## Simplified bond-hyperpolarizability model of second harmonic generation, group theory, and Neumann’s principle |

JOSA B, Vol. 31, Issue 3, pp. 526-533 (2014)

http://dx.doi.org/10.1364/JOSAB.31.000526

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### Abstract

We discuss the susceptibility third-rank tensor for second harmonic and sum-frequency generation, associated with low index surfaces of silicon (Si(001), Si(011), and Si(111)), from two different approaches: the simplified bond-hyperpolarizability model (SBHM) and group theory (GT). We show that the SBHM agrees very well with the experimental results for simple surfaces because the definitions of the bond vectors implicitly include the geometry of the crystal and therefore the symmetry group. However, for more complex surfaces it is shown that one can derive from GT the SBHM tensor, if Kleinman symmetry is allowed.

© 2014 Optical Society of America

**OCIS Codes**

(190.4350) Nonlinear optics : Nonlinear optics at surfaces

(240.4350) Optics at surfaces : Nonlinear optics at surfaces

(240.6700) Optics at surfaces : Surfaces

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: October 28, 2013

Revised Manuscript: January 10, 2014

Manuscript Accepted: January 10, 2014

Published: February 19, 2014

**Citation**

Adalberto Alejo-Molina, Hendradi Hardhienata, and Kurt Hingerl, "Simplified bond-hyperpolarizability model of second harmonic generation, group theory, and Neumann’s principle," J. Opt. Soc. Am. B **31**, 526-533 (2014)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-31-3-526

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