The light propagation through one-dimensional photonic crystal using Four-wave mixing (FWM) nonlinear process is modeled. The linear and nonlinear indexes of refraction are approximated with the first Fourier harmonic term. Based on this approximation, a complete set of coupled wave equations, including pump fields depletion, for description of FWM process and conversion efficiency from pump to signal and idler waves for periodic structures is presented. The derived coupled wave equations are evaluated numerically. Some of important system parameters effects on FWM performance are investigated. The obtained relations are suitable and can easily be applied for description of Wavelength Division Multiplexing (WDM) optical signals transmitted through (parametric process) nonlinear fiber Bragg Gratings compatible to optical fiber communications.
We demonstrate all-optical wavelength conversion at 10 Gb/s for differential phase-shift keyed (DPSK) data signals in the C-band, based on four-wave mixing (FWM) in a silicon ring resonator. Error-free operation with a system penalty of ~ 4.1 dB at 10-9 BER is achieved.
We present a theoretical analysis supported by comprehensive numerical simulations of quasi phase-matched four-wave mixing (FWM) of ultrashort optical pulses that propagate in weakly width-modulated silicon photonic nanowire gratings. Our study reveals that, by properly designing the optical waveguide such that the interacting pulses co-propagate with the same group-velocity, a conversion efficiency enhancement of more than 15 dB, as compared to a uniform waveguide, can readily be achieved. We also analyze the dependence of the conversion efficiency and FWM gain on the pulse width, time delay,…
Since the forward and backward waves are coupled with each other and a standing wave with no net propagation of energy is formed in the photonic bandgap, it is a commonsense of basic physics that, any kinds of effects associated with wave propagation including four-wave-mixing (FWM) are thought to be impossible. However, we lay great emphasis here on explaining that this commonsense could be broken under specific circumstances. In this article, we report with the first experimental observation of the energy conversion in the photonic bandgap into other channel via FWM. Owing to the phase manip…
We study the light propagation in one-dimensional photonic crystal via nonlinear Four Wave Mixing (FWM) process. The linear and nonlinear refractive indexes are approximated with the first Fourier harmonic term. A system of the nonlinear coupled mode equations (NLCMEs), including pump fields depletion is derived for FWM process and steady state analysis is presented numerically. Also some of important system parameters' effects on FWM process are investigated. It has been shown that, although we have considered pump depletion and used a medium with 3rd order succeptibility which is small compa…
We present a method by which the degree of longitudinal variation in photonic crystal fibre (PCF) may be characterised through seeded four-wave mixing (FWM). Using an iterative numerical reconstruction, we created a model PCF that displays similar FWM phasematching properties across all measured length scales. Our results demonstrate that the structure of our PCF varies by less than 1% and that the characteristic length of the variations is approximately 15 cm.
We theoretically investigate and optimize four-wave mixing (FWM) in silicon nitride (SiN) waveguides integrated with two-dimensional (2D) layered graphene oxide (GO) films. Based on extensive previous measurements of the material parameters of the GO films, we perform detailed analysis for the influence of device parameters including waveguide geometry, GO film thickness, length, and coating position on the FWM conversion efficiency (CE) and conversion bandwidth (CB). The influence of dispersion and photo-thermal changes in the GO films is also discussed. Owing to the strong mode overlap betwe…
We present a comprehensive theoretical analysis and computational study of four-wave mixing (FWM) of optical pulses co-propagating in one-dimensional silicon photonic crystal waveguides (Si-PhCWGs). Our theoretical analysis describes a very general set-up of the interacting optical pulses, namely we consider nondegenerate FWM in a configuration in which at each frequency there exists a superposition of guiding modes. We incorporate in our theoretical model all relevant linear optical effects, including waveguide loss, free-carrier (FC) dispersion and FC absorption, nonlinear optical effects su…
