Extremely efficient terahertz second-harmonic generation from organic crystals

Achieving efficient and intense second-harmonic generation(SHG)in the terahertz(THz)spectrum holds great potential for a wide range of technical applications,including THz nonlinear functional devices,wireless communications,and data processing and storage.However,the current research on THz harmonic emission primarily focuses on inorganic materials,which often offers challenges in achieving both efficient and broadband SHG.Herein,the remarkable efficiency of organic materials in producing THz harmonics is studied and demonstrated,thereby opening up a new avenue for searching candidates for frequency-doubling devices in the THz band.By utilizing DAST,DSTMS,and OH1 crystals,we showcase their superior frequency conversion capabilities when pumped by the narrowband THz pulses centered at 2.4,1.6,and 0.8 THz.The SHG spans a high-frequency THz domain of 4.8 THz,achieving an unprecedented conversion efficiency of∼1.21%while maintaining a perturbative nonlinear response.The highly efficient SHG of these materials is theoretically analyzed by considering the combined effects of dispersion,phonon absorption,polarization,and the nonlinear susceptibility of organic crystals.This work presents a promising platform for efficient THz frequency conversion and generation across a wide range of frequencies,offering new opportunities for novel nonlinear THz applications in next-generation electronics and optics.

Numerical Perspective of Second-Harmonic Generation of Circumferential Guided Wave Propagation in a Circular Tube

The effect of second-harmonic generation （SHG） by primary （fundamental） circumferential guided wave （CGW） propagation is investigated from a numerical standpoint. To enable that the second harmonic of the primary CGW mode can accumulate along the circumferential direction, an appropriate mode pair of primary and double frequency CGWs is chosen. Finite element simulations and evaluations of nonlinear CGW propagation are analyzed for the selected CGW mode pair. The numerical simulations performed directly demonstrate that the response of SHG is completely generated by the desired primary CGW mode that satisfies the condition of phase velocity matching at a specific driving frequency, and that the second harmonic of the primary CGW mode does have a cumulative effect with circumferential angles. The numerical perspective obtained yields an insight into the complicated physical process of SHG of primary CGW propagation unavailable previously.

Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate

Within the second-order perturbation approximation, this paper investigates the physical process of generation of the time-domain second harmonic by a primary Lamb wave waveform in an elastic plate. The present work is performed based on the preconditions that the phase velocity matching is satisfied and that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero. It investigates the influences of the difference between the group velocities of the primary Lamb wave and the double frequency Lamb wave, the propagation distance and the duration of the primary Lamb wave waveform on the envelope shape of the time-domain second harmonic. It finds that the maximum magnitude of the envelope of the second-harmonic waveform can grow within some propagation distance even if the condition of group velocity matching is not satisfied. Our analyses also indicate that the maximum magnitude of the envelope of the second-harmonic waveform is kept constant beyond a specific propagation distance. Furthermore, it concludes that the integration amplitude of the time-domain second-harmonic waveform always grows with propagation distance within the second-order perturbation. The present research yields new physical insight not previously available into the effect of generation of the time-domain second harmonic by propagation of a primary Lamb wave waveform.

Enhancement effect of cumulative second-harmonic generation by closed propagation feature of circumferential guided waves

On the basis of second-order perturbation approximate and modal expansion approach,we investigate the enhancement effect of cumulative second-harmonic generation(SHG)of circumferential guided waves(CGWs)in a circular tube,which is inherently induced by the closed propagation feature of CGWs.An appropriate mode pair of primary-and double-frequency CGWs satisfying the phase velocity matching and nonzero energy flux is selected to ensure that the second harmonic generated by primary CGW propagation can accumulate along the circumference.Using a coherent superposition of multi-waves,a model of unidirectional CGW propagation is established for analyzing the enhancement effect of cumulative SHG of primary CGW mode selected.The theoretical analyses and numerical simulations performed directly demonstrate that the second harmonic generated does have a cumulative effect along the circumferential direction and the closed propagation feature of CGWs does enhance the magnitude of cumulative second harmonic generated.Potential applications of the enhancement effect of cumulative SHG of CGWs are considered and discussed.The theoretical analysis and numerical simulation perspective presented here yield an insight previously unavailable into the physical mechanism of the enhancement effect of cumulative SHG by closed propagation feature of CGWs in a circular tube.

