Second Harmonic Research Articles

Wide-Field Polarimetric Second-Harmonic Imaging for Rapid and Nondestructive Investigation of Laser-Induced Crystallization Phenomena.

The selective and controlled formation of nanocrystals in glass is emerging as a versatile method to achieve functional photonics, optoelectronics, and quantum devices, such as single-photon emitters. Here, we investigate the use of wide-field polarimetric second-harmonic (SH) microscopy as a method to rapidly and nondestructively examine nanoscale crystal arrangements in laser-processed glass. As a case study, we investigate tellurite glass, where the formation of a trigonal tellurium (t-Te) nanocrystalline phase after femtosecond laser exposure was recently demonstrated. Combined with theoretical models, we show that wide-field polarimetric SH microscopy offers comprehensive information on the nanocrystals' orientation, distribution, and chirality. With its high imaging throughput and spatial resolution, this method has the potential not only to significantly accelerate investigations on laser-induced glass crystallization processes but also to provide a valuable tool for in situ process monitoring.

Theory of the interference tunability of second harmonic generation for two-dimensional materials in layered structures

We theoretically study how the intensity of second harmonic generation (SHG) for a sheet of two-dimensional (2D) material is controlled by an underlying layered structure. By utilizing the transfer matrix method with the inclusion of a nonlinear sheet current to describe the response of the 2D material, an explicit expression for the intensity of upward propagating second harmonic (SH) light is obtained, and the effects of the layered structure can be identified by a structure factor β, defined as the ratio of SH intensity from such a structure to that from a freely suspended 2D material. Our results show that the influence of a layered structure on the SHG intensity arises from interference effects of both the fundamental light and the SH light; the value of the structure factor is 0 ≤ β ≤ 64. Furthermore, when the incident light is pulsed, the interference effects are partially canceled due to the existence of many wave vectors and frequencies, and the cancellation becomes severe for thick films, small beam spots, and short pulses. For a specific structure of 2D material/dielectric film/substrate, the thickness of the dielectric film can effectively tune the value of β in an interval [βmin, βmax], and detailed discussions are performed for the thicknesses when these two extreme values can be obtained. When there is optical loss or the substrate is not perfectly reflective, the extreme value of βmax or βmin cannot reach 64 or 0. A large βmax requires two conditions to be fulfilled: (1) the substrate should be highly reflective, and (2) the refractive indices of the dielectric film at the fundamental and the SH frequencies should differ. Our results indicate how practical substrate structures can be used to achieve high SH signals, and the simple expression we give for the SH enhancement will be useful in characterizing the nonlinear susceptibility of 2D materials.

Efficient generation of octave-separating orbital angular momentum beams via forked grating array in lithium niobite crystal

Abstract The concept of orbital angular momentum (OAM) of light has not only advanced fundamental physics research but also yielded a plethora of practical applications, benefitting from the abundant methods for OAM generation based on linear, nonlinear and combined schemes. The combined scheme could generate octave-separating OAM beams, potentially increasing the channels for optical communication and data storage. However, this scheme faces a challenge in achieving high conversion efficiency. In this work, we have demonstrated the generation of multiple OAM beams at both fundamental frequency and second harmonic (SH) wavelengths using a three-dimensional forked grating array with both spatial χ (1) and χ (2) distributions in a lithium niobate nonlinear photonic crystal platform. The enhancements of the fundamental and SH OAM beams have been achieved by employing linear Bragg diffraction and nonlinear Bragg diffraction, respectively, i.e., quasi-phase matching. The experimental results show that OAM beams with variable topological charges can be enhanced at different diffraction orders via wavelength or angle tuning, achieving conversion efficiencies of 60.45 % for the linear OAM beams and 1.08 × 10−4 W −1 for the nonlinear ones. This work provides a promising approach for parallel detection of OAM states in optical communications, and extends beyond OAM towards the control of structured light via cascaded linear and nonlinear processes.

