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Abstract
Electrical corona discharge is employed in this work to deposit ions on the surface of an optical fiber, creating a strong electric field that is used for poling. Green laser light propagating in the core frees photocarriers that are displaced by the poling field. The technique presented can induce a higher optical nonlinearity than previously obtained in traditional optical poling with internal metal electrodes. To date, a maximum second order nonlinearity 0.13 pm/V has been achieved for a 15 kV corona discharge bias.
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1. Introduction
Silicate fibers do not exhibit a second-order optical nonlinearity because of the symmetry of the medium. Only a quadratic field dependence of the refractive index is present due to the Kerr effect. Poling can be used to induce a linear index dependence (Pockels effect), by breaking the glass symmetry [1,2]. In poling, a strong and temporary electric field is established inside the silicate fiber while carriers are made mobile using external excitation such as heat or visible radiation. The electric field displaces the mobile carriers, and when the external excitation is removed, the new charge distribution freezes. This gives rise to an electric field recorded in the fiber, which becomes an electret.
Thermal poling is the most widely used technique to pole fibers with internal electrodes, exploiting the displacement of cations such as Na+ from the anode(s) at high temperature [3–6]. The nonlinearity is induced adjacent to the anode, and the interaction of the optical field with the metal leads to loss in poled electrooptic fiber components. Another fiber poling technique used is optical poling [7–10], where photocarriers in the core are made mobile using short-wavelength light as excitation (e.g., UV, blue or green radiation). Strong poling fields are required to separate the photocarriers, and the maximum field recorded equals the poling field [9]. As a consequence, the induced nonlinearity obtained by optical poling is a few times lower than obtained by thermal poling. However, in optical poling the free charges are created primarily in the core of the fiber, regardless of where the electrodes are and how distant they are from the core (only the poling field strength matters). This makes it possible to draw fibers from drilled conventional single mode preforms with holes far from the core. Except for the holes, the fiber cross-section and doping are identical to standard telecom fiber (STF), resulting in devices that are easily integrated to available optical components. This opens the doors to lower loss, active devices, enabling applications in quantum optics, sensing and intra-cavity fiber lasers, where the loss can play a critical role. It is found that the higher the field established during optical poling, the higher the recorded field and the higher the linear electro-optic effect induced [9]. A typical value of the second order nonlinear coefficient obtained with optical poling in fibers is χ(2) ≈ 0.05 pm/V [8] and the highest value our group achieved with green light excitation was 0.1 pm/V [9].
Poling has improved over the years, and numerous electrodes configurations have been evaluated [11–14]. Traditionally, a parallel-plate anode-cathode configuration is used with fibers, but corona discharge has been employed for planar waveguides [15,16] and more frequently with nonlinear polymers [17–19]. In the configuration here, the corona discharge from a high voltage tungsten wire is used to create the poling field, through the deposition of ions on the fiber surface. The advantage of using a non-physically connected electrode is that it may help circumvent electric breakdown through the material. Corona poling has not been previously explored with optical fibers or fiber devices, subject of this work. This technique is demonstrated to be a possible strategy to increase the nonlinearity for low loss poled fiber devices.
2. Background
2.1 Theory
The refractive index of a transparent dielectric, under the influence of an electric field, can be written as:
Clearly, the higher the recorded field, the higher the effective second order nonlinearity. In an electrooptic fiber, the increase of the refractive index due to the electric field adds a phase shift to the optical wave guided in the fiber, expressed as:
where L is the optical path and λ is the wavelength used. If an interferometer is used to measure the phase change, the intensity of the transmitted light It is: where Iin is the input light intensity. With a poled fiber in one arm of the interferometer, the transmitted intensity from Eq. (2), (4) and (5), can be rewritten as:2.2 Principle
The main challenge addressed here is, without incurring in loss due to light-metal interaction, to increase the nonlinearity induced by poling with green light excitation. To this end, the increase in recorded field with poling voltage is exploited [21]. We remark that unlike in thermal poling, here the field applied across the core to displace photocarriers needs to be high [9]. Electrical breakdown (arcing) between internal fiber electrodes normally sets a limit to the highest bias that can be used in practice, and consequently limits the nonlinearity induced. Very high current supplied by a low resistance metal electrodes can flow through weak points in the fiber and result in catastrophic breakdown. The technique presented here makes use of the electrostatic deposition of charge on the non-conductive surface of the fiber to create a strong field across the fiber core. The release of distributed charges from the fiber surface is always slow, limiting the current flowing through any potentially weaker point along the fiber, where damage may initiate. Therefore, the absence of a physical electrode on the fiber surface makes it difficult for a nanosecond high-current discharge to take place, protecting the fiber from hard electrical breakdown.
