Theoretical analysis of phase-matched second-harmonic generation and optical parametric oscillation in birefringent semiconductor waveguides

We analyze the phase-matching conditions for second-harmonic generation (SHG) and optical parametric oscillation (OPO) in birefringent nonlinear semiconductor waveguides and apply these results to the model system of ZnGeP(2) on a GaP substrate. The analyses and numerical results show that phase matching can be achieved for OPO and SHG for reasonable guide thicknesses throughout much of the infrared, indicating significant potential applications for nonlinear birefringent waveguides. For the fundamental mode of a relatively thick guide the region of phase matching and the phase-matching angles are similar to those in bulk material. However, the waveguide has the added flexibility that phase-matched coupling can occur between the various modes of the guide. For example, the phase-matching region for SHG can be considerably extended by coupling the pump into the guide in the fundamental, m =, mode and phase matching to the m = mode of the second harmonic. Significantly, the results indicate, among other things, that ZnGeP(2) waveguides with harmonic output in the m = mode can be used for efficient SHG from input radiation in the 9.6-10.6-mum region where bulk efficiencies in this wavelength range are too small to be useful.     

Broadening of the second-harmonic phase-matching bandwidth in type II periodically poled KTP

We have theoretically demonstrated type II broadband second-harmonic generation (SHG) based on a quasi-phase-matching (QPM) configuration in periodically poled KTP (PPKTP). The wavelength dependence of QPM grating periods at different temperatures of 5 degrees C, 25 degrees C, and 45 degrees C is calculated with the crystal length of 1 cm. We find a very wide bandwidth, as large as 42.6 nm, of fundamental wavelength of 1.58 microm at the telecommunication band with the QPM period of 48.9 microm at 25 degrees C. The corresponding bandwidths of incident angle and temperature are found to be 4.24 degrees and 14.8 degrees C, respectively. The comparison among PPKTP, periodically poled lithium niobate (PPLN), and MgO:PPLN reveals the unique performance of PPKTP in the broadband SHG.     

Transmit beamforming for optimal second-harmonic generation

A simulation study of transmit ultrasound beams from several transducer configurations is conducted to compare second-harmonic imaging at 3.5 MHz and 11 MHz. Second- harmonic generation and the ability to suppress near field echoes are compared. Each transducer configuration is defined by a chosen f-number and focal depth, and the transmit pressure is estimated to not exceed a mechanical index of 1.2. The medium resembles homogeneous muscle tissue with nonlinear elasticity and power-law attenuation. To improve computational efficiency, the KZK equation is utilized, and all transducers are circular-symmetric. Previous literature shows that second-harmonic generation is proportional to the square of the transmit pressure, and that transducer configurations with different transmit frequencies, but equal aperture and focal depth in terms of wavelengths, generate identical second-harmonic fields in terms of shape. Results verify this for a medium with attenuation f1. For attenuation f1.1, deviations are found, and the high frequency subsequently performs worse than the low frequency. The results suggest that high frequencies are less able to suppress near-field echoes in the presence of a heterogeneous body wall than low frequencies.     

Extended sphere method for complete investigation of the phase-matching properties of sum- and difference-frequency generation

We demonstrate the feasibility of a complete experimental investigation of the phase-matching properties of sum- and difference-frequency generation in a single crystal cut as a sphere over its entire transparency range. The class of the studied crystal is the only initial data that is required. This feasibility study was carried out with rubidium titanyl arsenate.     

All-prism achromatic phase matching for tunable second-harmonic generation

Achromatic phase matching (APM) involves dispersing the light entering a nonlinear optical crystal so that a wide range of wavelengths is simultaneously phase matched. We constructed an APM apparatus consisting of six prisms, the final dispersion angle of which was optimized to match to second order in wavelength the type I phase-matching angle of beta barium borate (BBO). With this apparatus, we doubled tunable fundamental light from 620 to 700 nm in wavelength using a 4-mm-long BBO crystal. An analogous set of six prisms after the BBO crystal, optimized to second order in second-harmonic wavelength, realigned the output second-harmonic beams. Computer simulations predict that adjustment of a single prism can compensate angular misalignment of any or all the prisms before the crystal, and similarly for the prisms after the crystal. We demonstrated such compensation with the experimental device. The simulations also indicate that the phase-matching wavelength band can be shifted and optimized for different crystal lengths.     