INFINITELY MANY SOLITARY WAVES DUE TO THE SECOND-HARMONIC GENERATION IN QUADRATIC MEDIA

In this paper, we consider the following coupled Schrodinger system with χ^(2) nonlinearities {-Δu1+V1(x)u1=αu1u2,x∈R^N,-Δu2+V2(x)u2=α/2u^21+βu^22,x∈R^N.which arises from second-harmonic generation in quadratic media. Here V1(x) and V2(x) are radially positive functions, 2 ≤ N < 6, α > 0 and α > β. Assume that the potential functions V1(x) and V2(x) satisfy some algebraic decay at infinity. Applying the finite dimensional reduction method, we construct an unbounded sequence of non-radial vector solutions of synchronized type.

Experimental Observation of Cumulative Second-Harmonic Generation of Circumferential Guided Wave Propagation in a Circular Tube

The experimental observation of cumulative second-harmonic generation of the primary circumferential guided wave propagation is reported. A pair of wedge transducers is used to generate the primary circumferential guided wave desired and to detect its fundamental-frequency and second-harmonic amplitudes on the outside surface of the circular tube. The amplitudes of the fundamental waves and the second harmonics of the circumferential guided wave propagation are measured for different separations between the two wedge transducers. At the driving frequency where the primary and the double-frequency circumferential guided waves have the same linear phase velocities, the clear second-harmonic signals can be observed. The quantitative relationships between the second-harmonic amplitudes and circumferential angle are analyzed. It is experimentally verified that the second harmonics of primary circumferential guided waves do have a cumulative growth effect with the circumferential angle.

Analysis of Second-Harmonic Generation of Low-Frequency Dilatational Lamb Waves in a Two-Layered Composite Plate

We analyze the effect of second-harmonic generation（SHG） of primary Lamb wave propagation in a two-layered composite plate, and then investigate the influence of interfacial properties on the said effect at low frequency. It is found that changes in the interfacial properties essentially affect the dispersion relation and then the maximum cumulative distance of the double-frequency Lamb wave generated. This will remarkably influence the efficiency of SHG. To overcome the complications arising from the inherent dispersion and multimode natures in analyzing the SHG effect of Lamb waves, the present work focuses on the analysis of the SHG effect of low-frequency dilatational Lamb wave propagation. Both the numerical analysis and finite element simulation indicate that the SHG effect of low-frequency dilatational Lamb wave propagation is found to be much more sensitive to changes in the interfacial properties than primary Lamb waves. The potential of using the SHG effect of low-frequency dilatational Lamb waves to characterize a minor change in the interfacial properties is analyzed.

Broadband and continuous wave pumped second-harmonic generation from microfiber coated with layered GaSe crystal

The conversion-efficiency for second-harmonic(SH)in optical fibers is significantly limited by extremely weak second-order nonlinearity of fused silica,and pulse pump lasers with high peak power are widely employed.Here,we propose a simple strategy to efficiently realize the broadband and continuous wave(CW)pumped SH,by transferring a crystalline GaSe coating onto a microfiber with phase-matching diameter.In the experiment,high efficiency up to 0.08%W-1mm-1 is reached for a C-band pump laser.The high enough efficiency not only guarantees SH at a single frequency pumped by a CW laser,but also multi-frequencies mixing supported by three CW light sources.Moreover,broadband SH spectrum is also achieved under the pump of a superluminescent light-emitting diode source with a 79.3 nm bandwidth.The proposed scheme provides a beneficial method to the enhancement of various nonlinear parameter processes,development of quasi-monochromatic or broadband CW light sources at new wavelength regions.

