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A variety of systematic investigations aimed at exploring the onset of second order non- linearity in a glass matrix have been seeking the physical explanation of what looked to be an exception to the rule of nature. Among the others, neutron diffraction and inelas- tic scattering measurements (Cabrillo et al., 1998) have shown that the glass structure of poled silica becomes anisotropic and differs significantly from that of native sam- ples. From those data, crystallization of part of the glassy matrix into a cristobalite polymorph of silica appeared as a reasonable possibility. Direct evidence of deep struc- tural alterations induced by thermal poling in silica by means of inspection of poled and native samples by electron microscopy was also provided by Cabrillo et al. (2001) . The electron diffraction patterns of a poled silica glass revealed the presence of a large amount (of order 10%) of crystallites showing patterns consistent with partial crystal- lization of the silica matrix. The possibility that the χ(3) of the samples was enhanced by such a partial crystallization seemed therefore plausible (Xu et al., 2000a). Garcia et al. (2003) measured χ(3) _{enhancement of a factor of 2 after poling a channel waveg-}

uide, as Quiquempois et al. (2005b) did in Infrasil glass. This, in turn, would enhance the χ(2) induced by the frozen-in field, as postulated in the Equation 1.2. Yet, recent Rutherford backscattering investigations, as well as elastic recoil detection and resonant nuclear reaction have shown peculiar features introduced in silica by thermal poling. Nonetheless, the most widely accepted explanation for the generation of SON in glass does not invoke structural modifications within the glass to accomplish the breakdown of its radial symmetry. In a model first proposed by Stolen and Tom (1987) to explain self-induced second-harmonic generation, the nonlinear second-order χ(2) susceptibility

Chapter 2 Physical origin of the nonlinearity in thermally poled glass systems 17

was stated as rectified by the intrinsic nonlinear third-orderχ(3)susceptibility according to:

χ(2)∼= 3 2 ·χ

(3)_E

DC (2.9)

where EDC represent the permanent built-in electric field induced by charge migration

(Figure 1.1), and 3/2 accounts for the degeneracy factor which arises from the convention chosen to express the electric field in Equation 2.1. Assuming that this microscopic adjustment is responsible for theχ(2)susceptibility in poled silica glass, alkali metal ions constitute the only positive charge carriers. As mentioned in Section 1.1, this mechanism was supported by the fact that a nonlinearity of about 1pm/V was measured with a typical sodium weight percentage of 1ppm, whereas it was considerably reduced in synthetic silica and not observed at all in poled high-purity silica glasses which included negligible content of metallic impurities (Kameyama et al., 2001).

Evidence of an upper limit on χ(2) set by the breakdown electric field were copiously given for silica-based glasses, as described in Section 1.1.2. To account for larger second- order susceptibilities, one must invoke the dipole orientation mechanism, well known in organic nonlinear optical materials and commonly used in poled polymers (Suarez and Puma, 1998). Such a mechanism, along with formation of micro-crystallites, was also adopted to explain the origin of the nonlinearity induced in glass byU V poling (Fujiwara et al., 2000). In glass, dipoles take the form of polar bonds, defects or highly polarizable entities which could be oriented with the external electric field. The freezing of oriented dipoles would break the symmetry and lead to a second-order nonlinearity no longer forbidden in the whole bulk of the glass (Figure 2.3).

- + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + ₊- ₊- ₊- ₊- ₊- ₊-

Figure 2.3: Oriented dipoles: χ(2) located in the whole bulk

In this case, the χ(2) susceptibility would proportionally depend on the second-order hyperpolarizability tensorβ according to:

χ(2)∝N ·L(E)·βef f (2.10)

whereβef f can be written as a linear combination ofβ tensor coordinates,N is the con-

Chapter 2 Physical origin of the nonlinearity in thermally poled glass systems 18

under the total electric-field, E, within the material. If one assumes that the concen- tration of hyperpolarizable entities is sufficiently small so that the depolarization field is several orders of magnitude smaller than the charge migration field, the two models can be solved independently and the charge migration model determines the total electric field during the poling process.

According to Mukherjee et al. (1994) a combination of the two different mechanisms may be responsible for the induced second order nonlinear effect in thermally poled silica. The authors proposed a model based on charge transport of single mobile ions creating a depletion region, followed by reorientation of dipoles, as suggested by Kazansky and Russell (1994). The permanent induced second order nonlinearity can be expressed as the sum of both effects:

χ(2)∝χ(3)EDC+ (β/5kT)EDC (2.11)

The first term in Equation 2.11 is related to the interaction between the residual electric field EDC inside the material and the third order nonlinearity. The second term is

the resulting macroscopic second order nonlinearity induced by reorientation of polar bonds during the poling treatment, each of them with a permanent dipole moment and microscopic hyperpolarizability (β) corrected by the local field which is effectively seen by each dipole. An external electric field, of at most 5kV /mm, may or may not create a large permanent dipole moment in the silica glasses with the same order of second- order hyperpolarizability as that of the crystals. It could be concluded that the main contribution to the effective χ(2) in poled silica came from the nonlinear phase confined in a few microns below the anodic face, where Lesche et al. (1997) finally measured a large space-charge field by in-situ interferometric direct inspection during HF etching.