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We study the creation and erasure of the linear electrooptical effect in silicate fibers by optical poling. Carriers are released by exposure to green light and displaced with simultaneous application of an internal dc field. The second order nonlinear coefficient induced grows with poling bias. The field recorded (~108 V/m) is comparable to that obtained through classical thermal poling of fibers. In the regime studied here, the second-order nonlinearity induced (~0.06 pm/V) is limited by the field applied during poling (1.2 × 108 V/m). Optical erasure with high-power green light alone is very efficient. The dynamics of the writing and erasing process is discussed, and the two dimensional (2D) field distribution across the fiber is simulated.
© 2015 Optical Society of America
1. Introduction
Thermal poling has been used as the technique that allows reproducibly inducing a relatively large quadratic optical nonlinearity in silica fibers (a fraction of a pm/V) [1,2 ]. By heating the fiber and simultaneously applying high voltage to internal electrodes, ionic displacement allows recording electric fields in the range of 108 V/m [3]. Such fields act on the third-order nonlinear susceptibility and create a measurable and usable quadratic nonlinearity [1,4 ]. However, thermal excitation is not the only way to achieve carrier redistribution in glass fiber. Optical excitation in the form of infrared (1.06 µm wavelength) and its second harmonic is known to free charges from the silica fiber core in a spatially periodic way and form a frequency doubling grating [5,6 ]. Blue light has also been used in a fiber biased with internal electrodes for the creation of an effective χ(2), observed through the enhanced non-phase matched second harmonic (SH) [7]. In that early study, the poling process was reported to saturate for sufficiently large applied field (> 4 × 106 V/m) [7,8 ] and the second-order nonlinearity induced could not be erased with blue light alone. One common belief regarding optical poling is that the effective χ(2) induced is much weaker than that created by thermal poling [9], and indeed much higher conversion efficiencies have recently been achieved in quasi phase-matched thermally poled fibers [10,11 ]. The early promise of high nonlinear coefficients with UV poling [12] also failed to materialize [13]. Therefore, optical poling has come into disuse.
The erasure of the quadratic nonlinearity with green [14–17 ] and UV radiation [18–20 ] has also been reported in fibers poled with optical or thermal excitation. This effect has received attention, because intentional periodic UV erasure is nowadays used for creating a QPM grating in fibers poled uniformly [10,11 ] and because unintentional optical erasure may limit the ultimate efficiency of frequency doubling fibers [16,17 ]. Making use of a poled grating to accompany the χ(2) erasure by light is not always ideal. Since the phase-matched wavelength may change with high-power laser exposure, probing requires a broadband or tunable light source. Also, the dispersion of χ(2) brings about differences between the mechanisms in optical-wave mixing (e.g., frequency doubling) and in mixing optical frequencies with near-dc fields (e.g., electrooptical effect). Furthermore, erasure with green light propagating along the core can potentially create photoconductive paths for charges from one domain to the next domain of opposite sign laying only some 20 µm away. For these reasons, it is advantageous to study erasure of the electrooptical effect in fibers poled uniformly directly through the decay of the phase-shift induced by applied voltage, i.e., without resorting to frequency doubling.
The creation and erasure of the electrooptical effect in silicate fibers by optical poling at room temperature with green light and an applied dc field are the subject of the present paper. The nonlinearity is measured from the phase-shift for a given applied voltage. It is found that the maximum nonlinear coefficient induced grows with poling bias field and is of the same order as the one obtained through classical thermal poling. Optical poling, erasure and the field distribution induced with high-power green light are studied and discussed.