Topology-optimized photonic topological crystalline insulators with multiband helical edge states

Abstract Photonic topological crystalline insulators (PTCIs) with helical edge states provide an alternative way to achieve robust electromagnetic wave transport and processing. However, most existing PTCIs only involve a single topological bandgap, and generally support a pair of gapped helical edge states, restricting the scope of applications in various fields such as multiband waveguides, filters, and communication systems. Here, we design dual-band PTCIs, in which multiple helical edge modes appear within two distinct bulk gaps, for transverse electric (TE) and transverse magnetic (TM) modes, respectively, by introducing the topology optimization method into the photonic crystals with glide symmetry. For PTCIs with TE modes, the mismatched frequency ranges of edge modes hosted by two orthometric boundaries offer an opportunity to realize a photonic demultiplexer. For PTCIs with TM modes, we show the enhanced second harmonic (SH) generation through the coupling of multiband edge modes by matching the frequency ranges of edge modes within the first and second bandgaps to fundamental and SH waves, respectively. This work provides a new way for designing multiband PTCIs with helical edge states, having promising potentials in developing multiband topological photonic devices for both linear and nonlinear applications.

Dynamic Second Harmonic Imaging of Proton Translocation Through Water Needles in Lipid Membranes.

Proton translocation through lipid membranes is a fundamental process in the field of biology. Several theoretical models have been developed and presented over the years to explain the phenomenon, yet the exact mechanism is still not well understood. Here, we show that proton translocation is directly related to membrane potential fluctuations. Using high-throughput wide-field second harmonic (SH) microscopy, we report apparently universal transmembrane potential fluctuations in lipid membrane systems. Molecular simulations and free energy calculations suggest that H+ permeation proceeds predominantly across a thin, membrane-spanning water needle and that the transient transmembrane potential drives H+ ions across the water needle. This mechanism differs from the transport of other cations that require completely open pores for transport and follows naturally from the well-known Grotthuss mechanism for proton transport in bulk water. Furthermore, SH imaging and conductivity measurements reveal that the rate of proton transport depends on the structure of the hydrophobic core of bilayer membranes.

Extremely high extinction ratio electro-optic modulator via frequency upconversion to visible wavelengths.

Intensity modulators are fundamental components for integrated photonics. From near-infrared (NIR) to visible spectral ranges, they find applications in optical communication and quantum technologies. In particular, they are required for the control and manipulation of atomic systems such as atomic clocks and quantum computers. Typical integrated electro-optic modulators operating at these wavelengths show high bandwidth and low-voltage operation, but their extinction ratios are moderate. Here we present an integrated thin-film lithium niobate electro-optic (EO) modulator operating in the C-band, which uses a subsequent periodically poled waveguide to convert the modulated signal from 1536 to 768 nm using the second-harmonic (SH) generation. We demonstrate that the upconverted signal retains the characteristics of the modulated input signal, reaching a measured high bandwidth of 35 GHz. Due to the nature of the nonlinear process, it exhibits, with respect to the fundamental signal, a doubled extinction ratio of 46 dB, which is the highest, to the best of our knowledge, recorded for near-infrared light on this platform.

Cherenkov second harmonic generation of femtosecond laser pulses in a homogeneous nonlinear crystal

In experiments on second harmonic (SH) generation (SHG), a conical structure of radiation has been observed. In the present study, a non-stationary theory of SH excitation of ultrashort laser pulses with phase modulation has been developed, which explains the properties of such a structure as Cherenkov radiation. Under phase-mismatched interactions, a maximum of the SH spectrum is observed at the Cherenkov angle, which is determined by the ratio of the SH and laser radiation phase velocities. It is shown that tightly focused laser beams are preferred to observe Cherenkov SHG. The SH spectral width depends on the group velocity mismatch and is more complicated on the excited radiation spectrum. The SH energy can be proportional to the crystal length or group delay length depending on their ratio. We also demonstrate that a complex angular distribution of spectral components (an angular chirp) appears within the SH cross-section.

