Four-wave Mixing Signal Intensity Research Articles

Nonlinear plasmonic behavior of nanohole arrays in thin gold films for imaging lipids

We demonstrate linear and nonlinear plasmonic behaviors of periodic nanohole arrays in thin gold (Au) films with varying periodicities. As expected, the linear optical transmission spectra of the nanohole arrays show a red-shift of the resonance wavelength and Wood's anomaly with increasing hole spacing. The optical transmission and electric near-field intensity distribution of the nanohole arrays are simulated using the finite element method. The nonlinear plasmonic behavior of the nanohole arrays is studied by using picosecond pulsed excitation at near-infrared wavelengths. The characteristic nonlinear signals indicating two-photon excited luminescence (TPEL), sum frequency generation, second harmonic generation, and four-wave mixing (FWM) are observed. A maximum FWM/TPEL signal intensity ratio is achieved for nanohole arrays with a periodicity of 500 nm. Furthermore, the significant FWM signal intensity and contrast compared to the background were harnessed to demonstrate the ability of surface-enhanced coherent anti-Stokes Raman scattering to visualize low concentrations of lipids deposited on the nanohole array with a periodicity of 500 nm.

Time-delayed behaviors of transient four-wave mixing signal intensity in inverted semiconductor with carrier-injection pumping

An analytical expression of transient four-wave mixing (TFWM) in inverted semiconductor with carrier-injection pumping was derived from both the density matrix equation and the complex stochastic stationary statistical method of incoherent light. Numerical analysis showed that the TFWM decayed decay is towards the limit of extreme homogeneous and inhomogeneous broadenings in atoms and the decaying time is inversely proportional to half the power of the net carrier densities for a low carrier-density injection and other high carrier-density injection, while it obeys an usual exponential decay with other decaying time that is inversely proportional to half the power of the net carrier density or it obeys an unusual exponential decay with the decaying time that is inversely proportional to a third power of the net carrier density for a moderate carrier-density injection. The results can be applied to studying ultrafast carrier dephasing in the inverted semiconductors such as semiconductor laser amplifier and semiconductor optical amplifier.

Four-wave mixing signal intensity: Relaxation time effects on the absorptive and dispersive optical properties in a two-level system

A study of the effects of relaxation times on the Four-Wave Mixing (FWM) signal response in frequency space for a two-level system is presented where the collisional effects of the solvent and the presence of the electromagnetic field are considered. The model is a generalization of the conventional two-level approach in that it includes a simplified description of the molecular structure associated with the non-zero permanent dipole moments. Significant changes in both the FWM-intensity and nonlinear optical properties are observed, due mainly to changes in the ratio between the longitudinal and transversal relaxation times.

SOLVENT COLLISIONAL EFFECTS IN FOUR-WAVE MIXING

The stochastic effects of a thermal bath on a two-level molecular system interacting with a classical electromagnetic field are considered. The collective effects are modeled as a random Bohr frequency, whose manifestation is the broadening of the upper level according to a prescribed random function. A methodology based in cumulant expansions to obtain the average in the Fourier components associated with the coherence and populations, calculated by Optical Stochastic Bloch Equations (OSBE), is employed. The Four-wave mixing signal intensity as a function of the detuning of the pump beam, parametrized by the ratio of the relaxation times and other variables, is analyzed.

Switching enhancement and suppression of four-wave mixing via a dressing field

The switch between the enhancement and suppression of the four-wave mixing (FWM) process in an electromagnetically induced transparency (EIT) window via quantum interference has been demonstrated experimentally. The enhancement and suppression of the FWM signal, as well as the EIT window, switch with a change in the probe detuning. Also, by controlling the powers of the dressing and probe fields, the enhancement and suppression of the FWM signal can be switched and an optimized enhancement can be obtained. Such a switch of the enhancement and suppression of the FWM signal intensity can find potential applications in optical switches, optical communication and quantum information processes.