2. Experimental set-up
Experiments were carried out using the set-up illustrated in Fig. 1 . A frequency doubled Q-switched (1.2 kHz) and mode-locked (100 MHz) Nd:YAG laser operating at 1.064 µm wavelength and frequency doubled in a 3 mm KTP crystal was used as source of high-power green light. Each Q-switched laser train had ~20 mode-locked pulses above half-maximum intensity. The fundamental radiation was filtered out with a dichroic mirror (F1) and KG5 filters (F2). The green light could be blocked with a mechanical shutter. The creation and erasure of the electrooptical effect was monitored with a poled fiber in a Sagnac interferometer [21]. The radiation used for probing was purposely of very low coherence and was centered in the C-band at 1.55 µm wavelength. An Erbium-doped fiber amplifier (EDFA) provided ~5 mW of amplified spontaneous emission (ASE) after amplification in a second EDFA. This signal was coupled into port 1 of a 3-dB fiber splitter. The probe radiation was directed through port 2 of the splitter, collimating lens, red filter RG 7 (F3), semi-reflecting mirror (BS) and focusing lenses into the Sagnac interferometer. The Sagnac loop consisted of a fiber section, comprising a 20-m delay line (SMF28) spliced to a segment of twin-hole fiber with internal electrodes, and a free-space section that allowed for coupling the high-power green light into the fiber. Three 10x microscope objectives were used for focusing and collimation. The semi-reflecting mirror at 1.5 µm (BS) had high transmission (>80%) at 0.53 µm wavelength, and the fiber alignment was optimized so that most green light excited the fiber from one side only. The third port of the fiber splitter was coupled to a 1-ns response time InGaAs photodiode (Det in Fig. 1) and a high-speed digital oscilloscope. Filter F3 prevented green light from reaching the detector. Port 4 of the splitter was index-matched and terminated. It was found that even with the use of angled fiber-contacts, the sub-reflections at lenses and fiber-end surfaces caused much interference noise. This noise was greatly reduced by replacing with the ASE source a long coherence-length amplified DFB-diode originally use as probe light source. A mechanical polarization-controller was inserted in the delay fiber as a means of biasing the interferometer so that in the absence of control voltage the detected CW signal at 1.5 µm was maximized.
Fig. 1 Experimental set-up used for optical creation and erasure of the electrooptical effect in silica fibers.
The active component was fabricated with the twin-hole fiber. The fiber had diameter 125 µm, core dimensions 5.8 µm on the x-axis and 6.2 µm on the y-axis, separation between holes 25 µm, and distance between nearest hole and core 7.4 µm. The fiber is single-mode at 1.5 µm wavelength. Internal electrodes (BiSn) were provided by the technique described in [22]. The length of the electrodes was 25 cm. A few samples were used in the experiments, and most of these were used repeatedly. The device was connected via BNC cables to a 0-1500 V pulse generator for probing the phase-shift or to a 0-3.5 kV DC power supply during poling. The maximum average power of the green light coupled into the twin-hole fiber component was 18 mW, corresponding to a peak power 7.5 kW. The average power of the CW 1.5 µm wavelength radiation exiting both arms of the balanced Sagnac interferometer (clockwise and anticlockwise propagation) was 1.1 mW.
The non-symmetric position of the poled fiber in the Sagnac loop gave rise to a differential phase-shift upon application of voltage pulses. The duration of the electrical pulses used to measure the electrooptical phase response was chosen to be 100 ns, sufficiently long to exceed with good margin the risetime of the system and short enough to result in the formation of two separate pulses in the optical response [21], corresponding to the clockwise and anticlockwise propagation in the 20-m long delay fiber.
3. Phase-shift measurements
Figure 2(a) illustrates the typical response of the Sagnac interferometer to the application of pulses of 1500 V to a device poled optically with 3 kV bias. Prior to poling, the electrooptical response was several times weaker, but still measurable. The signal-to-noise ratio is good (~20:1), even if the amplitude is in the millivolt range. When the process studied evolved slowly, averaging was used to improve the reading further. Figure 2(b) shows the amplitude of the pulse measured when the applied voltage was varied (black dots).
Fig. 2 (a) Oscilloscope trace showing response of Sagnac interferometer with electrooptical fiber to the application of a 100 ns 1.5 kV pulse; (b) Amplitude of optical signal switched as a function of applied voltage. The red solid curve is fitted to the (black) experimental points using Eq. (1) below.
