Efficient Poling of Electro-Optic Polymers in Thin Films and Silicon Slot Waveguides by Detachable Pyroelectric Crystals



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Pyroelectric crystals are used as a conformal and detachable electric field source to efficiently pole electro-optic (E-O) polymers in both parallel-plate (transverse) and in-plane (quasi-longitudinal) configurations. Large Pockels coefficients in poled thin films and high tunability of resonance wavelength shift in hybrid polymer silicon slot waveguide ring-resonator modulators have been achieved using this method.

Pyroelectric materials can develop surface charges and generate high electric fields through modest change of temperatures. The switchable and patternable surfaces of pyroelectric crystals and epitaxial films provide an excellent platform for studying polarization-dependent surface chemistry of molecules,1–3 phase transition,4 and wettability of liquid matter.5 Field emission from pyroelectric crystals can also create high-energy (>100 keV) charged particles, yielding cheap and compact sources for x-rays, electrons, ions, and neutrons.6–8 However, these processes are transient in nature, which involve multiple time-varying parameters of the pyroelectric materials and their interacting substances. As a result, it greatly hinders the general application of pyroelectricity for polarizing dielectric functional materials and devices.

Here, we demonstrate that the electric field generated from pyroelectric crystals can be used to efficiently generate polar order in E-O polymers.9 The commonly used approach in poling E-O polymers is to apply high electric field at the glass-transition temperature (Tg) of the polymers to align the dipolar chromophores. This process is often performed using contact poling or corona poling, in which an external voltage source is needed. Although these protocols are quite well established, there do exist some challenging problems. For example, in contact poling, severe charge injection from metal electrodes often results in large current that causes dielectric breakdown of the films.10, 11 On the other hand, corona poling is usually performed under several kilovolts, which is difficult to control the homogeneity of the poling fields. In addition, it tends to create surface damage on the poled films due to various reactive (such as ozone or nitrogen oxides) and energetic species from the corona discharge.12 These problems can strongly inhibit the efficient poling of E-O polymers and other thin film dielectric materials, especially when newly developed high μβ EO systems with high conductivity and new generation of small footprint photonic devices with complicated geometries are involved.

Pyroelectric crystals, such as lithium niobate (LN) and lithium tantalate (LT), which can generate high electric field through less invasive pyroelectric charges on insulators, offer potential solutions to these problems.13 Under the equilibrium condition, the spontaneous polarization (Ps) of pyroelectric crystals is completely balanced by the surface screening charges (σsc). Heating or cooling of these crystals develop equal but opposite charges on both polar surfaces due to the change of Ps as a function of temperatures. However, only a small fraction of these charges exists as free carriers,14 and the relaxation time of pyroelectric charges can be adjusted by modifying the dielectric structures of the system. When E-O polymer is used as a thin film dielectric, several field-dependent parameters (such as poling-induced E-O activity and absorption changes) can be quantitatively measured to help understand the electrostatics in pyroelectric systems.

Figure1 shows the schematic drawing of a bilayer laminate comprising a pyroelectric crystal and a dielectric film, where the dielectric film is deposited onto the Z+ face surface of the crystal. This system can be considered as two capacitors in parallel, and the dielectric film is the recipient medium of pyroelectric field.13, 15 Under the equilibrium condition (Figure 1A), the bulk Ps is fully compensated by the surface σsc, therefore there is no electric field within the laminate. However, when the temperature is varied, it will alter the ionic and electronic forces within the bulk crystal and cause a change of spontaneous polarization (ΔPs).

Figure 1.

Schematic illustration of pyroelectric poling. The bilayer laminate comprises a pyroelectric crystal and a dielectric film (such as E-O polymer) on the Z+ face surface of the crystal. The large closed arrows in the layer of pyroelectric crystal denote the spontaneous polarization (Ps) of pyroelectric crystals, and the thickness and length of the arrows indicate relative magnitude of Ps at different temperatures. The generation of uncompensated charges (ΔPs) through the pyroelectric effect is the source of electric field (Edi) in the dielectric thin film, and the small open arrows at the thin layer of dielectrics represent the direction of electric fields. Not to scale.

