic argon and molecular nitrogen as examples. Coherent light sources in the range between 24 and 45 eV is generated by phase-matched cascaded four-wave mixing processes with a collinear configuration of laser fields 800 nm and 1400 nm. Motion of the electrons involving the excited states 3s3p6np (1P10) of argon gas, theF2Σg+ state and the predissociation state C2Σu+ of molecular nitrogen ion N2+ are unravelled through the ‘on-axis’ and ‘off-axis’ features of the two-dimensional spectra. Interpretation of the experimental data is supported by a theoretical dipole control model. Hence, results of this study may be promising for studies of dynamics of electrons in more complex systems.

Generation and application of four-wave mixing in collinear high harmonic generation

We describe a thorough study of the wave-mixing procedure in the extreme ultraviolet (XUV) region involving three laser fields (800 nm, 1400 nm and 1860 nm). In addition to the phase matched HHG spectrum generated by an 800-nm laser (driving field), non-integer order wave-mixing spectra are produced when the driving field and the control field (1400 nm or 1860 nm) are collinearly focused into krypton gas. In addition, the simultaneous presence of three laser fields generates resolvable four-wave mixing (FWM) frequencies that clearly indicate the contribution of each control field. We also discuss an application of the FWM scheme to extend the HHG cutoff region and generate the XUV quasi-continuum spectrum.

Enhanced intensity difference squeezing with a low gain off-resonant Four-Wave Mixing in potassium vapor

Although potassium stands out among alkalies by its smallest ground state hyperfine splitting, smaller than Doppler broadening, investigations of its four-wave mixing (FWM) quantum properties, like squeezing and entanglement, were neglected. Here we present measurements of quantum correlations in potassium vapor using far-detuned double Λ scheme for FWM. We obtained the relative intensity difference squeezing (IDS) of -6.1 dB, with the squeezing bandwidth between 0.9 to 4.5 MHz on the noise spectra. The squeezing maximum in potassium compares well with the best results obtained in Rb and Cs, and has larger value than previously reported IDS in potassium. This result agrees qualitatively well with the squeezing calculated using analytical expressions from the model of operators when with chosen parameters FWM generates both squeezing and probe at their maximums. The ultimate squeezing level in potassium, predicted by the model, when conjugate absorption in the cell and optical losses behind the cell are neglected, is −10.29 dB. This is among the largest predicting squeezing obtained by FWM in alkalies.

A 509 nm pulsed laser system for Rydberg excitation of cesium atoms

<sec>Single photon source is a non-classical light field with anti-bunching effect, which has a potential applications in the research of fundamental physics problems, quantum precision measurement, quantum communication, quantum computing, etc. The strong interaction between highly excited Rydberg atoms presents an excitation blockade effect. In a dense Rydberg atomic ensemble, the excitation of more than one Rydberg atom within a blockade volume is suppressed, where the interactions of Rydberg atoms shift the atomic states out of resonance with an excitation laser.</sec><sec>We consider here the generation of single photon source by using a four-wave mixing scheme in a room-temperature atomic vapor cell. In a homemade micrometer-sized atomic vapor cell, one-dimensional size is smaller than the radius of Rydberg blockade and the other two-dimensional size is limited by the size of focused laser beam. The blockade radius is on the order of a few micrometers, depending on the Rydberg atom states. An excitation blockade effect can be used to realize single photon source in thermal cesium vapor microcells. The micron cesium-cell is used to spatially localize atomic groups, which results in the atomic decoherence time on the order of microseconds or even nanoseconds. This requires a high-power pulsed laser to prepare the Rydberg atomic state at a nanosecond scale.</sec><sec>Four-photon excitation schemes with narrow linewidth lasers are also used experimentally. The cesium-Rydberg state can usually be excited by the lasers with optical wavelengths 852 and 509 nm, respectively. The laser system is well-stabilized so that the detuning is small compared with the spontaneous linewidth of Rydberg state, while the laser power and temporal mode need to be specified for ns-time coherence in thermal cesium vapor microcells. The 852 nm laser can be achieved by modulating the continuous laser beam with the help of an electro-optic intensity modulator (EOIM). While this remains a technical challenge for 509 nm laser with ns-laser pulse. There is no EOIM to generate the ns-laser pulse with high power.</sec><sec>We demonstrate a novel generation method of 509 nm laser system. In our experiments, a 1018 nm fiber laser is used to produce a continuous laser with a typical linewidth of ～8 kHz and power of 10 mW. The nanosecond pulse is generated with the help of an electro-optic intensity modulator (EOIM) by modifying the continuous laser beam. The peak power of modulated optical pulse is amplified to 4600 W by using a homemade fiber amplifier. The output beam of 1018 nm is then injected into a periodically poled lithium-niobate (PPLN) to generate the second harmonics laser of 509 nm. The typical peak power of 509 nm reaches 173 W by optimizing PPLN phase matching parameters. The pulse repetition frequency of the 509 nm laser can be continuously tuned in a range of 300 kHz–100 MHz, and the pulse width can be continuously tuned in a range of 1–100 ns. Peak power fluctuation of the pulses is about 1.3%. The power 509 nm laser with optimized pulse parameters can be used to excite the cesium atom with GHz bandwidth. Meanwhile the two seed source lasers is well established experimentally, which allows alternating pulses with a different wavelength. This is an essential capability for realizing a single photon source through four-wave mixing.</sec>

Phase regeneration of 8PSK signal using phase-sensitive amplification based on an organic-Ge hybrid waveguide.