Four-wave mixing (FWM) is an important nonlinear optical phenomenon that underlines many of the discoveries and device applications since the laser was invented. Examples include parametric amplification, mode-locked pulses and frequency combs, and in the quantum optics regime, entangled-photon generation, squeezed-state production and optical transduction from the visible to infrared wavelengths. For quantum dot systems, the basic understanding of FWM is limited by the conventional investigation method, which concentrates on the FWM susceptibility measured with optical amplifiers. This paper …
We experimentally demonstrated that infrared light imprinted with orbital angular momentum (OAM) was linearly converted into visible light using four-wave mixing (FWM) via a ladder-type configuration in 85Rb atoms. Simultaneously, we theoretically simulated this linear conversion process, and the theoretical analysis was in reasonable agreement with the experimental results. A large single-photon detuning process was used to reduce the absorption of the atoms to the up-converted light and to avoid pattern formation in the FWM process. The multi-mode image linear conversion process is important…
Nonlinear optical effects including stimulated Brillouin scattering (SBS) and four-wave mixing (FWM) play an important role in microwave photonics, optical frequency combs, and quantum photonics. Harnessing SBS and FWM in a low-loss and versatile integrated platform would open the path to building large-scale Brillouin/Kerr-based photonic integrated circuits. In this letter, we investigate the Brillouin and Kerr properties of a low-index (n=1.513 @ 1550 nm) silicon oxynitride (SiON) platform. We observed, for the first time, backward SBS in SiON waveguides with a Brillouin gain coefficient of …
The recent development of devices based on novel nonlinear materials like chalcogenides (ChGs), silicon (Si) and other semi-conductors has revolutionized the field of nonlinear photonics [1,2,3]. Among the nonlinear effects observed in these materials, four-wave mixing (FWM) is the process that finds the most applications including wavelength conversion [4], optical regeneration [5,6], optical delay [7], time-domain demultiplexing[8], temporal cloaking[9] and negative refraction[10]. Although FWM has been observed in several media including chalcogenides [11,12,13,14], silicon[15, 16], bismuth…
We numerically study supercontinuum (SC) generation in photonic crystal fibers pumped with low-power 30-ps pulses close to the zero dispersion wavelength 647nm. We show how the efficiency is significantly improved by designing the dispersion to allow widely separated spectral lines generated by degenerate four-wave-mixing (FWM) directly from the pump to broaden and merge. By proper modification of the dispersion profile the generation of additional FWM Stokes and anti-Stokes lines results in efficient generation of an 800nm wide SC. Simulations show that the predicted efficient SC generation i…
Four-wave mixing (FWM) in optical fibre is a leading technique for generating high-quality photon pairs. We report the generation of photon pairs by spontaneous FWM in photonic crystal fibre pumped by a 1.5 GHz repetition-rate vertical-external-cavity surface-emitting laser (VECSEL). The photon pairs exhibit high count rates and a coincidence-to-accidental ratio of over 80. The VECSEL's high repetition-rate, high average power, tunability, and small footprint make this an attractive source for quantum key distribution and photonic quantum-state engineering.
We demonstrate enhanced four-wave mixing (FWM) in doped silica waveguides integrated with graphene oxide (GO) layers. Owing to strong mode overlap between the integrated waveguides and GO films that have a high Kerr nonlinearity and low loss, the FWM efficiency of the hybrid integrated waveguides is significantly improved. We perform FWM measurements for different pump powers, wavelength detuning, GO coating lengths, and number of GO layers. Our experimental results show good agreement with theory, achieving up to ~9.5-dB enhancement in the FWM conversion efficiency for a 1.5-cm-long waveguide…
We study theoretically the cascaded four-wave mixing (FWM) in broadband tapered plasmonic nanoantennas and demonstrate a 300-fold increase in nonlinear frequency conversion detected in the main lobe of the nanoantenna far-field pattern. This is achieved by tuning the elements of the nanoantenna to resonate frequencies involved into the FWM interaction. Our findings have a potentially broad application in ultrafast nonlinear spectroscopy, sensing, on-chip optical frequency conversion, nonlinear optical metamaterials and photon sources.