Second-harmonic generation of ultrashort pulses in refractive index linearly modulating quantum dot structure

While other works use segments of nonlinear crystal to compensate for walk-off, this work utilizes a quantum dot (QD) nanostructure for such compensation. Such nanocrystal structures allow two benefits: the high nonlinear susceptibility in these nanocrystals and the high surface density of QDs in the structure. Good results are obtained for pre-chirping and modulation parameters. The results are computed at 10 and 100 kV/cm applied electric fields. Compared to ordinary nonlinear crystals, the pulse width, intensity, and efficiency of the second harmonic (SH) pulse are all higher in QD nanocrystals, even with a low electric field applied. Higher applied fields give higher results.

Two-dimensional solitons in second-harmonic-generating media with fractional diffraction

We introduce a system of propagation equations for the fundamental-frequency (FF) and second-harmonic (SH) waves in the bulk waveguide with the effective fractional diffraction and quadratic (χ(2)) nonlinearity. The numerical solution produces families of ground-state (zero-vorticity) two-dimensional solitons in the free space, which are stable in exact agreement with the Vakhitov–Kolokolov criterion, while vortex solitons are completely unstable in that case. Mobility of the stable solitons and inelastic collisions between them are briefly considered too. In the presence of a harmonic-oscillator (HO) trapping potential, families of partially stable single- and two-color solitons (SH-only or FF-SH ones, respectively) are obtained, with zero and nonzero vorticities. The single- and two-color solitons are linked by a bifurcation which takes place with the increase of the soliton’s power.

Enhanced Photon-Pair Generation Based on Thin-Film Lithium Niobate Doubly Resonant Photonic Crystal Cavity

In this work, a doubly resonant photonic crystal (PhC) cavity is proposed to enhance second harmonic generation (SHG) efficiency and photon pair generation rate (PGR). Through the exploration of geometry parameters, a band-edge mode within the light cone is identified as the first harmonic (FH) mode, and a band-edge mode outside the light cone is designated as the second harmonic (SH). Subsequently, by increasing the layers of the core region, a heterostructure PhC cavity is designed. The results showcase a doubly resonant PhC cavity achieving a 133/W SHG efficiency and a photon pair generation rate of 3.7 × 108/s. The exceptional conversion efficiency is attributed to the high quality factors Q observed in the FH and SH modes with values of approximately 280,000 and 2100, respectively. The remarkably high Q factors compensate for nonlinear efficiency degradation caused by detuning, simultaneously making the manufacturing process easier and more feasible. This work is anticipated to provide valuable insights into efficient nonlinear conversion and photon pair generation rates.

Second harmonic of higher-order Poincaré sphere beam with two orthogonal 5%MgO:PPLN crystals

In this work, the second harmonic (SH) of higher-order Poincaré sphere (HOPS) beam was introduced and demonstrated with two orthogonal 5%MgO:PPLN crystals. Based on the quasi-phase-matching technique, the vectorial coupled wave equations were derived to simulate the SH of HOPS beams through the two crystals, including the cylindrical vector beams (CVBs), elliptically polarized CVBs (EPCVBs), and circularly polarized vortex beams. Then, the experimental setup was established to reveal that the SH of CVBs and EPCVBs present the four-lobed structure and still exhibit vector characteristics. Meanwhile, the circularly polarized vortex beams become the linearly polarized vortex beams with double phase topology, confirming the conservation of orbital angular momentum. Moreover, the maximum SH conversion efficiency of CVBs, EPCVBs, and circularly polarized vortex beams can reach 25.3%, 23.4%, and 29.4%, respectively, which may be instructive for promoting the SH generation of vector vortex beams with high efficiency.