We numerically demonstrate the phase regeneration of eight-phase-shift keying (8PSK) in an organic-Ge hybrid waveguide with 10µm length. Through filling graphene oxide with a high Kerr coefficient and engineering of waveguide dimensions, an ultrahigh nonlinear coefficient with 5.86×106W-1m-1 is attained at 1550 nm. The phase regeneration of 8PSK signal is achieved by using phase-sensitive amplification of the dual-conjugated-pump degenerate four-wave mixing scheme. The error-vector magnitude (EVM), optical signal-to-noise ratio, as well as constellation diagrams of 8PSK signal are also used to evaluate the phase regeneration capacity quantitatively. A reduction of EVM from 39.25% to 1.34% for 8PSK signal is found. The results show great phase regeneration and noise-squeezing ability, which indicate that such a phase-sensitive amplifier of a waveguide can find critical promising applications in all-optical signal processing.

Stimulated Thermal Scattering in Two-Photon Absorbing Nanocolloids under Laser Radiation of Nanosecond-to-Picosecond Pulse Widths.

Recent discoveries in nonlinear optical properties of nanoparticle colloids make actual the challenge to lower the energy threshold of phase conjugation and move it into the domain of shorter pulse widths. A novel effect of the stimulated Rayleigh-Mie scattering (SRMS) in two-photon absorbing nanocolloids is considered as a promising answer to this challenge. We report the results of experimental and theoretical study of the two-photon-assisted SRMS in Ag and ZnO nanocolloids in the nanosecond-to-picosecond pulse width domain. For 12 ns 0.527 μm laser pulses, the four-wave mixing SRMS scheme provides lasing and amplification of backscattered anti-Stokes signal in Ag nanocolloids in toluene at the threshold 0.2 mJ and the spectral shifts up to 150 MHz. For 100 ps 0.532 μm pulses, we observed for the first time efficient (over 50% in signal-to-pump ratio of pulse energies) SRMS backscattering of the anti-Stokes signal in Ag nanocolloids in toluene and predominantly Stokes signal in ZnO nanocolloids in water, with the spectral shifts up to 0.25 cm−1. We develop the first order-in-perturbation model of the four-wave mixing two-photon absorption-assisted SRMS process which shows that at nanosecond pulses, amplification is predominantly due to the thermal-induced coherent oscillations of polarization while the slow temperature wave acts also as a dynamic spatial grating which provides a self-induced optical cavity inside the interaction region. At a picosecond pulse width, according to our model, the spectral overlap between pump and signal pulses results in formation of only the dynamic spatial temperature grating, and we succeeded at recovering the linear growth of the spectral shift with the pump power near the threshold.

Phase controllable four-wave mixing in the hybrid opto-electromechanical system

The future quantum networks will require reversible coherent conversion and modulation between microwave and optical photons to link the quantum information-processing ability of microwave and long-distance distribution ability of optical photons. Here, we present a scheme of bi-directional phase controllable four-wave mixing (FWM) between microwave and optical fields in the hybrid opto-electromechanical system. As an intermediate interface, a nanomechanical resonator optomechanically couples both optomechanical cavities in the optical and microwave frequency domains by the radiation pressure forces. We can find the four peaks of FWM, study the effects of the phases of the driven fields on the total, absolute, and cross correlation FWMs, and achieve the laws of phase control FWM based on quantum interference. In particular, we believe that such a hybrid opto- and electro-mechanical device incorporating highly coherent and compact mechanical elements on a chip has some potential functions for electro-optic modulation. We expect that such a modulator will have a broad range of applications including in optical communications and further quantum networks.

Engineering helical phase via four-wave mixing in the ultraslow propagation regime

We describe a theoretical investigation of a four-wave mixing (FWM) scheme in a six-level atomic system driven by a field with orbital angular momentum and making use of two electromagnetically induced transparency (EIT) control fields. The obtained results allow us to control the helical phase of the output FWM field by varying the intensities of the two EIT control fields as well as the detuning of the probe field. More interestingly, we can achieve FWM output fields that are very stable under variation of the system parameters and allow the helical phase twist to be manipulated and suppressed, if desired, by adjusting the probe detuning. In this way, our scheme may open a tool to control the helical phase in a compact, efficient, and robust way.

