1. Introduction

Many aerospace and telecommunications applications require greatly increased bandwidths and lower operating power for high-speed data transmission and analysis, which could, in principle, be enabled by lower power, higher speed electro-optic (EO) modulators than are currently available. One important application area requiring high-speed EO modulators with substantially lower driving power is RF photonics, which promises replacement of electrical RF transmission lines with much lighter weight, more power-efficient RF optical links. RF photonics, when fully developed, will have many application spaces, including antenna remoting, antenna beam formation, signal synthesis, frequency conversion and channelization, as well as radar and communications [1]. Another important application area that would benefit from ultra-low power EO modulators is efficient optical interconnects, which would enable next-generation microprocessors [2].

A critical performance requirement in RF photonics and optical interconnect design is that the operating power requirements of the enabling high-speed modulators be as low as possible so that minimum power semiconductor lasers can achieve efficient, near-unity RF-to-optical power conversion. For example, commercial LiNbO₃ modulators have switching voltages (also called the π-phase-shift or half-wave voltage, V_π) of 5V, an active length of L = 2cm, and an electrical terminal impedance of Z = 50Ω [3]. This means that the electrical power required to drive the modulator, given by P = V_π²/Z, is ~500mW, which is excessive in terms of electrical-to-optical signal power conversion since the semiconductor laser powers used in fiber optic communication are typically less than 10mW. Note that the required electrical power scales as (V_π)², so that there is a great advantage to reducing V_π. For example, a 5.0V→ 0.5V reduction in V_π reduces LiNbO₃ modulator driving power requirements 100-fold to 5mW, and if the total optical insertion loss is held below 6dB, a nearly one-to-one electrical-to-optical signal power conversion can be achieved with a 10mW semiconductor laser. Recently, there have been substantial advances in polymeric EO materials with r₃₃ coefficients reaching the impressive 200pm/V regime–more than 5x larger than that of LiNbO₃ [4–9]. EO modulators using these organic EO materials and conventional device structures [e.g., Fig. 1(a) ] have been reported with in-device r₃₃s from 140 - 170pm/V [11,12]. Although these devices have reached V_π = 0.66 – 1.0 V, the great potential of these new materials is not realized in conventional modulator designs, due to the large voltage drop across the thick cladding layers required to avoid metal electrode-induced optical loss. Typical interelectrode distances in these devices range from 8 - 15μm, and the corresponding active electrode lengths L_es are necessarily large, 2.4 - 3.5cm, since V_π scales inversely with L_e. However, such long active lengths limit the electrical bandwidth by increasing the RF-optical velocity mismatch and RF loss in the active region. Therefore, achieving sub-1V EO modulators with large modulation bandwidths and compact device lengths (sub-1cm) presents a daunting challenge for conventional modulator designs.

 

Fig. 1 Evolution of a conventional organic EO modulator structure to a TCO electrode-based organic EO modulator design using a side conduction geometry. (a) Conventional organic EO modulator structure having two thick waveguide cladding layers that separate the metal electrodes from the EO optical waveguide core to reduce metal-induced optical loss. (b) TCO-based modulator having a top-down conduction geometry utilizing a TCO material as the waveguide cladding layers to conduct the driving voltage directly from the metal electrodes to the EO waveguide core. This geometry is limited by the high refractive index of typical TCO materials versus that of organic EO materials. (c) TCO-based EO modulator design with a side conduction geometry utilizing a pre-etched trench structure in the bottom cladding layer to form an effective optical waveguide, and two thin TCO layers acting as bridge electrodes to laterally deliver the switching voltage to the waveguiding EO core from metal side electrodes.

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Here we report an alternative approach which builds on the attractions of these organic materials but drastically modifies the modulator design for maximum performance. This includes replacing the thick cladding layers with non-metallic transparent conducting oxide (TCO) bridge electrodes, or inserting thin TCO layers between the cladding and core layers. In both strategies, the TCO acts as a “bridge” to conduct the driving voltage from the metal transmission line directly to the EO layer. The interelectrode distance is then reduced from the thickness sum of the top cladding layer + the active layer + the bottom cladding layer, to the thickness of the active layer only.

In previous work, we briefly reported an early modulator design using side-conducting TCO electrodes, a top cladding arrangement (a horizontal multi-mode “effective” waveguide), and a low-r₃₃ organic EO material [10]. We also estimated the modulation bandwidth. In the present contribution, we now report: 1) a new, more easily fabricated “inverted rib waveguide” design with better polymer compatibility, 2) incorporation of a high-response organic EO material (AJCKL1) with a larger r₃₃ and greater thermal stability [4], 3) a comprehensive analytical model to optimize V_π , the optical insertion loss, and the modulation bandwidth based on full wave numerical simulation. 4) a new buried waveguide structure with a side conduction geometry which minimizes RF loss and velocity mismatch, yet maintains good electrical-optical confinement. The sum of these results shows that TCO electrode-based modulators combining current-generation EO polymers (r₃₃ = 100 - 200pm/V) offer V_π = 0.5V, high operation frequency potential (40-100GHz), and compact dimensions (5mm active length). Such devices should be ideal for RF photonics applications, with the compact sizes capable of on-chip integration with semiconductor lasers.

