Second-order Nonlinear Effects Research Articles

Modeling of photoinduced charge separation in germanosilicate optical fibers during UV-excited poling

We report numerical solutions of a proposed model for charge separation and trapping during poling of germanosilicate fiber in the presence of ultraviolet (UV) light. The model was solved quantitatively in the steady state to determine the space charge field distribution after UV-excited poling of a germanosilicate optical fiber with internal electrodes. The resulting internal electric field was found to be up to an order of magnitude higher than the initial poling field, sufficient to produce an effective second-order nonlinearity consistent with experimental observations by the internal field acting on the inherent third-order nonlinearity. The effects of core-cathode spacing, nonuniform defect distributions, and photo-electron recombination rate on the induced /spl chi//sub eff//sup (2)/ were also investigated. It is shown that a small core-cathode spacing is advantageous. Our UV-poled field solutions may also apply to thermal poling, provided we swap the anode and cathode designations. The results suggest that it is optimal to have the core located in the depletion region regardless of poling method.

All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide

We report efficient all-optical switching by using a periodically poled titanium-diffused lithium niobate (Ti:PPLN) waveguide. The periodically domain inversion of the Ti:PPLN waveguide is achieved by electric field poling. The switching is driven by the second-order nonlinear effect of the cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes. It is found that about 12% of the signal is switched by a 20-W gate power.

Comparisons of finite difference beam propagation methods for modeling second-order nonlinear effects

Three numerical methods, iterative finite difference (FD), split-step, and iterative split-step beam propagation methods (BPM's), for modeling second-order nonlinear effects are evaluated. All three methods are able to handle the depletion of the pump wave. The evaluation shows that both iterative methods are more accurate than the split step method. In addition, the iterative split-step method, even with its iterative nature, is more efficient than the split-step one. Between the two iterative methods, further comparisons indicate that, for a small stepsize, both have comparable accuracy. As the stepsize increases, the iterative split-step method is not as accurate as the iterative finite-difference one. However, the former method has a higher efficiency, suggesting that it is a better choice when the stepsize has to be small because of, for example, the quasiphase-matched geometrical configuration.

Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion

By specifying a discrete matrix formulation for the frequency–space modelling problem for linear partial differential equations (‘FDM’ methods), it is possible to derive a matrix formalism for standard iterative non-linear inverse methods, such as the gradient (steepest descent) method, the Gauss–Newton method and the full Newton method. We obtain expressions for each of these methods directly from the discrete FDM method, and we refer to this approach as frequency-domain inversion (FDI). The FDI methods are based on simple notions of matrix algebra, but are nevertheless very general. The FDI methods only require that the original partial differential equations can be expressed as a discrete boundary-value problem (that is as a matrix problem). Simple algebraic manipulation of the FDI expressions allows us to compute the gradient of the misfit function using only three forward modelling steps (one to compute the residuals, one to backpropagate the residuals, and a final computation to compute a step length). This result is exactly analogous to earlier backpropagation methods derived using methods of functional analysis for continuous problems. Following from the simplicity of this result, we give FDI expressions for the approximate Hessian matrix used in the Gauss–Newton method, and the full Hessian matrix used in the full Newton method. In a new development, we show that the additional term in the exact Hessian, ignored in the Gauss–Newton method, can be efficiently computed using a backpropagation approach similar to that used to compute the gradient vector. The additional term in the Hessian predicts the degradation of linearized inversions due to the presence of first-order multiples (such as free-surface multiples in seismic data). Another interpretation is that this term predicts changes in the gradient vector due to second-order non-linear effects. In a numerical test, the Gauss–Newton and full Newton methods prove effective in helping to solve the difficult non-linear problem of extracting a smooth background velocity model from surface seismic-reflection data.

Improved Temporal Stability of the Second-Order Nonlinear Optical Effect in a Sol−Gel Matrix Bearing an Active Chromophore

A second-order nonlinear optical (NLO) chromophore (disperse red 1) was reacted with (3-isocyanatopropyl)triethoxysilane to form a functionalized silicon alkoxide precursor (SGDR1). To improve the temporal stability of the second-order NLO effect, we employed a thermal cross-link between the organic side groups themselves. (3-Glycidoxypropyl)trimethoxysilane was mixed with SGDR1 in tetrahydrofuran (SGDR1/GPTS). We compared the temporal stability of the poled samples with SGDR1 and SGDR1/GPTS. We investigated second-order NLO properties of sol−gel films by virtue of second harmonic generation (SHG) and linear electrooptic (E/O) coefficient measurements for the purpose. We achieved much improvement in the temporal stability of second-order NLO effect at high temperature with the heterogeneous films.

An iterative finite difference beam propagation method for modeling second-order nonlinear effects in optical waveguides

An iterative finite difference beam propagation method based on the Crank-Nicholson scheme is presented to simulate continuous wave (CW) second-order nonlinear effects in optical waveguides with the depletion of the pump wave taken into account. This method is an extension of the linear finite difference beam propagation method and preserves the same order of accuracy. Comparisons with the previously published explicit finite difference beam propagation method and the rectangular approximation method are presented. Quasi-phase matched difference frequency generation in AlGaAs and quasi-phase-matched second harmonic generation in LiNbO/sub 3/ are considered in the evaluation, showing that one iteration for the IFD-BPM is sufficient for the simulation with good accuracy and without increasing much computation time.

