1. Introduction

In 1991 Myers et al. discovered that fused silica samples subjected to high temperature and high voltage (thermal poling) could frequency double a Nd:YAG laser operating at 1064 nm [1], with an induced second order susceptibility (χ⁽²⁾) of ~1 pm/V.

Glass [2], optical fiber [3] or a planar waveguide [4] becomes non-centrosymmetric when subjected to high voltage (~kilovolts) at high temperature (typically 300°C) for a few minutes. The temperature is decreased with the field still applied, and a frozen-in electric field remains inside the sample. This frozen-in electric field, in conjunction with the third order susceptibility of the glass (χ⁽³⁾), is responsible for the second order effects induced by poling, such as second harmonic generation (SHG) [5] and electro-optic modulation [6], forbidden before poling due to the centrosymmetry of the glass. The origin of this frozen-in electric field is still uncertain, but it is believed that impurities such as sodium, calcium, lithium, potassium, etc, migrate to the cathode, leaving a depletion region under the anode [7], full of anions, dangling bonds and/or electrons [8], or that dipoles are oriented [9]. It has been observed that glasses containing high concentration of germanium and subjected to poling could also generate defects like GeE’ [10], changing the optical properties of the glass, and inducing a non-linearity (d₃₃) of about 1.1 pm/V. Recently, Godbut et al. [11] reported on the square law dependence of the induced refractive index change through the measurement of the shift in the wavelength of a Bragg grating based Fabry-Perot interferometer fabricated in a short piece of un-poled double-side hole optical fiber. The quadratic electro-optic Kerr effect was estimated in Ref. 11 to be 3.07×10^-22 (m/V)². Thermal poling has been extensively investigated, led by the goal that it would be a very simple technique for changing the properties of the glass in order to produce cheap telecommunication devices such as frequency converters, electro-optic modulators, switches etc, competing with devices based on nonlinear crystals. Silica has other advantages such as low thermal expansion, excellent refractive index match for optical fibers making splicing easier, and a low dielectric constant for a high speed electro-optic response. Abe et al. [12] successfully demonstrated the first integrated device based on poling. In their work, a Mach-Zehnder configuration was photo-lithographed in a silica-based planar waveguide, and one of the arms was poled with 4 kV at 300°C. In order to measure the electro-optical effect induced by poling, a voltage was applied via electrodes at room temperature, and the linear phase shift gave an r-coefficient of 0.02 pm/V. However, this configuration provides not only the induced linear electro-optic effect, but also the Kerr effect present in all glasses, not reported by the authors. The contribution to the electro-optic effect from the Kerr nonlinearity has so far not been discussed in the literature. All publications to date have presented results on the measurement of the induced linear electro-optic coefficient, consequently masking contributions from the always present dc-Kerr effect.

We recently reported some of our results [23], however in this paper, we present details on thermal poling of a planar waveguide in a simple arrangement in order to measure the χ⁽³⁾, the frozen-in field, E_dc, and therefore χ⁽²⁾ and the r- coefficient induced by poling, as well as its development as a function of the poling field, and highlight how the dc-Kerr coefficient affects electro-optic modulation in the poled sample.

2. Theoretical background

There is some confusion in the literature over the equation relating to poling. The correct expression for the change in the refractive index due to an applied external field in a poled device is [13]:

Where, n₀ is the average refractive index of the glass, E_appl is the externally applied electric field, and E_dc is the internal frozen-in field in a poled sample. For ease of discussion, we refer to ${\chi }_{\mathit{\text{xxxx}}}^{\left(3\right)}$ as χ⁽³⁾ throughout the paper, also r_xx →r, where x refers to the polarisation direction of the applied electric field. The last term in Eq. (1) is the dc-Kerr effect (~χ⁽³⁾${{\mathrm{E}}^2}_{\text{appl}}$), while the second term is responsible for the induced electro-optic effect (~χ⁽³⁾E_dcE_appl). Therefore, for the high fields applied to a device (~ kilovolts over few microns) one cannot ignore the contribution from the dc-Kerr effect.

In our experiments, we used a planar configuration, with an unbalanced Mach-Zehnder waveguide interferometer which was custom made at British Telecom Research Laboratories. Light from port 1 or 2 is split in the first directional coupler (with a coupling length L₁ and coupling constant κ₁). Arm A has a length L_A, with arm B, L_B<L_A, and the light from both arms interferes at the second directional coupler (with a coupling length L₂ and coupling constant κ₂). The power can be measured at ports 3 and 4. Generically, for light coupled from port 2 (P₂) we can describe the interference power in port 3 and 4 by:

where P₃ and P₄ are the output power at ports 3 and 4 respectively, α is the intrinsic loss per cm in the waveguide and Δϕ is the phase change which depends on the wavelength λ and on the refractive index, n, and can be expressed as:

It is clear that the phase change has a strong dependence on the wavelength and on the refractive index, due to the difference in the path length. As discussed before, poling leaves a frozen-in field (E_dc) in the vicinity of the anode [14]. If arm A alone was poled, then for an externally applied electric field the refractive index would change as per Eq. (1). Therefore, the phase in A can be expressed as:

This equation enables the determination of χ⁽³⁾ before poling, and E_dc from ϕ₀ after poling. The induced χ⁽²⁾ and r-coefficient after poling can be inferred from χ⁽³⁾ and E_dc as [15]:

3. Apparatus and poling

The details on the channel waveguide are: the substrate of silicon was thermally oxidized to form a 15.6 µm (SiO₂) as a lower cladding, and a buried channel core was 5 µm square (~20 wt% GeO₂, ~80 wt% SiO₂) with an upper cladding of 16 µm. In order to make the poling process more efficient, the upper cladding was etched down to a thickness of 5 µm. A gold electrode, approximately 200 nm thick, was deposited on top of arm A alone (anode electrode). The silicon substrate was used as the cathode. L_A (optical path) was calculated from measurements to be 280 mm (coiled) L_B=53 mm (slightly curved), with data on n_cladding=1.4457, n_core=1.4558, L₁=L₂=615 µm supplied by BT Labs. The dimensions of the sample were 22×43 mm, and κ₁ and κ₂ were estimated to be 0.9/L₁ and 1.1/L₂ respectively at 1.55 µm, which corresponds to 60/40 and 70/30 couplers, respectively. The intrinsic loss of this channel waveguide was below 0.1 dB/cm estimated from total power measurements. With these parameters, it was possible to calculate that a π phase change would occur if the wavelength is changed by 3.65 pm according to Eq. (4).

A Teflon covered silver wire was attached to the gold electrode (see Fig. 1) in order to make the anode contact. The whole system was placed on top of an aluminum plate which formed the connection to the cathode silicon substrate. The plate was connected to a resistor of 510 kΩ to measure the poling current in the circuit and thus the voltage (with a boxcar integrator). The system was heated on a conventional hot plate up to 280°C, measured with a thermocouple. The high voltage was applied once the temperature was stable (±5°C). However, in order to avoid thermal runaway [16], the poling voltage was increased in steps of 600 V. The current resulting from the poling process demonstrated a fast initial spike and decay when the high voltage was applied. This indicates that the poling process in the sample is over within a couple of minutes. With the voltage still applied the temperature was lowered until it reached room temperature. After poling, the planar waveguide was placed in the experimental arrangement shown in figure 1. The measurement system was composed of a tunable laser with a 1 pm resolution as the light source, a wave-meter with a precision of 1 pm, and a power meter. The wave-meter and the power meter were connected to an EG&G boxcar integrator and an optical spectrum analyzer (OSA) was used to measure the transmission from the device. A polarization controller was used to maintain linear polarization. Light was butt-coupled in/out & to/from the planar waveguides with standard single mode optical fiber pigtails and refractive index matching oil, with the help of two, nano-XYZ controlled stages.

 

Fig. 1. Arrangement to measure the dc-Kerr and Electro-Optic effects. The gold electrode is shown in yellow and only covers the coiled region.

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4. Results

In the first measurement, the respective output powers in the poled sample were monitored, whilst the wavelength was stepped in 1 pm intervals. Figure 2 shows these measurements for both ports 3 and 4, when light was launched into port 2. The solid lines are the calculated curves using Eqs. 3 and 4, and they are in good agreement with the experimental results. For subsequent measurements a wavelength at the quadrature point was chosen, and an external voltage was applied. It is possible to choose two different quadrature points: one going up in the wavelength curve (up-going) and another going down (down-going) as seen in Fig. 2 for port 3 or port 4. When a dc field, E_appl is applied, the output optical power goes up and down (Fig. 3a). The equivalent phase change varies quadratically (Fig. 3(b)), as expected from Eq. (5). For an un-poled sample the phase change as a function of the applied field is a perfect parabola but is centered at zero (not shown). A permanent phase change in arm A after poling is clearly visible from Fig. 3(b): the offset in the phase at zero applied field. Fitting a parabola to the curves in Fig. 3(b) by using Eq. (5), one can estimate the values for χ⁽³⁾ and ηE_dc. η is the overlap integral of the mode-field with the frozen-in electric field which is distributed through the upper cladding, core and lower cladding. The shape of this distribution is still unknown, but it has been suggested that it could be exponential [1], Gaussian [17], or even constant [18] through the depletion region. The estimated values for the three cases are: the 1/e decay in the exponential case occurs at 8 µm [1] (η ~0.45), or for a buried depth of 2.5 µm and a 1/e decay of 8 µm in the Gaussian case [16] (η ~0.26), or for a depletion region of 8 µm with a constant E_dc (η ~0.35) [17].