2. Voltage-size figure-of-merit enhancement using TCO modulator electrodes

The voltage-size figure-of-merit for an EO modulator is given by the product of the half-wave voltage V_π and the length L of the device [Eq. (1)], where λ is the optical wavelength, n is the

Table 1. Projected enhancement of EO modulator power-size figure-of-merit using a TCO electrode-based device versus a conventional structure. A TCO-based structure can enhance an organic EO modulator power-size figure-of-merit by 10x-100x versus a conventional device structure using the same EO material. We assume n_EO = 1.6 and Г_EO = 80%.

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3. Modulator fabrication and evaluation results

New Device Structure. To demonstrate the low V_πL potential of the present TCO electrode-based EO polymer modulators, a proof-of-concept device was fabricated. We ultilize AJCKL1 with a larger r₃₃ and better orientational thermal stability than that used in earlier work [10]. A schematic and SEM cross-section image of the straight-channel phase modulator are shown in Fig. 2(a) ; Fig. 2(b) shows the waveforms of the applied switching voltage at 1KHz and the intensity of the modulated light beam. Note the differences from the first-generation design of Fig. 2(c) [10]. The new structure in Fig. 2(a) has far better compatibility with the EO material because the optical mode confinement in horizontal direction is realized with an inverted rib waveguide, formed by pre-etching a trench in the bottom cladding layer (SiO₂) before spin-coating and poling the EO polymer layer. This strategy avoids undesirable thermal exposure in the post-poling process–fabrication of the top cladding layer (NOA74 in Fig. 2(c) by photolithography and RIE etching as in previous work [10]. The deposition of the top TCO electrode (In₂O₃) after the EO poling process can be carried out at room temperature.TCO modulator fabrication. Process steps are shown in Fig. 3 . After fabrication of the inverted rib structure on a 3μm thick SiO₂ layer on Si by standard photolithography (step 1), a 60nm In₂O₃ TCO layer was grown by Ion-Assisted Deposition (IAD) at room temperature [23] to form the bottom TCO bridge electrode (step2). A 90nm SiO₂ layer was then grown on top of the TCO layer as protective layer to reduce EO polymer breakdown during electric field poling (step 3). A 150nm gold layer was then thermally evaporated/patterned by shadow masking on the side of the bottom TCO bridge electrode to act as the bottom contact (step 4). Next, a 1.5μm EO polymer layer was spin-coated onto the substrate. The AJ-CKL1 EO polymer was formulated by doping 30 wt% of chromophore AJY02 into a low-loss, high-Tg amorphous polycarbonate (APC) host. Thus, 32.0 mg of APC and 13.7 mg of AJY02 was dissolved in 770 mg of dibromomethane, and the mixture shaken for 3 h to obtain a homogeneous solution. This solution was then filtered through a 0.2 μm pore size PTFE filter and spin-coated onto the device substrate, followed by drying under vacuum at 80°C for 0.5 h. The film thickness was adjusted to ~1.5-1.8 μm using a 1100-1600 rpm spinning speed. Under these processing conditions, the EO polymer filled the trench and formed the desired inverted rib optical waveguide structure. The refractive indices of this polymer in its unpoled form were measured with a MetriCon 2010 Prism Coupler and are estimated to be 1.693 (TE) and 1.680 (TM) at 1300 nm; and 1.661 (TE) and 1.642 (TM) at 1550 nm(step 5). The EO polymer fills the trench and forms the desired inverted rib optical waveguide structure. Next, a solution of 20 wt% poly(4-vinylphenol) (PVP) in n-propanol was spin-coated on the top of the EO layer to deposit a 1.5µm PVP film (step 6). The PVP/EO bilayer was then thoroughly dried under vacuum at 80 °C. This PVP layer is used as a sacrificial buffer for poling, and is essential to produce poled EO films with acceptable surface quality. We explored the undoped version of PVP (resistivity ~1x10¹⁰Ω*m) and a PEDOT-PSS doped version (resistivity ~1x10⁶Ω*m), to see whether the doped PVP layer might enhance the poling efficiency versus the undoped PVP layer. After the PVP layer deposition and drying, a 100nm gold poling electrode was thermally evaporated onto the PVP layer (step7). The poling voltage applied to the EO/PVP stack was ~250V-300V for the device with undoped PVP layer and 150V – 250V for the device with a doped PVP layer. The film temperature was then ramped from 60°C to 135°C at a rate of 10°C/min. The poling current increased during the temperature ramp process. The maximum current observed during poling of the EO/PVP stack was 5μA for undoped PVP (250V poling voltage), and 30μA for doped PVP (225V poling voltage). Under the same poling profile, the maximum current during the poling of the single EO layer is 170μA, which means that the PVP protective layer reduces the maximum achievable poling current.

