Quadratic Nonlinear Materials Research Articles

Inverse design of nonlinear metasurfaces for sum frequency generation

Abstract Sum frequency generation (SFG) has multiple applications, from optical sources to imaging, where efficient conversion requires either long interaction distances or large field concentrations in a quadratic nonlinear material. Metasurfaces provide an essential avenue to enhanced SFG due to resonance with extreme field enhancements with an integrated ultrathin platform. In this work, we formulate a general theoretical framework for multi-objective topology optimization of nanopatterned metasurfaces that facilitate high-efficiency SFG and simultaneously select the emitted direction and tailor the metasurface polarization response. Based on this framework, we present novel metasurface designs showcasing ultimate flexibility in transforming the outgoing nonlinearly generated light for applications spanning from imaging to polarimetry. For example, one of our metasurfaces produces highly polarized and directional SFG emission with an efficiency of over 0.2 cm2 GW−1 in a 10 nm signal operating bandwidth.

Unit cell of three nonlinear layers for the design of tunable nonlinear metamaterials

Tang et al. (2012) and Kube (2017–2018) discussed the harmonic scattering of elastic waves from nonlinear inclusions through a theoretical perspective modeling early-stage damages as quadratic and cubic nonlinear elastic material models. Achenbach and Wang (2017–2018) studied the harmonic scattering of a wave from a single nonlinear layer embedded in a linear elastic material using the reciprocity theorem in elastodynamics and the concept of compensatory waves. They demonstrated sensitivity of the back and forward scattered waves towards the dimension and the intensity. Based on this understanding, a new unit cell is proposed in this study that can act as a tunable nonlinear metamaterial, where we can tune the amplitudes of the back and forward-scattered nonlinear waves. The unit cell contains three nonlinear layers of equal widths; the intensity of the central layer, along with the total width of the unit cell, is varied to tune the harmonic responses of scattered waves. Computational studies are carried out to demonstrate the presence and absence of harmonically backscattered waves from a unit cell. In some case studies, parameters are tuned so that the amplitudes of 2nd harmonics (2f) of forward, backscattered waves and waves recorded at the interfaces of the three nonlinear layers.

Gap solitons in one-dimensional χ(2) hetero-structures induced by the thermo-optic effect

The existence of stable optical spatial solitons in a one-dimensional periodic stack whose unit cell is composed of two quadratic nonlinear materials is demonstrated. The stack is subjected to an array of micro-heaters, arranged in such a way that a periodic temperature gradient imposed upon the original structure, induces a variation of the refractive index due to the thermo-optic effect. Within a multiple scale approach the governing wave equations are obtained. A linear stability analysis together with the numerical evolution of these equations are carried out, evidencing distinctive soliton dynamics. By varying parameters like the period and the depth of the temperature modulation one is able to steer these solitons, to change their shape and, move them independently.

A new dimension for nonlinear photonic crystals

The first three-dimensional nonlinear photonic crystals have been constructed thanks to the use of femtosecond laser writing in quadratic nonlinear materials.

Analysis of harmonics propagating in pipes of quadratic material nonlinearity using shell theory

Higher harmonics in pipes of quadratic nonlinear material behavior have been analyzed in this paper. Using shell theory, the mixing of axisymmetric longitudinal waves and torsional waves, and the self-interaction of axisymmetric longitudinal waves, have been investigated. The dispersion curves of longitudinal waves derived from the linear version of the governing equations show excellent agreement with the corresponding curves obtained from thick shell theory and three dimensional theory, presented elsewhere. For torsional waves, only the lowest mode is taken into consideration. Using the perturbation method, analytical expressions for the resonant torsional waves generated by the mixing of longitudinal and torsional waves have been obtained. The resonant waves with difference frequencies propagate in the opposite direction of the corresponding primary wave. The back-propagation effect has potential application for nondestructive evaluation. The nonlinear shell theory is further simplified for applicability to thin pipes, to obtain expressions for the cumulative second longitudinal harmonics generated by self-interaction of longitudinal waves. For this case, the phase-match conditions, which are used to determine phase-match points, are also presented in analytical form.

