Applications Of Four-wave Mixing Research Articles

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.

Nanoparticle Acoustic Resonance Enhanced Nearly Degenerate Four-Wave Mixing

Nanoparticles have acoustic resonances in the 10 GHz to THz range, which makes them interesting for resonantly enhanced four-wave mixing applications such as frequency conversion. Using a nearly degenerate four-wave mixing setup and comparing with Rayleigh–Gans–Debye scattering, we estimate a nonlinear refractive index, n2, of approximately 2 × 10–5 cm2/MW for 22 nm polystyrene nanospheres in water at a difference frequency of 43 GHz. This is nearly 3 orders of magnitude larger than the typical below-band-gap nonlinear response of semiconductors. This strong high-frequency response may be ideal for four-wave frequency conversion in all-optical information technologies, with appropriately chosen nanoparticle sizes.

Four-wave mixing experiments with extreme ultraviolet transient gratings.

Four wave mixing (FWM) processes, based on third-order non-linear light-matter interactions, can combine ultrafast time resolution with energy and wavevector selectivity, and enables to explore dynamics inaccessible by linear methods.1-7 The coherent and multi-wave nature of FWM approach has been crucial in the development of cutting edge technologies, such as silicon photonics,8 sub-wavelength imaging9 and quantum communications.10 All these technologies operate with optical wavelengths, which limit the spatial resolution and do not allow probing excitations with energy in the eV range. The extension to shorter wavelengths, that is the extreme ultraviolet (EUV) and soft-x-ray (SXR) range, will allow to improve the spatial resolution and to expand the excitation energy range, as well as to achieve elemental selectivity by exploiting core resonances.5-7,11-14 So far FWM applications at these wavelengths have been prevented by the absence of coherent sources of sufficient brightness and suitable experimental setups. Our results show how transient gratings, generated by the interference of coherent EUV pulses delivered by the FERMI free electron laser (FEL),15 can be used to stimulate FWM processes at sub-optical wavelengths. Furthermore, we have demonstrated the possibility to read the time evolution of the FWM signal, which embodies the dynamics of coherent excitations as molecular vibrations. This result opens the perspective for FWM with nanometer spatial resolution and elemental selectivity, which, for example, would enable the investigation of charge-transfer dynamics.5-7 The theoretical possibility to realize these applications have already stimulated dedicated and ongoing FEL developments;16-20 today our results show that FWM at sub-optical wavelengths is feasible and would be the spark to the further advancements of the present and new sources.

Designing photonic crystal waveguides for broadband four-wave mixing applications.

We present photonic crystal waveguide designs which exhibit large four-wave mixing efficiencies over a wide wavelength region. These designs are identified using an optimization process taking into account sophisticated figure-of-merits that depend on the pump bandwidth and the signal/pump tunability. The obtained designs achieve up to -18.9 dB conversion efficiency, tunable over a 10nm tunability range. We also present alternative designs that are less efficient but have smaller power requirements and are far more compact.

Analytical approach to the design of microring resonators for nonlinear four-wave mixing applications

An analytical approach for obtaining linear and nonlinear design parameters of microresonators is presented. The eigenmode/eigenfrequency problem of planar resonators is considered in detail, with an analytical closed-form approximation derived for resonators possessing a large radius to width ratio. The analysis permits the resonant frequencies and mode profiles to be determined together with the dispersion properties. The dependence of the effective nonlinear Kerr coefficient on the mode volume is further considered, and also the waveguide coupling together with estimates of the Q-value. Examples, which are in good agreement with numerical simulations, are presented for silicon resonators. The approach can be used for designing planar microring resonators for nonlinear four-wave mixing applications, such as optical Kerr frequency comb generation.

Designing slow-light photonic crystal waveguides for four-wave mixing applications

We discuss the optimization of photonic crystal waveguides for four-wave mixing (FWM) applications, taking into account linear loss and free-carrier effects. Suitable figures of merit are introduced in order to guide us through the choice of practical, high-efficiency designs requiring relatively low pump power and small waveguide length. In order to realistically perform the waveguide optimization process, we propose and validate an approximate expression for the FWM efficiency, which significantly alleviates our numerical calculations. Promising waveguide designs are identified by means of an exhaustive search, altering some structural parameters. Our approach aims to optimize the waveguides for nonlinear signal-processing applications based on the FWM.