 

Fig. 2 (a) Inverted rib waveguide structure used for the present demonstration of a TCO electrode-based organic EO modulator; and SEM cross-section image of the fabricated device; (b) Measured waveforms of the switching voltage and the detected output light intensity. The measurement was made at λ = 1.3µm, with a driving voltage frequency of 1kHz. (c) Earlier device structure from ref. [10]. (d) Mode pattern for TE / TM mode and a photo of the mode taken with a CCD camera. In the simulation, we assume n_EO = 1.68 and n_TCO = 2.0. The new structure has higher Г_EO ≥ 95% than in previous work because the top cladding layer is now air rather than NOA74. The optical mode overlapping factor in the top TCO layer, the EO layer and the bottom TCO layer for both TM and TE mode are listed. The total TCO overlapping factor is Г_TCO = 0.78% for TM mode and Г_TCO = 1.71% for TE mode.

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Fig. 3 Fabrication process for the side conduction TCO electrode-based EO modulator of Fig. 1(c).

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Once the maximum temperature is reached, the sample is slowly cooled to room temperature before terminating the voltage (step 8). After the EO poling process, the gold poling electrode was removed by wet etching and the PVP protective layer removed with ethanol (step 9). A 60nm In₂O₃ TCO layer was then grown by IAD at room temperature on top of the poled EO film to form the top TCO bridge electrode (step 10). Finally, a 150nm gold layer is thermally evaporated/patterned on top of the TCO bridge electrode to form the top metal contact (step11).Measurement of V_πL figure-of-merit. The EO phase shift was measured by converting the phase modulation to intensity modulation using a cross-polarization interference setup: input light from a 5mW 1310nm semiconductor laser was linearly polarized at + 45° to the direction of the switching electric field. The light was coupled into the straight waveguide using a 60x objective lens with a numerical aperture of 0.6. The output light from the waveguide was collected by another 60x objective lens and passed through a polarization analyzer oriented with an analyzed polarization at −45° to the direction of the switching electric field. Phase modulation was converted to intensity modulation after the analyzer. The intensity modulation is detected by a photo-detector and recorded with an oscilloscope.

For a number of devices fabricated, the observed voltage-size figure-of-merit ranged from 0.6V-cm to 0.9V-cm, after physically reasonable conversion of the directly measured V_πL to that for a push-pull geometry. We summarize details of the measurement results in Table 2 . As discussed above, for the sacrificial poling protective layer (PVP), we explored both un-doped and doped (conductive) PVPs. For each PVP formulation, we also varied the poling voltage. From Table 2 note that the device with the conductive PVP layer and higher poling voltage provides the smallest V_πL product voltage-size figure-of-merit, 0.6V-cm, which corresponds to a very low power-size figure-of-merit of 7.2mW-cm²–very close to the desired 5mW driving power in a 1.0cm long device. In our previous work, we reported V_π = 2.8V with in an 8mm straight waveguide device or V_πL = 0.75V-cm (converting to a push-pull value), with an inter-electrode distance of 1.5μm, based on a previous generation EO polymer (AJLS8/APC). While the best result of the present work is 0.56V-cm with an inter-electrode distance of 2μm (0.5μm larger than previously due to the trench in SiO₂ layer), there is an effective 45% reduction in V_πL (0.56V-cm/2μm versus 0.75V-cm/1.5μm).

Table 2. Detailed measurement results of TCO electrode-based organic EO modulators.

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Using cut-back methods, the measured waveguide loss of the present devices is ~4dB/mm for the TM mode and 8dB/mm for the TE mode, with a coupling loss of 9dB. In this work, In₂O₃ (α ~1000/cm, σ = 70S/cm) is used for both the top and bottom TCO electrodes. Since the bottom TCO layer has much larger mode overlapping factor Г_TTCO than the top TCO layer (from Fig. 2, Г_BTCO = 0.71% and Г_TTCO = 0.07% for the TM mode), the optical loss caused by the bottom In₂O₃ electrode is 10log(e^{-1000/cm*0.71%*L})/L = 3.1dB/mm and the optical loss caused by the top In₂O₃ is 0.32dB/mm, with the total TCO induced loss = 3.4dB/mm, close to the measured value. Therefore, in the new modulator structure, the waveguide loss mainly comes from the bottom TCO layer. Since the TCO induced optical loss is proportional to the product of α_TCO and Г_TCO, it can be reduced by engineering the TCO material to have a lower α_TCO, or by inserting thin buffer layers between the EO and TCO layers to reduce Г_TCO. The first method requires TCO materials development, and a systematic study of how to reduce the α_TCO while keeping a high σ_TCO during TCO deposition. This will be discussed in a later publication. In Section 3 we discuss the second strategy in detail.

4.Comprehensive modeling work for a new high speed modulator structures

In our previous work, we estimated the modulation bandwidth of the first generation TCO electrode-based organic EO modulator shown in Fig. 2(c). Although the structure is easy to fabricate and demonstrate operation at low frequencies, it is by no means optimized, especially for high speed operation, because: 1) horizontally it is a multimode optical waveguide since the lateral mode confinement is through an “effective” top cladding layer, 2) the overlapping area of the two TCO bridge electrodes must be as large as 4μm to achieve good electrical to optical mode overlapping, and this will cause a large RF loss in the TCO-EO active region, 3) the TCO layer thickness was deliberately kept thin to avoid refractive index mismatch and also to reduce the optical loss in the TCO layers. In that work, we used a 50nm thick bottom TCO electrode and a 20nm thick top TCO electrode. In the present study, we systematically analyze the interplay of half-wave voltage V_π, optical insertion loss, and modulation bandwidth. The effect of the TCO layers on the optical mode will be discussed based on a numerical simulation. We then optimize the structure to achieve better optical confinement in the EO waveguide core and lower optical mode overlapping with in the TCO layers. We also propose a new “buried waveguide” structure for high speed operation. The effect of TCO bridge electrodes on the RF loss of the EO active region, or the “TCO loading effects”, will be discussed in detail. Finally the modulation bandwidth will be predicted based on the numerical simulation results.