Corona discharge is used to supply the charge to the fiber surface. A thin wire at high voltage bias ionizes the air in the neighborhood of the fiber. Both positive and negative bias have been attempted successfully. One of the two internal electrodes is electrically grounded while the second one is left at a floating potential. The ions in air are attracted to the grounded electrode, migrating towards the fiber. The ionic charge finds an impermeable barrier consisting of the primary coating and much of the glass cladding, and is not able to reach the electrode, depositing instead on the outer fiber surface. The ionized air behaves as a finite conductance resistor, through which a distributed capacitor - the fiber with one grounded electrode - charges. Ionic migration ceases when the potential on the fiber surface nearly equals the fine wire bias. At this point in time, the outer surface of the fiber is at approximately the same potential as the corona voltage bias. It is found that voltage levels higher than previously used with direct bias of the internal electrodes are manageable with such a configuration.
The physics and chemistry of corona, the molecular subproducts created, the air resistivity and the electrical characteristics of the discharge depend on many parameters. These include the sign of the voltage bias, geometrical features such as the diameter of the wire and its distance to the fiber, and air humidity and its exact composition. COMSOL simulations of corona discharge using the plasma module reveal a ∼20% reduction of the voltage that develops on the fiber surface as compared to the voltage bias applied to the tungsten wire [22]. This reduction was considered acceptable and not studied further in the present paper.
2.3 Poling field simulation
A numerical study was made with COMSOL Multiphysics software to calculate the electric field and potential inside the fiber using Poisson’s equation due to the presence of corona discharge. This simulation is used to determine the poling field in the absence of free carriers inside the fiber. The ions are assumed to deposit uniformly on the fiber’s surface. One electrode is grounded, and the other one left at a floating potential. The numerical study reproduces the fiber used in the experiments, which had an 8-µm core and two symmetrically located electrodes of 32 µm in diameter, separated by 24.4 µm. The fiber is coated with a 12.5-µm thick layer of polyimide to minimize the distance between the deposited charges and the electrodes, as compared with a typical 62-µm thick acrylate coating, to maximize the field. The dielectric constant used for silica was 3.8, and for the polyimide coating 3.4.
The grounded electrode is represented by the letter ‘G’ in Fig. 1(a), which shows a color map of the field distribution inside the fiber when its surface is set at a uniformly distributed potential Vsurface = -15kV. Figure 1(b) shows a plot of the electric field (red, left axis) and the electric potential (blue, right axis) along a horizontal line across the center of the fiber. The field is strongest between the fiber surface and the outer side of the grounded electrode, peaking at 7.5×108 V/m. Noteworthily, grounding a single electrode and letting the other one float leads to the appearance of a strong field at the core. More than 2/3 of the voltage potential on the fiber surface appears between the internal electrodes (10.6 kV here, for 15 kV bias). This strong bias allows displacing photocarriers freed in the core by green light excitation.
Fig. 1. (a) Electric field distribution in the fiber when the surface is at -15kV potential. One electrode is electrically grounded and the other is left floating. The polyimide coating is preserved. (b) Electric field (red, left axis) and electric potential (blue, right axis) taken from a horizontal line across the center of the fiber. The electric field in the core is Ecore ∼3.9×108 V/m.
