I. Razdolski, R. Kapra, T. Murzina, O. Aktsipetrov, M. Inoue
Third-order nonlinear optical effects in photonic microcavities are studied. Significant light defocusing in the thin nonlinear microcavity spacer was observed. The polarization self-action effect was detected, when the large nonlinear polarization rotation angle arises when exciting the microcavity mode, being proportional to the radiation intensity.
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Photonic molecules, named by analogy with chemical molecules, are clusters of closely located electromagnetically interacting microcavities or "photonic atoms". As two or several microcavities are brought close together, their optical modes interact, and a rich spectrum of photonic molecule supermodes emerges, which depends both on geometrical and material properties of individual cavities and on their mutual interactions. Here, we discuss ways of controllable manipulation of photonic molecule supermodes, which improve or add new functionalities to microcavity-based optical components. We pres…
Second-harmonic and sum-frequency mixing phenomena associated with 3D-localized photonic modes are studied in InP-based planar photonic crystal microcavities excited by short-pulse radiation near 1550 nm. Three-missing-hole microcavities that support two closely-spaced modes exhibit rich second-order scattering spectra that reflect intra- and inter-mode mixing via the bulk InP chi(2) during ring-down after excitation by the broadband, resonant pulse. Simultaneous excitation with a non-resonant source results in tunable second-order radiation from the microcavity.
The latest achievements in the fabrication of black phosphorus thin layers, towards the technological breakthrough of a phosphorene atomically thin layer, are paving the way for a their employment in electronics, optics, and optoelectronics. In this work, we have simulated the optical properties of one-dimensional photonic structures, i.e. photonic crystals and microcavities, in which few-layer black phosphorus is one of the components. The insertion of the 5 nm black phosphorous layers leads to a photonic band gap in the photonic crystals and a cavity mode in the microcavity interesting for l…
Using a 3D fully-vectorial nonlinear time-domain analysis we numerically investigate the generation of terahertz radiation by pumping a photonic crystal microcavity out of resonance. High quality factors and a quadratic susceptibility lead to few-cycle terahertz pulses via optical rectification. Material dispersion as well as linear and nonlinear anisotropy is fully accounted for.
By numerically integrating the three-dimensional Maxwell equations in the time domain with reference to a dispersive quadratically nonlinear material, we study second harmonic generation in planar photonic crystal microresonators. The proposed scheme allows efficient coupling of the pump radiation to the defect resonant mode. The out-coupled generated second harmonic is maximized by impedance matching the photonic crystal cavity to the output waveguide.
A two-dimensional photonic crystal microcavity design supporting a wavelength-scale volume resonant mode with a calculated quality factor (Q) insensitive to deviations in the cavity geometry at the level of Q~2x10^4 is presented. The robustness of the cavity design is confirmed by optical fiber-based measurements of passive cavities fabricated in silicon. For microcavities operating in the lambda = 1500 nm wavelength band, quality factors between 1.3-4.0x10^4 are measured for significant variations in cavity geometry and for resonant mode normalized frequencies shifted by as much as 10% of the…
We demonstrate the first monolithically integrated linear photonic crystal microcavities in an advanced SOI CMOS microelectronics process (IBM 45nm 12SOI) with no in-foundry process modifications. The cavities were integrated into a standard microelectronics design flow meeting process design rules, and fabricated alongside transistors native to the process. We demonstrate both 1520nm wavelength and 1180nm cavity designs using different cavity implementations due to design rule constraints. For the 1520nm and 1180nm designs, loaded quality factors of 2,000 and 4,000 are measured, and intrinsic…
The optical properties of vanadium dioxide ($VO_2$) can be tuned via metal-insulator transition. In this work different types of one-dimensional photonic structure-based microcavities that embed vanadium dioxide have been studied in the spectral range between 900 nm and 2000 nm. In particular, $VO_2$ has been sandwiched between: i) two photonic crystals made of $SiO_2$ and $ZrO_2$; ii) two aperiodic structures made of $SiO_2$ and $ZrO_2$ that follow the Thue-Morse sequence; iii) two disordered photonic structures, made of $SiO_2$ and $ZrO_2$ in which the disorder is introduced either by a rand…
We design, fabricate, and experimentally demonstrate a compact thermo-optic gate switch comprising a 3.78 um-long coupled L0-type photonic crystalmicrocavities on a silicon-on-insulator substrate. A nanohole is inserted in the center of each individual L0 photonic crystalmicrocavity. Coupling between identical microcavities gives rise to bonding and anti-bonding states of the coupled photonic molecules. The coupled photonic crystalmicrocavities are numerically simulated and experimentally verified with a 6 nm-wide flat-bottom resonance in its transmission spectrum, which enables wider operatio…
We propose a scheme for efficient cavity-enhanced nonlinear THz generation via difference-frequency generation (DFG) processes using a triply resonant system based on photonic crystal cavities. We show that high nonlinear overlap can be achieved by coupling a THz cavity to a doubly-resonant, dual-polarization near-infrared (e.g. telecom band) photonic-crystal nanobeam cavity, allowing the mixing of three mutually orthogonal fundamental cavity modes through a chi(2) nonlinearity. We demonstrate through coupled-mode theory that complete depletion of the pump frequency - i.e., quantum-limited con…
Optical resonances in 1D photonic crystal microcavities are investigated numerically using finite-element light scattering and eigenmode solvers. The results are validated by comparison to experimental and theoretical findings from the literature. The influence of nanometer-scale geometry variations on the resonator performance is studied. Limiting factors to ultra-high Q-factor performance are identified.