The response is approximately sinusoidal because of the transmission of the Sagnac interferometer and the choice of bias point with the polarization controller. The value of Vπ for this component is 1600 V. Figure 2(b) also shows a red curve that fits well the experimental data, obtained by a minimum-square fit of the data using the expression [22]:
where Vm is the measured pulse amplitude, 2V0 the maximum measured pulse amplitude, L the length of the electrodes (0.25 m), λ the wavelength (1.55 µm), n the refractive index (1.46), d the separation between electrodes (25 µm), φ a phase determined by the bias point of the interferometer, Vappl the applied voltage, Erec the recorded field amplitude and Vrec = d × Erec. The “recorded voltage” Vrec is interpreted as the voltage that one needs to apply to the fiber electrodes to create an average field Erec across the core. The effect of poling is cancelled when the voltage applied is equal to Vappl = -Vrec. It is remarked that the value of Vrec is considered between the electrodes and is several times larger than the voltage that develops inside the fiber across the core only. Even before poling starts (i.e., Vrec = 0 V), Vm is finite because of the Kerr effect. The fit neglecting the Kerr term Vappl2 is significantly poorer, so both the Pockels and the Kerr effects must be taken into account in determining the phase-shift induced by the voltage pulse. The fit of the data to Eq. (1) only depends on the product χ(3) × Vrec, not on the individual values of χ(3) and Vrec, since the constant term Vrec2 is taken by the phase φ. Therefore, the value of χ(3) was measured in an independent experiment for this fiber, by applying different voltages and evaluating the parabolic phase-shift response, which depends on χ(3). The value found χ(3) = 1.62 × 10−22 m2/V2 is used as a parameter for the fitted curve. Likewise, the amplitude V0 is also treated as a parameter, equal to 2.55 mV. The remaining unknowns φ and Vrec are then allowed to vary, and the best-fit values found are 5.50 rad and 2.91 kV respectively. The fact that the recorded voltage (2.91 kV) is similar to the poling voltage (3 kV) indicates that the charges displaced during poling shield the field applied through the poling bias. In the fitting, the average field recorded across the center of the fiber core is Erec ~1.17 × 108 V/m. It is noted that in the simulations above, the fringing field resulting from the rounded electrode shape is neglected. Assuming the electrodes to be flat and infinite increases the estimated field and reduces the effective value of χ(3) by as much as 21%. Likewise, the spatial variation of the field in the core is neglected, and the field is attributed the average value it has at the core center.Equation (1) can be inverted to yield Vrec from the measured signal Vm,
where α = 3πLχ(3)/λnd2. The effective second-order optical nonlinearity is then determined using χ(2)eff = 3 χ(3)Erec. For χ(3) = 1.62 × 10−22 m2/V2 and Erec = 1.17 × 108 V/m one obtains χ(2) = 0.057 pm/V. This value is not much lower than the second-order nonlinearity induced in similar fibers by thermal poling with 3 kV bias voltage and a conventional anode/cathode electrode configuration, which amounts to 0.06 pm/V [23–25 ].4. Optical poling
The growth in time of the recorded χ(2)eff was determined using the characterization set-up described in section 2. The active fiber component was biased to 3 kV under high-power green light illumination. After a short exposure time (1-5 seconds), the visible beam was interrupted and the electrooptical effect was monitored at 1.55 µm wavelength using the Sagnac interferometer, while the active fiber was driven by 1.5 kV pulses. Real-time probing was not possible due to experimental limitations. This procedure was repeated several times. The voltage Vm measured in response to the pulses increased in a few minutes until saturation, as seen in Fig. 3 . Figure 3(a) illustrates the growth of the χ(2)eff as a function of poling time for two average powers (17 mW and 8.5 mW). For a given poling voltage, the nonlinearity recorded saturated at the same value after a few minutes exposure for both intensities, faster for the higher exposure levels. Figure 3(b) shows the growth of the recorded χ(2)for a piece of fiber poled (black trace), erased as described in section 5, and poled once more (red dots). The fiber could not be aligned to the high power laser beam without initiating the very poling effect to be monitored. Therefore, after poling saturated (after 6 minutes for the black dots data sequence) the alignment was optimized, increasing the output green power to 17 mW. After a few more minutes the nonlinearity grew to exactly the same value as in the second poling (0.051 pm/V), which did not require any realignment (red dots).
Fig. 3 (a) Increase in χ(2)eff for two average power intensities (17 mW and 8.5 mW); (b) Time evolution of χ(2)eff for consecutive poling procedures. After 6 minutes the exciting beam is realigned and subsequently the nonlinear coefficient reaches the same value as in the second poling; (c) Dependence of signal amplitude Vm on poling voltage. The Kerr effect ensures that the signal is non-zero even before poling starts. The phase-shift grows with poling voltage.
