Second-order Nonlinear Optical Processes Research Articles

Femtosecond Laser-Induced Emission of Coherent Terahertz Pulses from Ruthenium Thin Films.

We demonstrate emission of electromagnetic pulses with frequencies in the terahertz (THz) range from ruthenium thin films through a second-order nonlinear optical process. Ruthenium deposited on different substrates showed different THz emission properties. We provide evidence that for Ru on glass above a certain power threshold, laser-induced oxidation occurs, resulting in an increased slope of the linear dependence of the THz electric field amplitude on pump power. The THz electric field is mainly polarized parallel to the sample surface, pointing in the same direction everywhere. In contrast to Ru on glass, the electric field amplitude of the THz pulses emitted by Ru on sapphire and on CaF2 shows a simple single linear dependence on pump power, and it is polarized orthogonal to the sample surface. In this case, thermal oxidation in an oven enhances the emission and introduces an additional polarization component along the sample surface. This component also points in the same direction everywhere on the surface, similar to the as-deposited Ru on glass. Although the precise THz generation mechanism remains an open question, our results show a strong correlation between the emission strength and the degree of oxidation. Furthermore, the results highlight the importance of the interfaces, i.e., both the choice of the substrate and the chemical composition of the top surface in THz emission experiments. Knowledge of the state of the sample surface is therefore crucial for the interpretation of THz emission experiments from (nonmagnetic) metal surfaces.

Understanding the Correlation Between Structure and Entangled Photon Pair Properties with Metal–Organic Frameworks

Spontaneous parametric down conversion (SPDC) is a quantum second-order nonlinear optical process where the photons generated are frequently used in quantum information processing. Materials with large second-order nonlinearities (χ(2)) can be used as entangled photon sources with a high brightness. The source brightness scales as the square of the effective nonlinearity (deff), which is an intrinsic property of the material. Understanding material factors that can significantly alter this intrinsic property is useful in developing new materials that are SPDC efficient. In our work we focus on understanding factors affecting the entangled photon pair properties, such as the arrangements of ligands within the Zn(3-ptz)2 metal–organic framework (MOF) crystal and temperature. We find that the arrangement and alignment of the pyridine rings in the crystal structure significantly affect the deff and birefringence (Δn). Smaller pyridine ring alignments relative to the optic c-axis increase the Δn, which in turn leads to larger photon pair correlation times (τc) in coincidence measurements. Our work has significant implications in understanding the effect of ligand arrangement on deff and τc for any MOF crystal structure, providing a tool to rationalize the optimization of MOF crystals for the development of efficient nonlinear optical devices.

Degenerate optical parametric amplification in CMOS silicon

Silicon is a common material for photonics due to its favorable optical properties in the telecom and mid-wave IR bands, as well as compatibility with a wide range of complementary metal–oxide semiconductor (CMOS) foundry processes. Crystalline inversion symmetry precludes silicon from natively exhibiting second-order nonlinear optical processes. In this work, we build on recent works in silicon photonics that break this material symmetry using large bias fields, thereby enabling χ(2) interactions. Using this approach, we demonstrate both second-harmonic generation (with a normalized efficiency of 0.20%W−1cm−2) and, to our knowledge, the first degenerate χ(2) optical parametric amplifier (with an estimated normalized gain of 0.6dBW−1/2cm−1) using silicon-on-insulator waveguides fabricated in a CMOS-compatible commercial foundry. We expect this technology to enable the integration of novel nonlinear optical devices such as optical parametric amplifiers, oscillators, and frequency converters into large-scale, hybrid photonic–electronic systems by leveraging the extensive ecosystem of CMOS fabrication.

Enhanced surface second harmonic generation in nanolaminates.

Second-harmonic generation (SHG) is a second-order nonlinear optical process that is not allowed in media with inversion symmetry. However, due to the broken symmetry at the surface, surface SHG still occurs, but is generally weak. We experimentally investigate the surface SHG in periodic stacks of alternating, subwavelength dielectric layers, which have a large number of surfaces, thus enhancing surface SHG considerably. To this end, multilayer stacks of SiO2/TiO2 were grown by Plasma Enhanced Atomic Layer Deposition (PEALD) on fused silica substrates. With this technique, individual layers of a thickness of less than 2 nm can be fabricated. We experimentally show that under large angles of incidence (> 20 degrees) there is substantial SHG, well beyond the level, which can be observed from simple interfaces. We perform this experiment for samples with different periods and thicknesses of SiO2/TiO2 and our results are in agreement with theoretical calculations.