Atmospheric thermometry for metallic surfaces by laser-induced second-harmonic generation

To the best of our knowledge we report the first demonstration of surface thermometry using laser-induced second-harmonic generation (SHG) on a realistic metallic surface at atmospheric pressure. The surface is probed with a pulsed infrared laser beam and the SHG signal is monitored in reflection. For metallic silver, the SHG signal is found to be temperature dependent in the 25-120 οC range. The current accuracy of the method is ? οC. Future work with platinum should permit the application of SHG thermometry to much higher surface temperatures.     

Temporal properties of the second-harmonic generation of a short pulse

The time-dependent characteristics of the second-harmonic generation of a short pulse are investigated theoretically. Transient coupled-wave equations are necessary to describe the time-dependent process of the second-harmonic generation of a short pulse. It is found that the fundamental waves experience both pulse broadening and compression with different waveform distortion during the frequency-doubling process. The pulse width of a frequency-doubled wave broadens monotonically along the crystal length. There is no phase distortion in the case of exact phase matching. Phase modulation (i.e., chirp) occurs only when there is phase mismatch and chirp can be determined by the phase mismatch.     

Efficiency of non-phase-matched second-harmonic generation by Gaussian pulses

Conversion efficiency contour plots for second-harmonic generation by optical pulses exhibiting Gaussian temporal and spatial profiles are calculated numerically based on the monochromatic plane-wave theory. Comparison with a similar plot for pump pulses constant in time and space shows that Gaussian pulses convert less efficiently at low nonlinear drives and more efficiently in a specific range of high drives. This effect is due to the intensity-dependent period of conversion. We calculated the harmonic pulse shapes using the suggested computational routine and found them to depend on the magnitude of drive as well. The pulse shape is nearly Gaussian at low drives, but it becomes severely distorted at intermediate and high drives. It is shown that the conversion efficiency contour plots provide a convenient tool for evaluating the trade-off between the desirable efficiency and other parameters of the conversion process in the case of Gaussian pulses.     

On the analysis of second-harmonic modulators

Analysis of magnetic modulators, which includes low-level transducer amplifiers and magnetometers, usually is based on control-signal displacement of fixed hysteresis loops of some particular shape. Experience shows, however, that many qualitative aspects of the device operation do not agree with the analysis. In this paper, an analysis is based on thedphi/dtwidening of the hysteresis loop, which is applicable to metal alloy tape cores. The analysis makes possible the comparison of amplifiers using different magnetic materials by relating small-signal gain and output waveform to measurable properties of the material.     

Temperature and pulse-duration dependence of second-harmonic generation in CdGeAs2

A detailed investigation of frequency doubling of a transversely excited atmospheric CO2 laser operating at 9.55 microm with a CdGeAs2 crystal was carried out. The temperature of the crystal was varied between 80 and 295 K to maximize the frequency-doubled energy. The temporal shape of the generated beam at 4.775 microm was monitored to calculate its peak power. High values of midwave infrared pulse energy (16.65 mJ) and peak power (92 kW) were obtained, which can be of potential use in lidar systems.     

Intracavity testing of KTiOPO4 crystals for second-harmonic generation at 532 nm

We have developed a diode-pumped Nd:YVO(4) cw laser for testing KTiOPO(4) crystals designed for intracavity second-harmonic generation at 532 nm. We demonstrate that this source is extremely sensitive to defects inside the crystal, inducing losses at 1064 nm and an index mismatch between fundamental and harmonic waves.     

Simple method for determining the crystalline axes of nonlinear uniaxial crystal with second-harmonic generation

For uniaxial crystal the optic axis (Z axis) can be determined easily by means of observing its growth pattern or by linear optical methods such as conuscopy. However, determination of the other crystalline axes is not so trivial, normally requiring x-ray diffraction measurements. We propose a simple method for determining the other two axes of the nonlinear uniaxial crystal, using second-harmonic generation. For several uniaxial crystals (with 3m, 62m, 42m, and 32 point groups) the intensity change of the second-harmonic output is calculated as the crystal is rotated azimuthally with respect to the Z axis. The principle is demonstrated in an experiment with LiNbO(3) crystal to determine the X axis with 0.2 degrees accuracy.     

Relative measurements of second-order susceptibility with reflective second-harmonic generation

There is a strong demand for a simple and reliable technique for second-order susceptibility measurements of thin films. Since the Maker fringe technique is limited to transparent substrates we propose an experimental protocol based on reflective second-harmonic generation (SHG). The proposed protocol is based on relative measurements of Z-cut quartz. An analytical expression of the reflective SHG intensity dependence of the polarizer, analyzer, and sample azimuth is presented. An error analysis is also presented. Thin organic film of the side-chain polymer poly(Disperse Red 1 Methacrylate-Co-Methyl-Methacrylate) is investigated. Results for different wavelengths are reported.     

Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation

We present an extension of the rigorous coupled-wave analysis technique to analyze second-harmonic generation (SHG) in periodic optical nanostructures in the undepleted-pump approximation. We apply this method to analyze SHG in two example nanostructures for which we predict enhanced nonlinearity due to transverse near-field localization of the fundamental optical field in the nonlinear material. First, we examine a periodic nanostructure that yields up to twice the transmitted SHG intensity output compared with the bulk nonlinear material but only for small nanostructure depths because of mismatch of the fundamental and second-harmonic mode phase velocities. Second, we develop and analyze a modified nanostructure and find that this nanostructure concurrently achieves transverse localization and phase matching for SHG. In principle, this permits an arbitrary coherent interaction length, and for several specific nanostructure depths we predict a transmitted SHG intensity output more than two orders of magnitude greater than that of the bulk material.     

Organic materials for second-harmonic generation: advances in relating structure to function

The relationships between molecular structure and the nonlinear optical phenomenon second-harmonic generation (SHG) are discussed. New-found relationships built up from basic structural axioms that were deduced in the 1970s and 1980s are the particular focus of this article, using structural results from X-ray and neutron-diffraction studies. The molecular and supramolecular manifestations of the SHG effect are borne out, although ways to optimize the effect on the molecular scale feature predominantly, since control of SHG on the supramolecular scale remains difficult given present limitations. The use of a variety of templates to generate head-to-tail oriented host-guest species thereby bypassing such limitations is described. The paper concludes with a look ahead at next generation 'octupolar' SHG-active compounds, the prediction of new series of SHG-active compounds via data-mining computational procedures, and developments in diffraction technology that may enable structural movies of a molecule to be captured during the SHG process. A practical assessment of the viability of organic SHG materials for industrial application is reviewed with a positive outcome, thus indicating a promising future for organic SHG materials.     

Grating-enhanced second-harmonic generation in polymer waveguides: role of losses

A numerical study of second-harmonic (SH) generation in a corrugated polymer waveguide is performed with a rigorous electromagnetic theory. Comparison with experiment reveals the role of losses inside the waveguide-small losses do not significantly affect the nonresonant response and reduce the resonant enhancement of SH generation. High losses can lead to the opposite effect-instead of enhancement, dips in the SH efficiency are observed in the vicinity of guided-wave excitation. The peculiarities of the angular dependencies of SH generation are explained from the phenomenological point of view, and the role of phase matching is discussed.     

Far-field imaging of optical second-harmonic generation in single GaN nanowires

Means for assessing the nonlinear optical properties of nanoscale materials are of key importance for the advancement of active nanophotonics. By correlating second-harmonic generation (SHG) with electron backscattered diffraction from single GaN nanowires (NWs), we demonstrate that far-field microscopic imaging of SHG offers an approach for distinguishing crystallographic orientations of NWs lying on a substrate. The quasi-static approximation, which should prove useful in describing many nanophotonic behaviors, is shown to satisfactorily account for the SHG data.     

Composition dependence of thermally induced second-harmonic generation in chalcohalide glasses

By investigating the second-harmonic generation (SHG) of the series (100 − 2x)GeS₂·xGa₂S₃·xPbI₂ (x = 5, 10, 15, and 20) chalcohalide glass samples after thermal poling, it was found that there was an optimal poling temperature for each composition and there was also a relation between optimal poling temperature and glass transition temperature. With increasing x, the obtained second-order susceptibility χ⁽²⁾ shows an increase first and then decrease, and the maximum was seen at x = 15. A dipole reorientation model and structural relaxation causing by Ga₂S₃ and PbI₂ were proposed to explain the dependence of poling temperature on SH intensity for each composition and the presence of the maximum χ⁽²⁾ in this chalcohalide glass series.     

Simple method of detecting ferroelectric domains with non-phase-matched second-harmonic generation

We demonstrate a new method of detecting the presence of ferroelectric domains based on non-phase-matched second-harmonic generation. If a domain boundary is tilted relative to the input and output faces of the crystal, the far-field second-harmonic light consists of multiple beams, in contrast to the single beam generated in a single-domain crystal. The angular separation of the beams provides a measure of the tilt of the domain wall if the refractive-index difference n(2omega) - n(omega) is known.