We observed electromagnetically-induced-transparency-based four-wave mixing (FWM) in the pulsed regime at low light levels. The FWM conversion efficiency of 3.8(9)% was observed in a four-level system of cold 87Rb atoms using a driving laser pulse with a peak intensity of approximately 80 μW/cm^2, corresponding to an energy of approximately 60 photons per atomic cross section. Comparison between the experimental data and the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)] showed good agreement. Additionally, a high conversion efficiency of 46(2)% was demon…
We study topologically-protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time-reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large lifetime of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states within the topological bandgap can be achieved with pump power of less than 10 nW. In particular, we find tha…
We experimentally demonstrate wide-band (>100 THz) frequency down-conversion of near-infrared (NIR) femtosecond-scale pulses from an Er:fiber laser to the mid-infrared (MIR) using four-wave-mixing (FWM) in photonic-chip silicon-nitride waveguides. The engineered dispersion in the nanophotonic geometry, along with the wide transparency range of silicon nitride, enables large-detuning FWM phase-matching and results in tunable MIR from 2.6-3.6 um on a single chip with 100-pJ-scale pump-pulse energies. Additionally, we observe > 20 dB broadband parametric gain for the NIR pulses when the FWM proce…
We measure the time-energy correlation of broadband, spontaneously generated four wave mixing (FWM), and demonstrate novel time-frequency coupling effects; specifically, we observe a power-dependent splitting of the correlation in both energy and time. By pumping a photonic crystal fiber with narrowband picosecond pulses we generate FWM in a unique regime, where broadband (>100nm), sidebands are generated that are incoherent, yet time-energy correlated. Although the observed time-energy correlation in FWM is conceptually similar to parametric down conversion, its unique dependence on pump inte…
We theoretically investigate and optimize the performance of four-wave mixing (FWM) in microring resonators (MRRs) integrated with two-dimensional (2D) layered graphene oxide (GO) films. Owing to the interaction between the MRRs and the highly nonlinear GO films as well as to the resonant enhancement effect, the FWM efficiency in GO-coated MRRs can be significantly improved. Based on previous experiments, we perform detailed analysis for the influence of the GO film parameters and MRR coupling strength on the FWM conversion efficiency (CE) of the hybrid MRRs. By optimizing the device parameter…
Design of a mid-wave IR (MWIR) broad-band fiber-based light source exploiting four-wave mixing (FWM) in a meter long suitably designed highly nonlinear (NL) chalcogenide microstructured optical fiber (MOF) is reported. This superior FWM bandwidth (BW) was obtained through precise tailoring of the fibers dispersion profile so as to realize positive quartic dispersion at the pump wavelength. We consider an Erbium (Er3+) doped continuous wave (CW) ZBLAN fiber laser emitting at 2.8 micron as the pump source with an average power of 5 W. Amplification factor as high as 25 dB is achievable in the 3 …
One of the major difficulties in realizing a high-dimensional frequency converter for conventional optical vortex (COV) stems from the difference in ring diameter of COV modes with different topological charge numbers l. Here, we implement a high-dimensional frequency convertor for perfect optical vortex (POV) modes with invariant size through the four-wave mixing (FWM) process by utilizing Bessel-Gaussian beams instead of Laguerre-Gaussian beams. The measured conversion efficiency from 1530 nm to 795 nm is independent of l at least in subspace of {-6,...,6}, and the achieved conversion fideli…
Based on the interplay between photoionization and Raman effect in gas-filled photonic crystal fibers, we propose a new optical device to control frequency-conversion of ultrashort pulses. By tuning the input-pulse energy, the output spectrum can be either down-converted, up-converted, or even frequency-shift compensated. For low input energies, Raman effect is dominant and leads to a redshift that increases linearly during propagation. For larger pulse energies, photoionization starts to take over the frequency conversion process, and induces a strong blueshift. We have found also that the fi…
We demonstrate enhanced second harmonic generation in a gallium phosphide photonic crystal waveguide with a measured external conversion efficiency of 5$\times10^{-7}$/W. Our results are promising for frequency conversion of on-chip integrated emitters having broad spectra or large inhomogeneous broadening, as well as for frequency conversion of ultrashort pulses.
Transfer of amplitude and phase noise from a continuous wave optical pump to the repetition rate of a Kerr frequency comb is studied theoretically, with focus on generation of spectrally pure radio frequency (RF) signals via demodulation of the frequency comb on a fast photodiode. It is shown that both the high order chromatic dispersion of the resonator spectrum and frequency-dependent quality factor of the resonator modes facilitate the optical-to-RF noise conversion that limits spectral purity of the RF signal.