The modulus of the electric field in the core center is Ecore ∼3.9×108 V/m. A similar field would be created across the core with a bias voltage of 9.5 kV if both electrodes were used in a parallel-plate configuration, or 10.6 kV considering the electrode curvature correction for this fiber (η = 1.11) [20]. Fibers with internal wires are reported to have had fields applied as high as ∼109 V/m [23], although it has been difficult to bias fibers with BiSn electrodes as used here above 2×108 V/m through contacted internal electrodes without electrical breakdown [21].
Simulations were also performed of the electric field developing in the center of the core for various values of the potential on the fiber surface Vsurface. A linear dependence was found, described as:
For example, for a -25 kV potential, the field in the core center is ∼-6.5×108 V/m. The fiber length biased by corona discharge in the experiments here was shorter than the total length of fiber with internal electrodes. The fiber section with contacts was kept away from the corona discharge because better insulation was needed in the vicinity of the exposed electrodes. As a result, the uniform field between the equipotential metal electrodes was smaller than if all the fiber were exposed to corona ions. The entire fiber length is poled, but with the bias generated from the charge accumulated along only a section of the fiber [14]. From a charged capacitor point of view where Q = CV, the two sections of fiber (one exposed to corona ions, the other not) can be seen as two capacitors connected in parallel. Since one capacitor is uncharged, it does not contribute to the charge accumulation. Therefore, the total voltage that develops between the electrodes decreases, reducing the poling voltage along the entire fiber. In the experiments discussed below, as much as 1/3 of the length of fiber with electrodes was outside the poling region, reducing the poling voltage and the field in the core accordingly.
3. Experiments
The 125 µm optical fiber used in the experiments is a twin-hole polyimide coated fiber, shown in Fig. 2(a). The diameter of the holes is 32 µm and their edge-to-edge separation is 24.4 µm. The core has 8 µm, and the fiber has the same optical characteristics of a STF fiber, that is single mode at 1.55 µm and a numerical aperture of 0.12. The fiber is polyimide coated and the total diameter is 150 µm. Polyimide was chosen for coating because it can provide a thin insulating material. The electrodes are made filling the empty holes of the fiber with molten BiSn at ∼160°C, keeping the ends of the fiber free of metal for splicing [24]. When cooled to room temperature, the fiber is polished from the side and each electrode connected with thin tungsten wire, as described in [24]. The capacitance of the fiber with electrodes samples utilized in the experiments was ∼50 pF. As mentioned earlier, during the poling phase one electrode is left disconnected and the other one grounded. In later experiments, the polishing and contacting of the floating electrode was carried out only after poling to ensure the best possible insulation. Stronger poling fields were recorded by keeping the floating electrode enclosed inside the fiber without a connection while poling.
Fig. 2. (a) Cross section of fiber used in the experiments. The polyimide coating represented in dashed yellow gives a total diameter of 150 µm. (b) Experimental setup using corona discharge to charge the fiber during poling. One fiber electrode was grounded and the other was left at floating potential. (c) Photo of the set-up with green light exciting the fiber and corona discharge ionizing the air.
For the experiments, the fiber was positioned parallel to a 20-µm diameter tungsten wire, 9.5 cm apart from it, as schematically shown in Fig. 2(b). Two 2-cm thick acrylic legs represented in gray with small holes supported the fiber with electrodes and the tungsten wire. When biased with high voltage, the tungsten wire ionizes the air, creating the characteristic blue light of corona discharge seen in the photo in Fig. 2(c). The length of the wire was 37 cm, comprised entirely between the acrylic legs.
