Nonlinear Optical Processes Research Articles

Tutorial on the instrumentation of sum frequency generation vibrational spectroscopy: Using a Ti:sapphire based system as an example

Sum frequency generation vibrational spectroscopy (SFG-VS) is an intrinsically surface-selective vibrational spectroscopic technique based on the second-order nonlinear optical process. Since its birth in the 1980s, SFG-VS has been used to solve interfacial structure and dynamics in a variety of research fields including chemistry, physics, materials sciences, biological sciences, environmental sciences, etc. Better understanding of SFG-VS instrumentation is no doubt an essential step to master this sophisticated technique. To address this need, here we will present a Tutorial with respect to the classification, setup layout, construction, operation, and data processing about SFG-VS. We will focus on the steady state Ti:sapphire based broad bandwidth SFG-VS system and use it as an example. We hope this Tutorial is beneficial for newcomers to the SFG-VS field and for people who are interested in using SFG-VS technique in their research.

Large Exciton-Driven Linear and Nonlinear Optical Processes in Monolayers of Nitrogen Arsenide and Nitrogen Antimonide

We demonstrate that atomically thin nitrogen-based binary group V wide band gap indirect semiconductors (β-NX (X = As, Sb)) embody 3-fold valley degenerated band structures and strong linear and nonlinear optical activities. Contrary to NAs, the fundamental optical absorption in NSb is quite resilient toward the temperature variations between 0 and 450 K. In the absence of lattice vibrations, exciton in NSb is, however, less strongly bound (1.30 eV) compared to the tighter case in NAs (1.62 eV), leading to a more delocalized Mott–Wannier-type texture. The inhomogeneous excitonic line widths for both monolayers within these temperatures are within the 100–400 meV range. The most significant nonlinear second harmonic optical coefficients (2ω resonances) in NAs and NSb monolayers are obtained as ∼636 and 270 pm/V at 3.2 eV (387 nm) and 2.6 eV (477 nm), respectively. We also present a detailed analysis of in-plane biaxial strain on these structures and found that tensile strain dynamically stabilizes structures with no loss in absorbance spectra (and does not influence exciton binding energy in NAs). The nonlinear coefficient also significantly improves at the two most important 810 and 1560 nm wavelengths compared to the cases offered by the monolayer transitional metal dichalcogenides. Our analyses originate from a fully ab initio G0W0+Bethe-Salpeter excited-state theory. The temperature-dependent linear absorption spectra are evaluated by including the electron–phonon self-energies, whereas the nonlinear spectra are treated using the modern theory of polarization within the same perturbative approach. Our reference findings provide important advanced characteristics for applications of two-dimensional β-NX (X = As, Sb) materials and should motivate further theoretical and experimental investigations of these interesting materials.

Controlling the polarization and phase of high-order harmonics with a plasmonic metasurface

Nanostructured surfaces, or metasurfaces, allow exquisite control of linear and nonlinear optical processes by reshaping the amplitude, phase, and polarization of electric and magnetic fields near wavelength-scale heterogeneities. Recently, metasurfaces have broken new ground in high-field attosecond science where they have been utilized to amplify the emission of high-order harmonics of femtosecond infrared laser pulses, a notoriously inefficient process, by enhancing the incident field, and to shape the emitted high harmonics in space. Here we show control of the polarization and phase of high harmonics with a plasmonic metasurface. We design and fabricate perpendicularly aligned rectangular gold antennas on a silicon crystal that generate circularly polarized deep-ultraviolet high harmonics, from a circularly polarized infrared driver, providing a simple path for achieving circular emission from patterned crystals. Our metasurface enhances the circularly polarized harmonics up to ∼ 43 times when compared to the unpatterned surface, where harmonics are quenched. Looking forward, circularly polarized high harmonics will be useful tools for sensing chiral laser–matter interactions and magnetic materials. Our approach paves the way for polarization control at even shorter, extreme ultraviolet, wavelengths.

