Degenerate Four-wave Mixing Process Research Articles

Si metasurface supporting multiple quasi-BICs for degenerate four-wave mixing

Abstract Dielectric metasurfaces supporting quasi-bound states in the continuum (qBICs) enable high field enhancement with narrow-linewidth resonances in the visible and near-infrared ranges. The resonance emerges when distorting the meta-atom’s geometry away from a symmetry-protected BIC condition and, usually, a given design can sustain one or two of these states. In this work, we introduce a silicon-on-silica metasurface that simultaneously supports up to four qBIC resonances in the near-infrared region. This is achieved by combining multiple symmetry-breaking distortions on an elliptical cylinder array. By pumping two of these resonances, the nonlinear process of degenerate four-wave mixing is experimentally realized. By comparing the nonlinear response with that of an unpatterned silicon film, the near-field enhancement inside the nanostructured dielectric is revealed. The presented results demonstrate independent geometric control of multiple qBICs and their interaction through wave mixing processes, opening new research pathways in nanophotonics, with potential applications in information multiplexing, multi-wavelength sensing and nonlinear imaging.

Optical reciprocity-nonreciprocity-amplification conversion based on degenerate four-wave mixing

Optical nonreciprocity plays an important role in optical communication and quantum networks. In this research, we propose and demonstrate a conversion scheme of magnetic-free dual-channel optical reciprocal amplification (RA) and nonreciprocal amplification (NRA) based on the multiple degenerate four-wave mixing (FWM) process in hot atoms. In our experiment, the dual-channel NRA works with the action of a single pump field based on the establishment of FWM in the same direction and breaking in the opposite direction. Based on stable ground-state Zeeman coherence, by introducing a counter-propagating pump field again, NRA can be changed to RA in the opposite direction of the two original amplified conjugate signals. Moreover, the frequencies of RA signals are very dependent on those of co-propagating pump fields. The experimental realization of NRA-RA conversion may have applications for multichannel angular momentum spatial multiplexing and quantum gate manipulation.

Numerical study of generation mechanisms of narrow spectral modes, emerging in a raman fiber laser with randomly distributed feedback

The present paper discusses possible influence of nonlinear effects, namely – the degenerate four-wave mixing process – upon the build-up and attenuation of narrow spectral modes, emerging in radiation of a Raman fiber laser with randomly distributed feedback.

Combinations of orbital angular momentum in two degenerate four-wave mixing processes in Rb vapor

We present experimental measurements showing the combination of the orbital angular momentum (OAM) content of incident light beams in two distinct processes of degenerate four-wave mixing induced in hot rubidium vapor. These two processes, driven by the same fields, must satisfy distinct topological charge (TC) selection rules, which impose OAM conservation. These selection rules are readily obtained from the so-called overlap integral of the incident beams and allow us to control the relations between the two nonlinear signals, in particular, to characterize the conditions to obtain the two signals with symmetric or anti-symmetric TCs. The tilted lens method was employed to measure the OAM content of the output fields. We also discuss the transition from the near- to the far-field distributions of the generated signals.

Fabrication and characterization of tapered photonic crystal fiber for broadband 2 µm: four-wave mixing-based fibered OPCPA

We present the simulation, fabrication, and characterization of large area microstructured fiber tapers which enables broadband phasematching conditions of the four wave-mixing process. These silica-based tapers are intended to serve as a nonlinear gain medium for intense and high average power Fiber Optical Parametric Chirped Pulse Amplifier emitting at 2 upmu hbox {m} and strongly pumped at Yb wavelength. Different geometries (tapered/untapered, aspect ratio, etc.) are fabricated, analyzed and their broadening properties—key for supporting ultrashort pulses amplification—are compared and discussed. The characterization of nonlinear gain bandwidth of the tapers relies on a tunable source of stochastic pulses based on tunable amplified spontaneous emission in Yb-doped amplifiers. The strong overshoots of this source allows degenerate four-wave mixing process to occur thus generating broadband incoherent visible signal and mid-infrared idler waves at much lower average power than usually needed with coherent pumping. The idler centered around 1.85 mum is broadened due to zero-dispersion wavelength shift along the taper.

Intermodal Four-Wave Mixing Process in Strain-Induced Birefringent Multimode Optical Fibers.

