Time-Dependent SHG in Thin Film Germanium-Doped Silica Waveguides
- PDF / 307,834 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 11 Downloads / 176 Views
ABSTRACT The evolution of second harmonic generation (SHG) in germanium doped silica planar waveguides is simulated numerically. Based on the asymmetric photoionization model, the total current in the waveguide is taken to be the sum of an asymmetric current and a current due to the resulting dc field. The interplay between these two currents causes the SHG to saturate in time. The saturation of SHG in length is due to diffraction. INTRODUCTION Efficient frequency doubling of infra-red radiation was originally observed in germaniumdoped fibers [1]. The second harmonic signal was found to increase in time until finally saturating after several hours. It was later demonstrated that saturation could be reached much faster by simultaneously seeding the fiber with an intense infra-ced light and a small amount of green light (second harmonic) [2]. More recently, researchers have been able to observe this process in germanium-doped optical planar waveguides [3]. Since silica is centro-symmetric, it appears that the exposure of a germanium-doped silica medium to the optical fields somehow breaks down the inversion symmetry and produces an effective second-order susceptibility, X(-). A non-vanishing X(, however, is not sufficient for efficient SHG as due to dispersion effects, phase-matching generally cannot be maintained between the fundamental wave and its second harmonic. Thus one may conclude that the written X(2) grating is also periodic in the direction of propagation with a periodicity matching the phase mismatch between the fundamental wave and its second harmonic [2]. The mechanism responsible for such a process is not yet fully understood. Several theories have been proposed to explain this surprising phenomenon. It is now generally agreed upon that a semi-permanent spatially periodic dc electric field is produced via a third-order or higher optical process [4]. One promising model that explains the origin of the dc electric field is the asymmetric photoionization model [5]. In this model, one and two-photon absorption processes interfere, resulting in electrons being ejected into the conduction band in a preferential direction. The current associated with this process is of the form:
J. oc E*2 E2,,,
+ c.c.
261 Mat. Res. Soc. Symp. Proc. Vol. 392 e 19 9 5 Materials Research Society
(1)
where J=, represents the asymmetric current, and &, and E 2w represent the electric fields of the fundamental wave and the second harmonic, respectively. The ejected electrons are retrapped and the resulting dc electric field, Edt, interacts with the optical fields through a four-wave mixing process. Thus the effective X(2) grating is given by:
where
(3) X,,k1
(2)
(3) W(1
Xijk =
sXijklldc
(2)
represents the third-order susceptibility tensor.
We use the asymmetric photoionization model to examine the evolution of SHG in germanium-doped silica planar waveguides in which the seed waves are transverse magnetic (TM) waves. PHENOMENOLOGICAL MODEL To begin a description of the evolution of SHG in planar waveguides, we use th
Data Loading...