Efficient Quadrature Squeezing from Biexcitonic Parametric Gain in Atomically Thin Semiconductors.

Modification of electromagnetic quantum fluctuations in the form of quadrature squeezing is a central quantum resource, which can be generated from nonlinear optical processes. Such a process is facilitated by coherent two-photon excitation of the strongly bound biexciton in atomically thin semiconductors. We show theoretically that interfacing an atomically thin semiconductor with an optical cavity makes it possible to harness this two-photon resonance and use the biexcitonic parametric gain to generate squeezed light with input power an order of magnitude below current state-of-the-art devices with conventional third-order nonlinear materials that rely on far off-resonant nonlinearities. Furthermore, the squeezing bandwidth is found to be in the range of several meV. These results identify atomically thin semiconductors as a promising candidate for on-chip squeezed-light sources.

Towards compact phase-matched and waveguided nonlinear optics in atomically layered semiconductors

Nonlinear frequency conversion provides essential tools for light generation, photon entanglement, and manipulation. Transition metal dichalcogenides (TMDs) possess huge nonlinear susceptibilities and 3R-stacked TMD crystals further combine broken inversion symmetry and aligned layering, representing ideal candidates to boost the nonlinear optical gain with minimal footprint. Here, we report on the efficient frequency conversion of 3R-MoS2, revealing the evolution of its exceptional second-order nonlinear processes along the ordinary (in-plane) and extraordinary (out-of-plane) directions. By measuring second harmonic generation (SHG) of 3R-MoS2 with various thickness - from monolayer (~0.65 nm) to bulk (~1 {\mu}m) - we present the first measurement of the in-plane SHG coherence length (~530 nm) at 1520 nm and achieve record nonlinear optical enhancement from a van der Waals material, >10^4 stronger than a monolayer. It is found that 3R-MoS2 slabs exhibit similar conversion efficiencies of lithium niobate, but within propagation lengths >100-fold shorter at telecom wavelengths. Furthermore, along the extraordinary axis, we achieve broadly tunable SHG from 3R-MoS2 in a waveguide geometry, revealing the coherence length in such structure for the first time. We characterize the full refractive index spectrum and quantify both birefringence components in anisotropic 3R-MoS2 crystals with near-field nano-imaging. Empowered with these data we assess the intrinsic limits of the conversion efficiency and nonlinear optical processes in 3R-MoS2 attainable in waveguide geometries. Our analysis highlights the potential of 3R-stacked TMDs for integrated photonics, providing critical parameters for designing highly efficient on-chip nonlinear optical devices including periodically poled structures, resonators, compact optical parametric oscillators and amplifiers, and optical quantum circuits.

Robust enhancement of high-harmonic generation from all-dielectric metasurfaces enabled by polarization-insensitive bound states in the continuum.

The emerging all-dielectric platform exhibits high-quality (Q) resonances governed by the physics of bound states in the continuum (BIC) that drives highly efficient nonlinear optical processes. Here we demonstrate the robust enhancement of third-(THG) and fifth-harmonic generation (FHG) from all-dielectric metasurfaces composed of four silicon nanodisks. Through the symmetry breaking, the genuine BIC transforms into the high-Q quasi-BIC resonance with tight field confinement for record high THG efficiency of 3.9 × 10-4 W-2 and FHG efficiency of 4.8 × 10-10 W-4 using a moderate pump intensity of 1 GW/cm2. Moreover, the quasi-BIC and the resonantly enhanced harmonics exhibit polarization-insensitive characteristics due to the special C4 arrangement of meta-atoms. Our results suggest the way for smart design of efficient and robust nonlinear nanophotonic devices.