Ab initio nonlinear optics in solids: linear electro-optic effect and electric-field induced second-harmonic generation

Second-harmonic generation (SHG), linear electro-optic effect (LEO) and electric-field induced second-harmonic generation (EFISH) are nonlinear optical processes with important applications in optoelectronics and photovoltaics. SHG and LEO are second-order nonlinear optical processes described by second-order susceptibility. Instead, EFISH is a third-order nonlinear optical process described by third-order susceptibility. LEO and EFISH are only observed in the presence of a static electric field. These nonlinear processes are very sensitive to the symmetry of the systems. In particular, LEO is usually observed through a change in the dielectric properties of the material while EFISH can be used to generate a “second harmonic” response in centrosymmetric material. In this work, we present a first-principle formalism to calculate second- and third-order susceptibility for LEO and EFISH. LEO is studied for GaAs semiconductor and compared with the dielectric properties of this material. We also present how it is possible for LEO to include the ionic contribution to the second-order macroscopic susceptibility. Concerning EFISH we present for the first time the theory we developed in the framework of TDDFT to calculate this nonlinear optical process. Our approach permits to obtain an expression for EFISH which does not contain the mathematical divergences in the frequency-dependent second-order susceptibility that caused until now many difficulties for numerical calculations.

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.

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.

Second Harmonic Generation in Lithiated Silicon Nanowires: Derivations and Computational Methods

This research will examine the computational methods to calculate the nonlinear optical process of second harmonic generation (SHG) that will be hypothesized to be present during lithium ion insertion into silicon nanowires. First it will be determined whether the medium in which SHG is conveyed is non-centrosymmetric or whether the medium is inversion symmetric where SHG as a part of the second-order nonlinear optical phenomenon does not exist. It will be demonstrated that the main interaction that determines SHG is multiphoton absorption on lithium ions. The quantum harmonic oscillator (QHO) is used as the background that generates coherent states for electrons and photons that transverse the length of the silicon nanowire. The matrix elements of the Hamiltonian which represents the energy of the system will be used to calculate the probability density of second-order nonlinear optical interactions which includes collectively SHG, sum-frequency generation (SFG) and difference-frequency generation (DFG). As a result, it will be seen that at varies concentrations of lithium ions (Li+) within the crystallized silicon (c-Si) matrix the second-order nonlinear optical process has probabilities substantial enough to create second harmonic generation that could possibly be used for such applications as second harmonic imaging microscopy.

Unidirectional emission of phase-controlled second harmonic generation from a plasmonic nanoantenna

Abstract Shaping the emission pattern of second harmonic (SH) generation from plasmonic nanoparticles is important for practical applications in nonlinear nanophotonics but is rendered challenging by the complex second-order nonlinear-optical processes. Here, we theoretically and experimentally demonstrate that a pair of V- and Y-shaped gold nanoparticles directs the SH emission perpendicularly to an incident light direction. Owing to spatial overlap of two orthogonal plasmonic dipole modes at the fundamental and SH wavelengths of the individual particles, surface SH polarizations induced by the fundamental field is efficiently near-field coupled to the SH plasmon mode, resulting in dipolar SH emission from the individual particles. Moreover, the phase of this emission can be tuned simply by altering the part of the Y-particle shape, which changes the SH plasmon resonance while keeping the fundamental resonance. Our approach is a promising platform for engineering not only directional nonlinear nanoantennas but also nonlinear metamaterials.

Elucidating molecular mechanisms of two-dimensional chemical reactions

Elucidating molecular mechanisms of two-dimensional chemical reactions

High-performance quantum entanglement generation via cascaded second-order nonlinear processes

In this paper, we demonstrate the generation of high-performance entangled photon-pairs in different degrees of freedom from a single piece of fiber pigtailed periodically poled LiNbO3 (PPLN) waveguide. We utilize cascaded second-order nonlinear optical processes, i.e., second-harmonic generation (SHG) and spontaneous parametric downconversion (SPDC), to generate photon-pairs. Previously, the performance of the photon-pairs is contaminated by Raman noise photons. Here by fiber-integrating the PPLN waveguide with noise-rejecting filters, we obtain a coincidence-to-accidental ratio (CAR) higher than 52,600 with photon-pair generation and detection rate of 52.36 kHz and 3.51 kHz, respectively. Energy-time, frequency-bin, and time-bin entanglement is prepared by coherently superposing correlated two-photon states in these degrees of freedom, respectively. The energy-time entangled two-photon states achieve the maximum value of CHSH-Bell inequality of S = 2.71 ± 0.02 with two-photon interference visibility of 95.74 ± 0.86%. The frequency-bin entangled two-photon states achieve fidelity of 97.56 ± 1.79% with a spatial quantum beating visibility of 96.85 ± 2.46%. The time-bin entangled two-photon states achieve the maximum value of CHSH-Bell inequality of S = 2.60 ± 0.04 and quantum tomographic fidelity of 89.07 ± 4.35%. Our results provide a potential candidate for the quantum light source in quantum photonics.