Parametric amplification and self-compression of ultrashort tunable pulses

Using a 40-fs Ti:sapphire pump laser, we produced 20-fs infrared pulses in a /spl beta/-barium borate (BaB/sub 2/O/sub 4/) optical parametric amplifier without any external dispersion compensation. These results are in good agreement with a novel semi-analytical computer simulation. We also demonstrate that cascading of second-order nonlinear effects yields simultaneous production of ultrashort visible pulses from a near-infrared (NIR) pump.

Quantum-well intermixing for the control of second-order nonlinear effects in AlGaAs multiple-quantum-well waveguides

We present experimental evidence to demonstrate the feasibility of a promising new quasi-phase-matching technique in AlGaAs multiple-quantum-well waveguides. Non-phase-matched second-harmonic-generation measurements indicate that, for sub-half-bandgap excitation near 1.5 microm , quantum-well intermixing by impurity-free vacancy disordering results in a reduction of the nonlinear susceptibility chi((2))(zxy) (~340 pm/V) by 17%. Relatively low intermixed waveguide losses, and the high spatial resolution of the impurity-free vacancy disordering process, suggest that periodic intermixing along the direction of propagation should lead to useful frequency-conversion efficiencies.

Hydrogen bonded lambda-shaped packing motif based on 4-nitrophenylhydrazones: a promising design tool for engineering acentric crystals

Two newly developed 4-nitrophenylhydrazone derivatives, 4-diethylaminobenzaldehyde 4-nitrophenylhydrazone, DEANPH, and 5-bromothiophene-2-carbaldehyde 4-nitrophenylhydrazone, BTNPH, which exhibit very strong second harmonic signals that are three orders of magnitude greater than that of the urea standard were investigated by single crystal X-ray analysis. The structural comparison with three other strongly optically nonlinear hydrazones revealed that the hydrogen bond-directed lambda-shaped supramolecular assemblies are the key and fundamental bases of all these non-centrosymmetric crystal packings. The high occurrence within this class of acentric crystals is likely due to this hydrogen bonded lambda-shaped packing motif. Since the chromophores are preferentially arranged in a lambda-shape, the acentric crystals are generally optimized for second-order nonlinear optical effects such as second harmonic generation.

On the modelling of non-linear guided-wave optics for all-optical signal processing

The application of a reduced variational formalism, to model guided-wave optical signal processing devices is reviewed. The focus is mainly on second-order non-linearities. First, approximate analytical solutions (solitary waves) are derived for propagation in second-order non-linear media. Next, these analytical results are validated through numerical simulation of the governing equations. To show the potential of this formalism by means of a practical example, the analytical results are applied to a soliton-based LiNbO3 non-linear directional coupler exploiting second-order non-linear effects.

Polymer Physics and Structure/Property Relationships of Thermally Stable Polyarylene Ethers for Second-Order Nonlinear Optics

This paper describes the structure/property relationships including the polymer backbone structures and molecular weight, chromophore/polymer interactions, and chromophore functionalization that influence the chromophore orientational dynamics and polymer relaxations in a special class of thermally stable polymers that was recently developed for second-order nonlinear optical applications. These poly(arylene ether) polymers (synthesis and characterization reported elsewhere) are being investigated because of their high glass transition temperatures (>200 °C), which may minimize the randomization of chromophore orientation following electric field poling. They also have hydrogen-bonding sites that can interact with the chromophores, which may improve the temporal stability of chromophore orientation following poling. Generalization of the observed polymer dynamics to other second-order nonlinear optical polymers is discussed. Second harmonic generation, a second-order nonlinear optical effect, and dielectr...

Creation of second-order nonlinear optical effects by photoisomerization of polar azo dyes in polymeric films: theoretical study of steady-state and transient properties

It was shown recently that the application of a dc field across a polymer film containing polar azo dye chromophores at a temperature far below that of its glass transition leads to an appreciable polar order when the azo dyes undergo cis ⇔ trans isomerization. We present a detailed theoretical study of this phenomenon based on the enhanced mobility of the azo chromophores during the isomerization process. The equations representing this phenomenological theory are solved by recurrence relations of Legendre polynomials, and both the steady state and the dynamics are investigated. Analytical expressions are derived for the photoinduced polar order and its related anisotropy for both cis and trans molecular distributions.

Finite-Element Model for Thin-Walled Space Frame Flexible Connection Behavior

A finite-element formulation for modeling flexible connection behavior in space frames composed of thin-walled members is presented. The finite-element model is based on a distributed linear spring representation over the physical contact area of the connection that is capable of representing translational, rotational, and warping deformations of the connection. Second-order geometric and nonlinear moment-rotation response of the connection is considered. An updated Lagrangian formulation is used to model second-order geometric nonlinear effects. A Ramberg-Osgood representation is used to model the nonlinear moment-rotation connection behavior. Details for transforming the resulting stiffness equations for connection-to-member eccentricities are included. Results for a cubic, portal space frame composed of I-section and C-section members are presented to demonstrate the versatility of the developed element.