Coherent Control of the Nonlinear Emission of Single Plasmonic Nanoantennas by Dual‐Beam Pumping

AbstractThe control of nonlinear optical signals in nanostructured systems is pivotal to develop functional devices suitable for integration in optical platforms. A possible control mechanism is exploiting coherent interactions between different nonlinear optical processes. Here, this concept is implemented by taking advantage of the strong field enhancement and high optical nonlinearity provided by plasmonic nanostructures. Two beams, one at the angular frequency ω, corresponding to the telecom wavelength λ = 1551 nm, and the other at 2ω, are combined to generate a sum‐frequency signal at 3ω from single asymmetric gold nanoantennas. This nonlinear signal interferes with the third‐harmonic radiation generated by the beam at ω, resulting in a modulation up to 50% of the total signal at 3ω depending on the relative phase between the beams. Such a large intensity modulation of the nonlinear signal is accompanied by a rotation of its polarization axis, due to the lack of central symmetry of the nanostructure. The demonstration that the nonlinear emission can be coherently controlled through the phase difference of the two‐color illumination represents a promising route toward all‐optical logic operations at the nanoscale through nonlinear optical signal manipulation.

Ultra-low-power second-order nonlinear optics on a chip

Second-order nonlinear optical processes convert light from one wavelength to another and generate quantum entanglement. Creating chip-scale devices to efficiently control these interactions greatly increases the reach of photonics. Existing silicon-based photonic circuits utilize the third-order optical nonlinearity, but an analogous integrated platform for second-order nonlinear optics remains an outstanding challenge. Here we demonstrate efficient frequency doubling and parametric oscillation with a threshold of tens of micro-watts in an integrated thin-film lithium niobate photonic circuit. We achieve degenerate and non-degenerate operation of the parametric oscillator at room temperature and tune its emission over one terahertz by varying the pump frequency by hundreds of megahertz. Finally, we observe cascaded second-order processes that result in parametric oscillation. These resonant second-order nonlinear circuits will form a crucial part of the emerging nonlinear and quantum photonics platforms.

Saturation effects in nonlinear absorption, refraction, and frequency conversion: a review

Over the past few decades, there has been extensive research work carried out in the area of nonlinear optics and opened a myriad of applications in material science and engineering. In coherent light-matter interaction, the nonlinear optical processes exhibit a saturation behavior at high-intensity laser excitation. This review article was written based on most of the research articles published till now in such a way to provide complete information on saturation effects, generally seen in nonlinear optics. In this review article, we have given a brief discussion on the saturation effect which is taken place in nonlinear absorption, refraction, and frequency conversion. The saturation in single- and multi-photon absorption processes is discussed in detail. We have also given a detailed analysis of the saturation that occurred in the nonlinear refractive index and how the nonlinear gradient refractive index creates diffraction in the transmitted laser beam. Further, we discussed on the saturation involved in the nonlinear frequency conversion due to various factors. Our review will be of interest to the large community that seeks to use the applications of high-intensity light-matter interaction.

Numerical study of terahertz radiations from difference frequency generation with large spectral tunability and significantly enhanced conversion efficiencies boosted by 1D leaky modes

The nonlinear optical process of difference frequency generation (DFG) is a prominent technique to produce continuous-wave terahertz radiations while its low conversion efficiency calls for substantial enhancement using artificial structures. All-dielectric nanostructures supporting the quasi-bound states in the continuum (QBIC) appear as a promising approach to this end. To achieve the utmost of enhancement, both input lightwaves of the DFG should work at the QBIC conditions and in many cases a spectral tunability of the input wavelength is necessary. All these requirements go beyond the capability of conventional QBIC which can only happen within a narrow bandwidth for a given structure. In this work, we numerically demonstrate that these restrictions can be eliminated by using our recently proposed concept of one-dimensional leaky modes with ultrahigh Q factors and large operation bandwidth. Using an elaborately designed structures in the form of binary waveguide gratings (BWGs) made from LiNbO3 thin film, we demonstrate that a conversion efficiency enhanced by the order of 1011 can be achieved using the BWGs made from LiNbO3, compared to the case of a bare LiNbO3 thin film. Furthermore, enhanced THz generations over a large spectral range can be easily achieved by changing the incident angle of one input light beam while tuning its wavelength to match the requirement for the leaky resonance excitation at that angle.