The optical waveguide without the two TCO electrodes is shown in Fig. 4(a) . The refractive index of the EO material n_EO is assumed to be 1.6 which is typical for organic EO polymers. To efficiently confine the optical mode, the low index polymer CYTOP with n = 1.35 (ε = 2.1) was chosen as the material for the side and bottom cladding layers. The thickness and width of the waveguide core are: d_cor = 1.3μm and w_cor = 1.2μm, so that it is a single mode waveguide in both vertical and horizontal directions. The calculated optical energy confinement factor in the waveguide core Г_EO = 83%. If r₃₃ = 150pm/V and a dual drive structure are assumed (which means the effective EO coefficient r = 2r₃₃ = 300pm/V), then V_πL = (λd_el-sep)/(n³rГ_EO) = 0.205V-cm for λ = 1.55μm, and 0.173V-cm for λ = 1.31μm, and an L = 5mm long active length yields V_π = 0.41V for λ = 1.55μm operation and 0.34V for λ = 1.31μm operation. At this point we assume that d_el-sep = d_cor which means that the two TCO electrodes directly contact the waveguide core. However, since the TCO layers will cause optical loss in the waveguide due to free carrier absorption, the design of the two electrodes is crucial to the overall device performance. Since the optical insertion loss is proportional to the product of α_TCO and Г_TCO, an effective way to reduce the optical insertion loss is by reducing Г_TCO. Later we show that, by inserting thin buffer layers between the TCO electrodes and the EO waveguide core, Г_TCO can be reduced significantly, and this strategy allows the TCO electrodes to have much higher electrical conductivity without significantly increasing the V_πL product. A higher TCO electrode electrical conductivity will greatly benefit the modulation bandwidth by reducing both the RF loss in the TCO loaded EO active region and the horizontal voltage drop along the TCO electrodes.

 

Fig. 4 (a) Buried waveguide structure and the resulting optical mode pattern. The EO waveguide core (n_EO = 1.6) is buried within two side cladding layers (n_scl = 1.35) and a bottom cladding layer (n_bcl = 1.35). d_cor = 1.3μm and W_cor = 1.2μm . The optical waveguide is single mode in both the horizontal and vertical directions. The effective refractive index n_eff = 1.467 and the TM optical mode confinement factor in the waveguide core Г_EO = 83% (b) buried waveguide with two TCO electrodes (n_TCO = 1.9) and buffer layers, and the optical mode pattern. The bottom buffer layer is 300nm thick and the top buffer layer is 100nm thick. The arrows show the direction of the E-component of the optical mode.

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To determine the required TCO electrode dimensions, we must first analyze the optical loss requirements of an EO modulator. The total loss of an optical waveguide device with TCO layers is given by: I_out/I_in = T_TCO × T_Met × T_oth, where T_TC is the optical power transmission coefficient accounting for the optical loss caused by the TCO layer alone, which can be further described by: T_TCO = exp(-α_TCoptΓ_TCL), where L is the length of TCO layer in the device (it is also the modulator interaction length) and Γ_TCO is the percentage of optical mode energy overlapping with the TCO layer (the TCO optical-mode overlapping factor). T_Met is the transmission coefficient accounting for the optical loss due to the optical mode touching the metal transmission line on both sides and is given by T_Met = exp(-α_MetL). As mentioned above, for an optimal design, we can let T_Met = T_TCO. A typical commercial LiNbO₃ EO modulator has a device optical insertion loss of less than 6 dB (< 75% loss in optical power). The typical fiber coupling loss at the input and output ports can typically be lower than 30% (1.5dB) per port, yielding a total coupling loss of less than 50% (3dB). Assuming that other propagation losses, including EO material absorption loss, total to be less than 20% (1dB), T_oth will be no less than (1 − 0.3) × (1 − 0.3) × (1 − 0.2) ≈0.4 (4dB). To achieve a similar total device insertion loss of 6 dB for our modulator design, it is desirable to keep the optical propagation loss due to the TCO and metal to be less than 40%, i.e., keep (T_TCO × T_Met) > 0.6 (less than 2.2dB) or T_TCO > 0.775 (less than 1.1dB) assuming T_TCO = T_Met, so that (T_oth × T_TCO × T_Met) will be greater than 0.25 (< 75% loss or < 6 dB total device insertion loss). For here and all examples given below, we assume an RF-optical interaction length L = 0.5 cm, so that the optical transmission T_TCO will be > 0.8 if α_TCoptΓ_TC < ln(0.8)/L = 0.22/L (for L in cm) which requires α_TCopt Γ_TCO < 0.44/cm when L = 0.5cm. Table 3 summarizes the optical loss caused by each part of the TCO electrode-based EO modulator.