Nonlinear generation of vector beams by using a compact nonlinear fork grating

Vectorial beams have attracted great interest due to their broad applications in optical micromanipulation, optical imaging, optical micromachining, and optical communication. Nonlinear frequency conversion is an effective technique to expand the frequency range of the vectorial beams. However, the scheme of existing methods to generate vector beams of the second harmonic (SH) lacks compactness in the experiment. Here, we introduce a new way to realize the generation of vector beams of SH by using a nonlinear fork grating to solve such a problem. We examine the properties of generated SH vector beams by using Stokes parameters, which agree well with theoretical predictions. Then we demonstrate that linearly polarized vector beams with arbitrary topological charge can be achieved by adjusting the optical axis direction of the half-wave plate (HWP). Finally, we measure the nonlinear conversion efficiency of such a method. The proposed method provides a new way to generate vector beams of SH by using a microstructure of nonlinear crystal, which may also be applied in other nonlinear processes and promote all-optical waveband applications of such vector beams.

DC Voltage Induces Quadratic Optical Nonlinearity in Ion-Exchanged Glasses at Room Temperature

We demonstrate that applying DC voltage at room temperature to an ion-exchanged glass induces quadratic optical nonlinearity in a subsurface region of the glass. We associate this with the EFISH (Electric-Field-Induced Second Harmonic) effect due to the Maxwell–Wagner charge accumulation in the subsurface region of the glass, in which a conductivity gradient forms as a result of the ion exchange processing. The second harmonic (SH) signal from the soda–lime glass subjected to potassium-for-sodium ion exchange is comparable with one from the same glass after thermal poling. The signal linearly increases with the duration of the ion exchange. The lower mobility of the potassium ions results in a higher SH signal from the potassium-for-sodium exchanged glass than that from the silver-for-sodium ion-exchanged one. This phenomenon is resistant to thermal annealing: only a 500 °C anneal caused noticeable degradation of the SH signal after “charging” the specimen. The phenomenon found is of interest for characterizing graded conductivity regions and providing and controlling second-order optical nonlinearity in transparent isotropic media.

Two‐Dimensional Hybrid Simulation of the Second‐Harmonic Generation of EMIC Waves in the Inner Magnetosphere

AbstractTwo‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation.

Efficient Cascaded Third‐Harmonic Generation in Sampled‐Grating Periodically‐Poled Lithium Niobate Waveguides

AbstractPeriodically poled thin‐film lithium niobate (PPTFLN) waveguides enable efficient quadratic nonlinear processes due to the strong light confinement and the utilization of the largest nonlinear coefficient d33 of lithium niobate. Here, an efficient third harmonic (TH) generation is reported with a normalized conversion efficiency of 6481% W−2 cm−4 in a sampled‐grating PPTFLN waveguide under the pump of a continuous laser, which is improved by 4 orders of magnitude compared with reported results. Such an efficient TH generation is realized by cascaded second‐harmonic (SH) generation and sum‐frequency (SF) generation supported by a sampled‐grating domain structure with two Fourier coefficients of 0.44 and 0.37, respectively. Phase matching conditions for the SH and cascaded SF processes are simultaneously achieved by finely tuning the geometric dispersion, domain structure, and operating temperature of the PPTFLN waveguides.

Control of the spider-like interference structure in photoelectron momentum distributions of a helium atom in a few-cycle nonlinear chirped laser pulse.

We investigate theoretically the photoelectron momentum distributions (PMDs) of the helium atom in the few-cycle nonlinear chirped laser pulse. The numerical results show that the direction of the spider-like interference structure in PMDs exhibits periodic variations with the increase of the chirp parameter. It is illustrated that the direction of the spider-like interference structure is related to the direction of the electron motion by tracking the trajectories of the electrons. We also demonstrate that the carrier-envelope phase can precisely control the opening of the ionization channel. In addition, we investigate the PMDs when a chirp-free second harmonic (SH) laser pulse is added to the chirped laser field, the numerical results show that the interference patterns can change from only spider-like interference structure to both spider-like and ring-like interference structures.

