Effective Second-order Nonlinear Susceptibility Research Articles

A New Imaginary Term in the Second-Order Nonlinear Susceptibility from Charged Interfaces.

Nonresonant second harmonic generation (SHG) phase and amplitude measurements obtained from the silica-water interface at varying pH values and an ionic strength of 0.5 M point to the existence of a nonlinear susceptibility term, which we call χX(3), that is associated with a 90° phase shift. Including this contribution in a model for the total effective second-order nonlinear susceptibility produces reasonable point estimates for interfacial potentials and second-order nonlinear susceptibilities when χX(3) ≈ 1.5χwater(3). A model without this term and containing only traditional χ(2) and χ(3) terms cannot recapitulate the experimental data. The new model also provides a demonstrated utility for distinguishing apparent differences in the second-order nonlinear susceptibility when the electrolyte is NaCl versus MgSO4, pointing to the possibility of using heterodyne-detected SHG to investigate ion specificity in interfacial processes.

Difference-frequency generation in plasmonic nanostructures: a parameter-free hydrodynamic description

The efficiency enhancement of nonlinear optical processes in extremely confined volumes (∼100  nm3) is a great challenge in the field of nanophotonics, and has an important role in modern applications such as all-optical signal processing and ultrafast switching. Due to their opacity and large absorption, metals are usually considered a hindrance to high efficiency in traditional photonic systems. However, light interaction with metal nanoparticles, i.e., plasmonics, gives unmatched possibilities of both miniaturization and electromagnetic field enhancement. These properties, together with the large intrinsic nonlinear susceptibilities of metallic systems, make plasmonic systems ideal candidates for nonlinear optics applications. Here, we present the design of a plasmonic system for efficient difference frequency generation (DFG), performing a theoretical and numerical analysis of linear and nonlinear properties of the structure. In particular, we model the system using a hydrodynamic theory for the electron dynamics inside the metal. A key element for the implementation of these equations is to write the nonlocal contributions as purely surface current terms. This may be done by exploiting the particular mathematical form of the nonlinear surface terms, which can be approximated as a function of the bulk and external values of the electric field. As a result, we obtain a parameter-free model for DFG in plasmonic systems. Finally, as an application of our method, we have designed a doubly resonant gold nanostructure, estimating an effective second-order nonlinear susceptibility χeff(2)≈1  nm/V.

On the origin of second harmonic generation in silicon waveguides with silicon nitride cladding

Strained silicon waveguides have been proposed to break the silicon centrosymmetry, which inhibits second-order nonlinearities. Even if electro-optic effect and second harmonic generation (SHG) were measured, the published results presented plenty of ambiguities due to the concurrence of different effects affecting the process. In this work, the origin of SHG in a silicon waveguide strained by a silicon nitride cladding is investigated in detail. From the measured SHG efficiencies, an effective second-order nonlinear susceptibility of ~0.5 pmV−1 is extracted. To evidence the role of strain, SHG is studied under an external mechanical load, demonstrating no significant dependence on the applied stress. On the contrary, a 254 nm ultraviolet (UV) exposure of the strained silicon waveguide suppresses completely the SHG signal. Since UV irradiation is known to passivate charged defects accumulated in the silicon nitride cladding, this measurement evidences the crucial role of charged centers. In fact, charged defects cause an electric field in the waveguide that via the third order silicon nonlinearity induces the SHG. This conclusion is supported by numerical simulations, which accurately model the experimental results.

Selectively Plasmon-Enhanced Second-Harmonic Generation from Monolayer Tungsten Diselenide on Flexible Substrates.

Monolayer two-dimensional transition-metal dichalcogenides (2D TMDCs) exhibit promising characteristics in miniaturized nonlinear optical frequency converters, due to their inversion asymmetry and large second-order nonlinear susceptibility. However, these materials usually have very short light interaction lengths with the pump laser because they are atomically thin, such that second-harmonic generation (SHG) is generally inefficient. In this paper, we fabricate a judiciously structured 150 nm-thick planar surface consisting of monolayer tungsten diselenide and sub-20 nm-wide gold trenches on flexible substrates, reporting ∼7000-fold SHG enhancement without peak broadening or background in the spectra as compared to WSe2 on as-grown sapphire substrates. Our proof-of-concept experiment yields effective second-order nonlinear susceptibility of 2.1 × 104 pm/V. Three orders of magnitude enhancement is maintained with pump wavelength ranging from 800 to 900 nm, breaking the limitation of narrow pump wavelength range for cavity-enhanced SHG. In addition, SHG amplitude can be dynamically controlled via selective excitation of the lateral gap plasmon by rotating the laser polarization. Such a fully open, flat, and ultrathin profile enables a great variety of functional samples with high SHG from one patterned silicon substrate, favoring scalable production of nonlinear converters. The surface accessibility also enables integration with other optical components for information processing in an ultrathin and flexible form.

Broken Symmetry Induced Strong Nonlinear Optical Effects in Spiral WS2 Nanosheets.

Transition metal dichalcogenides (TMDs) have provided a fundamental stage to study light-matter interactions and optical applications at the atomic scale due to their ultrathin thickness and their appropriate band gap in the visible region. Here, we report the strong nonlinear optical effects, including second-harmonic generation (SHG) and third-harmonic generation (THG) in spiral WS2 structures. SHG intensity quadratically increases with layer numbers, other than diminishing the oscillation of 2H stacking TMDs. The contrary SHG behavior is attributed to the broken symmetry from twisted screw structures, revealed by aberration-corrected transmission electronic microscope observation. Furthermore, the twist angle of the screw structure (5 degrees) was obtained by high-resolution transmission microscope measurements and confirmed by polarization tests of SHG output. Moreover, we roughly estimate the effective second-order nonlinear susceptibility. The discovery and understanding of the accumulation of nonlinear susceptibility of spiral structures with increasing thickness will extend the nonlinear applications of TMDs.