The same nonlinear coefficient measured through the voltage pulses (cf. Figure 2) was obtained numerous times (~10), indicating that the write-erase process here is reversible. This is in contrast to thermal poling when ion-exchange takes place [26]. In the regime studied here, higher poling voltages resulted in a larger phase-shift, for a given applied voltage Vappl, as discussed in the following. Figure 3(c) shows a plot of the dependence of the voltage measured Vm on the poling bias, probed by 1500 V pulses. It is seen from the data points that without poling the value of Vm is ~1 mV due to the Kerr effect. As the poling voltage is increased, the phase-shift measured becomes larger. When the poling bias approaches 3 kV, the phase-shift caused by the probe pulses is approximately π-rad. For even larger poling bias, Vπ is exceeded. The data points shown are taken for different poling events at different poling voltages. The uncertainty in the data was estimated for a poling bias 3 kV, where four measurements gave a 6 mV average value and a standard deviation 0.39 mV (see bar in Fig. 3(c)). The functional dependence of Vm on the poling voltage Vpol is unknown. Assuming that Vπ ~Vpol-n [27], the experimental data in Fig. 3(c) are fitted using the function
where V1 = 3.5 mV, V0 = 2.5 mV, Vappl = 1500 V and the constant V22 = 4.65 × 106 V2. The resulting curve for Vm is plotted as a solid red line in Fig. 3(c). With a single free parameter, the best fit value of n is n = 0.99. The adequate fit and the proximity of n to unity indicates that the phase-shift increases approximately linearly with poling voltage, i.e., Vrec is proportional to the poling bias in this 0-3 kV range. This linear dependence has been reported in experiments and simulations of thermally poled fibers, where the recorded nonlinearity is also proportional to Vpol ([23], Fig. 10(c) in [25]).5. Optical erasure
Upon exposure to high-power green light without simultaneously applying a DC bias, the photocarriers released in the glass move to cancel the charge distribution recorded previously. The erasure is very fast, being completed in a couple of minutes for the typical green powers used. It is not possible to adjust the alignment during erasure. The poled fiber was driven by the short duration 1.5 kV pulses, and the phase-shift in the Sagnac interferometer was monitored at 1.5 µm while the high-power erasing beam exposed the fiber. A film was made of the decay measured on the oscilloscope with a running clock. One example of the film sequences is shown in Fig. 4 .
Fig. 4 Video illustrating the optical erasure of the linear electrooptic effect in an optically poled fiber under high power green light illumination. Even faster erasure is observed for higher optical powers. The erased fiber can be poled renewably (Visualization 1)
Afterwards, the amplitude Vm(t) measured at different times was read scanning the movie frames. One such measurement is shown in Fig. 5(a) . Once again, Eq. (2) is used to derive the decay of Vrec(t) and of χ(2)(t). The corresponding plot is illustrated in Fig. 5(b) (black dots). The decay curve has a slightly different shape than that for Vm. Figure 5(b) also shows the decay of χ(2) fitted to a single exponential (blue curve) and to a function of the type χ(2) = (at + b)−2 (red curve), as described in [14]. The single exponential [15] gives R2 = 0.991, and reproduces the data better for longer times, whereas the quadratic function fits the data better at earlier times and gives R = 0.993. Neither fit seems to fully account for all details of the erasure process.
Fig. 5 (a) Decrease of measured signal Vm from Sagnac interferometer; (b) Corresponding erasure of the effective χ(2) (black dots). Two fitting curves are shown. The blue line indicates an exponential decay where fit is poor for early times, and the red curve follows the function (at + b)−2 [14], which deviates from the data for longer times. (c) Decay of χ(2) under green light exposure plotted on a semi-log scale, with the fitting curves and data from Fig. 5(b).