This change can be described as ΔPs = γ ΔT, where γ is the pyroelectric coefficient of the crystal and ΔT is the change of temperature. When the temperature change is fast enough, there is not enough time for charge compensation to occur, leading to uncompensated charges of ΔPs in the form of excessive polarization charges (Figure 1B) or screening charges (Figure 1C). These “static” charges are the origin of electric field (Edi) creation inside the dielectric medium. If the loss of pyroelectric charges is small, it would yield

equation image((1))

where ϵ0, ϵcr, and ϵdi are the dielectric permittivities of free space, the pyroelectric crystal and the dielectric film, respectively. Lcr and Ldi are the thickness of the crystal along the polar axis and the dielectric film, respectively.

In this idealized model, a modest temperature change (10 to 50 °C) in a LT crystal will lead to a considerably large electrostatic field in a thin film dielectric material (Figure2).16 If the ϵdi of a typical amorphous organic thin film dielectrics is assumed to be 3, the maximum achievable potential on the charged surface can be as high as 15 kV, and the effective field strength in the dielectric films can vary from 50 to 350 V/μm over a broad range of thickness (from sub-micrometer to 100 μm). This level of static electric field is adequate to align the dipoles of the NLO chromophores or polarize other dielectric materials.

Figure 2.

Electric field generation (Edi) in pyroelectric poling as a function of temperature change (ΔT), thickness (Ldi), and dielectric constant (ϵdi) of thin film dielectric materials. The Z-cut lithium tantalate (LT) is selected as the pyroelectric crystal with a thickness (Lcr) of 1.0 mm, γ of 176 μC/(m2·°C) and ϵcr of 43 with respect to Equation 1.

To verify the validity of this idealized model, several physical parameters used in the experiments need to be considered. The leakage of pyroelectric charges through both the crystal and dielectric medium can cause the exponential decay of the generated electric fields at the ratio of exp[-t/(ReqCeq)], where t is the time in seconds, Req is the equivalent resistance in ohms (Req−1 = Rcr−1 + Rdi−1), and Ceq is the total capacitance in farads (Ceq = Ccr + Cdi) of the system, respectively. Rcr and Rdi are the resistance, and Ccr and Cdi are the capacitance of the crystal and dielectric layer, respectively. In previous studies, when the recipient medium has low permittivity and high resistivity (such as gaseous molecules under high vacuum), the values of ReqCeq are approximate to RcrCcr, which gives the relaxation time of greater than 105 sec due to very high resistivity (on the order of 1015 Ω·m) of LN and LT crystals. Therefore, the leakage due to the bulk conductivities of these systems could be negligibly small over a relatively long time.14, 15

However, for amorphous π-functional materials such as E-O polymers and organic semiconductors with resistivity on the order of 109 Ω·m or less, the values of ReqCeq are nearly equal to those of RdiCdi and the relaxation time will drop dramatically to around 10−2 sec. This indicates that the majority (>90%) of the static field from Equation 1 would vanish within 0.1 sec. This analysis underscores the fundamental challenge of pyroelectric poling of E-O polymers, where the relatively low resistivity of E-O polymers provides a pathway for rapid leakage of pyroelectric charges. To solve these problems, we have carefully designed heterogeneous dielectric structures suitable for the poling experiments.

A guest-host polymer was selected for this investigation and its linear optical and E-O properties of contact-poled films are established as a reference. The measured results of E-O coefficient (r33 values), maximum absorbance, and refractive index of the contact-poled films clearly showed their dependence on the poling field strength. This provides a reliable comparison with pyroelectrically poled results. The guest-host polymer is formulated by doping 15 wt% of a dipolar phenyltetraene chromophore AJLZ53 into poly(methyl methacrylate) (PMMA).

A thin layer of gold electrode was sputtered on top of the films of doped polymer, and poling were performed at the polymer's glass transition temperature (Tg ∼ 110 °C) with an electric field (Epol) of 100 V/μm. The resistivity of the films under this poling condition is around 1.3 × 109 Ω·m. The r33 values of poled films are ∼90 pm/V at the wavelength of 1.3 μm measured by using the Teng–Man reflection technique.17, 18 The r33 values are found to be linearly proportional to the Epol at a constant r33/Epol ratio of 0.90 nm2/V2, which agrees well with the oriented gas model commonly used for poled polymers.9

The efficiency of pyroelectric poling of this standardized E-O polymer is critically dependent on: 1) the air-gap-free contact between the E-O polymer film and crystal, 2) the balanced thermal profile to provide sufficient temperature change (ΔT) for generating static electric field and orientating dipolar chromophores, and 3) the optimized dielectric structures to prevent or limit the discharge pathways. Among numerous protocols used, a multi-layered structure that can enable very efficient pyroelectric poling of polymers is shown in Figure3. A thin layer (200 nm to 400 nm) of spin-on material, poly(vinylidene fluoridetrifluoroethylene) copolymer (P(VDF-TrFE), 65/35 copolymer) or poly(4-vinylphenol) (PVP) is inserted between ITO electrode and E-O polymer (1.5–3.5 μm thick) as a barrier.

