Relative bulk and interface contributions to optical second-harmonic generation in silicon

Peng, H-X; Adles, Eric J.; Wang, J.-F. T.; Aspnes, D. E.

doi:10.1103/physrevb.72.205203

Cited by 21 publications

(24 citation statements)

References 13 publications

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“…On the basis of the 58 vicinal (111) Si data, Lüpke et al [9] and McGilp [31] both concluded that the bulk contribution is significant. In contrast, in fitting lineshapes to data, and in particular examining the 98 vicinal results where the third-and fourth-rank tensor separation should be more distinct, Peng et al [27] came to the opposite conclusion. They pointed out that additional information could be obtained from the 7th harmonic, which is nonzero only if both third-rank and bulk forth-rank tensor contributions are present.…”

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confidence: 91%

“…Given the above success, we applied the same basic approach to fourth-harmonic generation (FHG) at the Si-SiO 2 interface [25], and third-harmonic (THG) [26] and dipole-forbidden SHG [27] from bulk Si. The FHG work, done with the objective of interpreting data obtained by the Downer group on surfaces of varying roughness [28], showed that interface angles were not always those of the bulk, a result also found by Kwon et al [5] Our most recent application, to amorphous (a-) SiO 2 [14], was intended as a first step toward understanding the data of Figliozzi et al [29] on crystalline Si nanoparticles embedded in SiO 2 .…”

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confidence: 98%

“…The bulk-quadrupole, relativistic, and field-gradient contributions differ only in that the final unit vector in the fourth-rank product involves a dot product withk o ,k, or the appropriate field gradients, respectively. Noting that a second intrinsic dipole-forbidden bulk contribution, the relativistic term [27], has only recently been identified, we recommend using ''bulk-quadrupole'' to refer to spatial dispersion arising from the phase of the driving plane wave, as done, for example, here and in [5]. Thus the symmetry analysis done for example in Ref.…”

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Bond models in linear and nonlinear optics

Aspnes

2010

Physica Status Solidi (b)

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Atomic-scale descriptions of linear-optical properties such as reflection are nearly a century old, but surprisingly, analogous models describing nonlinear-optical (NLO) properties as the natural dynamic response of bond charges driven by an external field are a recent development. These bond-charge models have proven to be particularly useful in describing the relevant physics of second-, third-, and fourth-harmonic generation, identifying previously unrecognized contributions to NLO responses, and uncovering well-disguised correlations in tensor parameters determined phenomenologically from symmetry conditions. Current capabilities are discussed, and opportunities for improved understanding noted. 1 Introduction The availability of continuum sources of radiation covering wide spectral ranges has not only made linear-optical spectroscopy possible, but also linear-optical techniques indispensable for determining information nondestructively about materials, interfaces, and structures. Owing to the higher-order tensors involved, in principle nonlinear-optical (NLO) probes are much more powerful, but spectroscopic data [1-5] have been difficult to acquire. However, commercial femtosecond systems that can tune over wide wavelength ranges are becoming available, and we are rapidly reaching the point where NLO spectroscopy will be routine.The potentially greater diagnostic power of NLO comes at a price, specifically the need to use more complex models and methods to interpret these more complex data. For most linear-optical applications, measurements can be analyzed using macroscopic parameters such as the dielectric function e, which for isotropic materials is a scalar and anisotropic materials a second-rank tensor. Here a return to fundamentals is generally unnecessary, and the last contact most linear-optical spectroscopists have had with atomic scale properties is the textbook derivation of the ClausiusMossotti relation [6], which relates the dielectric constant to local polarizabilities in the static limit.For NLO, quantities equivalent to e are the susceptibility tensors x ijk , x ijkl , etc. [7]. Symmetry-allowed NLO tensor components have been determined for all crystal classes, and

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Bond models in linear and nonlinear optics

Aspnes

2010

Physica Status Solidi (b)

