Parametric Four-wave Mixing Research Articles

Wavelength-tunable parametric third-harmonic generation in a photonic-crystal fiber

A photonic-crystal fiber (PCF) is used to demonstrate a fiber-optic format of efficient third-harmonic generation through a 3ω=2ω+2ω−ω parametric four-wave mixing, involving 1.24 μm radiation of a femtosecond Cr:forsterite laser (ω) and its second-harmonic output (2ω). The frequency of the 3ω fiber output is tuned within the range of wavelengths from 407to433 nm by changing the peak power of the 1.24 μm input laser pulses through cross-phase-modulation-induced instability. The 3ω field is shown to play a significant role in supercontinuum generation in a PCF, substantially enhancing the short-wavelength part of the supercontinuum spectrum.

Soliton pulses in an erbium-doped fiber ring laser and its use in supercontinuum generation

We present a source of soliton pulses in an erbium-doped fiber ring laser. The passive mode-locking is achieved by using the nonlinear polarization rotation technique. The system generates 352 fs pulses with repetition rate of 12.5 MHz and the 3dB spectrum width of about 7.8 nm at the central wavelength of 1563.3 nm. A low-cost erbium-doped fiber amplifier is employed to boost the peak power of the pulses. Single-mode supercontinuum is obtained by passing the amplified pulses through a photonic crystal fiber with the length of 101 nm. Further more, we show the evolution process of the supercontinuum with different optical pump power. It is shown that, with the low-intensity femtosecond pulses, the spectrum broadening is caused by the fission of the higher-order solitons. With the increase of the pump power, the threshold of stimulated Raman scattering (SRS) is achieved, and the energy transfer through SRS spreads toward the long wavelength and the short wavelength sides. On further increasing the pump power, the coupling between SRS and parametric four-wave mixing will result in the appearance of waves with new wavelengths, and the spectrum will become broader and more smooth.

Cross-phase-modulation-induced instability and efficient parametric frequency conversion of ultrashort light pulses

We experimentally demonstrate efficient controlled parametric frequency conversion of femtosecond laser pulses through cross-phase-modulation-induced instability in the presence of a copropagating pump field in a fused silica photonic-crystal fiber. The amplitudes and the frequency shifts of sidebands generated in the spectrum of the probe field at the output of the fiber as a result of parametric four-wave mixing are controlled by varying the intensity of the pump field.

Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP-InP racetrack microresonators

We demonstrate for the first time a nonlinear finite-difference time-domain (FDTD) analysis of optical parametric four-wave mixing (FWM) in an actual InGaAsP-InP-based racetrack microresonator, and the results are compared with measurements on an experimental prototype. It has been found from the two-dimensional (2-D) and three-dimensional FDTD analyses that the resonance frequencies can be reasonably predicted by an FDTD model by considering the strong material dispersion of the waveguide medium and that the wavelength conversion by FWM is not sensitive to the dimensionality of the model; thus, it is efficiently predicted by the 2-D FDTD model.

Four-wave mixing assisted self-stable 4×10 GHz actively mode-locked Erbium fiber ring laser

We proposed and developed a self-stable multiwavelength (4 cbannels) 10-GHz actively mode-locked Erbium-doped fiber ring laser with 0.8 nm wavelength spacing. A 1-km highly nonlinear fiber is incorporated in the laser cavity to eliminate the strong gain competitions in the homogeneously broadened EDF by multiple parametric four-wave mixing processes. The fiber nonlinearity is also helpful to provide phase locking and stabilize the output pulse. Stable laser pulses at 1556.55, 1557.36, 1558.17, and 1558.98 nm are successfully obtained simultaneously with supermode noise suppression ratio greater than 50 dB. The corresponding time-bandwidth products of four channels are 0.39 ~ 0.41.

Polarization of signal wave radiation generated by parametric four-wave mixing in rubidium vapor: Ultrafast(∼150−fs)and nanosecond time scale excitation