A technique is demonstrated which efficiently transfers light between a tapered standard single-mode optical fiber and a resonant mode of a high-Q photonic crystal cavity with mode volume less than a cubic wavelength in size. Cavity mode quality factors of 4.7 x 10^4 are measured, and a total fiber-to-cavity coupling efficiency of 44% is demonstrated.
Photonic Doping of Epsilon-Near-Zero Bragg Microcavities
本研究通过在超低损耗全介电ENZ平台中嵌入周期性介电米共振子，实现了光学频率下的光子掺杂，展示了超窄带米共振、增强磁光相互作用及多极选择性光谱等新应用。
The employment of magneto-optical materials to fabricate photonic crystals gives the unique opportunity to achieve optical tuning by applying a magnetic field. In this study we have simulated the transmission spectrum of a microcavity in which the Bragg reflectors are made with silica (SiO2) and yttria (Y2O3) and the defect layer is made with TGG (Tb3Ga5O12). We show that the application of an external magnetic field results in a tuning of the defect mode of the microcavity. In the simulations we have considered the wavelength dependence of the refractive indexes and the Verdet constants of th…
Photochemical reaction enabling the engineering of photonic spin-orbit coupling in organic-crystal optical microcavities
本文提出在有机单晶微腔中利用光化学反应控制人工Rashba-Dresselhaus自旋-轨道耦合，实现了光子模式自旋分裂的可逆转换及圆偏振与线偏振发射的光控切换，为片上集成提供新方法。
A large body of work has accumulated over the years in the study of the optical properties of single and coupled microcavities for a variety of applications, ranging from filters to sensors and lasers. The focus has been mostly on the geometry of individual resonators and/or on their combination in arrangements often referred to as photonic molecules (PMs). Our primary concern will be the lasing properties of PMs as ideal candidates for the fabrication of integrated microlasers, photonic molecule lasers. Whereas most calculations on PM lasers have been based on cold-cavity (passive) modes, i.e…
The authors study the ultrafast switching-on and -off of planar GaAs/AlAs microcavities. Up to 0.8% refractive index changes are achieved by optically exciting free carriers at 1720 nm and a pulse energy of 1.8 micro Joules. The cavity resonance is dynamically tracked by measuring reflectivity versus time delay with tunable laser pulses, and is found to shift by as much as 3.3 linewidths within a few picoseconds. The switching-off occurs with a decay time of around 50 ps. The authors derive the dynamic behavior of the carrier density and of the complex refractive index. They propose that the i…
We investigate a photonic device consisting of two coupled optical cavities possessing Rashba-Dresselhaus spin-orbit coupling, TE-TM splitting, and linear polarisation splitting that opens a tuneable energy gap at the diabolic points of the photon dispersion; giving rise to an actively addressable local Berry curvature. The proposed architecture stems from recent advancements in the design of artificial photonic gauge fields in liquid crystal cavities [K. Rechcińska et al., Science 366, 727 (2019)]. Our study opens new perspectives for topological photonics, room-temperature spinoptronics, and…