Four wave mixing at air-dielectric interfaces with a femtosecond laser excitation

In this article we report our experimental results on non collinear four-wave mixing (FWM) at air-dielectric interfaces. We generated FWM signal from the two interfaces of a 1mm thick fused silica slide with air using two 800 nm, 100 fs pump pulses in non-collinear pump-probe type geometry. We observe that there is a maximum peak shift of approximately 1.5 nm in FWM signals corresponding to the two interfaces of the same silica slide. Further, we find that the intensity of FWM signal observed at air to silica interface is less than that from silica to air interface. We briefly elaborate on this observation with systematic study of FWM in fused silica.

Observation of Sub-femtosecond Polarization Beats Using Twin Noisy Driving Fields

We study the phase-conjugate polarization interference in a V-type three-level system and obtain an analytic closed form for the second-order stochastic correlation of sum-frequency polarization beat. In our Na vapour atomic system pumped by laser pulse of nanosecond timescale duration, we experimentally demonstrate an ultrafast modulation of the four-wave mixing signal intensity with a sub-femtosecond timescale period, corresponding to the sum-frequency of the resonant transitions from 3S1/2 to 3P1/2 and 3P3/2.

Nonlinear propagation and wave mixing characteristics of pulses in semiconductor optical amplifiers

AbstractNonlinear propagation and wave mixing characteristics of pulses in semiconductor optical amplifiers (SOAs) are analyzed using the finite‐difference beam propagation method (FD‐BPM). From the analyzed output waveform it is found that the peak positions of pulses are shifted to the leading edge. The output spectra are red‐shifted and the dips are found at the higher frequency side in the frequency spectra. Two pulses propagate in SOAs and four‐wave mixing (FWM) characteristics are obtained. Next, all‐optical demultiplexing (DEMUX) characteristics of pulses in SOAs based on FWM are analyzed. From this analysis, it is clear that the SOAs with wider gain bandwidth are required for faster DEMUX operation. The DEMUX characteristics from the time‐multiplexed signals by the repetitive pump pulses are also analyzed. The FWM signal intensity decreases with the strong pump pulses. However, there is no pattern effect due to gain saturation of pulses, because the pump pulses are injected continuously. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1223–1227, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23350

Analysis of optical DEMUX characteristics based on four-wave mixing in semiconductor optical amplifiers

We have analyzed the basic characteristics of all-optical demultiplexing (DEMUX) based on four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) by solving a modified nonlinear Schrodinger equation by the finite-difference beam propagation method. Amplified spontaneous emission noise was not included in our model. The optimum pump pulsewidth for obtaining the high ON-OFF ratio is 1/spl sim/3 ps for 1 ps, 250 Gb/s probe pulses. The shorter limit of the pulsewidth is due to detuning between the pump and probe frequencies, which is determined by the gain bandwidth of the SOA. In order to achieve faster DEMUX operation, an SOA with broader gain bandwidth is required. We also simulated pattern effects in the FWM signal. Power fluctuation in the FWM signal can be reduced by using a strong energy pump pulse and/or weak energy probe pulse. The energy fluctuation of the FWM signal decreases to less than 1% for a 30-bit, 250-Gb/s input probe pulse train with a pulse energy of 0.01 pJ. This small fluctuation should not disturb DEMUX operation. We have also examined DEMUX from time multiplexed signals by repetitive pump pulses. Strong energy pump pulses decrease the FWM signal intensity. However, there is no pattern effect due to gain saturation because the pump pulses are injected continuously.

Theory of forward degenerate four-wave mixing in two-level saturable absorbers

A theoretical description for a forward degenerate four-wave mixing process in homogeneously broadened two-level absorbers with arbitrary intensities of all four beams is presented. Assuming no pump absorption and depletion, we obtain an analytical solution of forward degenerate four-wave mixing signal intensity in the limit of the strong pumps and weak probe and signal. In the case of low absorption or large detuning, this solution is shown to become equivalent to that of the phase-conjugate degenerate four-wave mixing derived by Abrams and Lind [Opt. Lett.2, 94 (1978)]. For arbitrary beam intensities and absorption parameters, the signal intensity is numerically calculated by solution of the coupled equations of complex wave amplitudes. Comparing the results of the numerical calculation with those of the analytical solution, we discuss the validity of using the analytical solution in practical experiments and show the saturation behavior that is due to the strong probe beam. The line shapes under the various ratios among the input beams and absorption parameters are also obtained and discussed.