 

Fig. 2. Output from ports 3 (open squares) and 4 (open circles) and their theoretical fits (lines).

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The increase in E_appl required to null this phase change is initially linear with increasing poling field, E_poling, for the same poling temperature, but saturates for E_poling >10⁸ V/m. E_appl needed to null the phase change is basically due to the E_dc frozen into the sample. From the dc-offset for different poling fields, the evolution of the frozen-in field, ηE_dc as a function of the poling field is plotted in Fig. 4(a). An external field exists throughout the intervening space between the electrodes and is uniform within it; however, the internal field may not be, and the calculation is therefore for an average value. The values from fig. 4a typically give an effective frozen-in field, ηE_dc from zero to approximately 4×10⁷ V/m, becoming constant for E_poling >~10⁸ V/m. The aperture of the parabola seen in Fig. 3(b) is smaller than in the un-poled sample, indicating that the coefficient of the quadratic term in the parabola increases: this mean χ⁽³⁾ must increase (see Eqs. (1) or (5)). Thermal poling causes a permanent increase in the χ⁽³⁾ by a factor of ~2, independent of the poling voltage as shown in Fig. 4b (increasing from an average of 5.2 (±0.4)×10^-22 (m/V)² to 10.3 (±0.3)×10^-22 (m/V)²). This was also reported by Fujiwara [10] in high-Ge-doped glasses, Wong [20] and Xu [21] in optical fibers, where an increase of the χ⁽³⁾ of ~15 times in the first case, and ~2, in the last two cases, was reported. Fujiwara attributes this increase to a phase change in the glass, i.e., the UV-poling, used in his case, creates crystallites. This is not very clear yet, but as the poling field is very high and charge carriers are present in large numbers, it might be reasonable to consider substantial changes in the characteristics of the glass matrix, and therefore in χ⁽³⁾. This step increase has been addressed recently by us and is the subject of another publication [22]. We can roughly estimate χ⁽²⁾ and the r-coefficient using our values of χ⁽³⁾, η and E_dc. χ⁽²⁾ and r increase in the same way as E_dc, and they reach values of approximately 0.03 pm/V and 0.01 pm/V respectively, using η=1. Note that the induced electro-optic coefficients are small, but comparable to the values obtained in the literature [11, 19].

From experimental results, the depletion region appears to extend well beyond the waveguide with high poling fields: the poled region is only 26µm and the waveguide is within 10 microns of the anode, possibly resulting in saturation of the internal field. It is evident from Eq. (5) that when an electric field is applied, the output will show both the electro-optic effect induced by poling, and the dc-Kerr effect present in all materials: i.e. the phase-modulation is not linear.

 

Fig. 3. (a) Output power at port 3 when an external field E_appl is applied in the waveguide. (b) The phase change due to E_appl. The open squares represent a quadrature point with the wavelength going “down”, while the open circles represent one going “up”. The dotted and solid lines are the parabolic fits to the curves going “up” and “down”, respectively.

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Abe et al. [11] showed the electro-optic effect alone, and ignored the Kerr effect contribution. Therefore their estimated coefficient is probably slightly smaller than reported. According to Eq. (1), we note that unless the frozen-in field, E_dc≫E_applied, there will always be a strong dc-Kerr effect visible, making the refractive index modulation non-linear. In our case, E_dc should be >10⁸ V/m, for the dc-Kerr contribution to be less than 10%.

 

Fig. 4. (a) Average ηEdc vs. E_poling. (b) Average increase of χ⁽³⁾ as a function of E_poling.

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5. Conclusions

χ⁽³⁾ and the induced internal electric field, ηE_dc after poling is inferred from measurements in a germania doped silica waveguide unbalanced Mach-Zehnder interferometer. The equation describing the influence of the dc-Kerr effect on electro-optic modulation has been presented and the contribution from the dc-Kerr effect after poling has been shown to be significant. The resulting electro-optic coefficient was also measured in poled devices and shown to be non-linear. A χ⁽³⁾ of 5.2 (±0.4)×10^-22 (m/V)² was measured for an unpoled Ge:silica planar waveguide, slightly higher than that reported in the literature [11]; after poling it increased to 10.3 (±0.3)×10^-22 (m/V)². The internal frozen-in field, ηE_dc increases with the poling field, and saturates for E_poling >10⁸ V/m. To our knowledge this is the first time that the frozen-in internal field has been inferred directly from measurements and shown how it varies with the poling field. The contribution from the dc-Kerr effect has been elucidated for the first time. Further insights to elucidate the step like increase in χ⁽³⁾ may be seen elsewhere [22].