Four-wave Mixing Efficiency Research Articles

Silicon‐Rich Nitride Refractive Index as a Degree of Freedom to Maximize Nonlinear Wave Mixing in Nanowaveguides

Silicon nitride is widely used in integrated photonics for optical nonlinear wave mixing due to its low optical losses combined with relatively high nonlinear optical properties and a wide‐range transparency window. It is known that a higher concentration of Si in silicon‐rich nitride (SRN) magnifies both the nonlinear response and optical losses, including nonlinear losses. To address the trade‐off, four‐wave mixing (FWM) is implemented in over a hundred SRN waveguides prepared by plasma‐enhanced chemical vapor deposition in a wide range of SRN refractive indices varying between 2.5 and 3.2 (measured in the C‐band). It is determined that SRN with a refractive index of about 3 maximizes the FWM efficiency for continuous‐wave operation, indicating that the refractive index of SRN is indeed a crucial optimization parameter for nonlinear optics applications. The FWM efficiency is limited by large nonlinear optical losses observed in SRN waveguides with indices larger than 2.7, which are not related to two‐photon absorption. Finally, the third‐order susceptibility and the nonlinear refractive index are estimated for multiple SRN refractive indices, and, specifically, the nonlinearities as large as and are estimated in a waveguide with an SRN refractive index of 3.2.

Maximizing Four-Wave Mixing in Four-Subband Semiconductor Quantum Wells with Optimal-Shortcut Spatially Varying Control Fields

In the present article, we derive optimal spatially varying control fields, which maximize the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, following analogous works in atomic systems. The control fields coherently prepare the medium, where a weak probe pulse is propagated and eventually converted to a signal pulse at the output. The optimal fields, which maximize the conversion efficiency for a given propagation length, are obtained by applying optimal control theory to a simplified form of propagation equations but are tested with numerical simulations using the full set of Maxwell–Schrödinger equations, which accurately describe the propagation of light pulses in the medium. For short propagation distances, the proposed optimal scheme outperforms a simpler spatially changing control protocol that we recently studied, while for larger distances, the efficiency of both protocols approaches unity. The present work is expected to find application in frequency conversion between light beams, conversion between light beams carrying orbital angular momentum, and nonlinear optical amplification.

Efficient four-wave mixing in four-subband semiconductor quantum wells using spatially modulated control fields with a linearly varying mixing angle

In this article, we use spatially modulated control fields to increase the four-wave mixing efficiency in a four-subband semiconductor asymmetric double quantum well, motivated by similar works in atomic systems. Using a simplified version of the propagation equations, we show analytically that for control fields with a constant amplitude and linearly varying mixing angles with the propagation distance, a conversion efficiency close to unity can be achieved even for relatively short propagation distances. Subsequently, we confirm these results by numerically simulating the full set of propagation equations.

Broadband quantum-dot frequency-modulated comb laser

Frequency-modulated (FM) laser combs, which offer a quasi-continuous-wave output and a flat-topped optical spectrum, are emerging as a promising solution for wavelength-division multiplexing applications, precision metrology, and ultrafast optical ranging. The generation of FM combs relies on spatial hole burning, group velocity dispersion, Kerr nonlinearity, and four-wave mixing (FWM). While FM combs have been widely observed in quantum cascade Fabry-Perot (FP) lasers, the requirement for a low-dispersion FP cavity can be a challenge in platforms where the waveguide dispersion is mainly determined by the material. Here we report a 60 GHz quantum-dot (QD) mode-locked laser in which both the amplitude-modulated (AM) and the FM comb can be generated independently. The high FWM efficiency of –5 dB allows the QD laser to generate FM comb efficiently. We also demonstrate that the Kerr nonlinearity can be practically engineered to improve the FM comb bandwidth without the need for GVD engineering. The maximum 3-dB bandwidth that our QD platform can deliver is as large as 2.2 THz. This study gives novel insights into the improvement of FM combs and paves the way for small-footprint, electrically pumped, and energy-efficient frequency combs for silicon photonic integrated circuits (PICs).