Figure 3.

The schematic drawings of multi-layered structures for pyroelectric poling of guest-host E-O polymers in the parallel-plate (transverse) design: A) unpoled films; B) poled films. The ellipses in the layer of E-O polymer represent the chromophores with the arrows directed along the chromophoric dipole moments. Note that the PDMS buffer layer provides the soft contact lamination for poling, and the poled films can be lifted off from the crystal for linear optical and E-O measurements. Not to scale.

To have a better lamination between the E-O polymer films and the crystal, an ultra-thin layer (70 nm) of polydimethylsiloxane (PDMS) elastomer is spin-coated onto both E-O polymer film and the Z+ surface of LT (or LN) crystal, and cured at 70 °C for 3 h. The optical grade Z-cut LT and LN crystals (size, 15 mm × 15 mm; height, 1.0mm) are used. The Z+ axis is defined as the direction of out-of-the-Z-surface that becomes positive upon cooling. Initially, the crystal flake is brought to the central area of E-O polymer film on ITO slides (size, 25.4 mm × 25.4 mm), and a wetting front propagates naturally across the sample, until the entire surface of the crystal is in gap-free contact with the polymer film.

Such a soft lamination is critical for pyroelectric poling, and the polymer film and the crystal flake can be separated easily from each other after poling. This protocol provides great convenience for characterizing linear optical and E-O properties of the samples. The Z surface and ITO electrode are grounded to complete the pre-poling preparation of samples.

The samples are initially inserted into a hot stage, heated to ∼120 °C and held for 10 min. The hot stage is digitally controlled and monitored by a central processor. The 10-min annealing step is to allow the screening charge and spontaneous polarization (Ps) of LT or LN crystal to reach a new equilibrium at elevated temperatures. Then the heating power is turned off and the hot stage is opened, exposing the whole system to the nitrogen atmosphere at ambient temperature. During the temperature change from 120 to 100 °C, the pyroelectric poling is expected to orient the chromophore dipoles in the polymer. This monotonic cooling protocol is necessary to provide large ΔT, and generate a steady and strong static electric field for poling.

After the samples were cooled to RT, the crystal flake is removed, and the residual PDMS on E-O films can be readily removed with isopropyl alcohol, leaving the stand-alone poled E-O films ready for characterization. The voltage drop to the stack of AJLZ53/PMMA was estimated using Equation 1 because it is difficult to measure directly. Any external measurement circuit added will act as an extra leakage pathway to affect the screening of in situ generated pyroelectric charges (on the level of 0.1 μC/cm2).

As shown in Table1, very high efficiency of pyroelectric field generation (90% to 100%) could be achieved compared to those obtained from conventional poling. The highest field strength (Etheo) can be estimated from Equation 1. The triple-layered structure of PDMS/E-O polymer/barrier can be considered as three capacitors linked in series. The change in temperature is defined as ΔT = Tmax–100 °C, where Tmax is the highest applied temperature. The lowest limit we choose here is 10 °C lower than the DSC measured Tg (110 °C) of this polymer composite. It is empirically selected as the lowest limit since the experience from contact poling suggests chromophore cannot rotate efficiently under 100 °C in this time scale. During pyroelectric poling, the electric field will continue to increase as we cool the system down below 100 °C, but further chromophore rotation is literally forbidden under the current experiment condition. With the ΔT varied between 20 and 30 °C, the Etheo of pyroelectric poling is around 75–124 V/μm for LT and 35–58 V/μm for LN, respectively.

