Nonlinear Four-wave Mixing Research Articles

Performance analysis and parameter optimization of all-optical encryption using the FWM effect in semiconductor optical amplifier

Abstract The demand for larger bandwidth to carry high capacity data in optical networks is increasing. Thus, it is expected to replace all digital logic with optical logic soon. Privacy and data security are also of utmost importance in all-optical networks. Generally, all-optical encryption has been carried out using (i) highly nonlinear fiber (HNLF) and (ii) Semiconductor Optical Amplifier (SOA) with interferometric structures. However, the former is limited by the requirement of a lengthy fiber and the latter one with more number of nonlinear components. In this work, an all-optical encryption process using nonlinear effects and four-wave mixing (FWM) in SOA without interferometric structure is presented for different number systems. The basic idea of the proposed system is to use delay operations which are carried out by duo binary modulation units whereas the encryption using single SOA is possible by FWM nonlinear effect. This combination of novel design for different number systems is optimized through SOA structural parameters, pump and probe signal power, and wavelength. Through optimization, the performance improvement is assured by a good extinction ratio of 11.5 dB for the active region length of less than 200 µm. Compared to the existing techniques, the quality factor is 2.28 times and 1.52 times better than HNLF and SOA-MZI, respectively.

Nonlinear optical induced lattice in atomic configurations

Traditional artificial lattice with untunable refractive index have been restricted to flexible applied to kinds of micro medium imaging. This study proposes a novel approach to quantifying lattice using nonlinear optically induced periodic lattice, which possesses a striking feature of tunable refractive index, to further broaden current knowledge of optical imaging equipment. We conduct self-dressed and dual-dressed nonlinear four-wave mixing (FWM) signal modulation in the atoms by using the dressing effect of standing waves, and then investigate the space amplitude modulation and synthetization (amplitude and phase) modulation of the electromagnetic induced lattice (EIL) of FWM signal at the atom surface. The EIL presented in the far-field diffraction region confirms that diffraction intensity of the FWM signal can be easily transformed from zero-order to higher-order based on the dispersion effects. The tunable EIL with ultra-fast diffraction energy change can contribute to a better understanding of nonlinear process and provides a further step toward developing two-dimensional nonlinear atomic higher-resolution.

PT -symmetry-breaking-enhanced cavity optomechanical magnetometry

$\mathcal{PT}$-symmetry-breaking enhanced cavity optomechanical magnetometer is proposed, which is achieved by monitoring the change of intensity of a nonlinear four-wave mixing (FWM) process in a gain-cavity-assisted cavity optomechanical system (COMS). Compared with the traditional single loss COMS, the FWM intensity can be enhanced by two orders of magnitude when the gain-cavity-assisted COMS operates at the $\mathcal{PT}$-symmetry-breaking phase. Meanwhile, the sensitivity of magnetic field sensing can be increased from $10^{-9}$T to $10^{-11}$T. This originally comes from the fact that the effective detuning and decay of loss-cavity can be effectively modified in the $\mathcal{PT}$-symmetry-breaking phase. Our work shows that an ultrahigh-sensitivity magnetometer can be achieved in the $\mathcal{PT}$-symmetry-breaking COMS, which will have wide applications in the field of quantum sensing.

The ion-pair character of the B[formula omitted] state of CuAg

In order to obtain fundamental insight into the bonding properties of transition metals, the (v′,0) B-X transitions (v′=0-2) of the heteronuclear CuAg dimer are re-investigated by applying non-linear four-wave mixing and laser-induced fluorescence spectroscopy. The CuAg molecules in a molecular beam are produced by laser ablation of a Cu/Ag alloy target. Rotationally resolved spectra of the B-X transition are recorded. The measurements yield accurate molecular constants for four isotopologues and an equilibrium distance re=2.4577±0.0003 Å for the B state. In particular, the B state is identified as an Ω=0+ ion-pair state. The results corroborate the important contribution of the charge-transfer state to the metal–metal bond. The results are in good agreement with the recent calculations at the MRCI level of theory (Alizadeh et al., 2014).

