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 grating-assisted nonlinear directional couplers are investigated by using the singular perturbation technique with multiple space scales. One of the waveguides of the nonlinear directional couplers has second order nonlinear cladding whose surface has a grating profile. The period of the grating is determined to satisfy the quasi-phase matching condition between the fundamental wave and second harmonic (SH) wave. From the solvability condition to have nontrivial solutions for each order, the coupled-mode equations between fundamental and SH waves are derived. In the numerical examples, lithium niobate (LiNbO/sub 3/) is chosen as second-order nonlinear medium. After the coupled-mode equations are examined numerically, it is found that the SH wave separates from the fundamental wave due to the difference of the coupling length between the fundamental and SH waves.

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.

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.

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.

We have found that the resonance energy of optical second-harmonic (SH) generation from Au films on NaCl(100) depends strongly on the film thickness. The resonance peak of the SH intensity was found at $2\ensuremath{\Elzxh}\ensuremath{\omega}=3.2\mathrm{eV}$ for the island film of mean thickness 0.4 nm, while it appeared at $2\ensuremath{\Elzxh}\ensuremath{\omega}=2.4\mathrm{eV}$ for the continuous film of thickness 40 nm. We suggest that the SH intensity peak observed at $2\ensuremath{\Elzxh}\ensuremath{\omega}=3.2\mathrm{eV}$ originates from a resonant transition from occupied to unoccupied electronic levels of the (100) surface on top of the Au islands. The SH intensity peak observed at $2\ensuremath{\Elzxh}\ensuremath{\omega}=2.4\mathrm{eV}$ for the film thickness of 40 nm originates from the roughness-induced linear dielectric property of the film.

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.

The thermal conductivity of 2000-9000-\AA{}-thick amorphous and crystalline films of Ge and GeTe has been measured in the temperature range 100-550\ifmmode^\circ\else\textdegree\fi{}K. No thickness dependence has been observed in these films down to 2000 \AA{}. The results show that crystalline Ge and amorphous Ge and GeTe films have a negligible electronic contribution in the measured thermal conductivity. However, as expected, crystalline GeTe films exhibit significant electronic contribution which is \ensuremath{\sim}25% of the measured value of the thermal conductivity. The thermal conductivity of both amorphous Ge and GeTe increases slowly with increasing temperature in contrast to the rapid decrease in the crystalline films. In the latter case, the lattice component of the thermal conductivity decreases approximately inversely with temperature. The observed temperature dependence of the thermal conductivity can be understood on the basis of a combination of (i) umklapp-scattering mechanism, (ii) scattering due to defects, and (iii) scattering by grain boundaries. The last term, which is primarily responsible for the observed thermal resistance in the case of amorphous films, leads to a temperature-independent phonon mean free path. The observed increase of thermal conductivity with temperature for amorphous films is, therefore, attributed to the increase of specific heat with temperature. The values of the phonon mean free path in amorphous films as deduced from the thermal-conductivity data are \ensuremath{\sim}3 \AA{} in amorphous GeTe and \ensuremath{\sim}5 \AA{} in amorphous Ge films. These values suggest a relatively longer short-range order (coherently scattering regions) in amorphous Ge, as compared with amorphous GeTe.

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.

We theoretically study the gain-assisted double plasmonic resonances to enhance second harmonic generation (SHG) in a centrosymmetric multilayered silver-dielectric-gold-dielectric (SDGD) nanostructure. Introducing gain media into the dielectric layers can not only compensate the dissipation and lead to giant amplification of surface plasmons (SPs), but also excite local quadrupolar plasmon which can boost SHG by mode matching. Specifically, as the quadrupolar mode dominates SHG in our nanostructure, under the mode matching condition, the intensity of second harmonic near-field can be enhanced by 4.43 × 102 and 1.21 × 105 times when the super-resonance is matched only at the second harmonic (SH) frequency or fundamental frequency, respectively. Moreover, the intensity of SHG near-field is enhanced by as high as 6.55 × 107 times when the nanostructure is tuned to double super-resonances at both fundamental and SH frequencies. The findings in this work have potential applications in the design of nanosensors and nanolasers.

A modal method for the study of second harmonic (SH) generation in nanostructures is depicted both for plane waves and focused beam illumination. It is based on the B-spline modal method, and relies on the undepleted pump approximation. The nonlinear polarization induced by an incident plane wave or a focused beam generates a source term at the doubled frequency. The latter is divided into a finite number of sub-sources, and the SH field is subsequently computed by integration of these sub-source contributions.

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.

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.

Second Harmonic Generation (SHG) has become a powerful tool for studying the surfaces of liquids and other centric systems [1], but due to the symmetry rule no Second Harmonic (SH) can be produced from their bulk. It is then of great interest that a number of recent experimental studies have shown strong SHG from randomly oriented suspension of finely fragmented purple membranes of Halobacterium halobium contain Bacteriorhodopsin (BR) [2 ], which belongs to the family of retinal proteins. The understanding of the nature of the SH signal itself still constitutes an obscure matter. Most of the mechanisms proposed for the description of this effect, have focused on the hyper-Rayleigh incoherent scattering, but some of them suggest also coherent nonlinear contributions into the SH signal.

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.