Four-wave Mixing Efficiency Research Articles

Optical cavity for enhanced parametric four-wave mixing in rubidium

We demonstrate the implementation of a ring cavity to enhance the efficiency of parametric four-wave mixing in rubidium. Using an input coupler with 95% reflectance, a finesse of 19.6$\pm$0.5 is achieved with a rubidium cell inside. This increases the circulating intensity by a factor of 5.6$\pm$0.5, and through two-photon excitation on the $5s_{1/2}\rightarrow5d_{5/2}$ transition with a single excitation laser, up to 1.9$\pm$0.3 mW of power at 420 nm is generated, 50 times what was previously generated with this scheme. The dependence of the output on Rb density and input power has been explored, suggesting the process may be approaching saturation. The blue output of the cavity also shows greatly improved spatial quality, combining to make this a promising source of 420 nm light for future experiments.

Efficiency of four-wave mixing between orthogonally polarized linear waves and solitons in a birefringent fiber

We analyze the interaction between orthogonally polarized solitons and dispersive waves via four-wave mixing in a birefringent fiber. We calculate analytically the efficiency of the phase-sensitive scattering between orthogonally polarized solitons and dispersive waves. Experiments performed by using a photonic crystal fiber perfectly match the analytical predictions.

Efficiency of four-wave mixing in injection-locked InAs/GaAs quantum-dot lasers

Frequency conversion using highly non-degenerate four-wave mixing is investigated in optically injection-locked InAs/GaAs quantum-dot Fabry-Perot lasers with different ridge waveguide dimensions. Conversion efficiencies up to -16 dB with a large optical signal-to-noise ratios of 36 dB are unveiled. The conversion bandwidth is extended to 4 THz with a quasi-symmetrical response between up- and down-converted signals.

All-Optical Wavelength Preserved Modulation Format Conversion From PDM-QPSK to PDM-BPSK Using FWM and Interference

Flexible conversion between multi-level modulation formats is one of the key processing functions to realize adaptive modulation techniques for flexible networking aimed at high spectral efficiency in optical fiber transmission. The authors have proposed an all-optical format conversion systems from binary phase-shift keying (BPSK) to quadrature PSK (QPSK) and its reverse conversion from QPSK to BPSK. The latter had an advantage of wavelength-shift-free conversion from an incident QPSK to simultaneous two BPSK outputs without loss of the transmitting data. However, it was limited only for a single polarization signal. In this paper, we propose a novel method of wavelength preserved conversion for polarization division multiplexed QPSK signal with arbitrary polarization rotation angle to the x-axis on the x-y polarization plane which is orthogonal to the propagation axis. The method is based on the orthogonal dual-pump four-wave-mixing (FWM) in the highly nonlinear fiber with a nonlinear optical loop mirror configuration, which has advantages that it separately outputs the original signal and the phase conjugate signal and has independent FWM efficiency of the signal polarization angle. We show the system performances such as bit-error-rate and optical signal-to-noise ratio penalty evaluated by numerical simulations.

Enhanced four-wave mixing with nonlinear plasmonic metasurfaces.

Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be further enhanced by increasing the excitation power. The dielectric nonlinear material placed in the nanogap is mainly responsible for the ultrastrong FWM response. Compact and efficient wave mixers and optical sources spanning different frequency ranges are envisioned to be designed based on the proposed nonlinear metasurface designs.

Optimal geometry of nonlinear silicon slot waveguides accounting for the effect of waveguide losses.

The optimal geometry of silicon-organic hybrid slot waveguides is investigated in the context of the efficiency of four-wave mixing (FWM), a χ(3) nonlinear optical process. We study the effect of slot and waveguide widths, as well as waveguide asymmetry on the two-photon absorption (TPA) figure of merit and the roughness scattering loss. The optimal waveguide core width is shown to be 220nm (symmetric) with a slot width of 120nm, at a fixed waveguide height of 220nm. We also show that state-of-the-art slot waveguides can outperform rib waveguides, especially at high powers, due to the high TPA figure-of-merit.

Semi-analytic modeling of FWM noise in dispersion-managed DWDM systems with DQPSK/DPSK/OOK channels

Semi-analytic models are developed to deterministically calculate the variances of degenerate and non-degenerate four-wave-mixing (FWM) noises for dispersion-managed dense wavelength division multiplexing (DWDM) systems with pure and mixed differential quadrature-phase-shift keying (DQPSK)/differential phase-shift keying (DPSK)/on-off-keying (OOK) channels. The semi-analytic models include various important propagation effects for exact numerical results. The novel dispersion map used here for dispersion management is composed of effective-area-enlarged positive dispersion fiber (EE-PDF), dispersion slope and dispersion compensating fiber (SCDCF) and nonzero dispersion-shifted fiber (NZ-DSF). It is numerically validated with the new models that, under the condition that all channels have the same average launch powers and baud rates, the impact of FWM noise for mixed DQPSK/OOK channels are more severe than that for pure DQPSK and mixed DQPSK/DPSK channels. It is also shown that the FWM efficiency is strongly dependent on the peak power of launched optical pulse for a large number of channels, as can be mainly attributed to the quasi-linear evolution of pulse shapes in pump channels induced by cross-phase modulation (XPM). Compared with some commercial optical-fiber transmission simulators, massive time-consuming can be avoided by using the newly derived semi-analytic models when transmission performances of such DWDM systems are numerically optimized and evaluated.