It is noted that a single exponential decay in time is governed by a rate equation of the type dχ(2)/dt = -a[χ(2)], whereas the decay described in [14] is written as dχ(2)/dt = -a[χ(2)]2. An attempt was also made to determine the coefficient n that lead to a best fit to the data using the function dχ(2)/dt = -a[χ(2)]n. The results from this procedure for four decay curves was inconclusive. The values of n found varied significantly without increasing R2 towards unity. It is possible that Eq. (2) does not fully describe the physical processes involved here, even if the fits shown in Fig. 5(b) and 5(c) may look acceptable. For example, a double-exponential decay with two time-constants gives excellent fit to the data in Fig. 5(b). This could indicate that two types of traps (one deep and one shallow) may be involved and are needed to describe optical erasure. Alternatively, it is possible that incorrect setting using the polarization control leads to erroneous values in the phase used in Eq. (2), which becomes particularly sensitive at lower signal amplitudes. This issue could not be resolved here.
6. Electric potential and field distribution in optical poling
In contrast to thermal poling where the mobile charges move from the anode to the cathode, in optical poling charges can only move where they are rendered mobile by the high-power green light excitation, i.e., in the fiber core. Therefore, the field and potential distribution in the present case is different from fibers poled thermally [25]. Figure 6 shows a numerical simulation using Comsol Multiphysics of the expected potential and electric field distributions in fibers poled optically. Poisson’s equation was solved before green light exposure with the poling bias of 3 kV applied to the fiber. The potential and electric field distributions are illustrated in Figs. 6(a) and 6(b), respectively, and the values along a horizontal line crossing the center of the core is shown in Fig. 6(c). The potential varies approximately linearly from 3 kV on the anode to zero on the cathode. The field is relatively uniform in the core vicinity at a value ~1.1 × 108 V/m, a little under the applied voltage divided by the electrode separation (1.17 × 108 V/m). The effect of the electrode roundness is quite apparent near the electrodes, where the field grows significantly. As high-power green light excites photocarriers, these drift towards the electrodes. The carriers are trapped near the core-cladding interface where the optical intensity is much weaker. The poling process saturates when the displaced charges cancel the external field. Here it was assumed that both electrons and holes move to the edges of the core. The charge concentration accumulating was assumed to be cosinusoidal, reflecting the extent of the area where the carriers are created (maximum at the center, zero at the poles of the circular core, positive on the right side of the core and negative on the left). Figures 6(d) and 6(e) show a 2D map of the potential and electric field when shielding is complete. The inset in Fig. 6(e) is a magnified view of the region between electrodes. The field is nearly zero and the potential quite uniform across the core, as seen in Fig. 6(f). The surface charge concentration needed to cancel the field here was found to be 0.00745 C/m2. This value corresponds to a positive and negative charge 1.09 × 10−8 C stored over the integration area 1.45 × 10−6 m2 (core diameter × 0.25 m). If one calculates the effective capacitance through Q = CV where the voltage across the core is 628 V (see Fig. 5 (i)), one finds C = 17.3 pF. For comparison, the less accurate parallel-plate capacitor model using C = εrε0A/d, where the relative dielectric constant is 3.8, gives a capacitance 8.5 pF. Attempts to measure the small current during poling failed. Figures 6(g) and 6(h) show an expanded view of the core region when poling ceases. Here it is assumed that the illumination has been interrupted, the voltage bias has been removed, and that the electrodes are grounded through an external circuit of equivalent resistance much lower than inside the glass fiber, which is several GΩ. It is seen that the cosinusoidal charge concentration creates a dipole [Fig. 6(g)] which gives rise to a uniform field in the core [Fig. 6(h)]. The map of the field and potential in Fig. 6(i) shows a linear potential across the core and a uniform field ~1.1 × 108 V/m, reversed in sign from the poling field. Interestingly, in contrast to thermal poling of thin samples [28] the presence of both positive and negative charges causes the field to be nearly zero on the electrode surfaces without necessarily attracting a large amount of new charge to cancel the field inside the metal [29].
Fig. 6 Spatial distribution of electrical potential (top row), electric field (middle row) and potential (blue) and field magnitude (red) along a horizontal line through the center of the core (bottom row). (a-c) before poling; (d-f) after poling is completed, the green excitation is switched-off but the high voltage is still applied to the electrodes; and (g-i) after the high voltage bias is switched off and the fiber is in steady-state with grounded electrodes.