(Invited) high speed densely dispersion-managed soliton and four-wave-mixing in dense periodical fibers and conventional dispersion-managed systems

I briefly reviewed the interesting densely dispersion-managed soliton (DDMS), and single channel high speed (40–160 Gbit/s) DDMS can transmit record distance at that time. I briefly reviewed the four-wave-mixing (FWM) of continous wave (CW) lasers in DPF when the EDFAs are located in the middle of dispersion section (z2 section), and our relative FWM efficiency formula was the first formula even for conventional dispersion-managed system (CDM) as well. We reached much lower FWM efficiency over a broad wavelength range in the well designed DPF than that in CDM and constant dispersion systems. We first found the FWM resonant condition for our dense periodical fiber (DPF) and CDM system. FWM strongly relates to the location of EDFAs. In this paper, I first report the analytical formula of relative FWM of CW lasers in DPF when the EDFAs are located right after the z1 section with dispersion D1, and our results are also suitable for CDM systems.

Broadband optical wavelength conversion through four-wave mixing in W3-type AlGaAs photonic crystal waveguides

We realized a wide-band wavelength conversion method through four-wave mixing in W3-type AlGaAs photonic crystal waveguides. AlGaAs exhibits a large third-order nonlinearity. Furthermore, because of its large bandgap, two-photon absorption can be avoided in the 1550 nm range. A four-wave mixing efficiency of −7 dB was obtained for a pump peak power of 7 W. Furthermore, by utilizing the two even guided bands of the W3-type photonic crystal waveguide, a conversion bandwidth greater than 38 nm was achieved with a conversion efficiency of −22 dB.

Performance enhancement of duobinary modulation-based DWDM system using particle swarm optimization

Abstract The next-generation light wave communication DWDM networks can accommodate large number of channels to efficiently utilize the bandwidth (BW). However, in the deployment of DWDM system mixing of two or more waves limits the performance due to four wave mixing (FWM) nonlinearity in fiber. This article, presents improved performance analysis of DWDM using a proposed improved duobinary modulation (IDBM), modified duobinary modulation (MDBM) and duobinary modulation (DBM) model for mitigation of FWM nonlinearities has been estimated experimentally through interference of noise on optical signal, FWM efficiency, FWM power etc. In IDBM, a unit delay in addition to time delay parameter is also utilized for generation of electrical duobinary pulses. The parameters of both delay blocks are tuned through particle swarm optimization (PSO) technique to improve the performance. The overall proposed IDBM effectively decreases the FWM. The results obtained for IDBM in terms of Q-factor 8.9, OSNR 18 dB, FWM power −87 dBm and FWM efficiency −70 dB shows substantial improvement with the recommended IDBM technique in comparison to DBM and MDBM schemes.

Convex-shaped silicon-on-insulator waveguide for linear and nonlinear applications

Dispersion engineering and enhanced light–matter interaction are the most desirable attributes for creating linear and nonlinear devices. It is always a challenging task to achieve both characteristics simultaneously. In this paper, we present a design of a silicon waveguide that provides not only enhanced light–matter interaction, measured through evanescent field strength, but also a platform to realize compact couplers and enhanced four-wave mixing efficiency. We make use of a convex-shaped design and numerically evaluate its modal characteristics. The design supports two zero dispersion wavelengths, from 1.2 µm to 1.3 µm and 1.7 µm to 1.8 µm, which can be tailored by changing the shape design parameters such as depth. Numerical simulations reveal that the depth of the convex shape affects both linear and nonlinear properties of the designed waveguide. We observe significant improvement of 15.2 dB in four-wave mixing efficiency when the waveguide is covered with a monolayer of graphene, illustrating the capabilities of such convex-shaped waveguides.

Demonstration of Ultra-High-Q Silicon Microring Resonators for Nonlinear Integrated Photonics.