Engineering nonlinear optical phenomena by arbitrarily manipulating the phase relationships among the relevant optical fields

Nonlinear optical processes are intrinsically dominated by the phase relationships among the relevant electromagnetic fields, including the phase of nonlinear polarization produced in them. If one can arbitrarily manipulate these phase relationships at a variety of desired interaction lengths, direct and highly designable manipulations for the nonlinear optical phenomenon could be achieved. Here, we report a proof-of-principle experiment in which a high-order Raman-resonant four-wave-mixing process is used as a representative nonlinear optical process and is tailored to a variety of targets by implementing such arbitrary manipulations of the phase relationships in the nonlinear optical process. We show that the output energy is accumulated to a specific, intentionally selected Raman mode on demand; and at the opposite extreme, we can also distribute the output energy equally over broad high-order Raman modes in the form of a frequency comb. This concept in nonlinear optical processes enables an attractive optical technology: a single-frequency tunable laser broadly covering the vacuum ultraviolet region, which will pave the way to frontiers in atomic-molecular-optical physics in the vacuum ultraviolet region.

Селектор импульсов для получения фемтосекундного излучения с управляемой фазой несущей относительно огибающей

In non-linear optical processes, such as obtaining attosecond pulses, it is extremely important to control the carrier envelope phase. To do this, various periodic trains of identical femtosecond pulses with a controlled phase can be created. In addition, since there is no frequency comb offset in such sequences, the process of measuring optical frequencies is greatly simplified. The pulse selector has been developed to obtain a sequence of identical femtosecond pulses with a controlled carrier – envelope phase. The selector makes it possible to obtain a “pure” sequence of identical femtosecond pulses at the modulator output (when every 125th pulse is selected from the original sequence with a repetition rate of 250 MHz) in a fairly wide range of control signal phase tuning. This range is 1.3 degrees. The phase tuning of the pulse selector provides the possibility of obtaining one hundred twenty-five such sequences with a phase tuning discreteness of 2π/125. The simplest way to reduce discreteness is to increase the ratio of the pulse repetition rate of a femtosecond laser to the shift of its frequency comb. The phase characteristic of the pulse selector was obtained by registering the time dependence of the synthesized sequence with a selector phase tuning step of 0.1 degrees. We measured the spectra of the sequences at different phases of the pulse selector, as well as the emission spectrum of the master laser at the minimum transmission of the modulator in the absence of modulation. The spectrum with the maximum amplitude corresponded to the case when identical pulses with the highest amplitude were selected from the original sequence. The difference between these spectra made it possible to isolate the spectrum of a pure sequence of identical femtosecond pulses without taking into account the "background" that occurs due to the modulator has a finite attenuation of –20 dB.

Nonlinear Quantum Optics With Structured Light: Tightly Trapped Atoms in the 3D Focus of Vectorial Waves

Atomic gases tightly trapped near the focus of an electromagnetic wave interact with photons that exhibit a complex structure, displaying strong gradients of field amplitude and local polarization that can lead to topological phase singularities. We illustrate the consequences of this structure on a paradigmatic nonlinear optical process: three-wave mixing. The process begins by proper selection of the pump field, whose spatial structure is tailored to present huge gradients of the EM field that enhance atomic excitations through forbidden transitions. Atoms can then be depopulated via two electric dipole decays in a cascade configuration, thus providing the three necessary waves. The properties of the down-converted photons are conditioned to those of the pump field through phase matching conditions. It is emphasized that the expression of the photons must incorporate both the structure of the vectorial EM modes and the spatial configuration of the atomic trap. Due to the three-dimensional focusing, the slowly varying envelope approximation becomes inadequate when describing the scattered EM field. We discuss an alternative using a Green function formalism valid for any configuration of the field that also allows to identify the phase matching conditions. Spherical vectorial waves exemplify most concepts here discussed, including the possibility of observing nonlinear quantum phenomena at the single photon level.