Erratum The dependence of broad band four-wave mixing signal intensity on the length of the interaction region

Erratum The dependence of broad band four-wave mixing signal intensity on the length of the interaction region

Four-Wave Mixing with Short Temporally Nonoverlapping Pulses

We predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.

Ultrafast Modulation Spectroscopy in Four-Level System

Based on the interference between two two-photon processes, we reported a four-level ultrafast modulation spectroscopy in Na vapor, where 3S, 3P, 5S, and 4D formed a four-level system. We studied the temporal behavior of the four-wave mixing signal intensity and obtained signal modulation with period 25 fs, corresponding to the splitting between 5S and 4D. This technique can achieve Doppler-free precision in the measurement of the energy level splitting between two excited states which are dipolar forbidden from the ground state.

The dependence of broadband four-wave mixing signal intensity on the length of the interaction region

Abstract A theoretical investigation of broadband four-wave mixing (FWM) signal intensity dependence on the length of the interaction region, L, is undertaken, for the case of weak intensity input beams. The phase diffusing model, PDM, is used to describe the statistics of the field fluctuations. A general result is derived which is in agreement with the quadratic L dependence obtained in previous work by Cooper et al. 1989, Phys. Rev. A, 40, 5707, where only the particular case of coherent lengths, L c , much greater than L was considered. We particularize our general result for the opposite case, L c ≰L, where retardation effects in the randomly fluctuating phases can no longer be neglected. In this case we find the FWM signal intensity to have a linear, rather than a quadratic, dependence on L. An intuitive and simple physical justification is provided for this new result in terms of the short length scale, coherent dipole, contributions to the FWM signal, along the interaction region.

The dependence of broadband four-wave mixing signal intensity on the length of the interaction region

Abstract A theoretical investigation of broadband four-wave mixing (FWM) signal intensity dependence on the length of the interaction region, L, is undertaken, for the case of weak intensity input beams. The phase diffusing model, PDM, is used to describe the statistics of the field fluctuations. A general result is derived which is in agreement with the quadratic L dependence obtained in previous work by Cooper et al. 1989, Phys. Rev. A, 40, 5707, where only the particular case of coherent lengths, L c , much greater than L was considered. We particularize our general result for the opposite case, L c ≰L, where retardation effects in the randomly fluctuating phases can no longer be neglected. In this case we find the FWM signal intensity to have a linear, rather than a quadratic, dependence on L. An intuitive and simple physical justification is provided for this new result in terms of the short length scale, coherent dipole, contributions to the FWM signal, along the interaction region.

Ultrafast modulation spectroscopy in a cascade three-level system.

Based on the polarization interference between one-photon and two-photon processes, we demonstrated an ultrafast modulation spectroscopy in a cascade three-level system (UMSCTS) in Na vapor, which showed a modulation of the four-wave mixing signal intensity with a 55-fs period, corresponding to the beating between the resonant frequencies of the transitions from 3${\mathit{S}}_{1/2}$ to 3${\mathit{P}}_{3/2}$ and from 3${\mathit{P}}_{3/2}$ to 4${\mathit{D}}_{3/2,5/2}$. We have also discussed the possibility of using UMSCTS to measure the energy levels of the excited states with Doppler-free precision.

Polarization Beats in a Cascade Three-Level System

Based on the interference between one-photon and two-photon processes, we report polarization beats in a cascade three-level system (PBCTS). We performed PBCTS experiments in Na vapor, which showed a modulation of the four-wave mixing signal intensity with period 55 fs, corresponding to the beating between the resonant frequencies of the transitions from 3S1/2 to 3P3/2 and from 3P3/2 to 4D3/2,5/2.

THE EFFECT OF THE STOCHASTIC PROPERTY OF LASER ON THE DEGENERATE FOUR-WAVE MIXING

The effect of the stochastic field on the degenerate four-wave mixing signal intensity hag been studied basing on the phase-diffusion model. It is shown that the ratio of the correlation time of the laser source to the relaxation time of the induced grating plays an important role. The effect of the stochastic property of laser source on the linewidth of mixing signal has also been discussed.