Our study investigated the partially degenerate intermodal four-wave mixing (IM-FWM) process in nonlinear multimode optical fibers with strain-induced birefringence. The difference in the refractive index along the two orthogonal directions was due to the photoelastic effect that occurred when the fiber under test (FUT) was subjected to uniformly applied diameter stress caused by winding on a cylinder of a given diameter. Our work analyzed how the nonlinear frequency conversion and the output modal field profiles depended on the degree of birefringence in FUT. The experimental results significantly affected the order of the excited moduli in fiber sections characterized by different amounts of birefringence. We also checked the efficiency of the FWM process for different polarizations of the pump beam to determine those for which the FWM process was most effective for the 532 nm sub-nanosecond pulses. More than 30% conversion efficiency was obtained for the FUTs with a length of tens of centimeters.

Topologically protected energy-time entangled biphoton states in photonic crystals

The concepts of topological phases have been widely exploited in quantum optics in recent years. Here we demonstrate a topological insulator implementing topological protection of correlated biphoton states. A degenerate four-wave mixing (FWM) process of pseudospin states propagating along the topological interface is numerically simulated. Strikingly, the signal and idler photons generated from the FWM process are clarified to be entangled between two degrees of freedom—the frequencies of photon pairs and their time of arrival. The topological edge states of the pump, signal, and idler are robust against the sharp bends and defects, revealing the topological protection of energy-time entangled biphoton states. These findings could pave the way for unprecedented topological quantum devices.

Modeling nonlinear high-pressure sensors based on degenerate four-wave mixing in photonic crystal fibers.

We propose a high-pressure sensing mechanism in solid-core silica photonic crystal fibers (PCF) that is based on the nonlinear optical process of degenerate four-wave mixing. A quite simple configuration for the pressure sensor is given and is theoretically investigated by obtaining signal gain spectra. We focus on the Stokes and anti-Stokes sidebands that are generated during propagation of the field along the PCF due to the interplay of dispersion and nonlinear optical effects. We have considered wave propagation in the normal dispersion regime with the inclusion of negative fourth-order dispersion. We have also considered a pumping field with wavelength of 1076 nm and peak power of 3000 W that propagates along a PCF with 40 cm of length. We have optimized sensitivity, varying lattice pitch and air-hole diameter, and we have obtained high sensitivities of the Stokes and anti-Stokes lines of 3.672 and -0.146nm/MPa, respectively. The proposed sensors have potential applicability in high-pressure environments.

Dispersion Tailoring and Four-Wave Mixing in Silica Microspheres with Germanosilicate Coating

Optical whispering gallery mode microresonators with controllable parameters in the telecommunication range are demanded for diverse applications. Controlling group velocity dispersion (GVD) in microresonators is an important problem, as near-zero GVD in a broad wavelength range could contribute to the development of new microresonator-based light sources. We demonstrated theoretically near-zero dispersion tailoring in the SCL-band in combination with free-spectral range (FSR) optimization for FSR = 200 GHz and 300 GHz in silica glass microspheres with micron-scale germanosilicate coating. As an illustration of a possible application of such a GVD, we also performed a theoretical study of degenerate four-wave mixing (FWM) processes in the proposed microresonators for pumping in the SCL-band. We found that in some cases the generation of two or even three pairs of waves–satellites in a FWM process is possible in principle due to the specific GVD features. We also determined optimal microresonator configurations for achieving gradual change in the satellite frequency shift for the pump wavelengths in the SCL-, S-, CL-, C-, and L-bands. The maximum obtained FWM satellite tunability span was ~78 THz for a pump wavelength change of ~30 nm, which greatly exceeds the results for a regular silica microsphere without coating.

Optical Frequency Combs Generated in Silica Microspheres in the Telecommunication C-, U-, and E-Bands

Optical frequency combs (OFCs) generated in microresonators with whispering gallery modes are demanded for different applications including telecommunications. Extending operating spectral ranges is an important problem for wavelength-division multiplexing systems based on microresonators. We demonstrate experimentally three spectrally separated OFCs in the C-, U-, and E-bands in silica microspheres which, in principle, can be used for telecommunication applications. For qualitative explanation of the OFC generation in the sidebands, we calculated gain coefficients and gain bandwidths for degenerate four-wave mixing (FWM) processes. We also attained a regime when the pump frequency was in the normal dispersion range and only two OFCs were generated. The first OFC was near the pump frequency and the second Raman-assisted OFC with a soliton-like spectrum was in the U-band. Numerical simulation based on the Lugiato–Lefever equation was performed to support this result and demonstrate that the Raman-assisted OFC may be a soliton.