Imaging the crystal orientation of 2D transition metal dichalcogenides using polarization-resolved second-harmonic generation

We use laser-scanning nonlinear imaging microscopy in atomically thin transition metal dichalcogenides(TMDs)to reveal information on the crystalline orientation distribution,within the 2D lattice.In particular,we perform polarization-resolved second-harmonic generation(PSHG)imaging in a stationary,raster-scanned chemical vapor deposition(CVD)-grown WS2 flake,in order to obtain with high precision a spatially resolved map of the orientation of its main crystallographic axis(armchair orientation).By fitting the experimental PSHG images of sub-micron resolution into a generalized nonlinear model,we are able to determine the armchair orientation for every pixel of the image of the 2D material,with further improved resolution.This pixel-wise mapping of the armchair orientation of 2D WS2 allows us to distinguish between different domains,reveal fine structure,and estimate the crystal orientation variability,which can be used as a unique crystal quality marker over large areas.The necessity and superiority of a polarization-resolved analysis over intensity-only measurements is experimentally demonstrated,while the advantages of PSHG over other techniques are analysed and discussed.

Optical second-harmonic generation of Janus MoSSe monolayer

The transition metal dichalcogenides(TMD)monolayers have shown strong second-harmonic generation(SHG)ow-ing to their lack of inversion symmetry.These ultrathin layers then serve as the frequency converters that can be intergraded on a chip.Here,taking MoSSe as an example,we report the first detailed experimental study of the SHG of Janus TMD monolayer,in which the transition metal layer is sandwiched by the two distinct chalcogen layers.It is shown that the SHG effectively arises from an in-plane second-harmonic polarization under paraxial focusing and detection.Based on this,the orientation-resolved SHG spectroscopy is realized to readily determine the zigzag and armchair axes of the Janus crystal with an accuracy better than±0.6°.Moreover,the SHG intensity is wavelength-dependent and can be greatly enhanced(~60 times)when the two-photon transition is resonant with the C-exciton state.Our findings uncover the SHG properties of Janus MoSSe monolayer,therefore lay the basis for its integrated frequency-doubling applications.

Review on second-harmonic generation of ultrasonic guided waves in solid media(Ⅰ): Theoretical analyses

Considering the high sensitivity of the nonlinear ultrasonic measurement technique and great advantages of the guided wave testing method, the use of nonlinear ultrasonic guided waves provides a promising means for evaluating and characterizing the hidden and/or inaccessible damage/degradation in solid media. Increasing attention on the development of the testing method based on nonlinear ultrasonic guided waves is largely attributed to the theoretical advances of nonlinear guided waves propagation in solid media. One of the typical acoustic nonlinear responses is the generation of second harmonics that can be used to effectively evaluate damage/degradation in materials/structures. In this paper, the theoretical progress of second-harmonic generation（SHG） of ultrasonic guided wave propagation in solid media is reviewed. The advances and developments of theoretical investigations on the effect of SHG of ultrasonic guided wave propagation in different structures are addressed. Some obscure understandings and the ideas in dispute are also discussed.

Analysis of second-harmonic generation microscopy under refractive index mismatch

On the basis of the vector diffraction theory and Green＇s function method, this paper investigates the effects of refractive index mismatch on second-harmonic generation （SHG） microscopy. The polarization distribution and SHG intensity are calculated as functions of the sample radius and probe depth. The numerical results show that refractive index mismatch can result in peak intensity degradation, increase secondary lobes and extension of second- harmonic polarization distribution. Because of the attenuation of polarization intensity, the detected SHG intensity significantly decreases with increasing probe depth, which can limit the imaging depth of SHG microscopy inside thick samples. Forward SHG intensity decays slowly than backward SHG, due to the combination of extension second-harmonic polarization distribution and strong dependency of forward SHG on sample radius.

