Second-harmonic Photon Research Articles

Spin Hall Effect of Nonlinear Photons (Laser Photonics Rev. 17(5)/2023)

Spin Hall Effect for Second-Harmonic Photons in Nonlinear Uniaxial Crystals In article number 2200681, Wenguo Zhu and colleagues demonstrate theoretically and experimentally the spin Hall effect for second-harmonic photons in nonlinear uniaxial crystals and unveil the interesting focal position-dependent spin Hall effect and vortex-generations for nonlinear fields.

Steering Nonlinear Twisted Valley Photons of Monolayer WS2 by Vector Beams.

Monolayer transition metal dichalcogenides have intrinsic spin-valley degrees of freedom, drawing broad interests due to their potential applications in information storage and processing. Here, we demonstrate the possibility of using cylindrical vector pumped beams, which are nonseparable in their polarization and spatial modes, to manipulate nonlinear valley-locked twisted-vortex emissions in monolayer tungsten disulfide (WS2). The second-harmonic (SH) photons from K and K' valleys are encoded with opposite optical vortices, thus allowing the SH beams to emerge as cylindrical vector beams with doubled topological orders compared to the fundamental beams. The conically refracted pumped beams allow us to generate the first-order SH cylindrical vector and full Poincaré beams via tuning the valley-locked emitted light field profiles. With fanshaped WS2 films breaking the axial symmetry of SH beams, the SH valley photons are routed to opposite directions. Our results pave the way to develop atomically thin nonlinear photonic devices and valleytronic nanodevices.

Optical Second-Harmonic Generation of Terahertz Field from n-type InSb Semiconductors

In this paper, optical second-harmonic generation of terahertz field from n-type InSb semiconductors is investigated. The inter-band transitions generate electron-hole charge carriers in narrow bandgap semiconductors. The nonlinear interaction of terahertz fields with charge carriers within the absorption depth produces a nonlinear current at twice of the fundamental THz frequency, which generates second-harmonic terahertz photons. The conversion efficiency of second-harmonic generation is enhanced by the resonant density perturbations of the charge carriers. The results based on computational fluid dynamics show the generation of second-harmonic radiation spectrally centered at 2 THz frequency with 8 MeV energy. This mechanism for optical second-harmonic generation of terahertz may open new realms of semiconductor characterization, for which terahertz techniques are ideally suited.

Second-Harmonic Generation in Mie-Resonant GaAs Nanowires

We investigate the enhancement of second-harmonic generation in cylindrical GaAs nanowires. Although these nanostructures confine light in two dimensions, power conversion efficiencies on the order of 10 − 5 with a pump peak intensity of ~ 1 GW / cm 2 are possible if the pump and the second-harmonic fields are coupled to the Mie-type resonances of the nanowire. We identify a large range of nanowire radii in which a double-resonance condition, i.e., both the pump and the second-harmonic fields excite normal modes of the nanowire, induces a high-quality-factor peak of conversion efficiency. We show that second-harmonic light can be scattered with large efficiency even if the second-harmonic photon energy is larger than 1.42 eV, i.e., the electronic bandgap of GaAs, above which the material is considered opaque. Finally, we evaluate the efficiency of one-photon absorption of second-harmonic light and find that resonant GaAs nanowires absorb second-harmonic light in the near-field region almost at the same rate at which they radiate second-harmonic light in the far-field region.

Coherent steering of nonlinear chiral valley photons with a synthetic Au–WS2 metasurface

Two-dimensional transition metal dichalcogenides (TMDCs) present extraordinary nonlinearities and direct bandgaps at the K and K′ valleys. These valleys can be optically manipulated through, for example, plasmon–valley-exciton coupling with spin-dependent photoluminescence. However, the weak coherence between the pumping and emission makes exploring nonlinear valleytronic devices based on TMDCs challenging. Here, we show that a synthetic metasurface, which entangles the phase and spin of light, can simultaneously enhance and manipulate nonlinear valley-locked chiral emission in monolayer tungsten disulfide (WS2) at room temperature. The second-harmonic valley photons, accessed and coherently pumped by light, with a spin-related geometric phase imparted by a gold (Au) metasurface, are separated and routed to predetermined directions in free space. In addition, the nonlinear photons with the same spin as the incident light are steered owing to the critical spin–valley-locked nonlinear selection rule of WS2 in our designed metasurface. Our synthetic TMDC–metasurface interface may facilitate advanced room-temperature and free-space nonlinear, quantum and valleytronic nanodevices. By entangling the phase and spin of light, a synthetic metasurface is shown to be able to coherently manipulate the valley-exciton-locked chiral emission in monolayer tungsten disulfide at room temperature. The findings will be of benefit to advanced room-temperature and free-space nonlinear, quantum and valleytronic nanodevices.