A reflowing photoresist and oxidation smoothing process is used to fabricate ultra-high-Q silicon microring resonators based on multimode rib waveguides. Over a wide range of wavelengths near 1550 nm, the average Q-factor of a ring with 1.2-μm-wide waveguides reaches up to 1.17 × 106, with a waveguide loss of approximately 0.28 dB/cm. For a resonator with 1.5-μm-wide waveguides, the average Q-factor reaches 1.20 × 106, and the waveguide loss is 0.27 dB/cm. Moreover, we theoretically and experimentally show that a reduction in the waveguide loss significantly improves the conversion efficiency of four-wave mixing. A high four-wave mixing conversion efficiency of −17.0 dB is achieved at a pump power of 6.50 dBm.

High-efficiency four-wave mixing in low-loss silicon photonic spiral waveguides beyond the singlemode regime

Low-loss optical waveguides are highly desired for nonlinear photonics such as four-wave mixing (FWM), optical parametric amplification, and pulse shaping. In this work, low-loss silicon photonic spiral waveguides beyond the single-mode regime are proposed and demonstrated for realizing an enhanced FWM process. In particular, the designed 2-µm-wide silicon photonic waveguides are fabricated with standard foundry processes and have a propagation loss as low as ∼0.28 dB/cm due to the reduced light-matter interaction at the waveguide sidewalls. In the experiments, strong FWM effect is achieved with a high conversion efficiency of -8.52 dB in a 2-µm-wide and 20-cm-long silicon photonic waveguide spiral, and eight new wavelengths are generated with the pump power of ∼80 mW (corresponding to a low power density of ∼195 mW/µm2). In contrast, the FWM efficiency for the 0.45-µm-wide waveguide spiral is around -15.4 dB, which is much lower than that for the 2-µm-wide waveguide spiral. It can be seen that silicon photonics beyond the singlemode regime opens a new avenue for on-chip nonlinear photonics and will bring new opportunities for nonlinear photonic applications.

Optimization of quantum light sources and four-wave mixing based on a reconfigurable silicon ring resonator.

Being a key component on a photonic chip, the microring usually specializes in a certain nonlinear optical process and can not simultaneously meet different working conditions for different processes. Here, we theoretically and experimentally investigate a reconfigurable silicon microring resonator to act as a optimization strategy for both classical four-wave mixing and quantum light sources. Experimental results show that the four-wave mixing efficiency with continuous wave and pulsed pump can be both optimized to a high value well matching numerical analysis. A variety of quantum light sources - including the heralded single-photon source, two-photon source and multi-photon source - are demonstrated to present a high performance and their key parameters including the pair generation rates (PGR), the heralding efficiency (HE) and the coincidence-to-accidental ratio (CAR) are controllable and optimizable. Such tunable nonlinear converter is immune to fabrication variations and can be popularized to other nonlinear optical materials, providing a simple and compact post-fabrication trimming strategy for on-chip all-optical signal processing and photonic quantum technologies.

Tip-enhanced four-wave mixing internally illuminated by an ultrafast vector light field.

A tip nanofocusing light field, with high electric-field intensity and nanoscale mode volume, can significantly improve nonlinear light scattering efficiency, thereby greatly promoting the development of strong-field nano-optics. Here, tip-enhanced four-wave mixing (FWM) is theoretically analyzed through two ultrafast radial vector beams internally illuminating an Ag-coated silica tip (ACST). Two femtosecond pulses, with radial electric vectors and pulse width of 100 fs, are adopted as excitation sources to illuminate the ACST. Degenerate tip-enhanced FWM (ωFWM = 2ω1-ω2) with a nonlinear conversion efficiency of ∼10-5 is achieved. The peak electric-field amplitude of the two pump pulses is 5 × 107 V/m, which is two orders of magnitude lower than that of the external excitation method. Further theoretical analysis shows that the conversion efficiency of the tip-enhanced FWM has strict frequency detuning dependence characteristics, and is closely related to the frequency response of the tip nanofocusing light field. This plasmonic tip provides an approach for enhancing nonlinear nano-optics, and may be used in the field of tip-based FWM nanoscopy.