Table 1. Summary of pyroelectric poling for the E-O polymer AJLZ53/PMMA.
Sample Entriesa)Barrier Layer (thickness)CrystalΔT [°C]b)r33 [pm/V]d)Eequiv [V/μm]f)Φe)Etheo [V/μm]c)Eequiv/Etheo [×100%]
  • a)

    a)Sample configuration is illustrated in Figure3;

  • b)

    b)ΔT = Tmax–100, where Tmax is the highest applied temperature, and 100 is selected as the lowest limit;

  • c)

    c)Etheo is calculated by the derived electrostatic analysis from equation 1, parameters being used for LT: Lcr of 1.0 mm, γ of 176 μC/(m2·°C) and ϵcr of 43; and for LN: Lcr of 1.0 mm, γ of 83 μC/(m2·°C) and ϵcr of 28 [Ref. 16];

  • d)

    d)r33 values are measured by Teng-Man reflection at 1.3 μm, and Veo is the portion of the total modulation voltage (Vmod) that drops across the E-O polymer. It is corrected by the model of two capacitors in series, Veo = Vmodϵbl/(ϵbl + ϵeoLbl/Leo), where ϵeo and ϵbl are the ambient temperature dielectric constant at 1 kHz, and Leo and Lbl are the thicknesses of E-O polymer and barrier layer, respectively;

  • e)

    e)Φ is the order parameters of poled samples, which is described as Φ = 1 − A/A0, where A0 and A are the integral absorbance for the unpoled and poled films at normal incidence;

  • f)

    f)Eequiv is the effective electric field strength of pyroelectric poling.

1PVP (200 nm)LT1560670.0587589%
2PVP (200 nm)LT2081900.0859991%
3PVP (200 nm)LT2578870.07412470%
4P(VDF-TrFE) (360 nm)LT155864-7585%
5P(VDF-TrFE) (360 nm)LT2078870.0769988%
7PVP (200 nm)LN2042470.03047100%

The actual field drop across the polymer films during pyroelectric poling can be estimated from their r33 values using the approximated r33/Epol ratio of 0.9 nm2/V2. The use of this simple and quantitative approach can avoid complicated local-field corrections. Furthermore, the interaction between the dipoles and the poling field is proportional to the induced absorption spectra changes of poled films.19 Through these systematic analyses, the Eequiv is calculated, and the efficiency of electric field generation through pyroelectric poling is determined as the ratio between Eequiv and Etheo. The field strength of pyroelectric poling is as high as 90 V/μm for LT and 47 V/μm for LN, which is linearly proportional to the γ values of two crystals, respectively. As a result, very high Eequiv/Etheo ratios (85% − 100%) and relatively large r33 values (up to 81 pm/V at the wavelength of 1.3 μm) were obtained for uniformly poled films. Also worth noting is that we observe relatively small r33 from samples poled by the LN crystals, but the electric field harvest rate from LN crystals is high (∼100%). The low r33 is mainly caused by the relatively small γ of the LN crystal, which is 83 μC/(m2·°C), or 47% of the LT crystal. Thus we focused most of our studies on the LT samples.

This study demonstrates the first efficient pyroelectric poling of E-O polymers without using an external voltage source. Due to the transient nature of pyroelectric charges, the insertion of both PDMS and a barrier layer (PVP or P(VDF-TrFE)) is necessary to prevent charges from leaking through the E-O polymer, which has a relatively low resistivity. This can be exemplified by comparing the poling efficiency between triple-layered (entries 1-5 and 7, Table 1) and double-layered samples (entries 6 and 8, Table 1). In addition to providing soft contact lamination, PDMS also functions as an insulating dielectric with stable electrical properties over a wide range of temperatures,20 which is one of the key factors in maintaining durability of pyroelectric charges on the Z+ face of crystals during poling.

Equally important, the insertion of a barrier layer (PVP or P(VDF-TrFE)) between the E-O polymer and ITO on the other side is also needed in order to stabilize the pyroelectric charges from the Z face of crystals. Although the resistivity of PVP and P(VDF-TrFE) are comparable to that of AJLZ53/PMMA,21, 22 significant charge trapping is expected at the interfaces between the adjacent dielectric layers following the Maxwell-Wagner polarization process,23 which prevent charges from leaking through the polar surfaces of pyroelectric crystals. It should be mentioned that the triple-layered structure of pyroelectric poling is generally applicable to the poling of conventional waveguide devices where E-O polymers are usually poled in the parallel-plate (transverse) configuration.24

To investigate the feasibility of in-plane pyroelectric poling, we select the same device configuration in a silicon-polymer hybrid slot waveguide ring-resonator modulator reported earlier (Figure4A).25 The hybrid slot waveguide devices are expected to be one of the key components that will enable high-speed optical modulation with low driven voltages and small footprints.26, 27 In this study, the geometry of the strip-loaded slot waveguide utilized for the modulator consists of 230 nm wide arms, and a 200 nm slot width. The ring resonators constructed out of this waveguide possess a bend radius of 60 μm.