Application of laser dispersion method in apparatus combining H atom Rydberg tagging time-of-flight technique with vacuum ultraviolet free electron laser

Photodissociation of H2S in the VUV region plays an important role in the atmospheric chemistry and interstellar chemistry. To date, however, few studies have been focused on this topic. In this article, we have described a laser dispersion method applied in the apparatus combining the high-n H atom Rydberg tagging time-of-flight technique with the vacuum ultraviolet free electron laser (VUV FEL). The Lyman-α laser beam (121.6 nm) used in the H-atom detection was generated by the difference frequency four-wave mixing schemes in a Kr/Ar gas cell. After passing through an off-axis biconvex LiF lens, the 121.6 nm beam was dispersed from the 212.6 nm and 845 nm beams due to the different deflection angles experienced by these laser beams at the surfaces of the biconvex lens. This method can eliminate the background signal from the 212.6 nm photolysis. Combined with the VUV FEL, photodissociation of H2S at 122.95 nm was studied successfully. The TOF spectrum was measured and the derived total kinetic energy release spectrum was displayed. The results suggest that the experimental setup is a powerful tool for investigating photodissociation dynamics of molecules in the VUV region which involves the H-atom elimination processes.

Coherent diffusion of partial spatial coherence

Partially coherent fields are abundant in many physical systems. While the propagation of partially coherent light undergoing diffraction is well understood, its evolution in the presence of coherent diffusion (i.e., diffusion of complex fields) remains largely unknown. Here we develop an analytic model describing the diffusion of partially coherent beams and study it experimentally. Our model is based on a diffusion analog of the famous Van Cittert–Zernike theorem. Experimentally, we use a four-wave mixing scheme with electromagnetically induced transparency to couple optical speckle patterns to diffusing atoms in a warm vapor. The spatial coherence properties of the speckle fields are monitored under diffusion and are compared to our model and to the familiar evolution of spatial coherence of light speckles under diffraction. We identify several important differences between the evolution dynamics of the spatial coherence under diffraction and diffusion. Our findings shed light on the propagation of partially coherent fields in media where multiple scattering or thermal motion lead to coherent diffusion.

High-efficiency four-wave mixing beyond pure electromagnetically induced transparency treatment.

We present a theoretical study of high-efficiency four-wave mixing (FWM) sum-frequency generation beyond a pure electromagnetically induced transparency (EIT) technique in a five-level atomic system. In our FWM scheme, with the assistance of two Λ-type subsystems utilized to create EIT and Autler-Townes splitting (ATS), a synergetic mechanism of EIT and ATS, or a dual-ATS mechanism is induced. These novel mechanisms can have a significant impact on the FWM process in the optically thick medium, and the FWM efficiency can be several orders of magnitude larger than that obtained from the pure EIT method. This Letter opens up a new perspective for exploring enhanced quantum nonlinear optical phenomena.

Rotational dependence of the branching ratios and fragment angular distributions for the photodissociation of 12C16O in the Rydberg 4p(2) and 5p(0) complex region (92.84-93.37 nm).

12C16O shows complicated absorption structures in the wavelength range of 92.84-93.37 nm caused by the mutual interactions among the Rydberg 4p(2) and 5p(0) complexes, and several diffuse valence states. Here, we systematically measured the branching ratios and fragment angular distributions for the photodissociation of 12C16O in the wavelength range using our mini-time-slice velocity-map imaging (mini-TSVMI) setup and a tunable vacuum ultraviolet (VUV) laser radiation source generated by the two-photon resonance-enhanced four-wave mixing scheme. Various patterns of rotational dependence for the photodissociation branching ratios have been observed for different vibronic states, and they are found to be consistent with previous spectroscopic investigations, revealing the complicated coupling schemes and predissociation dynamics in this region. Irregular angular distributions of the photofragments have been observed, especially in the Rydberg 5p(0) complex region. This has been attributed to the simultaneous excitation of multiple states with different symmetries in this region. The newly observed underlying continuum in the Rydberg 5p(0) complex region has been directly detected in the present study, and it is found to be of 1Σ+ symmetry and dissociates predominantly into the C(3P) + O(3P) channel. This study generally confirms the results of previous spectroscopic studies from a different perspective, and adds new knowledge for understanding the complicated predissociation dynamics of 12C16O in the titled wavelength range.

High efficiency four-wave mixing in double asymmetry quantum dots

A theory analysis of the four-wave mixing (FWM) scheme in a double asymmetry quantum dots (QDs) system is performed. The efficiency of the generated field decreases in an oscillating mode for the penetration depth and is significantly enhanced because of three-wave mixing (TWM). The dependence of the conversion efficiency on the three coupling laser fields and decay rate is also discussed. High conversion efficiency up to 0.8 is demonstrated with small propagation length at low temperature. Such a solid-state system may be more practical due to the flexibility of QDs to generate coherent short-wavelength radiation.