The experiment was kept inside a transparent acrylic enclosure for safety and to limit the volume of ionized air. Air humidity was ∼26%. Before green illumination the high voltage was applied to the wire, ionizing the air in the enclosure for ∼20 minutes. This was sufficient to saturate the charging process according to the experiments shown below. To pole the fiber optically, green light from a frequency doubled Q-switched (3.2 kHz), and mode-locked Nd:YAG laser was launched into the fiber, and two-photon excitation exploited to free photocarriers [25]. The infrared radiation from the laser beam was removed with a KG5 filter and a dichroic mirror. The average output power coupled into the fiber was between 15-20 mW. Details of optically poling fibers with a Nd:YAG laser can be found in [9]. After a ∼20 min poling time, the light from the laser was blocked and subsequently the high voltage applied to the tungsten wire removed.
Various samples of fiber with electrodes were prepared for poling. Voltages ranging from -3kV to -25kV were applied to the thin tungsten wire below the fiber. Positive voltages were also tried. Since abrupt movement of the wire was sometimes observed (probably due to an unidentified discharge), negative poling was preferred. The reason why positive bias led to instability but negative bias did not is unknown.
The electrooptic effect was characterized before and after poling using a Sagnac interferometer to measure the phase shift when pulsed voltage were applied to the fiber electrodes. A HV pulse generator (Behlke GHTS 100) and a Bertan 915 HV power supply were utilized to generate the high voltage pulses. Typically, 400 ns pulses of 10 ns rise and fall time were generated.
As mentioned above, the neighborhood of the fiber contacts was kept away from the corona discharge. As schematically shown in Fig. 2(b) and mentioned above, the section of the fiber with the contacts and lying outside the acrylic legs was not facing the wire creating the ions.
4. Results
An experiment was devised to evaluate the time needed for the ions to deposit on the fiber’s surface with the corona discharge. The Kerr response of the fiber was probed in real time as the charge accumulated on its surface. The fiber with electrodes was mounted off-center in the loop of a Sagnac interferometer probed with cw light from an Erbium doped fiber amplifier at 1.55 µm. The transmission of the Sagnac loop was monitored at very low rate (1 kHz) while high voltage pulses (4kV/400 ns) were applied to only one electrode. In the absence of the pulses, during poling, this electrode was grounded through a 1 MΩ resistor. The schematic of the Sagnac interferometer for electro-optic characterization is shown in Fig. 3.
Due to the low pulse rate and short duration of the pulses, the electrode connected was at ground potential for the vast majority of time. The other electrode was left at floating potential. This unconventional electrical configuration was necessary because grounding the other electrode to apply short duration pulses would mean that neither electrode would be at a floating potential as desired for corona charging. The intensity of the transmitted light during the 400 ns pulses was monitored with a photodetector while the thin tungsten was biased continuously with as much as -25 kV. The transmitted light intensity from the interferometer changed in time with a faster time constant (seconds) and a slower one, reaching saturation after ∼ 2 minutes, as seen in Fig. 4(a). The increase in the Kerr response of the interferometer due to the strong field Ecore created by the ionic charges on the fiber surface is apparent, as well as their relative slow accumulation.
Fig. 4. (a) Normalized photodetector response when 4 kV/400 ns pulses are applied to one electrode while the other is left floating and -25 kV is used to bias the tungsten wire. (b) Normalized peak intensities when -10 kV and -25 kV are applied to the tungsten wire. The dots are experimental data. In solid are double exponential fit to the experimental points. The results show that charge saturation occurs after ∼2 minutes.
Figure 4(b), illustrates the normalized peak intensities of the pulses measured when the tungsten wire was biased with -10kV and -25kV for different charging times. They show similar time dependence. The blue (red) solid line is a double exponential fit to the experimental points when -10 (-25) kV was used.
In order to quantify the electrooptic response of devices poled with the assistance of corona discharge, both fiber electrodes were connected to the pulse source, before and after poling. The Sagnac interferometer was used. Before poling, the electrooptic effect is quadratic, and the voltage necessary to change the optical phase by π rad (Vπ) was 2.04 kV, as seen in Fig. 5(a). χ(3) is calculated using Eq. (6) when Erec = 0, n0 = 1.47, L = 0.57 m, λ = 1550 nm, d = 24.4 µm and η = 1.11. A good fit (R2 = 0.9988) is obtained, and the calculated value of the third order nonlinear coefficient for the sample used is 2.02×10−22 m2/V2, very similar to the expected value for a silica waveguide, which is 2.0×10−22 m2/V2 [20]. The blue solid line shows the result of the fitted curve, and the dots represent experimental data points.