Figure 4.

Pyroelectric poling of EO polymers in hybrid E-O polymer silicon slot waveguide ring-resonator modulators: A) dark field optical microscopy image of the device; B) the partial cutaway view illustration of heterogeneous dielectric structures. A quasi-longitudinal polarization of the EO polymer is induced across the gap of two silicon slots, and the details of the hybrid structures are simplified to highlight the principal dielectric materials and electrical contact pads in the system for electrostatics analysis; C) the cross-sectional side view illustration of heterogeneous dielectric structures. The middle arrow in the silicon slot denotes the direction of electric fields within the slot during pyroelectric poling. Not to scale.

To compare with conventional poling, a reference device was poled at 100 V/μm across the slot by applying the poling voltage to the central pad (pad 2) and holding the outer two pads (pad 1) as ground. The DC tunability of the resonance wavelength device was determined to be 16.5 ± 0.6 pm/V by measuring transmission as a function of wavelength with the device biased at several DC voltages. This level of tunability is substantial to quantify the r33 values of E-O films that were poled at the in-plane geometry. The implied in-slot r33 value of 19 pm/V at 1.55 μm as compared to the peak value of 60 pm/V from contact-poled thin films, indicating low poling efficiency of the polymer in slot waveguides.25

In order to create the in-plane polarization of E-O polymers across the slot by using Z-cut LT crystal, a heterogeneous structure of dielectrics has been fabricated (Figure 4B and 4C). The chip is initially coated with a micron-thick layer of AJLZ53/PMMA, and the material was cleared from the central pad 2 using a laser ablation system, leaving the bare area that is re-coated with PDMS. The thickness of PDMS is controlled to be slightly thicker than that of E-O polymer, which provides the soft-contact lamination with the Z+ surface of a LT crystal. A secondary LT crystal is laminated at the bottom Z surface with an ultrathin spin-on PDMS layer. With the insertion of relatively thick (∼1 mm) SOI wafer, such a sandwiched structure between two crystals can generate higher effective field strength during pyroelectric poling than using a single crystal, while keeping the design of photonic dies unchanged. It also removes the potential complications of using the configured probe to ground one of the pads and adding an extra dielectric layer to the slot, which are very difficult to carry out in the 1 cm × 2 cm photonic die containing thousands of components.28 The poling of the stack follows the same protocol that was used for poling thin film samples. The in-plane poling of E-O polymer across the slot is induced by the potential difference between two pads, due to the difference in dielectric constants between PDMS (2.86) and E-O polymer (∼4.0).

To estimate the field strength of pyroelectric poling across the slot, we assume that the generated pyroelectric charges do not flow on the surfaces of LT crystals due to its high resistivity. The electric field in the design of heterogeneous dielectrics can be calculated layer by layer in each region (see Supplementary Information). The electric field from the grounded top surface to the pad is integrated to give the electric potentials on pad 1 and pad 2, respectively, resulting in a potential difference of 29 V across the 200 nm slot and electric field strength of 145 V/μm through the pyroelectric poling.

After pyroelectric poling and separation of the die from the LT crystal, the device shows a DC resonance wavelength tunability of 25 pm/V. This result is 60% higher than those obtained from contact-poled devices and it exceeds the best value reported for depletion-based ring modulators.29 The device has a 6 dB electrical bandwidth at around 800 MHz, which is the conclusive evidence of the E-O modulation for enhanced tunability of slot waveguides. The improved device performance and high electric field strength observed in this study indicate the great promises of using pyroelectric poling to introduce the in-plane polarization of E-O polymers that are essential to various designs of hybrid photonic devices.

In summary, we demonstrate a novel process using surface-modified LT and LN crystals as an effective conformal and detachable electric field source for efficient poling of E-O polymers. The employment of this approach not only helps to avoid the severe leakage current associated with conventional poling, but also provides poled devices with better uniformity and processibility. Through the modest temperature changes of pyroelectric crystals and careful design of heterogeneous dielectric systems, very large electric fields (50–350 V/μm) can be generated in both transverse and longitudinal configurations. More importantly, these high electric fields can be applied to amorphous dielectric films with a broad thickness variation. Considering that the polar surfaces of pyroelectric crystals are patternable and switchable, we expect that the electric field generated from pyroelectrics can be used to greatly facilitate the development of polarization-dependent functional materials and devices.