Design of coherent wideband radiation process in a Nd3+-doped high entropy glass system

We discover that the spatially coherent radiation within a certain frequency range can be obtained without a common nonlinear optical process. Conventionally, the emission spectra were obtained by de-exciting excited centers from real excited energy levels to the ground state. Our findings are achieved by deploying a high-entropy glass system (HEGS) doped with neodymium ions. The HEGS exhibits a much broader infrared absorption than common glass systems, which can be attributed to be high-frequency optical branch phonons or allowable multi-phonon processes caused by phonon broadening in the system. A broadened phonon-assisted wideband radiation (BPAWR) is induced if the pump laser is absorbed by the system. The subsequent low-threshold self-absorption coherence modulation (SACM) can be controlled by changing excitation wavelengths, sample size, and doping concentrations. The SACM can be red-shifted through the emission of phonons of the excited species and be blue-shifted by absorbing phonons before they are de-excited. There is a time delay up to 1.66 ns between the pump pulse and the BPAWR when measured after traveling through a 35 mm long sample, which is much longer than the Raman process. The BPAWR-SACM can amplify the centered non-absorption band with a gain up to 26.02 dB. These results reveal that the shift of the novel radiation is determined by the frequency of the non-absorption band near the absorption region, and therefore the emission shifts can be modulated by changing the absorption spectrum. When used in fiber lasers, the BPAWR-SACM process may help to achieve tunability.

Generalized Wilson loop method for nonlinear light-matter interaction

Nonlinear light–matter interaction, as the core of ultrafast optics, bulk photovoltaics, nonlinear optical sensing and imaging, and efficient generation of entangled photons, has been traditionally studied by first-principles theoretical methods with the sum-over-states approach. However, this indirect method often suffers from the divergence at band degeneracy and optical zeros as well as convergence issues and high computation costs when summing over the states. Here, using shift vector and shift current conductivity tensor as an example, we present a gauge-invariant generalized approach for efficient and direct calculations of nonlinear optical responses by representing interband Berry curvature, quantum metric, and shift vector in a generalized Wilson loop. This generalized Wilson loop method avoids the above cumbersome challenges and allows for easy implementation and efficient calculations. More importantly, the Wilson loop representation provides a succinct geometric interpretation of nonlinear optical processes and responses based on quantum geometric tensors and quantum geometric potentials and can be readily applied to studying other excited-state responses.

Phase Matching via Plasmonic Modal Dispersion for Third Harmonic Generation.

The overall effectiveness of nonlinear optical processes along extended nonlinear media highly depends on the fulfillment of the phase‐matching condition for pump and generated fields. This is traditionally accomplished by exploiting the birefringence of nonlinear crystals requiring long interaction lengths (cm‐scale). For nonbirefringent media and integrated photonic devices, modal phase matching can compensate the index mismatch. Here, the various interacting waves propagate in transverse modes with appropriate phase velocities, but they suffer from a low refractive index contrast and cm‐scale interaction lengths. This work harnesses modal phase matching for third‐harmonic generation (THG) in plasmonic waveguides using an organic polymer (poly[3‐hexylthiophene‐2,5‐diyl]) as the nonlinear medium. One demonstrates experimentally an effective interaction area as small as ≈ 0.11 µm2 and the phase‐matched modal dispersion results in THG efficiency as high as ≈ 10–3 W‐2 within an effective length scale of ≈ 4.3 µm. THG also shows a strong correlation with the polarization of the incident laser beam, corresponding to the excitation of the antisymmetric plasmonic modes, corroborating that plasmonic modal phase matching is achieved. This large reduction in device area of orders of magnitude is interesting for various applications where space is critical (e.g., device integration or on‐chip applications).