Four-wave mixing in Weyl semimetals

Weyl semimetals (WSMs) have unusual optical response originated from unique topological properties of their bulk and surface electron states. Their third-order optical nonlinearity is expected to be very strong, especially at long wavelengths, due to linear dispersion and high Fermi velocity of three-dimensional Weyl fermions. Here we derive the third-order nonlinear optical conductivity of WSMs in the long-wavelength limit and calculate the intensity of the nonlinear four-wave mixing signal as it is transmitted through the WSM film or propagates away from the surface of the material in the reflection geometry. All results are analytic and show the scaling of the signal intensity with variation of all relevant parameters. The nonlinear generation efficiency turns out to be surprisingly high for a lossy material, of the order of several mW per W$^3$ of the incident pump power. Optimal conditions for maximizing the nonlinear signal are realized in the vicinity of bulk plasma resonance. This indicates that ultrathin WSM films of the order of skin depth in thickness could find applications in compact optoelectronic devices.

Plasmon-induced enhancement of nonlinear optical processes in a double-resonant metallic nanostructure grating

Nanostructured gratings in a metal surface can highly enhance nonlinear optical processes. The geometrical parameters that characterize a grating can be optimized to achieve intense near-fields, which in turn enhance the nonlinear optical signals. For a nonlinear process that involves multiple frequencies, like four-wave mixing (FWM), the optimization of grating parameters necessary to enhance the radiation in-coupling for both frequencies is not trivial. Here, we propose, compute, and experimentally demonstrate a grating design that is resonant to two excitation frequencies and thus enhances the frequency mixing processes more efficiently. Second- and third-order nonlinear mechanisms are studied using two spatially and temporally overlapped laser pulses with different frequencies. Using our grating design, we achieve an unprecedented nonlinear FWM enhancement factor of 7×103.

Single Molecule Nonlinearity in a Plasmonic Waveguide.

Plasmonic waveguides offer the unique possibility to confine light far below the diffraction limit. Past room temperature experiments focused on efficient generation of single waveguide plasmons by a quantum emitter. However, only the simultaneous interaction of the emitter with multiple plasmonic fields would lead to functionality in a plasmonic circuit. Here, we demonstrate the nonlinear optical interaction of a single molecule and propagating plasmons. An individual terrylene diimide (TDI) molecule is placed in the nanogap between two single-crystalline silver nanowires. A visible wavelength pump pulse and a red-shifted depletion pulse travel along the waveguide, leading to stimulated emission depletion (STED) in the observed fluorescence. The efficiency increases by up to a factor of 50 compared to far-field excitation. Our study thus demonstrates remote nonlinear four-wave mixing at a single molecule with propagating plasmons. It paves the way toward functional quantum plasmonic circuits and improved nonlinear single-molecule spectroscopy.

Observation of optical nonlinearities in an all-solid transverse Anderson localizing optical fiber

An all-solid transverse Anderson localizing optical fiber (TALOF) was fabricated using a novel combination of the stack-and-draw and molten core methods. Strong Anderson localization is observed in multiple regions of the fiber cross section associated with the higher index strontium aluminosilicate phases randomly arranged within a pure silica matrix. Further, to the best of our knowledge, nonlinear four-wave mixing is reported for the first time in a TALOF.

Nonlinear four-wave mixing with enhanced diversity and selectivity via spin and orbital angular momentum conservation

Light that can carry orbital angular momentum (OAM) has found a variety of applications in super-resolution microscopy, optical communications, and laser machining, bringing up the need for pure OAM light generation at on-demand power levels and wavelengths. Parametric four-wave mixing is a promising platform for such source generation, and while investigations of higher-order fiber modes have revealed enhanced phase-matching possibilities, the role of the angular momentum of light in this process has not yet been substantially considered. Here, with a specially designed ring-core fiber in which over 16 OAM modes can be stably guided, we demonstrate the first experiments, to our knowledge, investigating nonlinear four wave mixing between OAM modes in an optical fiber. The large modal space as well as spin and OAM conservation rules enable a high diversity of phase matching conditions while also providing high selectivity. We report parametric wavelength translations of over 438 nm and the ability to obtain kilowatt peak-power level ∼ nanosecond pulses of pure OAM beams at user defined colors.