Experimental Section

Materials and Methods: All the polymers in this study were used as received without further purification: copolymer P(VDF-TrFE) (65:35, Solvay), PMMA (Aldrich 445746), poly(4-vinylphenol) (Aldrich 436224), and PDMS (Sylgard 184, Dow Corning). The E-O polymers used in this study is a guest-host system formulated by doping 15 wt% of dipolar phenyltetraene chromophore AJLZ53 into poly(methyl methacrylate) (PMMA). To formulate the E-O polymer, AJLZ53 was mixed with PMMA (Aldrich) in chlorobenzene at the 15wt% of chromophore loading to formulate the solution with the solid content of 10 wt%. The solution was filtered through a 0.2-μm poly(tetrafluoroethylene) (PTFE) filter and spin-coated onto the ITO glass substrates with or without barrier layers. The E-O films were baked overnight at 60 °C under vacuum to completely remove the residual solvent, leading to high optical quality films with a thickness of 2 to 3 μm. The procedure of coating the barrier layer onto ITO substrates is described in the following, respectively. The PVP barrier layer was prepared by spin-coating a 7 wt% cyclopentanone solution of the polymer onto ITO substrates at the spin speed of 2000 to 3000 rounds per minute (rpm). These films were soft baked at 65 °C for 10 minutes, followed by hard baking at 110 °C for 20 minutes, giving a thin layer (∼200 nm, measured by Dektek 3030 surface profiler) of PVP on ITO substrates. To prepare the P(VDF-TrFE) barrier layer, 7.5 wt% cyclohexanone solution was spin-coated onto ITO at the speed of 4k rpm. The films were baked at 65 °C for 10 minutes, followed by hard baking at 135 °C in vacuum oven for 1 hour. The resulting films have a thickness around 360 nm.

The LT and LN crystals used in this study were all 1 mm thick Z-cut flakes with the polar axis pre-determined. Prior to use, these crystals were cleaned by sequential sonication in soap solution, acetone and isopropyl alcohol, followed by 10-minute plasma treatment. Before performing pyroelectric poling, a 1:100 (by volume) hexane solution of PDMS was spin-coated onto the surface at of both the E-O polymer films and the crystals. After being cured at 70 °C for 3 hours, a ∼70 nm thin layer of PDMS elastomer was formed.

Characterization of E-O Polymer Films: The Pockels’ coefficients of poled AJLZ53/PMMA films were measured by Teng-Man reflection technique. The refractive indices and thicknesses of E-O films were measured by Metricon 2010 prism coupler. The UV-vis-NIR absorption of the poled polymer films were taken on a Perkin-Elmer Lambda 9 spectrophotometer. The absorption spectra of poled films were measured after removing the gold electrodes by KI/I2 gold etchant. These films were annealed at 110 °C for 5 minutes, which completely de-poled the sample, and then re-measured to give the spectra of unpoled films for comparison. The glass transition temperature of the E-O polymer was determined by analysis of differential scanning calorimeter (DSC), which was conducted in a sealed pan by a TA instruments DSC 2010 with a heating rate of 10 °C/min under the nitrogen atmosphere.

DC and RF Measurements of Silicon-Polymer Hybrid Slot Waveguide Ring-Resonator Modulator: The DC tunability of the device was determined by measuring transmission as a function of wavelength (around 1571 nm) with the device biased at several DC voltages, using a low-speed optical power detector. This was done in a non-sequential fashion to exclude thermal drift as the cause of the peak shifting behavior. High-frequency measurements were taken with a high frequency avalanche photodiode (APD). The optical wavelength of the ring is biased at the location of the steepest slope in the resonator wavelength spectrum and the drive signal was kept sufficiently small to ensure a linear response of the device. The ratio of the system detected RF power to the input RF power is used to measure the RF performance of the device. The S21 parameter relating the output to the input is indicating a 6 dB roll-off at around 800 MHz. This point corresponds to the half-power in the electro-optic response of the device and is a standard measure of the RF bandwidth.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.


The authors acknowledge financial support from the National Science Foundation (NSF-STC Program under Agreement Number DMR-0120967), Office of Naval Research (ONR), Air Force Office of Scientific Research (AFOSR) and the Boeing-Johnson Foundation.