Giant enhanced four-wave mixing efficiency via two-photon resonance in asymmetric quantum wells

We propose an efficient four-wave mixing (FWM) scheme in asymmetric semiconductor quantum wells (SQWs) via two-photon resonance. By using the coupled Schrödinger–Maxwell formalism, we derive explicitly the corresponding analytical expressions of the inter-probe pulse and generated FWM field in the linear regime under the steady-state condition. With the aid of cross coupling between one ground state and two closely adjacent excited states, the efficiency of the generated FWM field is found to be significantly enhanced, up to 60%. More interestingly, a wide region of the maximum FWM efficiency is demonstrated as the ratio of transition dipole moments is within the values ranging from 1.1 to 1.3, which can be maintained for a certain propagation distance (i.e. 100 μm).

Canonical logic units using bidirectional four-wave mixing in highly nonlinear fiber

All-optical canonical logic units at 40 Gb/s using bidirectional four-wave mixing (FWM) in highly nonlinear fiber are proposed and experimentally demonstrated. Clear temporal waveforms and correct pattern streams are successfully observed in the experiment. This scheme can reduce the amount of nonlinear devices and enlarge the computing capacity compared with general ones. The numerical simulations are made to analyze the relationship between the FWM efficiency and the position of two interactional signals.

Wavelength Multicasting at 22-GBaud 16-QAM in a Silicon Nanowire Using Four-Wave Mixing

We demonstrate 1-to-6 wavelength multicasting of a 22-GBaud 16-QAM single polarization ( $6\times 88$ Gb/s) signal based on four-wave mixing in a dispersion engineered silicon nanowire. All six multicast signals perform below the bit error rate forward error correction threshold of $3.8\times 10^{-3}$ , with a worst case power penalty of 8 dB. We compare our wavelength multicasting performance against the theoretical power transfer during a three-wave mixing process and show that the average power of degenerate idlers agrees with the predicted 6 dB difference with respect to that of nondegenerate idlers. When distinguishing the nonlinear conversion efficiency from the absolute idlers power at the output of the silicon nanowire, we also show the importance of the output grating coupler’s loss and how it impacts the multicasting performance, in conjunction with the four-wave mixing efficiency.

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.

Four-Wave Mixing in Microwires to All-Optical Signal Processing in Mode-Division Multiplexing Systems

Mode-division multiplexing requires all-optical signal processing techniques that are able to deal with a new coding dimension, the spatial mode. In this context, optical microwires emerge as a potential highly non-linear and multi-modal waveguide envisioning the development of all-optical signal processing devices to mode-division multiplexing systems based on the four-wave mixing process. The inter- and intramodal phase-matching conditions for the four-wave mixing process are mapped as a function of the microwire diameter and the wavelength of signals. Moreover, the efficiency of four-wave mixing considering a strong guiding regime is investigated in the multi-modal regime.

FWM Dynamics Under Dual-Pump Thermal Behavior in Silicon Microring Resonator

The silicon microring resonator is a superb platform for both fundamental studies and practical applications of various nonlinear optic phenomena. However, the highly enhanced light intensity in the ring cavity makes it quite sensitive to thermal variations and can in turn incur detrimental instability or degradation to the concurrent nonlinear processes. Here, we revisit the four-wave mixing effect in a silicon microring resonator by characterizing the detailed parametric dynamics under the influence of a dual-pump thermal behavior of the microring. We compare different pump scanning schemes and show that thermal variations of cavity modes can greatly impact the operation condition and efficiency of four-wave mixing. A synchronous pump scanning method is proposed and demonstrated to be the most applicable scheme to achieve high-efficiency parametric energy conversion in a thermally sensitive microring resonator.

Theory of intermodal four-wave mixing with random linear mode coupling in few-mode fibers.

We study intermodal four-wave mixing (FWM) in few-mode fibers in the presence of birefringence fluctuations and random linear mode coupling. Two different intermodal FWM processes are investigated by including all nonlinear contributions to the phase-matching condition and FWM bandwidth. We find that one of the FWM processes has a much larger bandwidth than the other. We include random linear mode coupling among fiber modes using three different models based on an analysis of the impact of random coupling on differences of propagation constants between modes. We find that random coupling always reduces the FWM efficiency relative to its vale in the absence of linear coupling. The reduction factor is relatively small (about 3 dB) when only a few modes are linearly coupled but can become very large (> 40 dB) when all modes couple strongly. In the limit of a coupling length much shorter than the nonlinear length, intermodal FWM efficiency becomes vanishingly small. These results should prove useful in the context of space-division multiplexing with few-mode and multimode fibers.