Ultra-low power all-optical wavelength conversion of high-speed data signals in high-confinement AlGaAs-on-insulator microresonators

Wavelength conversion technology is imperative for the future high-speed all-optical network. Nonlinear four-wave mixing (FWM) has been used to demonstrate such functionality in various integrated platforms because of their potential for the realization of a chip-scale, fully integrated wavelength converter. Until now, waveguide-based wavelength conversion on a chip requires a pump power beyond the reach of available on-chip lasers. Although high-quality factor (Q) microresonators can be utilized to enhance the FWM efficiency, their narrow resonance linewidths severely limit the maximal data rate in wavelength conversion. In this work, combining the ultrahigh effective nonlinearity from a high-confinement aluminum gallium arsenide waveguide and field enhancement from a microring resonator with a broad resonance linewidth, we realize all-optical wavelength conversion of a 10-Gbaud data signal by using a pump power, for the first time, at a submilliwatt level. With such a low operation power requirement, a fully integrated high-speed wavelength converter is envisioned for the future all-optical network. The waveguide cross-sectional dimension is engineered in a submicron scale to enhance the light confinement, which pushes the device effective nonlinearity to 720 W−1 m−1 while maintaining a broad operation bandwidth covering the telecom S-, C-, and L-bands. Moreover, we demonstrate that a single microring resonator is capable of handling a high-speed data signal at a baud rate up to 40 Gbit/s. All the wavelength conversion experiments are validated with bit-error rate measurements.

Resonant four-wave mixing microscopy on silicon-on-insulator based zero-contrast gratings

In this paper, we report large area four-wave mixing microscopy studies on silicon-on-insulator based partially etched two-dimensional zero-contrast gratings. The zero-contrast gratings offer an additional degree of freedom for the design of spectral resonances by varying the etch depth of the grating structures. This is leveraged by designing signal resonance at 1580 nm, operating in the sub-wavelength, zeroth-order diffraction region and pump fixed at 1040 nm operating in the higher order diffraction region. The zero-contrast gratings are fabricated on standard 220 nm silicon-on-insulator substrates with etch depth chosen as 140 nm. The fabricated structures are characterized to measure the linear transmission and nonlinear four-wave mixing performance. Multi-spectral four-wave mixing images acquired across the grating structures for varying input signal wavelength show maximum enhancement of four-wave mixing signal at 1575 nm, with the on-grating four-wave mixing signal enhanced by ∼ 450 times when compared to the un-patterned film. Zero-contrast gratings present a promising platform for realizing sub-wavelength scale nanostructured surfaces for nonlinear wave-mixing applications using standard silicon-on-insulator substrates. Such structures can find potential applications in wavelength conversion across widely separated wavelength bands and as substrates for nonlinear frequency conversion.

Fat‐tree‐based optical networks‐on‐chip with WDM: crosstalk noise exploiting

Wavelength division multiplexing (WDM) technology as an extension of optical networks-on-chip (ONoCs) performance, can be applied to further overcome shortages of low bandwidth and high-power consumption in multiprocessor systems-on-chip. Nevertheless, WDM-based ONoCs (ONoCs_W) can encounter performance degradation and network scalability constraints because of its power loss and intrinsic crosstalk noise, especially the non-linear four-wave mixing crosstalk noise. Here, a formal systematical exploiting for worst-case crosstalk noise and optical signal-to-noise ratio (OSNR) in arbitrary fat-tree-based ONoCs with WDM (FONoCs_W) is proposed. Meanwhile, the worst-case OSNR optical link candidates are identified. To verify the proposed analysis method, FONoCs_W employing an optical turnaround router with WDM (WOTAR) is used for case study. The study results demonstrate that crosstalk noise significantly diminishes OSNR and restricts scalability of FONoCs_W. For instance, when input optical signal power equals 0 dBm in worst case, the average OSNR is -9.47 dB, the mean power of crosstalk noise for eight wavelengths is slightly greater than that of signal when the number of processor cores is 64; when it equals to 128, the average OSNR is -34.37 dB, decreased by 24.90 dB compared with the network with 64 processor cores.