Optical Phase Conjugation Using Nonlinear SOA for Nonlinearity and Dispersion Compensation of Coherent Multi-Carrier Lightwave Systems

We study the use of nonlinear semiconductor optical amplifier (SOA) for generating optical phase conjugate towards compensation of distortions in short distance optical fiber transmission due to Kerr nonlinearity and chromatic dispersion in coherent multi-carrier lightwave signals. We experimentally demonstrate the effectiveness of the SOA-based phase conjugator to improve the link budget with a 100 km standard single mode fiber link for 20 GHz coherent OFDM signals, with QPSK and 16QAM modulations and a corresponding net bit-rate of 40 Gbps and 80 Gbps respectively. Mid-span spectral inversion scheme is employed where the optical phase conjugate is generated through a partially degenerate four-wave mixing process in a nonlinear SOA. We demonstrate a bit error rate performance within 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for an average launched power of up to 12 dBm (9 dBm) for QPSK (16QAM) coherent OFDM signals, in a 100 km fiber link. We also investigate the possible improvement in link budget using numerical simulation for 16QAM and 64QAM CO-OFDM signals with the proposed scheme.

Hybrid pulse propagation model and quasi-phase-matched four-wave mixing in multipass cells

We describe a nonlinear propagation model based on a generalized Schrödinger equation in the time domain coupled to Gaussian beam evolution through ABCD matrices that account for Kerr lensing in the spatial domain. This model is well suited to simulate propagation in mildly nonlinear systems such as multipass cells for temporal compression. It is validated against both a full ( x , y , z , t ) numerical model and recently reported experimental results in multipass cells, with excellent agreement. It also allows us to identify the physical mechanism for the recently reported parasitic appearance of spectral content in the 700–950 nm range in argon-filled multipass cells that are used to compress pulses at 1030 nm. We think this is due to a quasi-phase-matched degenerate four-wave mixing process. This process could be used in the future to perform wavelength conversion as is already done in fibers and capillaries.

Optimized design for a terahertz parametric oscillator based on degenerate four-wave mixing in silicon nitride

We propose terahertz wave generation using a parametric oscillator based on phase-matched and non-phase-matched degenerate four-wave mixing processes within a silicon nitride Fabry–Perot microcavity. The central frequency of the generated terahertz waves would be tunable over the frequency range of 3.6–5.73 THz by varying the wavelength of the pump wave. The best phase-matching condition is achieved at a frequency of 5 THz, and an optimum peak power of 329 W is obtained at a frequency of 4.29 THz.

Four-wave mixing in spin–orbit coupled Bose–Einstein condensates

We describe possibilities of spontaneous, degenerate four-wave mixing (FWM) processes in spin–orbit coupled Bose–Einstein condensates. Phase matching conditions (i.e., energy and momentum conservation laws) in such systems allow one to identify four different configurations characterized by involvement of distinct spinor states in which such a process can take place. We derived these conditions from first principles and then illustrated dynamics with direct numerical simulations. We found, among others, the unique configuration, where both probe waves have smaller group velocity than pump wave and proved numerically that it can be observed experimentally under proper choice of the parameters. We also reported the case when two different FWM processes can occur simultaneously. The described resonant interactions of matter waves is expected to play an important role in the experiments of BEC with artificial gauge fields. Beams created by FWM processes are an important source of correlated particles and can be used in the experiments testing quantum properties of atomic ensembles.

