1. Introduction

Thermal poling [1] is the most reliable way of introducing a permanent second order nonlinearity in optical fibers. In silicate fibers nonlinear coefficients ~0.5 pm/V [2] have been induced and although this value is much lower than that of e.g. lithium niobate, the low nonlinearity can be compensated for by increasing the interaction length. Various geometries have been employed, such as D-fibers [2], single-hole [3] and twin-hole fibers [4], and in the latter it is possible to manually insert thin wires into the holes by side polishing the fiber [5] and use these as electrodes. It is also possible to pump molten alloy into the holes to create long and uniform electrodes [6] and pole long lengths of fiber [7]. Since thermal poling creates a thin (~10 µm) depletion layer, it is generally assumed that the core must be placed within this layer in order to experience the recorded electric field. This means that the core is situated very close to the anode and therefore the evanescent optical field extending outside of the core interacts with the alloy, introducing a loss. Although this can be accepted in a proof-of-principle experiment, the loss is one factor that hinders the use of poled fibers in practical applications. As was recently shown for thin (100 µm) poled bulk samples [8], the electric field is not confined in the depletion layer, but is present throughout the sample with a change of sign at the edge of the depletion region. This indicates that it is possible to design a fiber with the core placed far from the anode, thus minimizing the loss caused by the electrode and yet subject the core to a strong recorded field. In the present paper, the poling process is time resolved, and shows for the first time that there is a strong recorded field outside of the depletion region in poled fibers.

2. Theory

When the fiber is poled, positive charges in the glass (e.g., Na⁺) migrate towards the cathode, creating a negatively charged depletion region close to the anode. The strong electric field injects new positive, low-mobility charges into this cation-depleted region to neutralize it (e.g., H₃O⁺) [9]. During poling, the applied field becomes concentrated mainly in the depletion region due to the higher resistivity caused by lack of conductive ions. If the depletion region is almost completely neutralized during poling, then to a good approximation the electric field observed after poling is caused by the presence of a thin negatively charged layer remaining at the edge of the depletion region. Once the poling high voltage is switched off, this negative layer attracts surface charges to cancel the field inside the metal electrodes (Fig. 1), so that positive charges accumulate on the surface of both anode and cathode [8]. The net charge of the whole sample becomes zero and the resulting field between the negatively charged layer and the metal surfaces is approximately constant in intensity. The potential difference between anode and cathode then drops to zero, implying ∫E dl=0, verified experimentally in [8]. As also shown in ref [8], the electric field is created both inside and outside of the depletion region in thin (100 µm) poled bulk samples, pointing from both outer edges of the sample towards the negative charge layer at the end of the depletion region. That is, after poling the direction of the electric field inside the depletion region is the same as that of the electric field applied during poling, while outside of the depletion region the direction is reversed.

 

Fig. 1. After poling, when the voltage bias is switched off, positive charges are attracted from the metal surfaces of both anode and cathode to shield the field in the metal. If the negative charges recorded in the poled fiber are closer to the cathode side, the field outside the depletion region is larger than inside it [8].

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In a bulk sample, the width of the depletion layer (~10 µm) is usually much smaller than the width of the whole sample so that the electric field is much larger inside the depletion region than outside it, following from ∫ E dl=0. In a fiber, however, the width of the depletion layer can be comparable to the distance between the electrodes (~20 µm) and so the electric field is of similar magnitude inside and outside the depletion region, but changing in sign. For short poling times the depletion layer may not yet overlap the core, and the electric field experienced by the core after poling may have opposite sign compared to the field applied during poling. For longer poling times, there should be an instant when the depletion layer extends half way into the core to give an effective recorded field equal to zero. Poling the fiber for even longer periods should extend the depletion layer to cover the entire core and results in an electric field in the core with the same sign as that of the applied poling field.