Interferograms of Votex FWM Beam for Nonlinear Spatial Filter in Photonic Band Gap

We analyze the properties and interferograms of vortex four-wave mixing (FWM) beams by varying the incident angle of the probe field. Based on the properties, we propose the model of a new type of nonlinear spatial filter without diffraction using a Bragg grating in the nonlinear FWM process. We show the evolutions of shapes and interferograms of probe transmission signal (PTS) and FWM by scanning the probe detuning, and demonstrate the Kerr nonlinearity can manipulate the shapes and spatial location of vortex PTS and FWM images. Further, we can determine the center position of the new type of nonlinear filter through interference patterns and use the Kerr nonlinearity of related fields to control the nonlinear filter precisely. In addition, the interferograms of the reflected signal from the photonic band gap (PBG) structure are studied both in experiment and theory. We demonstrate that the number of fork-like patterns of reflected signal changes from one to three, revealing that the superposition of first-order and third-order beams in the reflected signal from PBG structure creates an inverted fork-like pattern.

High-Quality-Factor AlGaAs-on-Sapphire Microring Resonators

We realize an AlGaAs-on-sapphire platform through Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -assisted direct wafer bonding and substrate removal processes. The direct wafer bonding process is optimized concerning the intermediate layer deposition and annealing temperature to obtain a high bonding strength between the AlGaAs and sapphire wafers. High quality-factor (Q) microring resonators are fabricated using electron-beam lithography in which the charging effect is mitigated by applying a thin aluminum layer, and a smooth pattern sidewall definition is obtained using a multi-pass (exposure) process. We achieve an intrinsic Q of up to ~460,000 which is the highest Q for AlGaAs microring resonators. Taking advantage of such high Q resonators, we demonstrate an ultra-efficient nonlinear four-wave mixing process in this platform and obtain a conversion efficiency of -19.8 dB with continuous-wave pumping at a power level of 380 μW. We also investigate the thermal resonance shift of microring resonators with different substrate layouts and observe superior temperature stability for devices in the AlGaAs-on-sapphire platform. The realization of the AlGaAson-sapphire platform also opens new prospects for AlGaAs devices in nonlinear applications in the mid-infrared wavelength range.

Ultrahigh-resolution interrogation of a fiber Bragg grating sensor based on higher order four-wave mixing.

The performance of a highly sensitive strain sensor based on nonlinear four-wave mixing (FWM) using a fiber Bragg grating (FBG) is investigated. The power change due to the wavelength shift induced by very small strain over the FBG is significantly magnified by a higher order FWM process. Strain sensitivity of 5.547 dBm/μϵ is achieved and minimum wavelength shift of 2.18×10-6 nm (which corresponds to a strain of 1.80×10-3 μϵ) is detected with uniform FBG, whereas in case of chirped FBG (CFBG) strain sensitivity of 0.3 dBm/μϵ with minimum detectable wavelength shift of 4×10-5 nm (which corresponds to a strain of 0.033 μϵ) is obtained.

Interference patterns of vortex beams based on photonic band gap structure.

We experimentally observe a vortex six-wave mixing (SWM), namely, enhanced four-wave mixing (FWM), signal with its orbital angular momentum transferred from a vortex probe via a photonic band gap (PBG) structure in a hot rubidium vapor cell. By analyzing spatial images and interference patterns, on the one hand, we demonstrate spatial shift and splitting of the images as well as shift of phase singularity for the probe transmission signal under the nonlinear phase of different dressing fields; on the other hand, we observe defocusing and shift of the images as well as shift of phase singularity for the reflected vortex SWM signal by scanning the frequency detuning of a related field. Moreover, we find the interference patterns of the vortex probe can be switched from parallel shape to spiral shape by changing its incident angle. Also, we further research the spiral interference patterns of the transmitted signal by scanning the probe detuning, observing that the number of forks changes with the detuning. We consider the transmitted signal as a combined beam of the linear probe and nonlinear FWM, which are separated under Kerr effect. It is the separation that causes the fork number to change with probe detuning. Our studies are useful for better understanding and manipulation of optical vortices and have wide applications in quantum communication and information processing.