7. Discussion
Inducing an uniform second order nonlinearity in fibers by optical poling, as demonstrated here, differs from thermal poling in a number of ways. In thermal poling, a small distance (few microns) between anode and core is desired because the χ(2) peaks near the anode surface. Therefore the fibers are non-symmetric (the core nearest to the anode) and the loss in the fiber with internal electrodes tends to be large. In contrast, optical poling is restricted to the core of the fiber. It is advantageous that the fiber used in optical poling has symmetric cross-section and the core distance to the electrodes can be increased to several microns. As long as the poling voltage is also increased, such low loss geometry does not lead to reduced second-order nonlinearity. Therefore, optical poling is fully compatible with fibers with standard telecom core numerical aperture and dimensions. Besides, long pieces of fiber could be poled with low loss.
In thermal poling, the amount of mobile ions available (Na+, for example) is fixed once the fiber is manufactured. In contrast, here the number of carriers released depends on the exposure dose to green light, which can be adjusted. In the regime studied in this paper, the amount of available charges from defects is in excess to those that can be driven by the poling field. The voltage bias used was limited by the experimental set-up, but it is anticipated that higher nonlinear coefficients will be reported in the near future.
Charge movement ceases in poling (optical and thermal) when the new charge distribution screens the field in the material. In optical poling, the maximum recorded field is equal to the field applied across the core. In thermal poling, the recorded field can be increased by a large factor if the sample thickness is much larger than the depletion region, as is the case in bulk poling [1]. In fibers, however, the distance between electrodes is typically only twice the width of the depletion layer, and besides, one looses a factor ~2 in recorded field once the bias voltage is switched off [28,29 ]. This explains qualitatively the similarity in nonlinear coefficient recorded by these distinct poling techniques, where even the type of carrier involved is believed to be different.
One additional aspect of the optical poling regime here that differs from previous work is the total effective poling time. Charge movement only occurs together with illumination by the 100 ps laser pulses. Within the 2 minutes that it takes to reach saturation, the fiber is effectively under green light exposure for only 560 µs. Likewise, the total effective time needed for erasure due to charge recombination is also sub-millisecond.
It is interesting to consider the photocurrent under a single mode-locked pulse. Using the mobility of electrons in silica 20 cm2/V.s [30], a field 1.1 × 108 V/m and a pulse duration 100 ps one finds that electrons could move by as much as ~22 µm during a single pulse. One 100 ps pulse is thus sufficient for the electrons to reach the core-cladding boundary.
Yet another aspect that deserves attention is optical erasure. The very ability to pole a fiber under high-power green light exposure is evidence that carriers in sufficient numbers are released by the relatively high energy photons and displaced by the field. When frequency doubling short wavelengths (e.g., 1.06 µm) in a fiber poled thermally, photocarriers are created, which can move to shield the field in the core. Therefore, the effort to stabilize the conversion efficiency in thermal poling could benefit from studies trying to minimize optical poling under high voltage bias.
In conclusion, the regime of optical poling to create the electrooptical effect in optical fibers has been studied. Poling takes place at room temperature, which can add to the simplicity of the process and ruggedness of the poled devices fabricated. Optical poling may also be advantageous in soft glass fibers with high third-order nonlinear susceptibility where thermal poling may be challenging [31]. It is found that high-power green light excitation is very efficient in exciting carriers which can be displaced by a poling field. The level of second-order nonlinearity demonstrated with the fiber geometry and bias voltage used in this work is ~0.06 pm/V, weak but similar to that obtained with the same fiber poled thermally with the same bias and similar anode/cathode configuration. The distance between core and electrodes in optical poling can be used to reduce the loss. The technique thus seems to be promising in some applications where the loss is of paramount importance. Future research work should include poling at higher voltages, investigations on the thermal stability of optically poled components and the possible use of layered core structures [32] for increased nonlinearity.
Acknowledgments
All special optical fibers used in this work were fabricated at Acreo Fiberlab. The authors acknowledge the experimental help by Dr. Luciene Demenicis (IME, Rio de Janeiro). Financial support from the ADOPT Linnaeus Center in Advanced Optics and Photonics, the Swedish Research Council (VR), the European Project CHARMING (FP7-288786), the CAPES-STINT 006/12 collaboration program for international fellowships and the Brazilian Agencies CNPq and FAPERJ (Rio de Janeiro) is gratefully acknowledged. The authors also thank Prof. F. Laurell for support.
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