Table 3. Details of the optical insertion loss caused by each modulator component

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Regarding TCO electrode composition, materials such as tin-doped indium oxide (ITO) are used widely in flat panel displays. While ITO is excellent for visible wavelength applications, it is not suitable for the 1550nm fiber-optic telecommunication wavelengths due to the high IR optical absorption. Since the modulators of interest are intended to operate at 1550nm, TCOs with low optical absorption in this region are essential. For such applications, TCOs such as undoped In₂O₃, ZnO, or CdO are more suitable due to their low optical absorption at 1300-1550nm [17–23], as given by the loss coefficient α_TCO. Besides the low loss requirement, an electrode TCO material must have a sufficiently high electrical conductivity, σ_TCO, to drive the modulator at high speed. While doping TCO materials with additional carriers increases σ_TCO, it also increases free carrier absorption at longer wavelengths, increasing α_TCO [17–24]. The electrical conductivity to optical absorption coefficient ratio, F_TCO = σ_TCO/α_TCO, is an intrinsic materials property at a given wavelength and an important TCO modulator figure-of-merit. As discussed before, the acceptable α_TCO is inversely proportional to Γ_TCO through the relationship α_TCoptΓ_TCO < 0.44 when L = 0.5cm, while σ_TCO is proportional to α_TCO when a certain F_TCO is assumed. Therefore, the optical mode overlapping factor Γ_TCO must be as small as possible to obtain as large a σ_TCO as possible. This can be achieved by either making the two TCO layers very thin, or adding thin buffer layers between the EO layer and the TCO layers. Table 4 shows the numerical simulation results for the relationship between Γ_TCO and the thicknesses of the TCO and buffer layers. The results are given by COMSOL, which is an FEM method based mode solver [26]. Here we define the optical mode overlapping factor in the bottom TCO layer to be Γ_BTCO and the optical mode overlapping factor in the top TCO layer to be Γ_TTCO. The total mode overlapping factor in the TCO layers is Γ_TCO = Γ_BTCO + Γ_TTCO. Note that if the TCO layers directly contact the EO layer, Γ_TCO is 2.9% and the corresponding α_TCopt = 15 /cm. Γ_BTCO is larger than Γ_TTCO because the refractive index top cladding layer (air) is smaller than the bottom cladding layer (CYTOP), and the optical mode is shifted towards the CYTOP side. However if there is a 300nm thick bottom buffer layer and 100nm top buffer layer in between the bottom TCO layer and the EO layer, Γ_TCO will be reduced to 0.77%, and the corresponding α_TCopt becomes 57 /cm . Here we make d_BBuff > d_TBuff to assure that Γ_BTCO ≈Γ_TTCO (i.e. separate bottom TCO layer away from the EO layer further than the top TCO layer). The thickness of the two TCO layers T_TCO is set here to 100nm. Assuming F_TCO = 1S, the corresponding σ_TCO = 57S/cm. Note that the 400nm thick buffer layer will only increase the V_π to 0.54V for λ = 1.55μm operation and to 0.44V for λ = 1.31μm operation. Later we will show that higher TCO electrode electrical conductivity will greatly reduce the RF loss and the horizontal TCO-RC voltage drop along the two TCO electrodes. Therefore we can choose d_Bbuff = 300 nm and d_Tbuff = 100nm. In Table 4 we also list the overlap integral η_overlap between the TM mode of the structure with TCO layers, and the TM mode of the structure without TCO layers, found by a commercial mode solver [27]. Here η_overlap is defined as

Table 4. Relationship between Г_TCO and the thicknesses of buffer layers. The thickness of the TCO layer T_TCO = 100nm, and here we assume λ = 1.55μm. The data is for TM mode.

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Note in Table 4 that the values of η_overlap are all close to 100% which means that the optical loss in the optical waveguide caused by the mode mismatch between the section without TCO layers and the TCO loaded section can be ignored.

In Fig. 5(b) , we show the values of n_eff and n_gopt at different optical wavelengths for the modulator structure with d_Bbuff = 300 nm and d_Tbuff = 100nm. Here n_gopt = n_opt – λ₀dn_opt/dλ. The group index optical waveguide n_gopt is found to be 1.642 at λ = 1.31μm and 1.643 at λ = 1.55μm–slightly higher than n_eff. Later in the RF simulation, n_gopt will be used to calculate the velocity mis-match. Figure 5(c) shows the relationship between Г_EO, Г_TCO, and λ. Note that Г_TCO at λ = 1.31μm is smaller than Г_TCO at λ = 1.55μm and therefore will allow the TCO layers to have a larger α_TCO. Figure 5(d) shows the relationship between α_Met (calculated from the extinction coefficient к) and W_gap. As discussed above, the metal-induced optical insertion loss is required to be <1dB. This requires that we find a W_gap at which T_Met = exp(-α_MetL) > 0.775, or α_Met < 0.44/cm when L = 5mm. In order to minimize W_gap, we first choose a large refractive index difference between the EO waveguide core (n_EO = 1.6) and the side cladding layer (n_scl = 1.35). This ensures a good horizontal mode confinement in the EO waveguide core region. Secondly, as shown in Fig. 5(a), the two metal electrodes are located on the two sides of the waveguide and the two TCO bridge electrodes extend to the top and bottom of the EO waveguide core region. The modulator will work in TM mode since its E-component is parallel to the RF electric field provided by the two TCO bridge electrodes. This arrangement also helps minimize W_gap because the TM mode has a better horizontal confinement in the EO waveguide core, compared with the TE mode case. In the numerical simulation, α_Met is found through the extinction coefficient к which is the imaginary part of the complex effective refractive index of a mode (n_c = n + iк) using the relationship: к = α_Metλ/(4π). We see from Fig. 5(d) that when W_gap > 1.6μm, α_Met is small enough (below 0.44/cm for both λ = 1.31μm and λ = 1.55μm).