Enhanced four-wave mixing efficiency in four-subband semiconductor quantum wells via Fano-type interference.

We propose and analyze an efficient way to enhance four-wave mixing (FWM) signals in a four-subband semiconductor quantum well via Fano-type interference. By using Schrödinger-Maxwell formalism, we derive explicitly analytical expressions for the input probe pulse and the generated FWM field in linear regime under the steady-state condition. With the aid of interference between two excited subbands tunneling to the common continuum, the efficiency to generate FWM field is found to be significantly enhanced, up to 35%. More interestingly, a linear growth rate in the FWM efficiency is demonstrated as the strength of Fano-type interference increases in presence of the continuum states, which can be maintained for a certain propagation distance (i.e., 50μm).

Enhanced continuous-wave four-wave mixing efficiency in nonlinear AlGaAs waveguides.

Enhancements of the continuous-wave four-wave mixing conversion efficiency and bandwidth are accomplished through the application of plasma-assisted photoresist reflow to reduce the sidewall roughness of sub-square-micron-modal area waveguides. Nonlinear AlGaAs optical waveguides with a propagation loss of 0.56 dB/cm demonstrate continuous-wave four-wave mixing conversion efficiency of -7.8 dB. Narrow waveguides that are fabricated with engineered processing produce waveguides with uncoated sidewalls and anti-reflection coatings that show group velocity dispersion of +0.22 ps²/m. Waveguides that are 5-mm long demonstrate broadband four-wave mixing conversion efficiencies with a half-width 3-dB bandwidth of 63.8-nm.

Tunable coupled-mode dispersion compensation and its application to on-chip resonant four-wave mixing.

We propose and demonstrate mode coupling as a viable dispersion compensation technique for phase-matched resonant four-wave mixing (FWM). We demonstrate a dual-cavity resonant structure that employs coupling-induced frequency splitting at one of three resonances to compensate for cavity dispersion, enabling phase matching. Coupling strength is controlled by thermal tuning of one cavity enabling active tuning of the resonant frequency matching. In a fabricated silicon microresonator, we show an 8 dB enhancement of seeded FWM efficiency over the noncompensated state. The measured FWM has a peak wavelength conversion efficiency of -37.9 dB across a free spectral range (FSR) of 3.334 THz (∼27 nm), which is, to the best of our knowledge, the largest in a silicon microresonator to demonstrate FWM to date. This form of dispersion compensation can be beneficial for many devices, including wavelength converters, parametric amplifiers, and widely detuned photon-pair sources. Apart from compensating dispersion, the proposed mechanism can alternatively be utilized in an otherwise dispersionless resonator to counteract the detuning effect of self- and cross-phase modulation on the pump resonance during FWM, thereby addressing a fundamental issue in the performance of light sources such as broadband optical frequency combs.

Triply resonant four-wave mixing in silicon-coupled resonator microring waveguides.

Silicon photonic four-wave mixing (FWM) devices intended for telecommunications applications must satisfy three requirements: achieve conversion efficiencies close to the detection threshold of typical receivers, while keeping pump power requirements modest and providing enough bandwidth for typical signal formats. Here, we report a continuous-wave FWM efficiency of -21.3 dB at 100 mW pump power and demonstrate wavelength conversion at 10 Gbps in a coupled-resonator optical-waveguide device.

Dynamic analysis of optical soliton pair and four-wave mixing via Fano interference in multiple quantum wells

We perform a time-dependent analysis of the formation and stable propagation of an ultraslow optical soliton pair, and four-wave mixing (FWM) via tunable Fano interference in double-cascade type semiconductor multiple quantum wells (SMQWs). By using the probability amplitude method to describe the interaction of the system, we demonstrate that the electromagnetically induced transparency (EIT) can be controlled by Fano interference in the linear case and the strength of Fano interference has an important effect on the group velocity and amplitude of the soliton pair in the nonlinear case. Then, when the signal field is removed, the dynamic FWM process is analyzed in detail, and we find that the strength of Fano interference also has an important effect on the FWM’s efficiency: the maximum FWM efficiency is ~28% in appropriate conditions. The investigations are promising for practical applications in optical devices and optical information processing for solid systems.

Theory of pulse propagation and four-wave mixing in a quantum dot semiconductor optical amplifier

A theory, combining the relations of pulse traveling into quantum dot (QD) semiconductor optical amplifier (SOA) with the four-wave mixing (FWM) theory in these SOAs, is developed. Carrier density pulsation (CDP), carrier heating (CH), and spectral hole burning (SHB) contributions on FWM efficiency are discussed. Effect of QD ground state and wetting layer are included. An additional parameter appears in the gain integral relation of QD SOAs. An equation formulating pulses in the QD SOAs is introduced. We have found that FWM in QD SOAs is detuning and is pulse width dependent. For short pulses, CH is dominant at high detunings (10–100 GHz) while at higher detunings (>100 GHz) the SHB is the dominant one. Undesired paunch behavior is shown in QD SOAs then, CDP must be reduced.