Fig. 5. Transmitted light measured with a photodetector in the Sagnac interferometer. (a) Before poling (in blue) the electrooptic effect responds quadratically to the voltage pulses applied to the electrodes. Vπ is 2.01 kV, and the calculated χ(3) is 2.02×10−22 m2/V2. (b) After poling for 20 minutes with -15kV applied to the tungsten wire gave a Vπ = 392 V, the recorded electric field, Erec, is calculated to be 2.1×108V/m, and the induced χ(2) = 0.13 pm/V. The poling has the effect of shifting the interferometric curve to the left.
The result of poling one sample (L = 0.53 m) with -15 kV applied to the tungsten wire for 20 minutes is shown in Fig. 5(b). It shows the transmitted intensity of the Sagnac interferometer as a function of the amplitude of the 400 ns voltage pulses applied to the fiber electrodes. The red dots represent the experimental points and the red solid curve the best fit to the data.
The results show that after poling, the zero-point transmitted light intensity response of the interferometer has shifted by ∼-5.7 kV. This voltage can be regarded as the “recorded voltage”, as if the applied pulses always had an extra bias due to the new charge distribution in the fiber due to poling. This shift from the origin makes the fringes change more rapidly for a given voltage interval, i.e., the electrooptic response of the fiber increases, gaining a linear term. A frozen electric field is recorded in the fiber core and an induced linear electrooptic effect is seen, cf. Eq. (2). Vπ is measured to be 392 V which is around 5 times lower than the Vπ measured without poling. The calculated recorded electric field is Erec = 2.1×108 V/m, assuming a third order nonlinear coefficient χ(3) = 2.02×10−22 m2/V2 obtained in the previous experiment before poling, as seen in Fig. 5(a). The induced second order nonlinear coefficient, χ(2) = 0.13 pm/V, was calculated using Eq. (3).
5. Discussions and conclusion
These experimental results show that a strong field is established across the fiber core even without the existence of a physical outer electrode where the charges are deposited. This is yet another example of unusual poling configurations [11–14] which evidence that the fiber poling problem should be regarded as an electrostatic one. In the corona poling arrangement described here, high fields can be used, approaching the theoretical limit of dielectric breakdown in silica, which is hardly ever reached with metallic electrodes. The square profile of the 400 ns pulses shown in Fig. 4 is evidence of the fact that no ionic redistribution takes place during the pulses, which would otherwise have a distorted shape. This corroborates the assumption that within a very short (∼1 ns) catastrophic discharge the ions can be treated as immobile. Hindering the delivery of high currents in ∼1 ns that could discharge through any fiber flaws or weaker points is a good strategy to increase the nonlinearity induced and make useful electrooptical fiber components.
We demonstrated here the use of corona discharge to establish an electric field inside the fiber during optical poling. The highest second order nonlinear coefficient obtained was χ(2)= 0.13 pm/V when the recorded electric field was 2.1×108V/m, in spite of the fact that the piece of fiber with electrodes had only 2/3 of its length directly exposed to the corona charges.
The induced nonlinear coefficient is in the range of what can be obtained using thermal poling with the advantage of being low loss. Conversely, thermal poling with ionic deposition via corona discharge may be a way to further increase the nonlinearity of poled fibers.
Funding
Horizon 2020 Framework Programme (ITN-FINESSE 722509); Marcus och Amalia Wallenbergs minnesfond; Vetenskapsrådet; Office of Naval Research Global (N62909-20-1-2033).
Acknowledgements
The authors thank Åsa Claesson, Håkan Olsson, Mats Erikson and the Fiberlab group for the fibers used in the work.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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