Quantized nonlinear Gaussian-beam dynamics: Tailoring multimode squeezed-light generation

We present a general, second quantization procedure for multi-transverse-spatial mode Gaussian beam dynamics in nonlinear interactions. Previous treatments have focused on the spectral density and angular distribution of spatial modes. Here we go a layer deeper by investigating the complex transverse-spatial mode in each angular-spatial mode. Furthermore, to implement the theory, we simulate four-wave mixing and parametric down-conversion schemes, showing how one can elucidate and tailor the underlying multi-transverse-spatial mode structure along with it's quantum properties.

Slowing 80-ns light pulses by four-wave mixing in potassium vapor

We experimentally and theoretically study propagation of 80-ns Gaussian-like probe pulses in hot potassium vapor under conditions of four-wave mixing (FWM). The atomic scheme for FWM is off-resonant, double-$\mathrm{\ensuremath{\Lambda}}$ atomic scheme, with pump and probe photons, mediated in the K vapor, generating new probe and conjugate photons. We define the subset of FWM parameters, one-photon pump detuning, two-photon pump-probe Raman detuning, vapor density, the pump Rabi frequencies, when slowed pulses exit the vapor are also Gaussian-like. When Gaussian-like pulses exit the cell we are able to compare theoretical and experimental results for fractional delays and broadening for the probe and conjugate. We have obtained fractional delays above 1. Results of the model are compared with the experiment, with and without the model of Doppler averaging, when the atom velocity distribution is divided into different number of groups. We analyze possible causes for pulse broadening and distortion of slowed probe pulses and show that they are the result of quite different behavior of the probe pulse in the FWM vapor. Besides presenting the first results of slowing 80-ns probe pulses, this work is a useful test of the numerical model and values of parameters taken in the model that are not known in experiments.

Tunable VUV photochemistry using vacuum ultraviolet free electron laser combined with H-atom Rydberg tagging time-of-flight spectroscopy.

In this article, we describe an experimental setup for studying tunable vacuum ultraviolet photochemistry using the H-atom Rydberg tagging time-of-flight technique. In this apparatus, two vacuum ultraviolet laser beams were used: one is generated by using a nonlinear four-wave mixing scheme in a Kr gas cell and fixed at 121.6 nm wavelength to probe the H-atom product through the Lyman α transition and the other beam, produced by a seeded free electron laser facility, can be continuously tunable for photodissociating molecules in the wavelength range of 50-150 nm with extremely high brightness. Preliminary results on the H2O photodissociation in the 4d (000) Rydberg state are reported here. These results suggest that the experimental setup is a powerful tool for investigating photodissociation dynamics in the vacuum ultraviolet region for molecules involving H-atom elimination processes.

Simultaneous Measurement of Salinity and Temperature in Gold-Coated D-Shaped Photonic Crystal Fiber Using Four-Wave Mixing Technique

We propose a novel nonlinear technique for simultaneous measurement of salinity and temperature of water in a gold coated D-shaped photonic crystal fiber (DPCF). In this novel nonlinear technique, the sensitivity is calculated numerically through a degenerate four-wave mixing scheme by tracking the wavelength shift of the Stokes and anti-Stokes lines for various concentrations of NaCl and temperatures. The optimized fiber design with lattice pitch of 4.49 $\mu$ m, airhole diameter of 2.892 $\mu$ m, and with a gold layer of 39.5nm enables effective sensitivities of 1.6nm/(kg/kg) for salinity and of 12.31nm/ $^{\circ }$ C for temperature when light is launched at the pumping wavelength of 1070.4nm in 2cm of length of a DPCF. To our knowledge, the obtained sensitivity is much higher than that of other simultaneous measurement techniques. This novel nonlinear sensor has been demonstrated with high resolution of about 8.625 $\times$ $10^{-4}$ (kg/kg) and 9.74817 $\times$ $10^{-7}$ $^{\circ }$ C for salinity and temperature measurements, respectively.

Frequency up-shift in the stimulated thermal scattering under two-photon absorption in liquids and colloids of metal nanoparticles

We report the results of the experimental and theoretical study of stimulated temperature scattering in toluene and hexane solutions of Ag-nanoparticles, as well as in pure toluene in the two-photon absorption regime. A four-wave mixing scheme with two counter-propagating pump waves of the same frequency is utilised to demonstrate the lasing effect and the amplification of the backscattered anti-Stokes signal. For the first time, we have measured anti-Stokes spectral shifts which turn out to appreciably exceed the Rayleigh line widths in those liquids. It is shown that the amplification effect is provided predominantly by thermally induced coherent polarisation oscillations, while the dynamic interference temperature grating causes the formation of a self-induced optical cavity inside the interaction region.