Impact of nonlocal response in plasmonic metasurfaces on four-wave mixing

We report the impact of nonlocal response in metallic nanostructures on four-wave mixing (FWM) process in nonlinear plasmonic metasurfaces which consist of Au nanostrips coupled with Au film spaced by an ultrathin dielectric film. When the dielectric film is linear and FWM only from the Au nanostructures, the FWM efficiency of around two orders of magnitude enhancement is obtained when the nonlocal effect of Au, not the traditionally local Drude model of Au, is considered. However, when the dielectric film is nonlinear and FWM from the Au nanostructures is negligible, the almost half FWM response from the nonlinear metasurface under the nonlocal, not the local model, of Au is confirmed. These results are both ascribed to the different local electric field distributions near the surface of Au nanostructures and in the gap at the local and nonlocal response of Au. The results have an important significance to design ultra-compacted integrated nonlinear optical devices or to explain the experimental measurements of nonlinear response involving plasmonic nanostructures of ultra-small gaps.

Design and Optimization of Four-Wave Mixing in Microring Resonators Integrated With 2D Graphene Oxide Films

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 parameters to balance the trade-off between the Kerr nonlinearity and loss, we achieve a high CE enhancement of ~18.6 dB relative to the uncoated MRR, which is ~8.3 dB higher than previous experimental results. The influence of photo-thermal changes in the GO films as well as variations in the MRR parameters such as the ring radius and waveguide dispersion on the FWM performance is also discussed. These results highlight the significantly improved FWM performance that can be achieved in MRRs incorporating GO films and provide a guide for optimizing their FWM performance.

A theoretical study of subcarrier-wave quantum key distribution system integration with an optical transport network utilizing dense wavelength division multiplexing

In this paper we study the performance of subcarrier-wave quantum key distribution (SCW QKD) in the presence of classical channels of optical transport network utilizing dense wavelength division multiplexing (DWDM). We consider the impact of spontaneous Raman scattering noise as well as the four-wave mixing and channel isolation efficiency. We calculate quantum bit error rate as well as the secure key generation rate of SCW-QKD protocol for different parameters of DWDM system and quantum channel allocations. Our calculations show, that quantum channel allocation at the wavelength of 1310 nm is preferable to allocation at C-band due to lower nonlinear noise, despite fiber’s larger attenuation at this wavelength.

Impact of System Parameters of Optical Fiber Link on Four Wave Mixing

Background: The invention of WDM technology in optical communication system has completely revolutionized the telecomm industry through its high data carrying capacity and efficiency of transmission. Advanced optical modulation formats with high spectral efficiency, advanced components like Reconfigurable Optical Add Drop Multiplexers (ROADMS), OXC, and large bandwidth requirements contributed significantly in existence of dynamic, flexible translucent and transparent networks. In these networks, it is common practice to increase the power levels as much as possible to overcome the power penalty effects and better transmission, but this introduces several non-linear impairments in the link and hence degrades the quality of signal flowing. These impairments arise when several high strength optical fields of different wavelengths interact with molecular vibrations and acoustic waves. The different non-linear impacts include Self Phase Modulation (SPM), Cross Phase Modulation (XPM), Four Wave Mixing (FWM) and scattering effects like Stimulated Raman Scattering (SRS), Stimulated Brillouin Scattering (SBS). The main cause of these impairments is variation in refractive index of fiber (also called Kerr effect) due to intensity of signal flowing through fiber. Due to the degradation impact posed by these impairments, it is crucial to analyze their cause, their influence on system performance and mitigation techniques so as to improve the overall quality of transmission. The monitoring of impairments is quite a challenging task due to their dependency on time, present state of network, signals flowing in adjoining channels and fibers. Objective: The present work aims to identify and describe the role of FWM in optical networks. The mathematical model of FWM is studied to know the parameters influencing the overall impact on system performance. The power of optical source, channel spacing, distance of transmission and presence of dispersion are considered as key factors influencing FWM power being developed. Their impact on FWM power and hence, FWM efficiency is calculated. In addition, the influence of FWM on Quality of transmission is quantified in terms of BER and Q-factor. Methods: The analysis is done through a two-channel transmitter system with varied power, channel spacing, distance of transmission and presence of other degradation factors (dispersion) is taken into account. The corresponding optical spectrums are analysed. Results: In this paper, the non-linear impairment FWM posing degradation effect on the signal quality has been discussed. The basics involved are presented along with the mathematical model. It has been found that FWM results in power transfer from one channel to generation of new waves which may lead to power depletion and interference. The new waves generated depend on the number of wavelengths travelling in the fiber and channel spacing. The influence of FWM on system performance is presented in terms of BER and Q-value. Conclusion: It has been concluded that the increased power of transmission and decreased channel spacing are the crucial factors increasing the magnitude of FWM and need to be closely monitored. On the other hand, increased distance of propagation and presence of certain level of dispersion leads to decrease in FWM power. Therefore, if selected carefully, they may act as source of FWM mitigation without requiring any external compensating device.