The polarization characteristics of the signal wave produced in Rb vapor by difference-frequency, parametric four-wave mixing (FWM) has been investigated for either ultrafast $(\ensuremath{\sim}150\phantom{\rule{0.3em}{0ex}}\mathrm{fs})$ or nanosecond time-scale excitation of the $5s\ensuremath{\rightarrow}\ensuremath{\rightarrow}5d$, $7s$ two photon transitions. The electronic configurations of the $5d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ and $7s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}$ states of Rb, as well as their energy separation $(\ensuremath{\sim}608\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1})$, offers the opportunity to examine separately the resonantly enhanced $5s\ensuremath{\rightarrow}\ensuremath{\rightarrow}7s$, $5d\ensuremath{\rightarrow}6p\ensuremath{\rightarrow}5s$ FWM pathways on the nanosecond time scale and then to drive both channels simultaneously with an ultrafast pulse of sufficient spectral width. As expected, dye laser $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{ns})$ excitation of the $5s\ensuremath{\rightarrow}\ensuremath{\rightarrow}5d$ $(J=5∕2)$ transition produces a signal wave $({\ensuremath{\lambda}}_{s}\ensuremath{\sim}420\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ having the same ellipticity as the driving optical field. Two photon excitation of Rb $(7s)$ on the same time scale, however, generates an elliptically polarized signal when the pump is linearly polarized $(\ensuremath{\epsilon}=1)$, a result attributed to $7s\ensuremath{\rightarrow}6p$, $5p$ amplified spontaneous emission at $\ensuremath{\sim}4\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ and $\ensuremath{\sim}741\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, respectively. Simultaneous excitation of the $5s\ensuremath{\rightarrow}\ensuremath{\rightarrow}7s$, $5d$ transitions with $\ensuremath{\sim}150\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ pulses centered at $\ensuremath{\sim}770\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ yields polarization characteristics that can be approximated as a superposition of those for the individual transitions, thus displaying weak coupling between the two FWM channels. Also, the influence of molecular contributions to the FWM signal is observed for Rb number densities above $\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.

Computation of the intensities of parametric holographic scattering patterns in photorefractive crystals

The present work represents a first attempt to perform computations of output intensity distributions for different parametric holographic scattering patterns. Based on the model for parametric four-wave mixing processes in photorefractive crystals and taking into account realistic material properties, we present computed images of selected scattering patterns. We compare these calculated light distributions to the corresponding experimental observations. Our analysis is especially devoted to dark scattering patterns as they make high demands on the underlying model.

Polarization- and mode-dependent anti-Stokes emission in a birefringent microstructure fiber

We have studied the polarization dependence of frequency-upconversion of 35-fs pulses of 820-nm Ti : sapphire laser radiation in a birefringent microstructure fiber with a high air-filling-fraction cladding. The central wavelength of frequency-upconverted radiation and its transverse intensity profile are controlled in our experiments through a selective coupling of the pump field into higher order modes of the fiber and polarization-sensitive phase matching in parametric four-wave mixing, allowing the central wavelength of the anti-Stokes fiber output to be tuned and its transverse intensity profile to be modified by varying the polarization state of the input pump field.

Quantum coherent effects in cavity exciton polariton systems

The non-linear emission from semiconductor microcavities in the strong coupling regime exhibits specific coherence properties that can be interpreted by parametric polariton four-wave mixing. In a geometry corresponding to degenerate four-wave mixing, we predict and observe a phase dependence of the amplification which is a signature of a coherent polariton wave mixing process. This process is also expected to lead to bistability and squeezed light generation. Spatial effects in the non-linear regime are evidenced, and spatial filtering is required in order to optimize the measured squeezing which is observed close to the bistability turning point. Moreover, the presence of strong coupling inside the microcavity allows to produce a new type of squeezing involving a part-light, part-matter field, the polariton.

A simple and rigorous verification technique for nonlinear fdtd algorithms by optical parametric four-wave mixing

A rigorous quantitative verification technique is presented for nonlinear finite-difference time-domain (FDTD) algorithms by analyzing parametric four-wave mixing (FWM) in an optical Kerr medium without involving other numerical techniques. This technique allows quick and reliable verification of complicated nonlinear FDTD algorithms, hence enhancing the application of nonlinear FDTD analysis to more realistic optical problems. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 88–91, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21270

Broad-band tunable wavelength conversion using Raman-assisted parametric four-wave mixing in highly nonlinear fibers with double-pass geometry

Efficient wavelength conversion using distributed Raman gain and the Raman-assisted parametric four-wave mixing in 1 km of highly nonlinear fibers (HNLFs) is demonstrated in this letter. We present the theoretical analysis of the Raman-assisted parametric process and investigate the mechanism of wavelength conversion between parametric Stokes and anti-Stokes light. The system is implemented in a double-pass Raman amplifier where a tunable optical bandpass filter and a wide-band reflector are used to form a laser oscillation in the normal dispersion region of HNLF. The lasing light acts as the parametric pump to enable the wide-band wavelength conversion about the pump wavelength. Conversion efficiency greater than 0 dB over 50 nm is obtained and the converted idler wavelength can be adjusted more than 10 nm continuously by tuning the tunable optical filter. Hence, an arbitrary new wavelength can be converted within the tunable range of optical filter with high efficiency.

Resonantly enhanced parametric four-wave mixing in sodium vapour

The conical and axially propagating UV emissions have been registered in sodium vapour excited with picosecond light pulses. The near-resonant two-photon excitation of 4D sodium level and efficient generation of coherent radiation in 330 nm spectral region (near the frequencies of 3S–4P1/2,3/2 sodium transitions) have been obtained for the pump wavelength tuned between 578.5 and 586 nm. The spectral and angular properties of the emitted radiation are discussed in terms of the phase matched parametric four-wave mixing.

High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser.