Generation of the second, fourth, and eighth harmonics by a hyperelastic longitudinal planewave: numerical simulation

The generation of the first, second, fourth, and eighth harmonics of a harmonic longitudinal plane wave propagating in quadratic nonlinear materials described by the classical Murnaghan model is numerically modeled. This situation was also analyzed analytically. The materials are fibrous composites with micro- and nanoscale structure. Using such materials introduces additional real restrictions on the main parameters and allows simulating various real situations: from the generation of all harmonics for feasible distances and times to the generation of the second harmonics for feasible distances and times. The contribution of each approximation to the overall wave pattern is analyzed. It is shown that these approximations affect the prediction of the evolution of the initial wave profile: first there is a tendency to the generation of the second harmonic which then transforms into a tendency to the generation of the fourth and eight harmonics

Analyzing the propagation of a quadratic nonlinear hyperelastic cylindrical wave

The perturbation method (small-parameter method) is used to analyze the propagation of a cylindrical wave in a quadratic nonlinear hyperelastic material described by the classical Murnaghan model. The exact representation of the first-order solution in terms of squared Hankel functions of zero and first orders and their product is derived. A simplification of the new solution is considered

Generation of the second, fourth, eighth, and subsequent harmonics by a quadratic nonlinear hyperelastic longitudinal plane wave

The perturbation (small-parameter) method is used to obtain the first three approximations for the problem of a harmonic longitudinal plane wave propagating in a quadratic nonlinear hyperelastic material described by the classical Murnaghan model. The subsequent approximations are discussed. The contribution of each approximation to the overall wave pattern is analyzed. It is shown that the third approximation corrects the prediction of the evolution of the initial wave profile. Which of the harmonics dominates depends on the distance traveled by the wave: the second harmonic is generated first, then it transforms into the fourth harmonic, and finally, as the distance increases, the eighth harmonic shows

ChemInform Abstract: Synthesis and Properties of Organic Lambda (λ) Shape Molecules as Quadratic Nonlinear Optical Materials

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Universal Charts for Optical Difference Frequency Generation in the Terahertz Domain

We present a universal and rigorous approach to study difference frequency generation in the terahertz domain, especially when reaching for the quantum efficiency limit. Through the definition of a suitable figure of merit, we have been able to keep the number of degrees of freedom to a minimum, in order to draw up suitably normalized charts, that enable to predict the optical-to-terahertz conversion efficiency of any efficient system based on wave propagation in quadratic nonlinear materials. The predictions of our approach take into account the effects of both terahertz absorption and optical pump depletion, and are found to be in good agreement with the best experimental results reported to date. This enabled also to estimate the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sub> nonlinear coefficient of high quality GaSe.

Analysis of a quadratic nonlinear hyperelastic longitudinal plane wave

The perturbation (small-parameter) method is used to analyze the propagation of a harmonic longitudinal plane wave in a quadratic nonlinear hyperelastic material described by the classical Murnaghan model. The three first approximations are obtained, and the contribution of each of them into the wave pattern is analyzed. It is shown that the third approximation somewhat improves the prediction of the evolution of the initial waveprofile: the tendency to generate the second harmonic goes over into the tendency to generate the fourth harmonic

Nonlinear photonic structures for all-optical deflection

We present a new type of photonic structures in quadratic nonlinear materials that enable efficient and continuous all-optical deflection. The structures are based on two-dimensional modulation of the nonlinear coefficient and consist of a set of symmetric or anti-symmetric arcs that form a periodic pattern in the propagation direction and a chirped pattern in the transverse direction. Stoichiometric lithium tantalite structures were tested by second harmonic generation. Varying the pump wavelength from 1545 nm to 1536 nm resulted in continuous angular deflection of the second harmonic wave up to approximately 2.3 degrees . Continuous deflection was also obtained by varying the crystal temperature at a fixed pump wavelength.