Optical second-harmonic generation imaging for identifying gastrointestinal stromal tumors

Gastrointestinal stromal tumors(GISTs)are the most common mesenchymal tumors arising in the digest tract.It brings a challenge to diagnosis because it is asymptomatic clinically.It is well known that tumor development is often accompanied by the changes in the morphology of collagen fibers.Nowadays,an emerging optical imaging technique,second-harmonic generation(SHG),can directly identify collagen fibers without staining due to its noncentrosymmetric properties.Therefore,in this study,we attempt to assess the feasibility of SHG imaging for detecting GISTs by monitoring the morphological changes of collagen fibers in tumor microenvironment.We found that collagen alterations occurred obviously in the GISTs by comparing with normal tissues,and furthermore,two morphological features from SHG images were extracted to quantitatively assess the morphological difference of collagen fibers between normal muscular layer and GISTs by means of automated image analysis.Quantitative analyses show a significant difference in the two collagen features.This study demonstrates the potential of SHG imaging as an adjunctive diagnostic tool for label-free identification of GISTs.

Phase Effects at Second-Harmonic Generation in ZnO/PMMA Nanocomposite Films

In this paper analysis of constant-intensity approximation of nonlinear interaction of the second-harmonic generation in ZnO/PMMA nanocomposite films for different concentrations of ZnO was carried out with regard to the losses and phase changes of all the interacting waves. The investigated samples were manufactured on the basis of ZnO nanoparticles embedded into polyvinylchloride polymeric matrix （PMMA） by the method of electrochemical deposition. The main goal of work is the exploration of the ZnO morphology and parameters of the second order susceptibilities. It is verified that the surface effects in ZnO/PMMA structures will give a larger contribution than the volume effects. The factors restricting the efficiency of the process of frequency conversion have been analyzed.

Second-harmonic generation in periodic fork-shaped χ^((2)) gratings at oblique incidence

Three-dimensional(3D) nonlinear photonic crystals have received intensive interest as an ideal platform to study nonlinear wave interactions and explore their applications. Periodic fork-shaped gratings are extremely important in this context because they are capable of generating second-harmonic vortex beams from a fundamental Gaussian wave, which has versatile applications in optical trapping and materials engineering. However, previous studies mainly focused on the normal incidence of the fundamental Gaussian beam, resulting in symmetric emissions of the second-harmonic vortices. Here we present an experimental study on second-harmonic vortex generation in periodic fork-shaped gratings at oblique incidence, in comparison with the case of normal incidence. More quasi-phase-matching resonant wavelengths have been observed at oblique incidence, and the second-harmonic emissions become asymmetric against the incident beam.These results agree well with theoretic explanations. The oblique incidence of the fundamental wave is also used for the generation of second-harmonic Bessel beams with uniform azimuthal intensity distributions. Our study is important for a deeper understanding of nonlinear interactions in a 3D periodic medium. It also paves the way toward achieving highquality structured beams at new frequencies, which is important for manipulation of the orbital angular momentum of light.

Broadband second-harmonic generation in thin-film lithium niobate microdisk via cyclic quasi-phase matching

Whispering-gallery-mode(WGM)microresonators can greatly enhance light-matter interaction,making them indispensable units for frequency conversion in nonlinear optics.Efficient nonlinear wave mixing in microresonators requires stringent simultaneous optical resonance and phase-matching conditions.Thus,it is challenging to achieve efficient frequency conversion over a broad bandwidth.Here,we demonstrate broadband second-harmonic generation(SHG)in the x-cut thinfilm lithium niobate(TFLN)microdisk with a quality factor above 107by applying the cyclic quasi-phase-matching(CQPM)mechanism,which is intrinsically applicable for broadband operation.Broadband SHG of continuous-wave laser with a maximum normalized conversion efficiency of~15%/m W is achieved with a bandwidth spanning over 100 nm in the telecommunication band.Furthermore,broadband SHG of femtosecond lasers,supercontinuum lasers,and amplified spontaneous emission in the telecommunication band is also experimentally observed.The work is beneficial for integrated nonlinear photonics devices like frequency converters and optical frequency comb generator based on second-order nonlinearity on the TFLN platform.