Nonlinear photonic crystals for completely independent asymmetric holographic imaging.

Nonlinear photonic crystals (NPCs) are microstructures characterized by a spatially modulated second-order nonlinear coefficient that have been extensively used for the generation and beam-shaping of coherent light at new frequencies. NPCs for asymmetric optical transmission have a significant impact on novel and multifunction photonic devices. However, nonreciprocal NPCs capable of completely independent asymmetric holographic imaging for the opposite propagation directions have not been reported. Here, we propose a holographic combiner for a different independent image generation at the second-harmonic (SH) wavelength when illuminated from opposite sides of NPCs. The design of the holographic combiner is based on a 3D nonlinear detour phase holography and an orbital angular momentum (OAM) multiplexing nonlinear holography. This work achieves completely independent asymmetric holographic imaging at the SH frequency by using NPCs, which may have potential applications in classical and quantum optical devices.

A chip-scale second-harmonic source via self-injection-locked all-optical poling

Second-harmonic generation allows for coherently bridging distant regions of the optical spectrum, with applications ranging from laser technology to self-referencing of frequency combs. However, accessing the nonlinear response of a medium typically requires high-power bulk sources, specific nonlinear crystals, and complex optical setups, hindering the path toward large-scale integration. Here we address all of these issues by engineering a chip-scale second-harmonic (SH) source based on the frequency doubling of a semiconductor laser self-injection-locked to a silicon nitride microresonator. The injection-locking mechanism, combined with a high-Q microresonator, results in an ultra-narrow intrinsic linewidth at the fundamental harmonic frequency as small as 41 Hz. Owing to the extreme resonant field enhancement, quasi-phase-matched second-order nonlinearity is photoinduced through the coherent photogalvanic effect and the high coherence is mapped on the generated SH field. We show how such optical poling technique can be engineered to provide efficient SH generation across the whole C and L telecom bands, in a reconfigurable fashion, overcoming the need for poling electrodes. Our device operates with milliwatt-level pumping and outputs SH power exceeding 2 mW, for an efficiency as high as 280%/W under electrical driving. Our findings suggest that standalone, highly-coherent, and efficient SH sources can be integrated in current silicon nitride photonics, unlocking the potential of χ(2) processes in the next generation of integrated photonic devices.

Mid-infrared second harmonic generation in p-type Ge/SiGe quantum wells: Toward waveguide integration

In this work we investigate a structure based on p-doped Ge/SiGe asymmetric-coupled quantum wells (ACQW) that enables the second harmonic generation in SiGe waveguide by double-resonant intersubband transitions (ISBTs). These transitions lead to χ(2) coefficients in the range 104-105 pm/V, significantly higher compared to the one of conventional nonlinear materials. We developed a model for the integration of Quantum Wells (QWs) into the active region of the waveguide through an adiabatic taper. Furthermore, we modelled the second harmonic (SH) conversion efficiency as a function of the propagation length, under both non-phase matching and phase-matching conditions. Our work demonstrates that the SiGe ACQWs can be used in spectral ranges not covered by the majority of conventional non-linear crystals, while allowing for the ready-integration with the CMOS technologies.

A kinetic theory approach to second harmonic generation by high power laser in magnetized plasma with nonextensive distribution

The present study presents a kinetic theory approach to second-harmonic generation (SHG) through high-power laser in collisionless plasma with nonextensively-distributed electrons. The study applied a relativistic Vlasov equation to obtain nonlinear current density and second-harmonic (SH) conversion efficiency. It was observed that the power conversion efficiency (PCE) of second-harmonic generation depends on plasma and laser parameters such as dimensionless cyclotron frequency, plasma density, normalized thermal velocity, the nonextensive q-parameter, and laser intensity. Moreover, cyclotron frequency associated with plasma electrons has been found to play an important role in increasing the power conversion efficiency of SH generation.