Transversely Divergent Second Harmonic Generation by Surface Plasmon Polaritons on Single Metallic Nanowires.

Coherently adding up signal wave from different locations are a prerequisite for realizing efficient nonlinear optical processes in traditional optical configurations. While nonlinear optical processes in plasmonic waveguides with subwavelength light confinement are in principle desirable for enhancing nonlinear effects, so far it has been difficult to improve the efficiency due to the large momentum mismatch. Here we demonstrate, using remotely excited surface plasmon polaritons (SPPs), axial collimated but transversely divergent second harmonic (SH) generation in a single silver nanowire-monolayer molybdenum disulfide hybrid system. Fourier imaging of the generated SH signal confirms the momentum conservation conditions between the incident and reflected SPPs and reveals distinct features inherent to the 1D plasmonic waveguides: (i) the SH photons are collimated perpendicular to the nanowire axis but are divergent within the perpendicular plane; (ii) the collimation (divergence) is inversely proportional to the length of the active region (lateral confinement of the SPPs); and (iii) the SH emission pattern resembles that of an aligned dipole chain on top of the substrate with an emission peak at the critical angle. Our results pave the way to generate and manipulate SH emission around subwavelength waveguides and open up new possibilities for realizing high efficiency on-chip nonlinear optics.

Enhanced second-harmonic generation and photon drag effect in a doped graphene placed on a two-dimensional diffraction grating

We theoretically investigate the second harmonic generation and photon drag effect induced by an incident plane wave to a doped graphene placed on a two-dimensional diffraction grating. The relevant nonlinear conductivity of the graphene is obtained by a semi-classical treatment with a phenomenological relaxation. The grating acts not only as a plasmon coupler but also as a dispersion modulator of the graphene plasmon. As a result, the second harmonic generation is strongly enhanced by exciting the graphene plasmon polariton of the first- and/or second-harmonic frequencies. The photon drag effect is also strongly enhanced by the excitation of the plasmon at the first-harmonic frequency. The direct current induced by the photon drag effect flows both forward and backward directions to the incident light, depending on the modulated plasmon mode concerned.

Second-Harmonic Scattering from Metallic Nanoparticles in a Random Medium

We report the second-harmonic scattering intensity from silver nanoparticles dispersed in a linear random medium. The medium is formed by an aqueous solution of 80 nm diameter silver nanoparticles acting as nonlinear optical sources and 200 nm diameter latex nanospheres used as scattering centers. At photon scattering mean free paths longer than the ballistic photon path length, the second-harmonic intensity decreases exponentially due to the linear scattering of both the fundamental and harmonic beams. However, below a critical photon scattering mean free path, the decrease of the nonlinear optical intensity levels off. Polarization analysis further provides details about the transition from the ballistic to scattered second-harmonic photons. Because of the incoherent nature of the second-harmonic scattering process, we suggest that a lengthening of the interaction time of the fundamental photons with the nonlinear medium occurs.

Coherent control of multiphoton dynamics and high-order-harmonic generation driven by two frequency-comb fields with a relative envelope delay

We present a theoretical investigation of the coherent control of multiphoton dynamics and a high-order-harmonic generation (HHG) process driven by two frequency-comb fields, via the interference of multiphoton transition paths by tuning the relative envelope delay between fields. The many-mode Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and frequency-comb laser fields. The case of two frequency-comb fields with the same repetition frequency and the carrier frequencies of fundamental and second harmonics, respectively, is considered. Due to the coupling of the second harmonic controlling the frequency-comb laser field, multiphoton transitions involving both fundamental- and second-harmonic photons occur. Different multiphoton transition paths can be superpositioned when the matching condition for carrier-envelope-phase shifts is satisfied, offering the possibility of coherent control of HHG power spectra via the interference of paths by tuning the relative envelope delay between fields. The calculated HHG power spectra present both sub-cycle oscillation and multi-cycle modulation behavior when the relative envelope delay is varied. It is also found that, under the condition of multiphoton resonance, the HHG power spectra can be further enhanced by about 10 times via the interference of multiphoton transition paths by tuning the relative envelope delay.

Investigation about relationships between the symmetries of ferroelectric crystal Ca0.28Ba0.72Nb2O6 and second-harmonic patterns

The broadband quasi-phase matching (QPM) process in a uniaxial ferroelectric crystal Ca0.28Ba0.72Nb2O6 (CBN-28) was demonstrated with the second-harmonic wavelength range from 450 nm to 650 nm, and the relationship between the symmetries of CBN-28 and the second-harmonic patterns was experimentally and theoretically investigated based on the random anti-parallel domains in the crystal and QPM conditions. The dependences of frequency-doubled patterns on the wavelength and anisotropy of the nonlinear crystal were also studied, and the frequency-doubled photons were found to be trapped on circles. By analyzing the light-matter interacting Hamiltonians, the trapping force for second-harmonic photons was found to be centripetal and tunable by the fundamental lasers, and the variation tendencies of the rotational velocity of second-harmonic generation photons could also be predicated. The results indicate that the CBN-28 ferroelectric crystal is a promising nonlinear optical material for the generation of broadband frequency-doubled waves, and the analysis on centripetal force based on the interaction Hamiltonians may provide a novel recognition for the investigation of QPM process to be further studied.