Single-shot fourth-order autocorrelator

The temporal contrast is one of the most important parameters of an ultra-high intense laser pulse. Third-order auto-correlator or cross-correlator have been widely used to characterize the temporal contrast of an ultra-intense laser pulse in the past decades. Here, a novel and simple single-shot fourth-order auto-correlator to characterize the temporal contrast with higher time resolution and better pulse contrast fidelity in comparison to third-order correlators is proposed. The single-shot fourth-order autocorrelation consists of a frequency degenerate four-wave mixing process and a sum-frequency mixing process. The proof-of-principle experiments show that a dynamic range of approximately 10^11 compared with the noise level, a time resolution of approximately 160 fs, and a time window of 65 ps can be successfully obtained using the novel single-shot fourth-order auto-correlator, which is the highest dynamic range with simultaneous high time resolution for single-shot temporal contrast measurement so far. Furthermore, the temporal contrast of laser pulse from a PW laser system is successfully measured in single-shot with a dynamic range of about 2*10^10 and simultaneous a time resolution of 160 fs.

All-optical modulation format conversion from star-QAM to PSK and ASK signals

An all-optical modulation format conversion scheme from star-QAM to ASK and PSK signals is proposed by employing four-wave mixing (FWM) in highly nonlinear fibers. The phase modulation information of star-QAM signal is firstly converted to the PSK format by a degenerate FWM process under gain saturation, and then the amplitude modulation information of star-QAM signal is mapped into the ASK format by means of a non-degenerate FWM associated with the resulting PSK signal. The detailed signal processing is presented by theory and simulation. As examples, the bit-error-ratio performances of 8QAM and 16QAM signals are evaluated by a non-degenerate FWM-based aggregation scheme for ASK and PSK formats.

Numerical Investigation of Phase-Conjugate Wave Generation as a Pulse Cleaner in Femtosecond Petawatt Laser Systems

We report on comprehensive research regarding the potential of phase-conjugate wave (PCW) generation via backward degenerate four-wave mixing process as a pulse cleaner in femtosecond high-power laser systems. We analyzed the performance of this technique by investigating the contrast enhancement capability, gain bandwidth, and energy conversion efficiency. All of these parameters are important in pulse cleaning. The numerical calculations verified that a considerably large efficiency bandwidth product and an excellent contrast enhancement capability can be realized by finding a balance between each physical effect. The simulation results based on this study provide guidance for the application of this technique in laser systems with different bandwidths. The method, which is based on PCW generation, provides new insights for femtosecond petawatt laser systems as pulse cleaners.

Full characterization of 8 fs deep UV pulses via a dispersion scan.

We report on, to the best of our knowledge, the first characterization of deep ultraviolet (UV) pulses by the dispersion scan (d-scan) technique. Negatively chirped 8fs deep UV pulses are generated via the phase transfer of shaped few-cycle near-infrared pulses in a sum frequency generation process with narrowband second harmonic. The pulses are characterized by a d-scan technique incorporating a cross-polarized wave (XPW) generation nonlinearity. Being a single-beam degenerate four-wave mixing process, XPW does not acquire frequency conversion and, thus, is ideally suited for characterizing pulses in the UV, where the material dispersion severely limits phase matching. The characterization method is benchmarked by measuring the dispersion effect of a known fused silica plate on the pulses.

Spatial intensity distribution of controlled-NOT gate carrying orbital angular momentum via photonic band gap structure

By employing the different topological charges of a Laguerre–Gaussian beam as a qubit, we experimentally demonstrate a controlled-NOT (CNOT) gate with light beams carrying orbital angular momentum via a photonic band gap structure in a hot atomic ensemble. Through a degenerate four-wave mixing process, the spatial distribution of the CNOT gate including splitting and spatial shift can be affected by the Kerr nonlinear effect in multilevel atomic systems. Moreover, the intensity variations of the CNOT gate can be controlled by the relative phase modulation. This research can be useful for applications in quantum information processing.

Modulation of controlled-not gate using light beams carrying orbital angular momentum in a nonlinear atomic vapor

We propose and experimentally demonstrate a controlled-not gate with light beams carrying orbital angular momentum (OAM) through a degenerate four-wave mixing process via a photonic band gap structure satisfying the phase-matching condition. By employing the different topological charges of a Laguerre-Gaussian beam as a qubit in this nonlinear process, the controlled-not gate with OAM can be realized. Moreover, we investigate the evolution of the controlled-not gate, which can be modulated by the frequency and the power of the incident beam, i.e., under electromagnetically induced transparency conditions. The study results are useful for applications in quantum communication and information storage.