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“…Accordingly, in this paper, we generalize the SBHM to a more complete description, the anisotropic bond model ͑ABM͒, which includes charge motion transverse to the bond, RD, SD, and MG effects, including SD effects arising from beam geometry, and SHG signals for off-axis observation angles, i.e., the role of diffraction. In developing our expressions, we follow the approach of Peng et al, 8 framing the calculations in terms of the fundamental four-step process of optics: ͑1͒ evaluate the local field at any given charge site that results from the driving ͑source͒ field, ͑2͒ solve the mechanical equation F ជ = ma ជ to obtain the acceleration of the charge, ͑3͒ calculate the radiation that results from the acceleration, and ͑4͒ superpose the radiation from all contributing charges. For random media, we show that step ͑4͒ factors into two parts: ͑4a͒ average over all possible bond orientations at a single site, and then ͑4b͒ calculate the properties of the emerging beam by Fourier transforming the envelope function of the incident radiation.…”

Section: Introductionmentioning

confidence: 99%

Application of the anisotropic bond model to second-harmonic generation from amorphous media

Adles

Aspnes

2008

Phys. Rev. B

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As a step toward analyzing second-harmonic generation ͑SHG͒ from crystalline Si nanospheres in glass, we develop an anisotropic bond model ͑ABM͒ that expresses SHG in terms of physically meaningful parameters and provide a detailed understanding of the basic physics of SHG on the atomic scale. Nonlinear-optical ͑NLO͒ responses are calculated classically via the four fundamental steps of optics: evaluate the local field at a given bond site, solve the force equation for the acceleration of the charge, calculate the resulting radiation, then superpose the radiation from all charges. Because the emerging NLO signals are orders of magnitude weaker and occur at wavelengths different from that of the pump beam, these steps are independent. Paradoxically, the treatment of NLO is therefore simpler than that of linear optics ͑LO͒, where these calculations must be done self-consistently. The ABM goes beyond previous bond models by including the complete set of underlying contributions: retardation ͑RD͒, spatial-dispersion ͑SD͒, and magnetic ͑MG͒ effects, in addition to the anharmonic restoring force acting on the bond charge. Transverse as well as longitudinal motion is also considered. We apply the ABM to obtain analytic expressions for SHG from amorphous materials under Gaussian-beam excitation. These materials represent an interesting test case not only because they are ubiquitous but also because the anharmonic-force contribution that dominates the SHG response of crystalline materials and ordered interfaces vanishes by symmetry. The remaining contributions, and hence the SHG signals, are entirely functions of the LO response and beam geometry, so the only new information available is the anisotropy of the LO response at the bond level. The RD, SD, and MG contributions are all of the same order of magnitude, so none can be ignored. Diffraction is important in determining not only the pattern of the emerging beam but also the phases and amplitudes of the different terms. The plane-wave expansion that gives rise to electric quadrupole magnetic dipole effects in LO appears here as retardation. Using the paraxial-ray approximation, we reduce the results to the isotropic case in two limits, that where the linear restoring force dominates ͑glasses͒ and that where it is absent ͑metals͒. Both forward-and backscattering geometries are discussed. Estimated signal strengths and conversion efficiencies for fused silica appear to be in general agreement with data where available. Predictions that allow additional critical tests of these results are made.

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“…In the intervening years since this debate first took place a consensus has developed among researchers that materials like Si are characterized by intrinsic nonlinear surface anisotropy with surface dipolar and bulk quadrupolar sources [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] divided in almost equal parts. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths

et al. 2012

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We study second and third harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths in bulk and cavity environments. Second harmonic generation is due to a combination of spatial symmetry breaking, the magnetic portion of the Lorentz force, and quadrupolar contributions from inner core electrons. The material is assumed to have a nonzero, third-order nonlinearity that gives rise to most of the third harmonic signal. Using the parameters of bulk silicon we predict that cavity environments modify the dependence of second harmonic generation on incident angle, while improving third harmonic conversion efficiency by several orders of magnitude relative to bulk silicon. This occurs despite the fact that the harmonic signals may be tuned to a wavelength range where the dielectric function of the material is negative: A phase-locking mechanism binds the generated signals to the pump and inhibits their absorption. These results point the way to alternative uses and flexibility of materials such as silicon as nonlinear media in the visible and UV ranges.

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Relative bulk and interface contributions to optical second-harmonic generation in silicon

Cited by 21 publications

References 13 publications

Bond models in linear and nonlinear optics

Bond models in linear and nonlinear optics

Application of the anisotropic bond model to second-harmonic generation from amorphous media

Dynamical model of harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths

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