Second-harmonic generation from metallic arrays of rectangular holes

The generation process of second harmonic (SH) radiation from holes periodically arranged on a metal surface is investigated. Three main modulating factors affecting the optical response are identified: the near-field distribution at the wavelength of the fundamental harmonic, how SH light couples to the diffraction orders of the lattice, and its propagation properties inside the holes. It is shown that light generated at the second harmonic can excite electromagnetic modes otherwise inaccessible in the linear regime under normal incidence illumination. It is demonstrated that the emission of SH radiation is only allowed along off-normal paths precisely due to that symmetry. Two different regimes are studied in the context of extraordinary optical transmission, where enhanced linear transmission either occurs through localized electromagnetic modes or is aided by surface plasmon polaritons (SPPs). While localized resonances in metallic hole arrays have been previously investigated, the role played by SPPs in SH generation has not been addressed so far. In general, good agreement is found between our calculations (based on the finite difference time domain method) and the experimental results on localized resonances, even though no free fitting parameters were used in describing the materials. It is found that SH emission is strongly modulated by enhanced fields at the fundamental wavelength (either localized or surface plasmon modes) on the glass metal interface. This is so in the transmission side but also in reflection, where emission can only be explained by an efficient tunneling of SH photons through the holes from the output to the input side. Finally, the existence of a dark SPP at the fundamental field is identified through a noninvasive method for the first time, by analyzing the efficiency and far-field pattern distribution in transmission at the second harmonic.

Managing orbital angular momentum in second-harmonic generation

We propose a convenient approach for managing orbital angular momentum (OAM) of second-harmonic photons generated by a quadratic nonlinear interaction under noncolinear type-I phase matching condition. Since the OAMs of two fundamental photons can be flexibly controlled by using computer-generated holograms, we were able to realize arbitrary combination of both OAMs and experimentally confirm the OAM conservation selection rule ${\ensuremath{\ell}}_{2\ensuremath{\omega}}={\ensuremath{\ell}}_{\ensuremath{\omega}}^{\ensuremath{'}}+{\ensuremath{\ell}}_{\ensuremath{\omega}}^{\ensuremath{'}\ensuremath{'}}$ in general cases. In particular, our approach could be used to generate the second-harmonic photon states with fractional and odd-order OAMs.

Generation of exciton-polaritons in ZnO microcrystallines using second-harmonic generation

We report an observation and detail mapping of exciton-polaritons (polaritons hereafter) on both lower-polariton and upper-polariton branches in ZnO microcrystallines using second-harmonic generation. Our investigations reveal that those polaritons can be well described by the dispersion curves of nanowires at certain diameter. The polaritons in the tree-like microcrystallines evolve as a function of incident wavelength in a similar fashion as that in a single nanowire. Hence, the origin of polaritons generated in the wire-based microcrystallines is the coupling between the excitons and the nanowire-cavities. The resonance profile of the polaritons reveals that the enhancement is due to the strong coupling between second-harmonic photons and the A, B and C excitons in ZnO. The high photon–polariton conversion efficiency suggests a new strategy for harvesting solar energy.

Nonlinear Plasmon-Photon Interaction Resolved byk-Space Spectroscopy

Metallic nanostructures support extreme localization and enhancement of optical fields via surface-plasmon (SP) resonances. Although SP are associated with giant enhancements of nonlinear phenomena such as second-harmonic generation (SHG), the role of SP in the process, whether as a field-enhancing catalyst or as a quasiparticle converted in the interaction, has remained experimentally elusive. We demonstrate how k-space spectroscopy can distinguish between the plasmonic and photonic SHG processes that occur in a metal nanofilm when it is optically driven via the Kretschmann geometry. The results revealed a nonlinear interaction where two SP annihilate to create a second-harmonic photon. This knowledge has implications for realizing the inverse process, plasmonic parametric down-conversion, which could act as a coherent source of entangled SP pairs.

Second harmonic spectroscopy of copper nanowire arrays on the (110) faceted faces of NaCl crystals

We have investigated the spectral dependence of the optical second harmonic (SH) signal from Cu nanowires deposited on the NaCl (110) faceted templates as a function of the SH photon energies from 2.4 to 4.6 eV. The SH response exhibited a peaked resonance near the SH photon energy of 2hΩ = 4.4 eV for the p-in/p-out and s-in/p-out polarization combinations. At this photon energy the SH response due to the resonant coupling between the fundamental field and the local plasmons in the wires is suggested to be dominant.