Pentamethylcyclopentadienyl ruthenium complexes as potential optically non-linear materials

Several alkoxystilbazole derivatives were π-bound to the [Cp ∗Ru] + fragment and the resulting complexes were examined for potential second-order non-linear optical effects.

Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect.

We show both theoretically and experimentally that the combined processes of optical rectification and the linear electro-optic effect lead to an effective nonlinear refractive index ${n}_{2}$ in noncentrosymmetric materials. This cascaded second-order nonlinear optical effect arises in addition to the well-known contribution due to second-harmonic generation and difference-frequency mixing and is of comparable magnitude. However, it has the advantage of a broad acceptance angle because no precise phase matching is needed. Experimental results in KNb${\mathrm{O}}_{3}$ crystals are presented.

Optical harmonic mixers

Mixing of optical signals in a waveguide via the second-order nonlinear effect in semiconductors was studied theoretically and experimentally. The InP-based material system was the main focus of the investigations. Both the up-conversion leading to second-harmonic generation and the down-conversion leading to optical rectification were analyzed and experimentally verified. Experiments in nonlinear optical waveguide structures at 1.55 /spl mu/m wavelength have shown the existence of both the quadratic second-harmonic signals as well as the linearly dependent optical rectification signals. Quantitative estimates confirmed a good agreement between the theory and the experiment. Some interesting applications for high-speed optical data processing required in transparent optical telecommunication systems have been identified. Most attractive functions proposed to be implemented with these types of devices are, for example, flexible-to-bit-rate all-optical clock extraction in a transparent high-performance optical telecommunication network or accurate and fast measurement of optical frequency for optical synchronization needs in wavelength-division-multiplexing systems. >

Electric-field enhancement and extinguishment of optical second-harmonic generation in asymmetric coupled quantum wells

The second-harmonic susceptibilities of asymmetric coupled quantum wells (ACQW) and compositionally asymmetric coupled quantum wells (CACQW) under the influence of the applied electric field are investigated theoretically. Analytic forms of the second-harmonic susceptibility are derived by using the density matrix formalism. Coupled one-dimensional Schrodinger equation and Poisson's equation are solved self-consistently to find the subband eigenenergies and the envelope wavefunctions for the ACQW and CACQW structures. Dipole moment matrix elements for the ACQW and CACQW are evaluated from the resulting envelope wavefunctions and large nonlinear optical effects are predicted for these two structures. Based on the theoretical calculations, the second-harmonic susceptibilities of 50 nm/V and 35 nm/V can be achieved for the ACQW and the CACQW, respectively. This is more than two orders of magnitude enhancement as compared to that of the bulk GaAs. By a suitable choice of the composition of CACQW, a novel structure which the second-order nonlinear optical effect can be turned on or off by the applied electric field is proposed based on the results of the theoretical calculation. This phenomenon is attributed to the symmetry restoration of envelope wavefunctions of the CACQW under the quenching electric field F/sub off/. A simple physical model to estimate the F/sub off/ has also been developed successfully. >

Modeling second-order nonlinear effects in optical waveguides using a parallel-processing beam propagation method

In this work, we present a simple efficient numerical solution for the three-dimensional coupled wave equations containing a second-order nonlinearity, using an explicit finite difference beam propagation method (EFD BPM). The linear EFD-BPM is known to be very efficient and to gain large speed up when implemented on parallel computers. The new nonlinear version of the EFD-BPM has the same features of the linear counterpart in using two separate computational windows, one for the fundamental field and the other for the second-harmonic field. We demonstrate the implementation and discuss the application of this method to a nonlinear rib waveguide using the quasi-phase-matching technique.

Ultraviolet second harmonic generation in radio-frequency sputter-deposited aluminum nitride thin films

Optical second harmonic generation in radio-frequency sputter-deposited AlN thin films has been studied for harmonic wavelengths from ultraviolet to near infrared. The effective second-order nonlinearity χ(2)(ω) was determined to have a nonresonant background value of ∼5×10−9 esu for second harmonic wavelengths longer than 400 nm, and it increases dramatically as the second harmonic frequency approaches the bandgap of 6.2 eV. This is likely due to resonance of the second harmonic frequency with the critical point transition associated with the direct bandgap of AlN.

Second-Order Nonlinear Optical Effects in Stacked Assemblies of Ultrathin Polymer Films with Amphiphilic Ruthenium Complex

Ultrathin poly(vinyl chloride) films with asymmetric surface properties were prepared by incorporating an amphiphilic ruthenium complex at the air-water interface. Stacked assemblies of the films were constructed to examine second-order nonlinear optical effects under specified conditions: (1) number of stacked films, (2) orientation of the asymmetric surface, and (3) presence (or absence) of gaps between the stacked films. The second harmonic light (SHL) intensity quadratically increased with the number of stacked films, when the films with the same surface orientation were separated by gaps. In the absence of gaps, the SHL intensity increased less sharply with the number of films. Appreciable modification of nonlinear optical properties was suggested on each component of the laminated films