Bound states in the continuum (BICs) in photonic crystal slabs represent the resonances with an infinite quality(Q)-factor, occurring above the light line for an infinitely periodic structure. We show that a set of BICs can turn into quasi-BICs with a very high Q-factor even for two or three unit cell structures. They are explained by a viewpoint of BICs originating from the tight binding of individual resonances of each unit cell as in semiconductors. Combined with a reciprocal-space matching technique, the microcavities based on quasi-BICs can achieve a Q-factor as high as defect-based PhC m…
A driven high-Q Si microcavity is known to exhibit limit cycle oscillation originating from carrier-induced and thermo-optic nonlinearities. We propose a novel nanophotonic device to realize synchronized optical limit cycle oscillations with coupled silicon (Si) photonic crystal (PhC) microcavities. Here, coupled limit cycle oscillators are realized by using coherently coupled Si PhC microcavities. By simulating coupled-mode equations, we theoretically demonstrate mutual synchronization (entrainment) of two limit cycles induced by coherent coupling. Furthermore, we interpret the numerically si…
Hydrophobic Silica Microcavities with Sustainable Nonlinear Photonic Performance
针对二氧化硅微腔在空气中Q值易退化的问题，提出一种新型疏水超高Q二氧化硅微腔，能防止Q值随时间退化并实现可持续超低阈值的光学频率梳，推动下一代光子应用。
Inorganic-organic perovskites semiconductors are becoming increasingly interesting due to their remarkable optical properties, such as a high photoluminescence quantum yield and the possibility to show optical gain in a broad range of wavelengths. We have here simulated microcavities that embed MaPBI3 and 2D hybrid organic inorganic perovskite semiconductors by sandwiching such active layers between periodic, aperiodic and disordered photonic structures. We have carefully considered the refractive index dispersion of all the materials employed, such silicon dioxide, titanium dioxide and the pe…
Purcell Effect in Epsilon-Near-Zero Microcavities
本文提出全介质Bragg反射微腔作为低损耗ENZ谐振平台，研究其Purcell效应并推导出区分于传统谐振器的标度定律，为增强非线性与量子光子学中的光物质相互作用提供设计见解。
Metal halide perovskites are materials that show unique characteristics for photovoltaics and light emission. Amplified spontaneous emission and stimulated emission has been shown with these materials, together with electroluminescence in light-emitting diodes and light-emitting transistors. An important achievement that combine stimulated emission and electroluminescence could be the fabrication of electrically driven metal halide perovskite lasers. In this work, the integration of metal halide perovskite light-emitting field-effect transistors with photonic microcavities is proposed. This ca…
Optical microcavities based on zero-group-velocity surface modes in photonic crystal slabs are studied. It is shown that high quality factors can be easily obtained for such microcavities in photonic crystal slabs. With increasing of the cavity length, the quality factor is gradually enhanced and the resonant frequency converges to that of the zero-group-velocity surface mode in the photonic crystal. The number of the resonant modes with high quality factors is mainly determined by the number of surface modes with zero-group velocity.