Electronic resonant images of an ion implanted Si(111) substrate observed by wavelength tunable optical second harmonic microscopy

This paper demonstrates that the spatial distribution of electronic states of an arsenic ion implanted Si(111) substrate can be observed by using a wavelength tunable second harmonic (SH) microscope in a wide photon energy range from 2ℏω=1.96to5.19eV. The contrast in the SH intensity images between the As-doped area and the nondoped area depends greatly on the SH photon energy. For 2ℏω>3eV, optical second harmonic generation (SHG) from the nondoped area was stronger than from the doped area, and the contrast was reversed for 2ℏω⩽2.33eV. The contrast in the SH intensity images was considerably different from that in the linear optical reflection images, indicating that spectroscopic SH microscopy can provide different informations on electronic levels from that associated with the linear optical response. It is suggested that the larger SH intensity from the nondoped area for 2ℏω>3eV results from the resonant SHG enhancement effect associated with the bulk Si E1 (3.4eV) and E2 (4.3eV) gaps. In the case of the doped area, a small resonant enhancement of the SH intensity was observed around 2ℏω=2.33eV. This resonance may result from an energy level created by the ion implantation.

Ab initiocalculation of optical second harmonic generation at the rutileTiO2(110)surface

Optical second harmonic (SH) response of rutile $\mathrm{Ti}{\mathrm{O}}_{2}(110)$ surface was studied by the self-consistent full potential linearized augmented plane-wave method within the local-density approximation. The calculated SH response of the relaxed surface agrees with the measured SH intensity as a function of the excitation photon energy and the sample rotation angle around its surface normal. In order to clarify the origin of the large surface SH response at the SH photon energy of about $2\ensuremath{\hbar}\ensuremath{\omega}=4\phantom{\rule{0.2em}{0ex}}\mathrm{eV}$, SH intensities from various Ti-O bonds on the surface were calculated. The result revealed that the zigzag chains consisting of bridging oxygen and neighboring sixfold coordinated titanium atoms on the top surface layer dominantly contribute to the SH response of the $\mathrm{Ti}{\mathrm{O}}_{2}(110)$ surface.

Optical second-harmonic interferometric spectroscopy ofSi(111)−SiO2interface in the vicinity ofE2critical points

The direct electron transitions at the $\mathrm{Si}(111)\ensuremath{-}{\mathrm{SiO}}_{2}$ interface are studied by combined second-harmonic (SH) intensity and phase spectroscopy with the SH photon energy range from 3.5 eV to 5 eV. A strong resonant behavior of the quadratic optical response is observed in the vicinity of the ${E}_{2}(X,\ensuremath{\Sigma})$ critical points (CP's) of the silicon band structure. Good representation of the experimental SH intensity and phase spectra is provided by a line shape of the quadratic susceptibility calculated both with excitonic and two-dimensional (2D) types of ${E}_{2}(X,\ensuremath{\Sigma})$ CP's. The line-shape dependence of resonance energies, namely, repulsion of nearby ${E}_{2}(X,\ensuremath{\Sigma})$ resonances in the case of a 2D CP in comparison with the excitonic ones, is observed.

Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum wells

Size effects in the resonant nonlinear optical response of amorphous Si/SiO2 multiple quantum wells (MQW) are studied by second-harmonic generation (SHG) spectroscopy in a spectral interval of second-harmonic photon energies from 2.5 to 3.4 eV. The sensitivity of SHG spectroscopy to thickness-dependent electronic structure (sub-band energy position and density of states line shape) of MQW is demonstrated. A monotonic red shift of central energies of SHG resonances by 120 m eV upon increase of the well thickness from 2.5 to 10 A is observed. This is interpreted as a size dependence of the position of singularities in the combined density of states for a 2D gas of electrons moving in an effective potential well. It is shown that, for agreement with experiment, the simplest (rectangular) shape of the well should be modified in order to take into account the lattice-potential distortion at the interfaces.

Second-harmonic interferometric spectroscopy of buried interfaces of column IV semiconductors

The technique of combined optical second-harmonic (SH) intensity and phase spectroscopy, which is the spectroscopic modification of SH phase measurements, is proposed to study the nonlinear optical response of semiconductor interfaces with spectrally close resonant contributions. The spectral dependences of SH intensity and phase from oxidised Si (111) and Ge (111) surfaces are studied in the range of 3.5- to 5-eV SH photon energy. The resonant behaviour of combined SH spectra is associated with a superposition of contributions from direct interband transitions at several critical points of Si and Ge band structures.