 

Fig. 5 (a) Buried waveguide structure with two TCO electrodes and buffer layers. Two side copper electrodes are also included to find the metal induced optical loss coefficient α_Met. n_scl = n_bcl = 1.35. d_cor = 1.3μm, W_cor = 1.2μm, d_Bbuff = 300nm, d_Tbuff = 100nm, d_TCO = 100nm. (b) Effective refractive index and group index of the optical waveguide for TM mode c) The optical mode confinement factor in the EO waveguide core Г_EO and the optical mode overlapping factor in the two TCO layers Г_TCO = Г_BTCO + Г_TTCO, under different wavelength. d) Metal-induced optical loss coefficient α_Met versus the width of the gap W_gap.

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Before going into the details of the RF transmission line design, we first analyze the theoretical upper limit of the acceptable values of the microwave attenuation coefficient α_RF and TCO-RC voltage drop coefficient r_RC. Figure 6 shows the standard RF model for the TCO electrode-based EO modulator. An RF source launches the RF wave into the active region (a TCO bridge loaded transmission line) through a standard Z_s = 50Ω feeding transmission line. A Z_L = 50Ω termination is assumed at the end of the active region.

 

Fig. 6 Transmission line model for the TCO electrode-based EO modulator. The entrance point of the TCO loaded EO active region is defined as x = 0. The termination point is defined as x = L.

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Assuming the voltage applied to the feeding transmission line is V_appl, then the instantaneous RF voltage seen by the optical packet along the active region is given by:

Here γ_RF = α_RF + jβ_RF is the complex propagation constant of the RF wave and ω = 2πf is the angular frequency. α_RF is the microwave attenuation coefficient which accounts for the RF loss in the TCO loaded active region. β_RF is the propagation constant which determines the traveling speed of RF wave in the active region. RF reflection often happens when the characteristic impedance of the active region Z_m is not equal to Z_s and Z_L, and this is accounted for by Г_s = (Z_s-Z_m)/ (Z_s + Z_m), which is the RF reflection coefficient at the entrance of the active region, and Г_L = (Z_L-Z_m)/(Z_L + Z_m), which is the RF reflection coefficient at the termination of the active region. T = 1- Г_s is defined as the RF transmission coefficient at the entrance of the active region. Because the TCO electrodes are often thin layers with limited conductivity, the voltage they conduct to the EO waveguide core will drop below the voltage on the metal transmission line, due to the TCO-RC loading effect, especially at the high frequency. This fact is accounted for by adding an RC voltage drop coefficient: r_RC = V_EO/V_metal. The average switching voltage applied to the optical packet after it leaves the active region, is found by integrating V_eff(x,ω) along 0 to L:

Here γ_FW and γ_BW are given by γ_FW = α_RF + j (ω/c)(n_RF-n_gopt) and γ_BW = α_RF + j (ω/c)(n_RF + n_gopt).

Equation (4) gives the complete analytical model to predict how the effects of the applied voltage will change with increased frequency. Note that our model is only slightly different from the model given in [28] because here we add the TCO-RC drop factor r_RC into the model and also we define the entrance of the transmission line as x = 0.

The challenging part of designing a high-speed (3dB optical bandwidth>40GHz) TCO based organic EO modulator is to manage the RF propagation loss along the TCO loaded EO active region (denoted by α_RF) and the voltage drop along the TCO bridge electrodes (denoted by r_RC). To find the theoretical upper limit of the RF loss, we can assume perfect impedance matching between the feeding transmission line and the active region, and a perfect velocity match between the RF wave and the optical wave, by setting Z_m = Z_s = Z_L. and β_RF = ω/v_RF = ω/v_gopt (which means n_gRF = n_gopt). Later we will show that this can be achieved by carefully selecting the dielectric materials and tuning the transmission line dimensions. Then, (ω/v_gRF) − β_gRF = 0 and Eq. (4) becomes:

We can see that now the averaged effective switching voltage V _av-eff(f) is determined by two factors: one is the TCO-RC voltage drop factor r _RC(f), which is a function of frequency f, and the other is the RF decay factor (1 − e^-x)/x, in which x = α _RF(f)L. The RF decay factor is also a function of frequency f because the microwave attenuation coefficient α _RF(f) will increase with frequency f. The modulation bandwidth of an EO modulator can then be found by solving for the frequency f _BW at which the V _av-eff drops to V _appl/2 (optical 3dB bandwidth, 3dBo) or

In other words, if we have a targeted bandwidth f _BW, the requirement for α_RF(f)L is given by:

The solution of Eq. (7) is:

Here W(x) is the Lumbert W function [25]. Assuming r_RC(f_BW) = 1, or no RC voltage drop along the TCO electrodes, then α _RF(f)L = W(−2e⁻²) + 2 = 1.6, or α _RF(f) = 3.2 /cm if L = 0.5cm. Here α_RF is defined as the microwave attenuation coefficient of the electric field amplitude of the RF wave, therefore 3.2/cm corresponds to 20log(e^3.2L)/L = 27.7dB/cm. For example, if the target 3dB optical bandwidth is 40GHz, then the theoretical upper limit of α _RF(40GHz) is 3.2/cm for a device with a 5mm long active length. If the TCO-RC voltage drop along the TCO electrode factor r_RC is taken into consideration, then the upper limit of α_RF(f_BW) will be reduced to a lower value. Figure 7 shows the theoretical upper limit of α_RF(f_BW) under different r_RC values. It can been seen that if the frequency cutoff is already determined by the TCO-RC voltage drop frequency cutoff factor (e.g., when r_RC(f) ~0.5), there is little room for the RF loss, and a small α_RF(f) will push it to the cutoff (when the voltage drops to half). More importantly, when L is increased from 5mm to 2cm, the theoretical upper limit of α_RF when r_RC = 1 (no TCO-RC voltage drop effect) reduces by 4x to only 6.9dB/cm. This means the room left for RF loss shrinks with increased active length.

 

Fig. 7 Theoretical upper limit of the microwave attenuation coefficient α_RF versus r_RC under different active lengths L. Here we assume perfect impedance match and velocity match.

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In a TCO-enabled organic EO modulator, the RF loss comes from the metal transmission line and the loading effect of the TCO electrodes in the EO active region. The metal transmission line loss in the organic EO modulator structure is mainly caused by the skin-effect of the metal electrodes and can be reduced [14,16]. Assuming the RF loss from the metal transmission line to be as high as 7.7dB/cm at 40GHz, we still have 20dB/cm left for TCO-induced RF loss. The actual RF loss in the TCO electrode loaded region depends on the device structure and the TCO electrical conductivity. Later we will discuss the RF loss in detail using a specific example. Note here that the active length L plays an important role in the theoretical upper limit of the RF loss and the TCO-RC voltage drop. For example, in a conventional organic EO modulator with a typical d_el-sep = 9μm (6x larger than a TCO-based structure), the required active length L becomes 3cm, and the acceptable α_RF(f) is reduced by 6x to 0.53 /cm, or 4.63dB/cm, which is only enough for the metal transmission line loss.

Therefore, we see that the TCO electrode-based EO modulator has high speed potential (f_3dBo > 40GHz) because it can be made short (<5mm active length) while still achieving low switching voltages (V_π < 0.5V with dual drive) with currently available organic EO materials (in device r₃₃ = 150pm/V).

Now we give a specific example of an RF design based on full wave simulation to show the effect of the two TCO electrodes on the device performance and how to optimize the structures to achieve large modulation bandwidths. Figure 8 shows the proposed buried waveguide with a coplanar slot transmission line and TCO side conduction geometry. In this structure, the two parallel metallic plates to the left and right of the EO waveguide core form a high-frequency RF transmission line. In the active region, the TCO material forms “bridge electrodes” to transmit the voltage laterally from the metallic transmission line to the active EO material region.

 

Fig. 8 High frequency structure design for a TCO-electrode based organic EO modulator. The structure comprises a pair of high speed metallic transmission lines and two TCO electrodes conducting the voltage from the metallic transmission line to the EO optical waveguide core. In the numerical simulation, we use W_cor = 1.2μm, W_gap = 1.6μm, W_copper = 250μm, d_cor = 1.3μm, d_Tbuff = 100nm, d_Bbuff = 300nm, d_el-sep = d_copper = d_cor + d_Bbuff + d_Tbuff = 1.7μm, d_TCO = 100nm, d_bcl = 3μm, d_sub = 100μm, ε_EO = ε_TCO = 3, ε_scl = ε_bcl = ε_sub = 2.1. In practice, a low-k substrate is required.

