Second harmonic generation in grating-assisted nonlinear directional couplers

In this paper, noise characteristics of second-harmonic generation (SHG) in periodically poled lithium niobate (PPLN) using the quasi-phase-matching (QPM) technique are studied experimentally. In the experiment, a 0.78-mm second-harmonic (SH) wave was generated when a 1.55-mm fundamental wave passed through a PPLN crystal (bulk or annealed proton-exchanged waveguide). The fundamental and SH waves were then separated through a beam splitter and sent to two photodetectors, respectively. The time-domain and frequency-domain characteristics of the fundamental and SH waves were analyzed. By using the pump-probe method, the noise characteristics were studied further when 532-nm irradiation light co-propagated with the 1.55-mm fundamental light in the PPLN crystals. It is found that for the bulk and waveguides of PPLN crystals, the SH wave has a higher relative noise level than the corresponding fundamental wave. For the same fundamental wave, the SH wave has lower noise in a bulk crystal than in a waveguide, and in MgO-doped PPLN than in undoped PPLN. In addition, the photorefractive effect incurred by the irradiation light can influence the SHG noise.

The visibility of inverted domain structures using the second harmonic generation (SHG) microscope is discussed based upon the three-wave coupling equations. Without reference second harmonic (SH) waves (non-interference case), the SHG intensity at a domain boundary decreases steeply along the perpendicular direction to the domain wall, which is observed as a dark line. Thus the non-interference SHG microscope reveals the location of domain boundaries but not the domain polarity which the SHG interference microscope can do. In the case of periodically poled domain structures, the clear observation criterion is expressed with the wave-number offset between the fundamental and SH waves.

High-order harmonic generation (HHG) has been studied in various laser-produced plasma plumes using a two-color orthogonally polarized beam with a 12:1 energy ratio between the fundamental and second-harmonic (SH) components. The influence of the relative phase between the fundamental and SH waves on the HHG efficiency has been investigated. Odd and even harmonic generation in plasma plumes containing nanoparticles, fullerenes, carbon nanotubes, and other samples was optimized. The effect of the variation in the SH intensity on the HHG conversion efficiency in carbon aerogel and silver plasma plumes has also been studied. It is shown that by increasing the SH intensity, one can generate only even harmonics by suppressing the odd harmonics.

We demonstrate a nonlinear frequency conversion strategy that transforms a Gaussian fundamental beam (carrying no orbital angular momentum, OAM) into a second-harmonic (SH) vortex wave with engineered OAM across an ultrabroad bandwidth. By implementing spiral-chirped quasi-phase-matching (QPM) in a femtosecond-laser-poled Sr0.61Ba0.39Nb2O6 (SBN) crystal, our system simultaneously imposes an azimuthal phase modulation to generate OAM in the SH wave and a longitudinal period chirp to achieve spectral broadening. This dual modulation converts collimated Gaussian beams (1200-1300 nm) into OAM-entrained SH vortices, exhibiting a spectral acceptance bandwidth significantly surpassing conventional helical-phase-matched systems while maintaining stable efficiency. This controllable second-harmonic OAM generation method opens new possibilities for applications including tunable structured light sources, high-capacity optical imaging using OAM multiplexing, and quantum light generation with tailored spectral properties, pushing forward the field of nonlinear optics that combines spectral and spatial control.

In this paper, a 1D nonlinear plasma photonic crystal (NPPC) structure composed of polarized ferroelectric crystals and nonlinear plasma periodic alternation is proposed. The transfer matrix method is employed to analyze the second harmonic generation (SHG) problem of this structure. In the designed NPPCs, the fundamental wave (FW) operates in the gigahertz (GHz) band and the nonlinear plasma is controlled by an external high‐intensity control wave (CW). Numerical simulations are performed to investigate the effects of different incident angles and external CW intensities on the total conversion efficiency (T‐con) of the second harmonic wave (SHW). Additionally, the internal electric field distribution and incident light intensity within the nonlinear structure are analyzed. The importance of the relationship between the FW frequency and photonic band gap (PBG) in enhancing SHG is summarized. The results demonstrate that the optimal structure can be obtained by changing the structural parameters, such that the FW and SHW are tuned to the edge of the PBG. At this point, the electromagnetic field density is large, the group velocity is small, the local field is enhanced, and the nonlinear optical interaction is increased, resulting in a significant increase in the T‐con of the SHW.