Visualization of Oil Body Distribution in Jatropha curcas L. by Four-Wave Mixing Microscopy

Jatropha curcas L. (jatropha) is a superior oil crop for biofuel production. To improve the oil yield of jatropha by breeding, the development of effective and reliable tools to evaluate the oil production efficiency is essential. The characteristics of the jatropha kernel, which contains a large amount of oil, are not fully understood yet. Here, we demonstrate the application of four-wave mixing (FWM) microscopy to visualize the distribution of oil bodies in a jatropha kernel without staining. FWM microscopy enables us to visualize the size and morphology of oil bodies and to determine the oil content in the kernel to be 33.2%. The signal obtained from FWM microscopy comprises both of stimulated parametric emission (SPE) and coherent anti-Stokes Raman scattering (CARS) signals. In the present situation, where a very short pump pulse is employed, the SPE signal is believed to dominate the FWM signal.

Ring Resonator Lasers using Passive Waveguides and Integrated Semiconductor Optical Amplifiers

We present a review of our work on ring lasers using passive waveguides and couplers (directional and multimode interference) integrated with semiconductor optical amplifiers (SOAs). Two architectures are given in this paper. The first architecture includes the SOA inside the ring cavity. The second architecture also known as ring resonator coupled laser, consists of passive ring resonators having SOAs in the bus waveguides. The increased photon lifetime in the cavity and the tunability of the ring response can be used to make compact, narrow linewidth, and widely tunable lasers. Four-wave mixing applications are also addressed.

Four-wave mixing in laser diodes for difference-frequency synthesis

Laser diodes are not only good laser-light sources but highly efficient nonlinear elements. The mixing signal power as a function of pump frequency differences of as much as 3 THz for three- and four-color four-wave mixing configurations is investigated experimentally and theoretically. The influence of phase matching, mode-spacing dispersion, and resonance effects is described by a round-trip model yielding an effective nonlinearity from the experimental data. The values obtained are in good agreement with the theoretical results. The phase-coherent bisection of a frequency interval and heterodyne detection with a coherent local oscillator are demonstrated as examples of application of four-wave mixing in laser diodes in frequency synthesis and spectroscopy.

Optimum pump pulse selection for demultiplexer application of four-wave mixing in semiconductor laser amplifiers

We report on an analysis of four-wave mixing in semiconductor laser amplifiers used for demultiplexing time-division multiplexed data streams at ultra-high bit rates. The analysis is focused on the optimum control pulse energy and width with respect to the switching efficiency, channel crosstalk, and jitter tolerance. We use a simple model of the time resolved gain saturation and four-wave mixing. It turns out, that an optimum pulse energy exists with respect to the switching efficiency. The requirements on the pulse width are contrary for the channel crosstalk and the jitter tolerance. Results for an optimum system design are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Phase noise of four-wave mixing in semiconductor lasers

A simple theoretical analysis shows that the linewidth of the conjugate wave produced in four-wave mixing in semiconductor lasers is equal to the linewidth of the probe plus four times the linewidth of the pump. Experimental results in good agreement with the theory are presented. This result implies an enormous enhancement in the phase noise of the conjugate wave and sets a limitation on some practical applications of four-wave mixing.

Theory and applications of four-wave mixing in photorefractive media

The development of a theory of four-wave mixing in photo-refractive crystals is described. This theory is solved in the undepleted pumps approximation with linear absorption and without using the undepleted pumps approximation for negligible absorption. Both the transmission and reflection gratings are treated individually. The results are used to analyze several photorefractive phase conjugate mirrors, yielding reflectivities and thresholds. The use of photorefractive crystals as optical distortion correction elements and experimental demonstrations of several of the passive phase conjugate mirrors are described.

DEGENERATE FOUR-WAVE MIXING IN SEMICONDUCTORS AND FERROELECTRICS

Semiconductors and ferroelectrics are promising candidate materials for a variety of applications of degenerate four-wave mixing. In this talk, we will review nonlinear mechanisms in each material and compare the performance of both types of materials for degenerate four-wave mixing applications.