3. Experiments

An etching experiment was designed to try to reveal the evolution of the depletion region. It is know in previous studies in bulk [10] and in fibers [11] that the linear electrooptic coefficient first grows but then decreases in time, and this is associated with the creation and expansion of a space charge region. Additionally, in fibers part of the change of the nonlinear coefficient experienced by light travelling in the core is caused by the growing width of the layer, and the alteration of its overlap with the core. Repeating the etching measurements of [12] should then show the spatial evolution of the region. Etching measurements are, however, destructive. In order to study this evolution without having to pole one fiber for every time interval, the fiber was placed in the thermal gradient at the edge of a hotplate during poling. It is assumed that poling at a slightly lower temperature is equivalent to shortening the poling time. This is a good assumption if the process is diffusive and dominated by a single time constant – not the case in poling. Nevertheless, the experiment is then simplified and still gives useful information about the evolution of the depletion layer.

The fiber used here had outer diameter 125 µm and was fabricated by drilling a modified chemical vapor deposition (MCVD) preform. A high temperature acrylate coating was applied to make the fiber resist the heat during electrode insertion and poling, and to keep it transparent after the thermal treatments. The fiber was designed as most fibers for poling with the anode hole placed closer to the core to ensure good overlap between the core and the poled region. In order to minimize the loss caused by the electrodes and confine the optical mode, the core was highly doped with Ge, to give a refractive index step Δn=0.033 and N.A.=0.31. The diameter of the core is 3.4 µm and the fiber is single-mode at 1550 nm. The edge-to-edge distance between the core and the nearest hole is 5.5 µm and farthest hole 9 µm. The two holes are 30 µm in diameter and have a separation d=17.9 µm.

The alloy used to create the electrodes consists of 80 % wt Au and 20 % wt Sn, with a melting point of 280 °C and resistivity 1.6×10^-5 Ω cm. This alloy was chosen because it can be inserted at 300 °C in molten form and poling can take place with the metal in its solid phase at a temperature 250–270 °C, close to the optimum for poling. The AuSn alloy was placed in a small pressure cell heated to 300 °C and pushed into the holes of the heated fiber by applying a pressure of 6 bars [6, 13]. The length of the electrodes in the present work was 70 cm, a compromise between maximizing the phase shift and keeping the loss caused by the electrodes reasonably small. Electric contact with the electrodes was established by side-polishing the fiber [5] and then attaching 20 µm thick gold coated tungsten wires to the alloy using conductive epoxy or plain thermal bonding. The fiber was placed at the edge of a hotplate and poled for 33 minutes by applying 4.3 kV. The hottest part of the fiber in this study was kept at 255 °C while the coldest part was at ~150 °C. After poling, in order to reveal the depletion region the coating was removed and the fiber cleaved several times in the poled region. The cleaved ends of the fiber pieces were then etched in 40 % hydrofluoric acid (HF) for 45 seconds [2, 12], rinsed in deionized water and dried at 150 °C in air, after which the samples were inspected with an optical phase contrast microscope.

The sequence of pictures in Fig. 2 shows how the depletion layer evolves in the region between electrodes. It is seen that the alloy electrodes fill the cross-section of the holes entirely. In Fig. 2(a, b), no distinct depletion region can be identified. In Fig. 2(c), it is clear that the depletion region formed has not yet reached the core after the 33 minutes poling interval. At yet higher temperatures Fig. 2(d–h), the region extends further and further, and in Fig. 2(i) it extends well past the core. The pointed shape of the region formed in Fig. 2(i) can be attributed to the electric field distribution during poling, as shown in [7]. In Fig. 2(f, g), the nonlinear layer covers approximately half the core, and according to Fig. 1, the effective electric field experienced by the core should be nearly zero. Some additional features are seen in the neighborhood of the core that are not accounted for in a simple model. In Fig. 2(h, i) a substructure is seen between the core and anode electrode, and it could be associated with the formation of a shielding field that slows down the expansion of the space charge [14]. Another possible explanation is that the substructure is caused by the high germanium concentration in the core acting as a barrier to the mobile sodium ions. The slower expansion of the depletion region in the Ge-doped core seems to be clear in Fig. 2(h).

 

Fig. 2. Spatial evolution of the depletion region measured by etching, temperature is increasing from upper left to lower right picture. The overlap with the core improves with increasing temperature until the region encompasses the entire core. Note the substructure in the lower right picture indicating that the core is slowing down the evolution of the depletion layer.