A kinetic model for the equilibrium dynamics of absorption and scattering processes in four-wave mixing spectroscopy

We construct a kinetic model, analogous to a simple chemical reaction, to describe the spatial propagation of the electromagnetic fields in four-wave mixing spectroscopy in a two-level molecular model, explicitly taking into account the stochastic effects of the solvent. We show that in this case, the nonlinear optics processes (absorption and scattering) along the optical path can be described using an analogy with the kinetic processes that occur in a chemical reaction. A key result is that it is possible to define an apparent equilibrium constant that regulates the competition of the photonic processes that take place, an idea conceptually similar to Einstein’s model for spontaneous emission and how it can be connected to induced emission in atoms and molecules but including an extension to nonlinear optical and relaxation processes. Our model can be generalized to describe a variety of phenomena in nano-photonics and plasmonic systems.

Ultrafast dynamic switching of optical response based on nonlinear hyperbolic metamaterial platform

The pursuit of high-speed and on-chip optical communication systems has promoted extensive exploration of all-optical control of light-matter interactions via nonlinear optical processes. Here, we have numerically investigated the ultrafast dynamic switching of optical response using tunable hyperbolic metamaterial (HMM) which consists of five pairs of alternating layers of indium tin oxide (ITO) and SiO2. The nonlinearity of the HMM is analyzed by the ultrafast dynamics of the hot electrons in the epsilon-near-zero (ENZ) ITO. Our approach allows large and broad all-optical modulation of the effective permittivity and topology of the HMM on the femtosecond time-scale. Based on the proposed HMM platform, we have shown considerable tunability in the extinction ratio and Purcell enhancement under various pump fluence. In addition, we have achieved all-optical control of the coupling strength through depositing plasmonic resonators on the HMM platform. A significant tuning of the coupled resonance is observed by changing pump fluence, which leads to a switching time within 213 fs at a specific wavelength with a relative modulation depth more than 15 dB.

Classical and quantum photonic sources based upon a nonlinear GaP/Si-superlattice micro-ring resonator

We present a theoretical investigation, based on the tight-binding Hamiltonian, of efficient second- and third-order nonlinear optical processes in the lattice-matched undoped (GaP)N/(Si2)M short-period superlattice that is waveguide-integrated in a microring resonator on an opto-electronic chip. The nonlinear superlattice structures are situated on the optically pumped input area of a heterogeneous “XOI” chip based on silicon. The spectra of χzzz(2)(2ω,ω,ω), χxzx(2)(2ω,ω,ω), χxxxx(3)(3ω,ω,ω,ω) and the Kerr refractive index (n2), have been simulated as a function of the number of the atomic monolayers for “non-relaxed” heterointerfaces; These nonlinearities are induced by transitions between valence and conduction bands. The large obtained values make the (GaP)N/(Si2)M short-period superlattice a good candidate for future high-performance XOI photonic integrated chips that may include Si3N4 or SiC or AlGaAs or Si. Near or at the 810-nm and 1550-nm wavelengths, we have made detailed calculations of the efficiency of second- and third-harmonic generation as well as the performances of entangled photon-pair quantum sources that are based upon spontaneous parametric down conversion and spontaneous four-wave mixing. The results indicate that the (GaP)N/(Si2)M short-period superlattice is competitive with present technologies and is practical for classical and quantum applications.

Controlled sputtering time growth, ultrafast nonlinear absorption and carrier dynamics properties of vertically WSe2 films under photoexcitation

In this work, the vertically-grown-WSe2-films were successfully prepared using the RF magnetron sputtering. Their structure, morphology, growth mechanism and nonlinear optical properties were investigated by adjusting the growth time. The special "worm-like" structure was characterized by scanning electron microscopy, attributing to the two growth orientations in C-axis type I (C//) and type II (C⊥). The X-ray diffraction results confirmed the preferential growing on (002) and (008). The nonlinear optical properties were studied by femtosecond Z-scan to reveal the nonlinear absorption mechanism. WSe2 films exhibited the nonlinear optical process from saturable absorption to reverse saturable absorption with the growing time. The NA coefficient for WSe2 films is ∼10−9 m/W. The carrier relaxation time was determined by femtosecond transient absorption spectroscopy. This proposed WSe2 films will be an excellent candidate for developing optoelectronic devices due to the excellent nonlinear optical properties.