Layer-by-layer analysis of second harmonic generation at a simple surface
J.E. Mejía*, C. Salazarba, and B.S. Mendozab
* Centro de Investigaciones en Optica, A.C., León Guanajuato, México.
a Alumno del Verano de la Ciencia patrocinado por la Academia Mexicana de Ciencias. Estudiante de la licenciatura en Física y Electrónica de la U. de Guadalajara.
b e-mail: bms@cio.mx.
]]>Recibido el 19 de noviembre de 2002.
Aceptado el 18 de agosto de 2003.
Abstract
We present a general scheme, based on a a microscopic formulation, to obtain the second harmonic signal produced by each atomic layer of a semi-infinite crystal. Using the simple Si(111):H (1 x 1) surface as an example, we obtain that the nonlinear polarization in the bulk does not decay to zero due to the lack of centrosymmetry of the individual layers. However, the sum of this polarization follows the physically correct picture that the second harmonic signal is zero at the centrosymmetric bulk and finite in the selvedge as the surface is approached and the centrosymmetry is broken. The results show that the selvedge region includes the surface and just a few layers below it.
Keywords: Non-linear optics; second harmonic generation; surfaces.
Resumen
Presentamos un procedimiento general, basado en una formulación microscópica, para obtener la señal del segundo armónico producida por cada capa atómica de un cristal semi-infinito. Usando la superficie sencilla Si(111):H (1 x 1) como un ejemplo, obtenemos que la polarización no lineal en el bulto no decae a cero debido a la falta de centrosimetría de las capas individuales. Sin embargo, la suma de esta polarización sigue el comportamiento físicamente correcto, mediante el cual la señal del segundo armónico es cero en el bulto centrosimétrico y finita en la región superficial conforme se aproxima la superficie y la centrosimetría se pierde. Los resultados muestran que esta región superficial incluye la superficie misma y tan sólo unas cuantas capas por debajo.
]]> Descriptores: Óptica No-lineal; generación de segundo armónico; superficies.
PACS: 42.65.Ky; 42.65.An; 78.66.-w
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Acknowledgments
We acknowledge partial support from CONACyT-México under grant 36033-E. CS thanks the AMC for the scholarship while at CIO.
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