We propose and design photonic crystal cavities (PCCs) in hexagonal boron nitride (hBN) for diverse photonic and quantum applications. Two dimensional (2D) hBN flakes contain quantum emitters which are ultra-bright and photostable at room temperature. To achieve optimal coupling of these emitters to optical resonators, fabrication of cavities from monolithic hBN is therefore required, to maximize the overlap between cavity optical modes and the emitters. Here, we design 2D and 1D PCCs using anisotropic indices of hBN. The influence of underlying substrates and material absorption are investiga…
Lithium niobate (LN) is an excellent nonlinear optical and electro-optic material that has found many applications in classical nonlinear optics, optical fiber communications and quantum photonics. Here we review the recent development of thin-film LN technology that has allowed the miniaturization of LN photonic devices and microcavities with ultrahigh quality factors. We discuss the design principle of LN devices that makes use of the largest nonlinear coefficients, various device fabrication approaches and resulting device performances, and the current and potential applications of LN micro…
We review a novel method for characterizing both the spectral and spatial properties of resonant cavities within two-dimensional photonic crystals (PCs). An optical fiber taper serves as an external waveguide probe whose micron-scale field is used to source and couple light from the cavity modes, which appear as resonant features in the taper's wavelength-dependent transmission spectrum when it is placed within the cavity's near field. Studying the linewidth and depth of these resonances as a function of the taper's position with respect to the resonator produces quantitative measurements of t…
We present the design of two-dimensional photonic crystal microcavities in thin diamond membranes well suited for coupling of color centers in diamond. By comparing simulated and ideal field distributions in Fourier and real space and by according modification of air hole positions and size, we optimize the cavity structure yielding high quality factors up to Q = 320000 with a modal volume of V = 0.35 (lambda/n)^3. Using the very same approach we also improve previous designs of a small modal volume microcavity in silicon, gaining a factor of 3 in cavity Q. In view of practical realization of …
Electrically tunable momentum space polarization singularities in liquid crystal microcavities
本文针对动量空间偏振奇点原位可调性稀缺的问题，提出利用高双折射平面液晶微腔产生并电调谐该奇点，结果与理论预测一致，为其集成到自旋光子技术提供可能。
Quasibound states in the continuum in photonic-crystal-based optomechanical microcavities
本文研究了基于光子晶体的光机械微腔中的连续谱准束缚态，提出用悬浮光子晶体板与分布式布拉格反射镜组合简化系统，使腔损耗仅由材料吸收主导，预计光学品质因子超过10^5。
Bosons hopping across sites and interacting on-site are the essence of the Bose-Hubbard model (BHM). Inspired by the success of BHM simulators with atoms in optical lattices, proposals for implementing the BHM with photons in coupled nonlinear cavities have emerged. Two coupled semiconductor microcavities constitute a model system where the hopping, interaction, and decay of exciton polaritons --- mixed light-matter quasiparticles --- can be engineered in combination with site-selective coherent driving to implement the driven-dissipative two-site optical BHM. Here we explore the interplay of …
Engineering Tunable Synthetic Su-Schrieffer-Heeger Chains in Liquid Crystal Microcavities
本文提出了一种在液晶微腔中实现可调合成Su-Schrieffer-Heeger链的方法，通过电压控制极化分裂和光子自旋轨道耦合，展示了其作为有效赝自旋自由度的应用。
This paper introduces a new approach to neuromorphic photonics in which microcavities exhibiting strong exciton-photon interaction may serve as building blocks of optical spiking neurons. The experimental results demonstrate the intrinsic property of exciton-polaritons to resemble the Leaky Integrate-and-Fire spiking mechanism. It is shown that exciton-polariton microcavities when non-resonantly pumped with a pulsed laser exhibit leaky-integration due to relaxation of the excitonic reservoir, threshold-and-fire mechanism due to transition to Bose-Einstein condensate, and resetting due to stimu…
Observation of Zitterbewegung in photonic microcavities
本研究在平面半导体微腔及蜂窝晶格耦合微腔中实验观测到极化子的Zitterbewegung效应，验证了理论模型与能带结构参数的一致性，为该相对论效应的光子模拟提供了实验证据。
Multicomponent Bose-Einstein condensates, quantum Hall systems, and chiral magnetic materials display twists and knots in the continuous symmetries of their order parameter, known as Skyrmions. Originally discovered as solutions to the nonlinear sigma model in quantum field theory, these vectorial excitations are quantified by a topological winding number dictating their interactions and global properties of the host system. Here, we report the first experimental observation of a stable individual second order meron, and antimeron, appearing in an electromagnetic field. These complex textures …