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The structure is modeled using HFSS, which is a commercial finite element method (FEM) solver [29]. The simulated electric field pattern of the RF mode in the TCO-EO core region is shown in Fig. 8. It can be seen that in the EO waveguide core region, the RF electric field is perpendicular to the TCO bridge electrodes and the electric field strength is uniform across the entire EO waveguide core region. This ensures a good RF electric field - optical mode overlapping in the EO waveguide core. Figure 9 shows the numerical simulation results of the RF loss, the TCO-RC voltage drop factor r_RC, the characteristic impedance Z₀, and the RF transmission line effective group index n_gRF. Figure 9(a) and 9(b) show that the structure is optimized so that Z₀ is tuned to match 50Ω and the n_gRF also matches n_gopt (~1.64). This means that the effects of the impedance mismatch and RF-optical velocity mismatch are minimized. From Fig. 9(c) and 9(d) we can see that α_RF and r_RC depend on the electrical conductivity of the TCO electrodes which is in turn dependent on the TCO material figure of merit F_TCO = σ_TCO/α_TCO where α_TCO = 57/cm is determined by the optical insertion loss requirement discussed before. We explored the F_TCO = 0S, 0.2S, 0.5S and 1S cases and the corresponding σ_TCO = 0S/cm, 11.4S/cm, 28.5S/cm and 57S/cm, cases, respectively. The curve with σ_TCO = 0S/cm represents the case in which only pure copper coplanar slot transmission lines are present. Note that α_RF in this case can be quite small. At 40GHz, the predicted α_RF in this situation is as low as 0.1328/cm or 1.15dB/cm. However, when the two TCO electrodes are loaded in the active region, α_RF will increase significantly. Note from Fig. 9(c) that when σ_TCO = 11.4S/cm or F_TCO = 0.2S, α_RF at 40GHz becomes 1.0898/cm, or 9.466dB/cm. This is because the RF wave interacts with the two TCO electrodes which have only finite electrical conductivity. Although α_RF is significantly higher than the value when there are only pure metallic transmission lines (0.1328/cm or 1.15dB/cm), it is still below the theoretical upper limit because in this case r_RC = 0.81718 [Fig. 9(d)] and from Fig. 7 we find that the corresponding theoretical upper limit of α_RF at 40GHz is 2.15/cm or 18.68dB/cm. Note that the structure is already optimized to achieve near impedance and velocity match. More importantly, with TCO materials having larger F_TCO values (0.5S or 1S), σ_TCO can be increased to 28.5S/cm or 57S/cm. In these cases, at 40GHz, α_RF will fall to 0.58/cm (5.3dB/cm) for F_TCO = 0.5S, or 0.37/cm (3.21dB/cm) for F_TCO = 1S. And at the same time, r_RC increases to 0.956 for F_TCO = 0.5S, and 0.984 for F_TCO = 1.0S, which can be seen from Fig. 9(d). This result shows the importance of the TCO figure of merit because a larger F_TCO will allow higher σ_TCO values, which in turn lead to lower α_RF and higher r_RC. From this trend, note also the importance of short active length L and the buffer layers. For a device with a short active length (~5mm), α_TCO can be larger than the value in a conventional structure with a 2cm long active length. Similarly, the buffer layers reduce the optical mode overlapping factor with the TCO layers Г_TCO and this in turn leads to larger α_TCO (as shown in Table 4). When F_TCO is fixed, larger α_TCO values mean larger σ_TCO.

 

Fig. 9 Simulation results for modulators having a TCO electrode loaded coplanar transmission line (the active region), as shown in Fig. 8. (a) Characteristic impedance Z₀ under different σ_TCO. (b) Effective RF refractive index c) Microwave attenuation coefficient α_RF d) TCO-RC voltage drop coefficient r_RC.

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Note that the size of TCO overlapping area has a significant impact on the microwave attenuation coefficient α_RF. Figure 10 shows the value of α_RF under different overlapping widths W_overlap. When the TCO overlapping area width drops from 3.2μm to −0.8μm, α_RF drops from 0.445/cm or 3.86dB/cm to 0.195/cm or 1.69dB/cm. Here the σ_TCO is set to be 57S/cm (F_TCO = 1S case). This is because the two overlapped TCO bridge electrodes act as a loading capacitor with two series resistors. Increasing W_overlap will increase the loading capacitance and the series resistance per unit length and therefore causes a larger RF loss along the active region. To achieve good electrical-optical mode overlapping, the two TCO electrodes must cover the entire EO waveguide core, meaning W_overlap ≥ W_cor Therefore, in the design of the optical waveguide, we chose a low index material (CYTOP with n = 1.35) to be the side cladding material, in order to minimize the width W_cor of the EO waveguide core. The overall frequency response of the average applied voltage V_av is found by plugging the results in Fig. 9(a)–9(d) into Eq. (4), and the final result of V_av is shown in Fig. 11 . Note that 3dB optical bandwidths (at which the average effective voltage drops to half the DC value) of 40GHz-100GHz can be achieved. Table 5 summarizes the complete device performance of the proposed buried waveguide structure with coplanar metal transmission lines and the TCO side conduction geometry.

 

Fig. 10 Microwave attenuation coefficient α_RF versus the width of the TCO overlapping area in the modulator structure shown.

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Fig. 11 Overall frequency response of the average applied voltage found by plugging the numerical results given in Fig. 9 into Eq. (4).

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Table 5. Complete modeling result of the TCO based EO modulator.

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7. Conclusions

We have shown here that a transparent conducting oxide (TCO) electrode-based organic EO modulator structure can be used to achieve substantially higher power-size performance than conventional modulator designs. An optimized high-speed structure is proposed and its performance carefully analyzed based on full wave numerical simulation. A compact device (5mm long device) with 0.5V driving voltage and 40GHz – 100GHz optical bandwidth is predicted. Note that a 0.5 V modulator operating at 40 Gbps in NRZ format has a switching energy on the order of 63 fJ/bit. Experimentally, we have demonstrated a new EO modulator structure which features an inverted ridge waveguide geometry offering a simpler fabrication process, better thermal compatibility with the organic EO material, and a high-response EO polymer active layer. Initial results demonstrate a power-size figure-of-merit of 7.2mW-cm². Compared with our previous experimental results, this represents an effective 45% improvement.