Enhancing second-harmonic generation with electron spill-out at metallic surfaces

Second-order nonlinear optical processes do not manifest in the bulk of centrosymmetric materials, but may occur in the angstroms-thick layer at surfaces. At such length scales, quantum mechanical effects come into play which could be crucial for an accurate description of plasmonic systems. In this article, we develop a theoretical model based on the quantum hydrodynamic description to study free-electron nonlinear dynamics in plasmonic systems. Our model predicts strong resonances induced by the spill-out of electron density at the metal surface. We show that these resonances can boost second-harmonic generation efficiency up to four orders of magnitude and can be arbitrarily tuned by controlling the electron spill-out at the metal surface with the aid of thin dielectric layers. These results offer a possibility to artificially increase nonlinear susceptibilities by engineering optical properties at the quantum level.

Nonlinear optical process of second-order nonlinear optical susceptibility χ133(2) in an organic nonlinear optical crystal DAST.

A large unexamined second-order nonlinear optical (NLO) process is found in a 4-N,N-dimethylamino-4'-N'-methyl stilbazolium tosylate (DAST) crystal, which has a large figure of merit among NLO crystals. In second-order NLO processes using a DAST crystal, the χ111(2) process of light excitation is commonly used, involving a-axis polarized light excitation with light generation of a-axis polarized light. However, there have been few studies of other second-order NLO susceptibility processes to date. In this Letter, terahertz (THz) wave generation via second-order NLO processes based on the χ133(2) second-order NLO susceptibility of the DAST crystal was investigated. By adjusting the polarization direction of the excitation light using a prism-coupled Cerenkov phase-matching method, efficient generation of THz waves was achieved using a process involving χ133(2). The magnitude of the NLO constant χ133(2) estimated from the THz intensity ratio was 77.8 pm/V. These results indicate that prism-coupled Cherenkov phase matching can be used to identify undiscovered NLO processes for NLO crystals.

Giant photogalvanic effect and second-harmonic generation in magnetic axion insulators

The second-order nonlinear optical (NLO) processes, such as photogalvanic effect and second-order harmonic generation (SHG), play crucial roles in probing and controlling light-matter interactions for energy and device applications. Combining quantum perturbation theory and first-principles simulations, we predict a giant injection-current photogalvanic effect and SHG in a family of emerging axion insulators, the even septuple layers of $\mathrm{MnB}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{4}$ (MBT) materials. Their amplitudes of photocurrent and SHG are about 1--2 orders of magnitude larger than those of proper ferroelectrics and antiferromagnetic $\mathrm{Cr}{\mathrm{I}}_{3}$. Moreover, unlike the widely studied injection current observed under circularly polarized light, the injection photocurrent of MBT only emerges under linearly polarized light, making it suitable for device applications. These unique characters are from a combination effect of parity-time symmetry and significant spin-orbit coupling. Our predicted enhanced NLOs are valuable for characterizing subtle magnetic orders and shed light on infrared photodetecting and photovoltaic applications based on magnetic topological materials.

Tailoring second-order nonlinear optical effects in coupled quantum dot-metallic nanosphere structures using the Purcell effect

We study the modification of second-order nonlinear optical processes, like nonlinear optical rectification and second-harmonic generation, of a quantum dot that is coupled to a metallic nanosphere. We show that the strong variation of the spontaneous decay rate of the quantum dot near the metallic nanosphere can lead to strong enhancement or suppression of the nonlinear optical rectification and second-harmonic generation coefficients depending on the distance of the quantum dot from the surface of the nanosphere and on the direction of the electric dipole moment of the quantum dot. The nonlinear optical coefficients are also strongly influenced by the pure dephasing rate of the quantum dot.