Mode-locked self-pumping and squeezing photons model in a nonlinear micro-ring resonator

Photon squeezing and self-pumping within a nonlinear microring GaAsInP/P resonator are modeled and simulated, based on practical, published device parameters. A slowly varying amplitude pulse is input to the system, with a pulse width of 20 ns, a wavelength of 1.55 µm and peak power of 100 mW. The nonlinear effect resulting from the photons within the nonlinear ring resonator can be increased by adding external nonlinear coupling where, in this case, two nonlinear side rings are provided. The Dirac approach is used to generate the squeezed photons within the system. Three different device structures have been investigated, which include an add-drop filter, and a modified add-drop filter with two inner and outer side ring coupling resonators, where the nonlinear four-wave mixing effect is introduced. By using the commercial Opti-wave and MATLAB programs (in which suitable parameters have been chosen), the balance between the creation and annihilation operators can form the squeezed photons, which can be seen at the edge and center rings. The results obtained have shown that the squeezed center photon optical path (between 0 and 1 nm can be obtained) can be useful for interferometry, photon sources, and security code and sensor applications.

Hamiltonian approach for optimization of phase-sensitive double-pumped parametric amplifiers.

In this work we applied a Hamiltonian formalism to simplify the equations of non-degenerate nonlinear four-wave mixing to the one-degree-of-freedom Hamiltonian equations with a three-parameter Hamiltonian. Thereby, a problem of signal amplification in a phase-sensitive double-pumped parametric fiber amplifier with pump depletion was reduced to a geometrical study of the phase portraits of the one-degree-of-freedom Hamiltonian system. For a symmetric case of equal pump powers and equal signal and idler powers at the fiber input, it has been shown that the theoretical maximum gain occurs on the extremal trajectories. However, to reduce the nonlinear interaction of waves, we proposed to choose the separatrix as the optimal trajectory on the phase plane. Analytical expressions were found for the maximum amplification, as well as the length of optical fiber and the relative phase of interacting waves allowing this amplification. Using the proposed approach, we optimized of the phase-sensitive parametric amplifier. As a result, the optimal parameters of the phase-sensitive amplifier were found and the maximum possible signal amplification was realized in a broad range of signal wavelengths.

Tunable VUV photochemistry using vacuum ultraviolet free electron laser combined with H-atom Rydberg tagging time-of-flight spectroscopy.

In this article, we describe an experimental setup for studying tunable vacuum ultraviolet photochemistry using the H-atom Rydberg tagging time-of-flight technique. In this apparatus, two vacuum ultraviolet laser beams were used: one is generated by using a nonlinear four-wave mixing scheme in a Kr gas cell and fixed at 121.6 nm wavelength to probe the H-atom product through the Lyman α transition and the other beam, produced by a seeded free electron laser facility, can be continuously tunable for photodissociating molecules in the wavelength range of 50-150 nm with extremely high brightness. Preliminary results on the H2O photodissociation in the 4d (000) Rydberg state are reported here. These results suggest that the experimental setup is a powerful tool for investigating photodissociation dynamics in the vacuum ultraviolet region for molecules involving H-atom elimination processes.

Generation of quadripartite entanglement from a hybrid scheme with a four-wave mixing process and linear beam splitters

We theoretically propose a hybrid scheme with nonlinear four-wave mixing process and linear beam splitters to generate continuous-variable quadripartite entanglement. To expose the entanglement properties of the generated state, the coupling strength matrix is derived to reveal the interactions of the resulting modes at first. The generated state is verified to be a H-graph state with a non-full rank coupling strength matrix by using graphical calculus for Gaussian pure states. Then based on the eigenmodes for the generated state, we find that the introduction of beam splitters does not alter the deduced eigenmodes of the nonlinear four-wave mixing process, and only contributes to generate quadripartite entanglement. In the end, we quantitatively investigate the internal entanglement structure of this scheme. Our work paves the way to generate quadripartite entanglement from a hybrid scheme with nonlinear four-wave mixing process and linear beam splitters.