Synthesis of second-order nonlinearities in dielectric-semiconductor-dielectric metamaterials

We demonstrate a large effective second-order nonlinear optical susceptibility in electronic optical metamaterials based on sputtered dielectric-semiconductor-dielectric multilayers of silicon dioxide/amorphous silicon (a-Si)/aluminum oxide. The interfacial fixed charges (Qf) with opposite signs on either side of dielectric-semiconductor interfaces result in a non-zero built-in electric field within the a-Si layer, which couples to the large third-order nonlinear susceptibility tensor of a-Si and induces an effective second-order nonlinear susceptibility tensor χeff(2). The value of the largest components of the effective χeff(2) tensor, i.e., χ(2)zzz, is determined experimentally to be 2 pm/V for the as-fabricated metamaterials and increases to 8.5 pm/V after the post-thermal annealing process. The constituents and fabrication methods make these metamaterials CMOS compatible, enabling efficient nonlinear devices for chip-scale silicon photonic integrated circuits.

Quantitatively extracting the contribution of asymmetric local-field to χ(2) in cross-shaped Ag nanoholes.

We systematically study the contribution of local-field distribution to second-harmonic generation (SHG) in cross-shaped Ag nanohole arrays, which is usually covered by resonance enhancement effect. By increasing one arm-length of the centrosymmetric cross-shaped Ag nanohole, the local-field distribution varies from centrosymmetric to non-centrosymmetric, while the localized surface plasmon resonance peak is red-shifted to the wavelength of the pumping laser accordingly. Both experimental and stimulated results indicate that the contribution of the asymmetric local-field distribution to SHG is quantitatively separated from a strong resonance enhancement effect. It shows that the pure effective second-order nonlinear susceptibility increases as the asymmetric degree of local-field distribution increases, and the largest effective second-order nonlinear susceptibility is ~2.5 times to that in a centrosymmetric local-field distribution. Our results provide evidence for optimizing the design of nonlinear plasmonic nanoantennas and metasurfaces.

Second Harmonic Generation in WSe2

Second harmonic generation of single- and few-layer mechanically exfoliated tungsten diselenide (WSe2) samples are studied. The value of the effective second-order nonlinear susceptibility for monolayer WSe2 is obtained, being three orders of magnitude larger than the values usually reported for other nonlinear bulk crystals. The presence of a monolayer is certified by symmetry analysis of the Raman modes and the occurrence of a direct band gap. Our results on WSe2 solidify the family of transition metal dichalcogenides as two-dimensional systems with ultra high second-order nonlinear susceptibility.

Terahertz Generation in an Electrically Biased Optical Fiber: A Theoretical Investigation

We propose and theoretically investigate a novel approach for generating terahertz (THz) radiation in a standard single-mode fiber. The optical fiber is mediated by an electrostatic field, which induces an effective second-order nonlinear susceptibility via the Kerr effect. The THz generation is based on difference frequency generation (DFG). A dispersive fiber Bragg grating (FBG) is utilized to phase match the two interacting optical carriers. A ring resonator is utilized to boost the optical intensities in the biased optical fiber. A mathematical model is developed which is supported by a numerical analysis and simulations. It is shown that a wide spectrum of a tunable THz radiation can be generated, providing a proper design of the FBG and the optical carriers.

Plasmon-Enhanced Second-Harmonic Generation from Ionic Self-Assembled Multilayer Films

We have demonstrated large enhancements of the effective second-order nonlinear susceptibility (chi(2)) of ionic self-assembled multilayer (ISAM) films, causing a film with just 3 bilayers to be optically equivalent to a 700-1000 bilayer film. This was accomplished by using nanosphere lithography to deposit silver nanoparticles on the ISAM film, tuning the geometry of the particles to make their plasmonic resonances overlap the frequency of optical excitation. An enhancement in the efficiency of second harmonic generation (SHG) by as much as 1600 times was observed. Even though this is already a large value, we suggest that further refinements of the techniques are expected to lead to additional enhancements of similar or larger magnitude.

Second-harmonic generation from an array of sub-wavelength metal apertures

We demonstrate the generation of second-harmonic radiation in transmission through periodic and disordered arrays of sub-wavelength metallic apertures. For circular apertures in a square lattice, the second-harmonic signal peaks at incidence angles corresponding to enhanced transmission of the fundamental beam of 800 nm wavelength except at small incidence angles where the local symmetry minimizes the effective second-order nonlinear susceptibility of the apertures. Even though the linear transmission of the fundamental beam can be more than five times greater through the periodic array as compared to a disordered array, the strength of the second harmonic from the disordered array is greater at large incidence angles. By breaking the local symmetry through the use of apertures of non-centrosymmetric shape, the second-harmonic output occurs at fundamental transmission resonances at small incidence angles.

The optical second-harmonic generation from porous silicon

Second-harmonic generation from porous silicon with a magnitude of two orders greater than that from the original silicon crystalline wafers is discussed. The measured effective second-order nonlinear susceptibility X/sup (2)//sub ps.eff/ for a p-type porous silicon is 1.96*10/sup -7/ esu. The susceptibility is estimated on the base of a bulk property rather than on quantum confinement owing to its large surface to volume ratio. >