Swapping of orbital angular momentum states of light in a quantum well waveguide

We study the effect of orbital angular momentum transfer between optical fields in a semiconductor quantum well waveguide with four energy levels in a closed-loop configuration via four-wave mixing. The waveguide is driven by two strong control fields and two weak probe fields. We consider three different cases for the light-matter interaction in order to efficiently exchange optical vortices. In the first two cases, the system is initially prepared in either a lower electromagnetically induced transparency or a coherent population trapping state, while the last case prepares the system in an upper state, enabling to induce the electron spin coherence. We find that for appropriate parameters and via the spin coherence effect, the efficiency of four-wave mixing is much higher in the quantum well waveguide. Working in the electron spin coherence regime, we then study the light-matter interaction under the situation where only one of the control fields has an optical vortex. The orbital angular momentum of the vortex control beam can be efficiently transferred to a generated probe field via the spin coherence. We also show that the spatially dependent optical effects of the waveguide can be strongly modified by the electron spin coherence.

Optimization of four-wave mixing wavelength conversion in a quantum-dot semiconductor optical amplifier based on the genetic algorithm

A novel approach based on the artificial neural network (ANN) and the genetic algorithm (GA) is presented for optimization of four-wave mixing (FWM) wavelength conversion in a quantum dot semiconductor optical amplifier (QD-SOA). First of all, we propose a simple, accurate, and fast model based on the feedforward ANN for the characteristics of FWM in a QD-SOA. To train the ANN, we collect the required data from a numerical model. In this model, the efficiency of FWM is obtained numerically taken into account the effect of pump/probe and the occupation probability of energy levels by using the slice technique. Then, the optimal design of QD-SOA as the FWM wavelength converter is performed using the GA.

Generation of visible-wavelength-tunable ultrashort laser pulses through femtosecond laser filamentation in air: strong external focusing effect

Wavelength-tunable ultrashort laser pulses in the visible spectral range are generated in a femtosecond laser filament in air through four-wave mixing of an intense 808-nm near-infrared (NIR) laser pulse and a weak tunable infrared (IR: 1.3–2.2 µm) laser pulse. We found that the external focusing geometries strongly influence the four-wave mixing efficiency in air filament. The measurements of the resultant four-wave mixing laser intensity reveal that changing both the tilting angle and the focal length of the focal lens can optimize the four-wave mixing signal. We interpret the process based on the strong influence of the external focusing on the plasma density and the volume of the filament during the filament formation.

Measurements of the nonlinear refractive index of AgGaSe2, GaSe, and ZnSe at 10 µm

We measure the four-wave mixing efficiency of dual-frequency, 300 ns, 10 µm C O 2 laser pulses to determine the effective nonlinear refractive index of the quadratic nonlinear crystals GaSe, A g G a S e 2 , and ZnSe relative to GaAs. The effective nonlinear refractive index of GaSe and A g G a S e 2 does not depend on the phase-matching conditions for second-harmonic and sum-frequency generation. This suggests that these measurements are representative of the intrinsic Kerr index and usable for infrared applications.