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4. Electro-optic characterization

It has been shown that etching a cleaved poled fiber reveals the location of the depletion region, but so far the magnitude and sigh of the recorded field cannot be extracted from such measurements. Therefore, an electro-optic characterization was performed in order to measure the recorded electric field. A new fiber was prepared, of similar type as the one used previously but with anode core separation of 7 µm instead of 5.5 µm. This time the entire fiber piece was heated to 255 °C using a hotplate and the whole 70 cm long piece was poled for a short time. The hotplate was turned off and the fiber allowed to cool down to room temperature after which it was placed in a 2×2 Mach-Zehnder interferometer [2,4,15] consisting of two 3 dB couplers and the poled fiber as the active arm. The passive arm consisted of a standard telecom fiber. Applying a voltage to the electrodes of the fiber in the active arm results in a refractive index change, thereby introducing a relative phase shift between the two arms. The electro-optic response was characterized by applying a linear voltage ramp to the fiber in the active arm while at the same time monitoring the optical power in one of the two output ports of the interferometer. The response is shown in Fig. 3 (left). From the optical response it is possible to estimate the introduced phase shift. This is shown as a parabola in Fig. 3 (left). The parabola has a minimum where the applied voltage cancels the recorded electric field. This is also seen as a symmetry point in the optical response as indicated by the arrow in the figure. In this case the symmetry point is located at +800V, indicating that the recorded voltage is -800V. Fig. 3 (right) shows the result of several such measurements done for increasing poling times. The recorded field was measured for each poling time and the result is displayed on a log scale (horizontal axis) to expand the shorter time intervals. It is clear that until approximately 20 minutes, the recorded field has negative sign, i.e., it points from the cathode to the anode. It is also clear that when the edge of the depletion region crosses the core position, the sign of the field changes. In this and another similar measurement the maximum field recorded after long poling times (many hours) is similar to the largest field obtained with opposite sign for short poling times (i.e., the magnitude of the recorded field at t=9 and at t=1000 minutes is comparable). This is expected from the geometry of the fiber used. The conclusion from the measurements is that indeed the recorded field experienced by the core can point in either direction depending on the position of the core and the extent of the depletion region. It is also concluded that after poling a strong electric field is observed outside of the depletion region. In the present study, the effective second-order nonlinearity induced was χ ⁽²⁾=0.036 pm/V.

 

Fig. 3. (left figure) Intensity vs. voltage response to find recorded field. The arrow indicates a symmetry point in the Mach-Zehnder interferometer where the applied voltage cancels the recorded field. (right figure) Time evolution of the recorded electric field. The recorded field first has negative sign. After 23 minutes of poling the recorded field is zero after which the sign changes to be the same as that of the applied voltage.

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5. Conclusions

In thermally poled fibers it is important to make use of a design where the recorded electric field overlaps the core. Previously, the strong electric field was only considered to be present in the depletion region. Following the results from [8] in bulk glasses, it is shown in the present paper that a strong field is also present outside of the depletion region in poled fibers. This gives a new degree of freedom when designing the fiber for poling, since it is possible to position the core far from the electrodes, and thereby minimize the loss caused by the metal. The new insight gained can also be used to give an alternative interpretation to previously reported results [14]. As demonstrated there, an electro-optic coefficient can appear when turning off the poling voltage in a fiber if the anode is positioned far from the core while the cathode is close to the core. The explanation given there was that during poling a shielding field is recorded in the fiber to oppose the applied field, and that after removal of the poling bias the shielding field gives rise to the electro-optic effect. The cancellation of the field experienced by the core during poling would imply that the shielding field of [14] appears across the core during poling. According to our results, the charge distribution is not static when the high voltage bias is switched off and thus the experiment of [14] can be explained in a different way. During poling the voltage drop is confined to the depletion region that never reaches the core, and therefore the field experienced by the core during poling drops to zero as the space charge region is established. When the external bias is switched off, however, positive charges are attracted to the surface of both electrodes and the core becomes subjected to a DC field. A nonlinear coefficient would then appear when the high voltage is switched off. According to this interpretation, the creation of a shielding field across the core would not be required.