Polarization is one of the most important properties of light, which is also a typical dimension for light field manipulation. With specially designed meta-atoms and tailorable phase distribution, metasurfaces have been employed to achieve arbitrary polarization state in linear regime. Moreover, metasurface is also a platform for various nonlinear light generation, which can be used to realize an integrated polarized light source combined with its powerful capability of polarization manipulation. Here, we demonstrate a nonlinear plasmonic metasurface that is able to simultaneously realize nonlinear light generation and polarization manipulation. Split-ring resonators (SRRs) and complementary split-ring resonators (CSRRs) rotated by 90 degrees are selected to generate orthogonal polarizations of second harmonic (SH) components under the same linear polarized fundamental wave (FW), respectively. Phase difference and amplitude ratio between SH components can be tailored by adjusting the arm length of SRRs and CSRRs. By introducing spatial offset between adjacent basic supercells, we can achieve phase difference between two orthogonal components and thus realize polarization control of output SH emission and beam splitting at the same time. Two separated SH beams with orthogonal circular polarizations are achieved from a linearly polarized FW, and illuminated by circularly polarized FW, the same nonlinear plasmonic metasurface can generate linearly polarized SH, which can be viewed as a SH quarter-wave plate. Furthermore, arbitrary elliptical polarized SH can also be obtained from properly designed nonlinear metasurfaces. Our design provides a new approach for miniaturized light source for special polarization requirement, which may have potential applications in integrated optics.

Second harmonic generation in selenium-metal structures

In this paper, we investigated the second harmonic (SH) and the third harmonic (TH) generations in nanorods and nanotubes. Nonlinear free and bound electrons responses of metal combined with the third-order nonlinearity of dielectric core were utilized to study the nonlinear response of nanotubes made of noble metals such as gold. The impacts of the dielectric constant of core medium, thickness of metal shell, and size of nanotube on the SH and TH conversion efficiency are reported. The physical interpretations behind the results are discussed. Finally, we have shown that enhancement of the SH and TH generations are more noticeable and adjustable by varying the core-shell parameters compared to those of nanorods.

The combination of scanning near-field optical microscopy (SNOM) and second-harmonic generation (SHG) spectroscopy provides a superior way, sensitive on an atomic scale, to analyze surface structures in a subwavelength resolution. We apply the self-consistent integral equation formalism to investigate the optical near field of SHG for mesoscopic nonlinear surface structures excited by a total internal-reflection beam. SHG near field is shown to strongly depend on the polarization state of excitation light. However, in various polarization states, they all exhibit a much stronger lateral localization effect than fundamental wave. This contrast can be attributed to the different interference features of elementary and secondary near field for fundamental and second-harmonic waves. Such a strong three-dimensional localization effect of SHG near field is of much convenience to an experimental observation of mesoscopic surface structures with use of SNOM.

Backward phase matching, which describes counterpropagating fundamental and harmonic waves in a negative‐index medium, is one of the most intriguing phenomena in nonlinear metamaterials. Predicted theoretically decades ago, however, it is still a challenging task to be applied for efficient second harmonic (SH) generation in a nonlinear metamaterial with ultrathin geometry and ultralow loss. Here, a negative‐index spoof plasmonic metamaterial is reported, which is composed of an ultrathin symmetrical corrugated metallic strips loaded with nonlinear active devices. The simulated and measured power spectra and surface near‐field distributions show that a peak SH signal can be generated at the backward phase‐matched frequency point in a 120° curved surface with high efficiency, thanks to the ultrathin flexible geometry, significant confinement effect, and large propagation length of the spoof surface plasmons. The results open new technological challenges from nano‐ and micro‐nonlinear photonics to science and engineering of compact, broadband, and efficient frequency‐mixing metamaterials and electromagnetic devices.