We performed measurements of photon correlation [$g^{(2)}(τ)$] in driven nonlinear high-$Q$ silicon (Si) photonic crystal (PhC) microcavities. The measured $g^{(2)}(τ)$ exhibits a damped oscillatory behavior when input pump power exceeds a critical value. From comparison between experiments and simulations, we attribute the measured oscillation of $g^{(2)}(τ)$ to self-pulsing (a limit cycle) emerging from an interplay between photon, carrier, and thermal dynamics. Namely, the oscillation frequency of $g^{(2)}(τ)$ corresponds to the oscillation period of the limit cycle, while its finite cohere…
Microstructured organic cavities with high-reflective flat reflectors fabricated by using a nanoimprint-bonding process
提出一种基于UV纳米压印技术的纳米压印键合工艺，用于制备高反射率微结构有机微腔，实现了空间局域光子模式、高精度光子能带及拓扑边缘态，推动了有机光子器件发展。
Parametrically encircled higher-order exceptional points in anti-parity-time symmetric optical microcavities
本研究在反PT对称法布里-珀罗型微腔中实现高阶奇异点，通过参数环绕方案揭示三阶及以下奇异点的分支点行为，优化微腔设计，为光学超材料和新型光子器件研究提供新思路。
Exceptional-point-controlled mode interaction in three-dimensional microcavities represented by generalized Husimi functions
本文将Husimi函数推广到三维微腔，通过二维投影表征TE与TM偏振模式相互作用，并揭示其动力学由折射率与腔倾角参数空间中的例外点网络支配，为高效光子器件设计提供新方法。
Electro-optical control of on-chip photonic devices is an essential tool for efficient integrated photonics. Lithium niobate on insulator (LNOI) is an emerging platform for on-chip photonics due to its large electro-optic coefficient and high nonlinearity [1]. Integrating quantum emitters into LNOI would extend their versatile use in classic photonics to quantum computing and communication [2, 3]. Here, we incorporate single rare-earth ions (REI) quantum emitters in electro-optical tunable lithium niobite (LN) thin films and demonstrate control of LN microcavities coupled to REI over a frequen…
Multiple Interacting Photonic Modes in Strongly Coupled Organic Microcavities
该研究通过对真实多模光学谐振腔内分子系综的微观量子描述，揭示低精细度多模下分子偶极子与非共振腔模耗散通道的部分杂化会限制光-物质相干程度，指出真空拉比分裂是光与物质相干混合的必要非充分条件。
Van der Waals functionalization of ultrahigh-Q silica microcavities for $χ^{(2)}$-$χ^{(3)}$ hybrid nonlinear photonics
本文提出通过原子级二硒化钨对超高Q二氧化硅微腔进行功能化，构建了二阶与三阶非线性磁化率可灵活调节的混合光子平台，实现了低功率下的二阶谐波与和频产生。
We present an experimental and theoretical study of the optical properties of metal-dielectric-metal structures with patterned top metallic surfaces, in the THz frequency range. When the thickness of the dielectric slab is very small with respect to the wavelength, these structures are able to support strongly localized electromagnetic modes, concentrated in the subwavelength metal-metal regions. We provide a detailed analysis of the physical mechanisms which give rise to these photonic modes. Furthermore, our model quantitatively predicts the resonance positions and their coupling to free spa…
Optical microcavities are often used to realize enhanced nonlinear optical interactions for highly efficient second-harmonic generation. With increased pump power, the efficiency of nonlinear frequency conversion can be increased further, while some other unwanted nonlinear effects will also emerge, leading to complicated dynamics or instability. Here, we study the interplay between cascaded second- and third-order nonlinear processes and investigate their impact on the second-harmonic generation in microcavities. It is found that the non-degenerate optical parametric oscillation (OPO) appears…
Reversing Annealing-Induced Optical Loss in Diamond Microcavities
本文研究高温高真空退火对金刚石微盘谐振器品质因数的损害，发现非金刚石层导致光学损耗，并证明三酸清洗可恢复其光学性能。
Self-aligned photonic defect microcavities with site-controlled quantum dots
提出一种无需额外纳米加工的自对准应变诱导位点控制量子点微腔，通过AlAs/Al2O3埋入式应力源尺寸定制微腔特性，实现激光特征且无热效应，为可扩展微型激光器制造铺路。
High-Q optical resonances in photonic microcavities are investigated numerically using a time-harmonic finite-element method.
Solitons are wavepackets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fiber waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities thereby bringing the power of microfabrication methods to future applications. This work repo…
The Moebius strip, as a fascinating loop structure with one-sided topology, provides a rich playground for manipulating the non-trivial topological behavior of spinning particles, such as electrons, polaritons, and photons in both real and parameter spaces. For photons resonating in a Moebius-strip cavity, the occurrence of an extra phase, known as Berry phase, with purely topological origin is expected due to its non-trivial evolution in the parameter space. However, despite numerous theoretical investigations, characterizing optical Berry phase in a Moebius-strip cavity has remained elusive.…
We use a phenomenological Hamiltonian approach to derive a set of coupled mode equations that describe light propagation in waveguides that are periodically side-coupled to microcavities. The structure exhibits both Bragg gap and (polariton like) resonator gap in the dispersion relation. The origin and physical significance of the two types of gaps are discussed. The coupled-mode equations derived from the effective field formalism are valid deep within the Bragg gaps and resonator gaps.