Nonlocal description of X waves in quadratic nonlinear materials

We study localized light bullets and X waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multidimensional nonlinear waves. For X waves we show that a local cascading limit in terms of a nonlinear Schrödinger equation does not exist-one needs to use the nonlocal description, because the nonlocal response function does not converge toward a function. Also, we use the nonlocal theory to show that the coupling to the second harmonic is able to generate an X shape in the fundamental field despite having anomalous dispersion, in contrast to the predictions of the cascading limit.

Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials.

We show theoretically that the frequency shifts that result from phase-mismatched cascaded processes under conditions of strong group-velocity mismatch can be significantly enhanced by local control of the nonlinearity with propagation. This control is possible with continuous variation of the poling period of quasi-phase-matched structures and can allow one to avoid saturation of the frequency shift. We theoretically demonstrate its applicability to high-quality, efficient frequency shifting of infrared pulses.

Multicolor soliton clusters

We present a comprehensive theoretical investigation of the formation and propagation of multicolor ringlike soliton clusters in quadratic nonlinear materials under conditions for type I second-harmonic generation. We show the several existing propagation regimes for the soliton clusters, which include fusion, expansion, and quasi-stationary propagation. The physical mechanism that leads to each evolution is elucidated and discussed. In the case of purely expanding clusters, accurate estimates of the expansion rate are obtained with a Hamiltonian approach. The experimental formation of the different soliton clusters by induced breakup techniques is discussed in detail, and the practical limitations of the concept of quasi-stationary clusters are highlighted.

Strategic placement of stereogenic centers in molecular materials for second harmonic generation.

Basic aspects of the nonlinear optical phenomenon of second harmonic generation (SHG) and the assembly of molecular materials for SHG are reviewed. Extensive use of chirality as a convenient tool to generate noncentrosymmetricity in molecular lattices, an essential requirement for the development of quadratic nonlinear optical materials, is noted. An overview of our investigations of chiral diaminodicyanoquinodimethanes is presented, which provides insight into a systematic approach to the effective deployment of chirality to achieve optimal molecular orientations for enhanced solid state SHG. Extension of these ideas to the realization of strong SHG in materials based on helical superstructures is outlined.

Modulational instability in periodic quadratic nonlinear materials.

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

Accurate switching intensities and length scales in quasi-phase-matched materials

We consider unseeded type I second-harmonic generation in quasi-phase-matched quadratic nonlinear materials and derive an accurate analytical expression for the evolution of the average intensity. The intensity-dependent nonlinear phase mismatch that is due to the cubic nonlinearity induced by quasi phase matching is found. The equivalent formula for the intensity of maximum conversion, the crossing of which changes the one-period nonlinear phase shift of the fundamental abruptly by pi , corrects earlier estimates [Opt. Lett. 23, 506 (1998)] by a factor of 5.3. We find the crystal lengths that are necessary to obtain an optimal flat phase versus intensity response on either side of this separatrix intensity.

On the phase matching conditions in applications of one-dimensional photonic band gap structures for nonlinear frequency conversion

Band edge effects such as increased density of modes, large field enhancement, and low group velocity will provide highly efficient parametric interaction if the proper phase matching conditions are established in one-dimensional photonic band gap (PBG) structures. The analysis of the dispersion properties of one-dimensional PBG structure allows us to define the suitable phase matching conditions for parametric interaction when quadratic nonlinear materials constitute the layered geometry.

Dynamic Y-branched structures in quadratic nonlinear media

A selfsplitting of the beams entering a waveguide made of a quadratic nonlinear material is observed numerically. Relative π phase differences between harmonics as positively contributing to linear diffraction are shown to trigger the effect. Formation of solitons out of this energy so that a Y-branched structure is nonlinearly induced, is shown to be dependent on input and material parameters. Simple setups should provide the means for experimental observation of the predicted phenomena.