Depending on the chosen fabrication process, nonlinear waveguides realized in periodically oriented material such as periodically poled lithium niobate (PPLN) can present different fabrication errors. In this paper, we present a detailed numerical study of the impact on the nonlinear performances of one or several stitching errors occurring during the realization of the periodic domains by e-beam writing. This study shows that contrary to what was expected, a single finite stitching error does not simply decrease the nonlinear efficiency but splits the second harmonic (SH) signal into a double peak spectrum, where the position of the peaks and their width at half-maximum depend not only on the poling period, the total length of the grating, and the waveguide parameters, but also on the amplitude and the position of the defect. The numerical results are confirmed by second harmonic generation (SHG) experiments performed in PPLN waveguides obtained by Soft Proton Exchange and where the nonlinear grating was composed of one to four e-beam-written 1.5-mm-long PPLN sections between which important stitching errors can occur. In this case the spectrum can be quite complicated. It is worth noting that similar errors (domains merging or missing domains) can occur also in the e-field poling process but they are randomly distributed along the propagation path. Therefore, this study is a first attempt to take them into account to explain experimental results and indicate the steps that have to be taken to improve the quality of the components.

We present a new technique for the efficient and simple production of amplitude-squeezed light with high coherent excitation, using a frequency doubler, in which only the fundamental wave is resonantly enhanced. Our theory predicts up to nearly 90% squeezing in the second-harmonic wave under ideal conditions. In our first experiment we measured up to 30% squeezing [having taken into account the limited quantum efficiency (63%) of our detection system] in a stable 50 mW beam. Compared to doubly resonant frequency doubling our new approach has considerable technical advantages.

Generation of an ultrabroadband optical pulse with a fluent frequency-dependency of the phase is important, for example, for shaping multi-wavelength optical pulses and monocyclization. When two optical pulses, one fundamental, the other generated by second harmonic generation, are co-propagated in a nonlinear waveguide, induced-phase modulation (IPM) between them, as well as self-phase modulation (SPM), can be used to broaden the spectrum of each pulse. Since the second-harmonic wave as well as the fundamental wave are generated from one common femtosecond pulse, the carrier-phase difference between their waves is constant and these can be synthesized constructively after propagation. For a case where a capillary fiber filled with noble gas is used as an almost-dispersionless, nonlinear waveguide, we analysed the optimum delay between two pulses and powers required for covering spectrum between two pulses and it was predicted that the generation of the optical pulses whose spectrum covers from near-ultraviolet to near-infrared was possible. To verify these predictions, experimental studies have been performed.

Temporal dynamic of the non-linear mirror: an analytical description

The transient oscillatory behavior of the nonlinear response of a two-level electron-spin system is experimentally investigated in a sample of glassy silica with ${E}_{1}^{\mathcal{'}}$ centers (S=(1/2)) at microwave frequency at T=4.2 K. The transient regime, excited by an intense step-modulated radiation tuned to double-quantum (DQ) resonance, is monitored by revealing the second-harmonic (SH) wave radiated by the spins undergoing DQ transitions. Time- and frequency-domain results show that the emitted SH wave has two components: the former, which vanishes at the DQ resonance, exhibits an overdamped transient regime, the latter consists of damped oscillations at a frequency which depends on the intensity and the polarization of the input radiation but not on its detuning from the DQ resonance condition. Using a vectorial model of the DQ resonance in an S=1/2 spin system we relate the observed oscillatory behavior to the transient nutations induced by the DQ processes; the calculated DQ Rabi frequency and its dependence on the input radiation are found in quantitative agreement with the experimental results. Moreover, we calculate that the inhomogeneous broadening of the resonance line strongly affects the time dependence and the spectral content of the emitted radiation, and in particular it makes its oscillation frequency independent of the input radiation detuning, in agreement with the experimentally observed behavior. The relationship, with recent discussions on the suitability of Bloch equations to describe coherent effects in randomly diluted solids, is also examined.