Typically, photonic waveguides designed for nonlinear frequency conversion rely on intuitive and established principles, including index guiding and band gap engineering, and are based on simple shapes with high degrees of symmetry. We show that recently developed inverse-design techniques can be applied to discover new kinds of microstructured fibers and metasurfaces designed to achieve large nonlinear frequency conversion efficiencies. As a proof of principle, we demonstrate complex, wavelengthscale chalcogenide glass fibers and gallium phosphide metasurfaces exhibiting some of the largest n…
Four-wave mixing is observed in a silicon W1 photonic crystal waveguide. The dispersion dependence of the idler conversion efficiency is measured and shown to be enhanced at wavelengths exhibiting slow group velocities. A 12-dB increase in the conversion efficiency is observed. Concurrently, a decrease in the conversion bandwidth is observed due to the increase in group velocity dispersion in the slow-light regime. The experimentally observed conversion efficiencies agree with the numerically modeled results.
An asymmetric double quantum wells (QWs) structure with resonant tunneling is suggested to achieve high efficient four wave mixing (FWM). We analytically demonstrate that the resonant tunneling can induce high efficient mixing wave in such a semiconductor structure with a low light pump wave. In particular, the FWM conversion efficiency can be enhanced dramatically in the vicinity of the center frequency. This interesting scheme may be used to generate coherent long-wavelength radiation in solid-state system.
Efficiency is a critical factor limiting the applications of nonlinear plasmonic devices. We show by theory and experiments that high efficiency four-wave mixing (FWM) is achieved in nanometer size plasmonic hotspots, which open up opportunities for nanoscale light manipulation. First, we present a classical calculation on the efficiency of frequency conversion by quadruple-enhanced FWM for a Kerr nonlinear material loaded in the plasmonic hotspot of a gold nanosphere dimer. The results indicate the viability to achieve over 10% efficiency in a nanometer volume under milliwatts of pump power c…
We report on nonlinear frequency conversion from the telecom range via second harmonic generation (SHG) and third harmonic generation (THG) in suspended gallium nitride slab photonic crystal (PhC) cavities on silicon, under continuous-wave resonant excitation. Optimized two-dimensional PhC cavities with augmented far-field coupling have been characterized with quality factors as high as 4.4$\times10^{4}$, approaching the computed theoretical values. The strong enhancement in light confinement has enabled efficient SHG, achieving normalized conversion efficiency of 2.4$\times10^{-3}$ $W^{-1}$, …
Layered 2D graphene oxide (GO) films are integrated with silicon nitride (SiN) waveguides to experimentally demonstrate an enhanced Kerr nonlinearity via four wave mixing (FWM). Owing to the strong light matter interaction between the SiN waveguides and the highly nonlinear GO films, the FWM performance of the hybrid waveguides is significantly improved. SiN waveguides with both uniformly coated and patterned GO films are fabricated based on a transfer free, layer by layer GO coating method together with standard photolithography and lift off processes, yielding precise control of the film thi…
Broadband-tunable sources of circularly-polarized light are crucial in fields such as laser science, biomedicine and spectroscopy. Conventional sources rely on nonlinear wavelength conversion and polarization control using standard optical components, and are limited by the availability of suitably transparent crystals and glasses. Although gas-filled hollow-core photonic crystal fiber provides pressure-tunable dispersion, long well-controlled optical path-lengths, and high Raman conversion efficiency, it is unable to preserve circular polarization state, typically exhibiting weak linear biref…
Coherent ultraviolet (UV) light has many uses, for example in the study of molecular species relevant in biology and chemistry. Very few if any laser materials offer UV transparency along with damage-free operation at high photon energies and laser power. Here we report efficient generation of deep and vacuum UV light using hydrogen-filled hollow-core photonic crystal fiber (HC-PCF). Pumping above the stimulated Raman threshold at 532 nm, coherent molecular vibrations are excited in the gas, permitting highly efficient thresholdless wavelength conversion in the UV. The system is uniquely press…
Four-wave mixing and secondary radiations generated by nonharmonic two-color filaments in air: Influence of the Kerr and plasma nonlinearities
Vilnius University（维尔纽斯大学）；Université de Bordeaux-CNRS-CEA（波尔多大学-CNRS-CEA）；The Extreme Light Infrastructure ERIC, ELI Beamlines Facility（极强光基础设施ERIC，ELI光束线设施）