High-power supercontinua are demonstrated in highly nonlinear, dispersion-shifted fibers with a continuous-wave Raman fiber laser. Supercontinuum growth is experimentally studied under different combinations of fiber length and launch power to show output powers as high as 3.2 W and bandwidths greater than 544 nm. Modulation instability (MI) is observed to seed spectral broadening at low launch powers, and the interplay between MI and stimulated Raman scattering plays an important role in the growth of the continuum at high launch powers. The effect on continuum generation of parametric four-wave mixing coupled with the higher-order dispersion properties of the fiber is investigated.

Generation of femtosecond anti-stokes pulses through phase-matched parametric four-wave mixing in a photonic crystal fiber.

Phase-matched parametric four-wave mixing in higher-order guided modes of a photonic crystal fiber is shown to result in an efficient decay of 40-fs 800-nm Ti:sapphire laser pump pulses into an anti-Stokes signal with a central wavelength around 590-600 nm and a Stokes signal centered at 1.25 microm. The photonic crystal fiber is designed in such a way as to minimize the group-velocity dispersion at the pump wavelength, phase match the parametric four-wave-mixing process, and reduce the group delay between the pump and the anti-Stokes pulses. The duration of the anti-Stokes pulse under these conditions, as shown by cross-correlation frequency-resolved optical gating measurements, is less than 200 fs.

Broadband source generated by stimulated Raman scattering and four-wave mixing in a highly nonlinear optical fiber ring cavity.

A novel high-power broadband source based on the combined action of stimulated Raman scattering and parametric four-wave mixing in a highly nonlinear dispersion-shifted fiber ring cavity is investigated experimentally. An output spectrum of 1510-1580 nm with a stable power of 91 mW is demonstrated with a dual-wavelength pumping scheme.

Squeezing in semiconductor microcavities in the strong-coupling regime

We report squeezed polariton generation using parametric polariton four-wave mixing in semiconductor microcavities in the strong coupling regime. The geometry of the experiment corresponds to degenerate four-wave mixing, which gives rise to a bistability threshold. Spatial effects in the nonlinear regime are evidenced, and spatial filtering is required in order to optimize the measured squeezing. By measuring the noise of the outgoing light, we infer a 9 percent squeezing on the polariton field close to the bistability turning point.

Production and Probing of Atomic Wavepackets With Ultrafast Laser Pulses: Applications to Atomic and Molecular Dynamics

We demonstrate that atomic wavepackets can serve as sensitive detectors for investigating atomic and molecular dynamics. In concert with parametric four-wave mixing, the interference between coherent superpositions of atomic excited states produced by ultrafast (/spl sim/150 fs) pump and probe pulses provides a new and powerful tool with which fundamental processes, such as molecular dissociation and Rydberg-Rydberg atomic collisions, can be observed with the extraordinary sensitivity afforded by a coherent nonlinear optical process. Experiments are described in which the dissociation of an electronically excited molecule (Rb/sub 2/) and the distribution of atomic fragments into excited states spanning >10 000 cm/sup -1/ are observed. Also, resonant collisions between Rb atoms in the 7s and 5d states are detected by monitoring the shift in the frequency of an atomic wavepacket induced by the dipole-dipole interaction.

Complete experimental characterization of the influence of parametric four-wave mixing on stimulated Raman gain.

We present what is to our knowledge the first complete measurement of the dependence of Raman gain on chromatic dispersion, fully revealing the influence of parametric four-wave mixing on stimulated Raman scattering. In particular, a threefold increase of the Raman gain is observed under phase-matching conditions, in excellent agreement with theoretical predictions. Our experiments, which were performed in a photonic crystal fiber, demonstrate that these unique fibers can be exploited to boost the performances of fiber Raman amplifiers.

Molecular dissociation observed with an atomic wavepacket and parametric four-wave mixing

We report the observation of the dissociation of an electronically-excited molecule (Rb2) with an atomic wavepacket and time-delayed parametric four-wave mixing. The dynamics of the molecular dissociation transient are captured by the temporal histories of the relative number densities of the Rb product states, determined by reference to the amplitude and phase of the Fourier (spectral) components of the wavepacket. Clear experimental evidence of the appearance of atomic fragments (7s, 5d, 6p, 4d, and 5p) generated by dissociation is observed in the pressure-dependent temporal behavior of the amplitude of the 608 cm−1 (7s–5d) wavepacket spectral component.

A microstructure-fiber-based 10-GHz synchronized tunable optical parametric oscillator in the 1550-nm regime

We demonstrate a microstructure-fiber (MF)-based supercontinuum source and a synchronously pumped optical parametric oscillator in the 1550-nm regime. By using a 12.5-m-long MF, we obtained a 10-GHz repetition-rate picosecond-pulse source that is capable of /spl sim/120-nm wavelength tunability due to the wide-gain bandwidth of the combined processes of stimulated Raman scattering and parametric four-wave mixing.