Ultrabroadband second-harmonic generation via spatiotemporal-coupled phase matching

We propose a spatially chirped quasi-phase-matching(QPM)scheme that enables ultrabroadband second-harmonic-generation(SHG)by using a fan-out QPM grating to frequency-convert a spatially chirped fundamental wave.A“zerodispersion”4f system maps the spectral contents of ultrabroadband fundamental onto different spatial coordinates in the Fourier plane,where the fundamental is quasi-monochromatic locally in picosecond duration,fundamentally canceling high-order phase mismatch.A fan-out QPM grating characterized by a linear variation of the poling period along the transverse direction exactly supports the QPM of the spatially chirped beam.We theoretically demonstrate the SHG of an 810-nm,12.1-fs pulse into a 405-nm,10.2-fs pulse with a conversion efficiency of 77%.

Flat-top beam illumination for polarization-sensitive second-harmonic generation microscopy

Wide-field second-harmonic generation (SHG) was used to obtain the second-harmonic signal from the entire image area for rapid imaging, despite the fact that conventional Gaussian beam illumination has low energy utilization efficiency,which makes it easy to overexpose the intensity of the image center area. However, flat-top beam illumination has uniform spatial distribution, thereby improving the photon excitation efficiency in the entire image region and reducing laser damage and thermal effect. By combining flat-top beam illumination and wide-field SHG polarization measurement, we can calculate more myosin fibril symmetrical axis orientations through polarization analysis of 16 images at a fast imaging speed while expanding the field of view. More importantly, the application of a flat-top beam can further improve the capability of polarization measurement in SHG microscopy.

Atomically phase-matched second-harmonic generation in a 2D crystal

Second-harmonic generation(SHG)has found extensive applications from hand-held laser pointers to spectroscopic and microscopic techniques.Recently,some cleavable van der Waals(vdW)crystals have shown SHG arising from a single atomic layer,where the SH light elucidated important information such as the grain boundaries and electronic structure in these ultra-thin materials.However,despite the inversion asymmetry of the single layer,the typical crystal stacking restores inversion symmetry for even numbers of layers leading to an oscillatory SH response,drastically reducing the applicability of vdW crystals such as molybdenum disulfide(MoS_(2)).Here,we probe the SHG generated from the noncentrosymmetric 3R crystal phase of MoS_(2).We experimentally observed quadratic dependence of second-harmonic intensity on layer number as a result of atomically phase-matched nonlinear dipoles in layers of the 3R crystal that constructively interfere.By studying the layer evolution of the A and B excitonic transitions in 3R-MoS_(2) using SHG spectroscopy,we also found distinct electronic structure differences arising from the crystal structure and the dramatic effect of symmetry and layer stacking on the nonlinear properties of these atomic crystals.The constructive nature of the SHG in this 2D crystal provides a platform to reliably develop atomically flat and controllably thin nonlinear media.

Full vectorial feature of second-harmonic generation with full Poincaré beams

We demonstrate the full vectorial feature of second-harmonic generation(SHG), i.e., from infrared full Poincaré beams to visible full Poincaré beams, based on two cascading type I phase-matching beta barium borate crystals of orthogonal optical axes. We visualize the structured features of the vectorial SHG wave by using Stokes polarimetry and show the interesting doubling effect of the polarization topological index, i.e., a low-order full Poincaré beam is converted to a high-order one. However, the polarization singularities of both C points and L lines are found to keep invariant during the SHG process. Our scheme could offer a deeper understanding on the interaction of vectorial light fields with media and can be generalized to other nonlinear optical effects.