The enhancement of Er$^{3+}$-based up-conversion for photovoltaics in multilayer porous silicon photonic structures is considered theoretically and experimentally. Transfer matrix simulations are used to assess the increased photonic density of states that results from the slowing of energy propagation at the short-wavelength edge of one-dimensional photonic band gaps. An indirect calculation of Er$^{3+}$ absorption enhancement within slow-light modes is then used to illustrate an increase in absorption over the bulk value: the effective absorption coefficient is shown to increase by more than…
While two-dimensional (2D) materials have intriguing second-order nonlinearities with ultrahigh coefficient and electrical tunability, their atomic layer thicknesses hinder explorations of other optical frequency-conversions (OFCs) than second harmonic generation (SHG) due to inefficient light-coupling and unachievable phase-matching. We report, by resonantly pumping a photonic crystal cavity integrated with a few-layer GaSe, it is possible to realize multiple second-order nonlinear processes in GaSe even with microwatts continuous wave pumps, including SHGs, sum-frequency generations (SFGs), …
The unique ring-shaped intensity patterns and helical phase fronts of optical vortices make them useful in many applications. Here we report for the first time efficient Raman frequency conversion between vortex modes in twisted hydrogen-filled single-ring hollow core photonic crystal fiber (SR-PCF). High fidelity transmission of optical vortices in untwisted SR-PCF becomes more and more difficult as the orbital angular momentum (OAM) order increases, due to scattering at structural imperfections in the fiber microstructure. In helically twisted SR-PCF, however, the degeneracy between left- an…
Cylindrical vector (CV) beams are a set of transverse spatial modes that exhibit a cylindrically symmetric intensity profile and a variable polarization about the beam axis. They are composed of a non-separable superposition of orbital and spin angular momentum. Critically, CV beams are also the eigenmodes of optical fiber and, as such, are of wide-spread practical importance in photonics and have the potential to increase communications bandwidth through spatial multiplexing. Here, we derive the coupled amplitude equations that describe the four-wave mixing (FWM) of CV beams in optical fibers…
We demonstrate second harmonic generation in photonic crystal nanocavities fabricated in the semiconductor gallium phosphide. We observe second harmonic radiation at 750 nm with input powers of only nanowatts coupled to the cavity and conversion efficiency $P_{\rm out}/P_{\rm in, coupled}^2 = 430%/{\rm W}$. The large electronic band gap of GaP minimizes absorption loss, allowing efficient conversion. Our results are promising for integrated, low-power light sources and on-chip reduction of input power in other nonlinear processes.
Low-noise frequency conversion of single photons is a critical tool in establishing fibre-based quantum networks. We show that a single photonic crystal fibre can achieve frequency conversion by Bragg-scattering four-wave mixing of source photons from an ultra-broad wavelength range by engineering a symmetric group velocity profile. Furthermore, we discuss how pump tuning can mitigate realistic discrepancies in device fabrication. This enables a single highly adaptable frequency conversion interface to link disparate nodes in a quantum network via the telecoms band.
Integrated nonlinear wavelength converters transfer optical energy from lasers or quantum emitters to other useful colors, but chromatic dispersion limits the range of achievable wavelength shifts. Moreover, because of geometric dispersion, fabrication tolerances reduce the accuracy with which devices produce specific target wavelengths. Here, we report nonlinear wavelength converters whose operation is not contingent on dispersion engineering; yet, the output wavelengths are controlled with high accuracy. In our scheme, coherent coupling between counter-propagating waves in a photonic crystal…
We present a photonic reservoir computing, relying on a non-linear phase-to-amplitude mapping process, able to classify in real-time multi-Gbaud time traces subject to transmission effects. This approach delivers an all-optical, low-power neuromorphic dispersion compensator.
We show how the ability to slow down, amplify, and capture fast transient events can produce high-throughput real-time instruments ranging from digitizers to imaging flow cytometers for detection of rare diseased cells in blood.
We propose to use the integrated aluminum nitride waveguide with engineered width variation to achieve optical frequency conversion based on $χ^{(2)}$ nonlinear effect on a photonic chip. We show that in an adiabatically tapered waveguide, the frequency conversion has a much broader bandwidth and the efficiency within the bandwidth is almost constant, which is favorable for short pulses. We demonstrate both analytically and numerically an "area law" for the frequency conversion, i.e. the product of bandwidth and efficiency is conserved as long as peak conversion efficiency does not saturate. T…