We present a joint theoretical and experimental characterization of thermo-refractive noise in high quality factor ($Q$), small mode volume ($V$) optical microcavities. Analogous to well-studied stability limits imposed by Brownian motion in macroscopic Fabry-Perot resonators, microcavity thermo-refractive noise gives rise to a mode volume-dependent maximum effective quality factor. State-of-the-art fabricated microcavities are found to be within one order of magnitude of this bound. We confirm the assumptions of our theory by measuring the noise spectrum of high-$Q/V$ silicon photonic crystal…
The realization of exciton-polaritons -- hybrid excitations of semiconductor quantum well excitons and cavity photons -- has been of great technological and scientific significance. In particular, the short-range collisional interaction between excitons has enabled explorations into a wealth of nonequilibrium and hydrodynamical effects that arise in weakly nonlinear polariton condensates. Yet, the ability to enhance optical nonlinearities would enable quantum photonics applications and open up a new realm of photonic many-body physics in a scalable and engineerable solid-state environment. Her…
Some properties of defect modes of cholesteric liquid crystals (CLC) are presented. It is shown that when the CLC layer is thin the density of states and emission intensity are maximum for the defect mode, whereas when the CLC layer is thick, these peaks are observed at the edges of the photonic band gap. Similarly, when the gain is low, the density of states and emission intensity are maximum for the defect mode, whereas at high gains these peaks are also observed at the edges of the photonic band gap. The possibilities of low-threshold lasing and obtaining high-Q microcavities have been inve…
We present an oxide aperture microcavity with embedded quantum dots that utilizes a three contact design to independently tune the quantum dot wavelength and birefringence of the cavity modes. A polarization splitting tuning of $\sim$5 GHz is observed. For typical microcavity polarization splittings, the method can be used to achieve perfect polarization degeneracy that is required for many polarization-based implementations of photonic quantum gates. The embedded quantum dot wavelength can be tuned into resonance with the cavity, independent of the polarization tuning.
Dual orthogonally-polarized lasing assisted by imaginary Fermi arcs in organic microcavities
本研究针对单个有机微激光器难同时产生两种正交偏振模式的问题，利用填充有机单晶的微腔中偏振相关损耗形成的虚费米弧与光子自旋轨道耦合，实现了正交偏振双激光同时发射，为线偏振激光器开发及相关光子学研究提供新路径。
We investigate the optical properties of microcavities with suspended subwavelength structured mirrors, such as high-contrast gratings or two-dimensional photonic crystals slabs, and focus in particular on the regime in which the microcavity free-spectral range is larger than the width of a Fano resonance of the highly reflecting structured mirror. In this unusual regime, the transmission spectrum of the microcavity essentially consists in a single mode, whose linewidth can be significantly narrower than both the Fano resonance linewidth and the linewidth of an equally short cavity without str…
Optical microcavities are essential in numerous technologies and scientific disciplines. However, their application in many areas relies exclusively upon discrete microcavities in order to satisfy challenging combinations of ultra-low-loss performance (high cavity-Q-factor) and cavity design requirements. Indeed, finding a microfabrication bridge connecting ultra-high-Q device functions with micro and nanophotonic circuits has been a long-term priority of the microcavity field. Here, an integrated ridge resonator having a record Q factor over 200 million is presented. Its ultra-low-loss and fl…
Formation of Quasi-Bound States in the Continuum in a Single Deformed Microcavity
本文提出在单个变形微腔中通过边界变形构建共享单向辐射通道并诱导外部强模式耦合，实验实现Friedrich-Wintgen准BIC，使长寿命共振的Q因子提升超过3倍，为增强光学微腔Q因子提供实用途径。
Nonlinear optical signals in the condensed phase are often accompanied by sequences of lower-order processes, known as cascades, which share the same phase matching and power dependence on the incoming fields and are thus hard to distinguish. The suppression of cascading in order to reveal the desired nonlinear signal has been a major challenge in multidimensional Raman spectroscopy, i.e., the $χ^{(5)}$ signal being masked by cascading signals given by a product of two $χ^{(3)}$ processes. Since cascading originates from the exchange of a virtual photon between molecules, it can be manipulated…
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