Symmetry-breaking-induced nonlinear optics at a microcavity surface

Second-order nonlinear optical processes lie at the heart of many applications in both classical and quantum regimes1,2,3. Inversion symmetry, however, rules out the second-order nonlinear electric-dipole response in materials widely adopted in integrated photonics (for example, SiO_2, Si and Si_3N_4). Here, we report nonlinear optics induced by symmetry breaking at the surface of an ultrahigh-Q silica microcavity under a sub-milliwatt continuous-wave pump. By dynamically coordinating the double-resonance phase matching, a second harmonic is achieved with an unprecedented conversion efficiency of 0.049% W^(−1), 14 orders of magnitude higher than that of the non-enhancement case. In addition, the nonlinear effect from the intrinsic symmetry breaking at the surface can be identified unambiguously, with guided control of the pump polarization and the recognition of the second-harmonic mode distribution. This work not only extends the emission frequency range of silica photonic devices, but also lays the groundwork for applications in ultra-sensitive surface analysis.

Quantum optical measurement with tripartite entangled photons generated by triple parametric down-conversion.

Parametric down-conversion is a second-order nonlinear optical process annihilating a pump photon and creating a pair of photons in the signal and idler modes. Then, by using two parametric down-converters and introducing a path indistinguishability for the two generated idler modes, a quantum coherence between two conjugate signal beams can be induced. Such a double spontaneous or stimulated parametric down-conversion scheme has been used to demonstrate quantum spectroscopy and imaging with undetected idler photons via measuring one-photon interference between their correlated signal beams. Recently, we considered another quantum optical measurement scheme utilizing W-type tripartite entangled signal photons that can be generated by employing three spontaneous parametric down-conversion crystals and by inducing coherences or path-indistinguishabilities between their correlated idler beams and between quantum vacuum fields. Here, we consider an extended triple stimulated parametric down-conversion scheme for quantum optical measurement of sample properties with undetected idler and photons. Noting the real effect of vacuum field indistinguishability on the fringe visibility as well as the role of zero-point field energy in the interferometry, we show that this scheme is an ideal and efficient way to create a coherent state of W-type entangled signal photons. We anticipate that this scheme would be of critical use in further developing quantum optical measurements in spectroscopy and microscopy with undetected photons.

Hybrid Three-Dimensional Spiral WSe2 Plasmonic Structures for Highly Efficient Second-Order Nonlinear Parametric Processes.

Two-dimensional (2D) layered materials, with large second-order nonlinear susceptibility, are currently growing as an ideal candidate for fulfilling tunable nanoscale coherent light through the second-order nonlinear optical parametric processes. However, the atomic thickness of 2D layered materials leads to poor field confinement and weak light-matter interaction at nanoscale, resulting in low nonlinear conversion efficiency. Here, hybrid three-dimensional (3D) spiral WSe2 plasmonic structures are fabricated for highly efficient second harmonic generation (SHG) and sum-frequency generation (SFG) based on the enhanced light-matter interaction in hybrid plasmonic structures. The 3D spiral WSe2, with AA lattice stacking, exhibits efficient SH radiation due to the constructive interference of nonlinear polarization between the neighboring atomic layers. Thus, extremely high external SHG conversion efficiency (about 2.437×10−5) is achieved. Moreover, the ease of phase-matching condition combined with the enhanced light-matter interaction in hybrid plasmonic structure brings about efficient SHG and SFG simultaneously. These results would provide enlightenment for the construction of typical structures for efficient nonlinear processes.

On-chip second-harmonic generation and broadband parametric down-conversion in a lithium niobate microresonator.

Nonlinear wavelength conversion is essential for many classical and quantum pho-tonic applications. The underlying second-order nonlinear optical processes, however, generally exhibit limited spectral bandwidths that impact their application potential. Here we use a high-Q X-cut lithium niobate microdisk resonator to demonstrate both second-harmonic generation and spontaneous parametric down-conversion on chip. In particular, our lithium niobate microresonator, with its wide-range cyclic phase matching and rich optical mode structures, is able to achieve ultra-broadband spontaneous parametric down-conversion, with a bandwidth over 400 nm, inferred from recorded spectra of the down-converted photons. The produced biphoton pairs exhibit strong temporal correlation, with a coincidence-to-accidental ratio measured to be 43.1. Our device is promising for integrated quantum photonics where optical frequency could be used as a degree of freedom for signal processing.

Phase-matched nonlinear optics via patterning layered materials.

The ease of integration and a large second-order nonlinear coefficient of atomically thin layered two-dimensional (2D) materials presents a unique opportunity to realize second-order nonlinearity in a silicon compatible integrated photonic system. However, the phase-matching requirement for second-order nonlinear optical processes makes the nanophotonic design difficult. We show that by nano-patterning the 2D material, quasi-phase-matching can be achieved. Such patterning-based quasi-phase-matching could potentially compensate for inevitable fabrication errors and significantly simplify the design process of the nonlinear nanophotonic devices.