An EO phase modulator having transparent conducting oxide electrodes and an inverted rib waveguide structure is demonstrated. This new modulator geometry employs an EO polymer having an in-device r33 = 60pm/V. The measured half-wave voltage Vπ of these devices ranges from 5.3V to 11.2V for 3.8 and 1.5 mm long devices, respectively. The lowest VπL figure-of-merit corresponds to 0.6V-cm (7.2mW-cm2 of power length product) in a dual-drive configuration. The trade-off between Vπ, insertion loss and modulation bandwidth is systematically analyzed. An optimized high-speed structure is proposed, with numerical simulation showing that this new structure and an in-device r33 = 150pm/V, can achieve Vπ = 0.5V in a 5mm long active length with dual drive operation. The insertion loss is targeted at 6dB, and a 3dB optical modulation bandwidth can reach > 40GHz.
© 2010 OSA
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 . Another important application area that would benefit from ultra-low power EO modulators is efficient optical interconnects, which would enable next-generation microprocessors .
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, Vπ) of 5V, an active length of L = 2cm, and an electrical terminal impedance of Z = 50Ω . This means that the electrical power required to drive the modulator, given by P = Vπ2/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 (Vπ)2, so that there is a great advantage to reducing Vπ. For example, a 5.0V→ 0.5V reduction in Vπ 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 Vπ = 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 Les are necessarily large, 2.4 - 3.5cm, since Vπ scales inversely with Le. 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.
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 . 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 , 3) a comprehensive analytical model to optimize Vπ , 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 Vπ = 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 Vπ and the length L of the device [Eq. (1)], where λ is the optical wavelength, n is the11]. The r33 coefficient defines the refractive index change in the modulating electric field direction. In many applications, it is equally meaningful to specify the power-size figure-of-merit given by: PπL2 = (Vπ2L2)/Z0, where Z0 is the transmission line impedance that is typically 50Ω. We see from Eq. (1) that Vπ is proportional to the electrode-electrode distance del-sep. For the conventional modulator of Fig. 1(a), del-sep is much larger than the EO layer thickness dcor due to the necessity of having two thick cladding layers (top layer thickness = dtcl and bottom layer thickness = dbcl) required to separate the metal electrodes from the EO active region to suppress metal-induced optical loss (i.e., del-sep = dcor + dtcl + dbcl). Typical organic modulators operating at 1550nm have del-sep ranging from 8 −15µm with a typical value of 12 µm and dcor ≈1.5µm [11–15]. However, note that if the cladding layers have sufficient optical transparency and electrical conductivity, they can introduce the switching voltage directly from the metal electrode to the EO layer, thus greatly reducing Vπ. However, a limitation is that typical TCO materials have high refractive indices at telecommunication wavelengths, nTCO > 1.7 (e.g., nIn2O3 = 1.75 - 2.05, depending on the doping density), significantly greater than those of typical organic EO materials, nEO = 1.4 - 1.7 [4–6], thus rendering TCOs unsuitable cladding materials. Furthermore, even if TCOs could be used as cladding, their optical loss may be too large for efficient waveguiding. To address this limitation, we employ the approach of Fig. 1(c). Here two thin TCO layers conduct the voltage from metal side electrodes to the top and bottom parts of the EO waveguide core, thereby reducing del-sep from del-sep = dcor + dtcl + dbcl to del-sep = dcor. Table 1 below compares the voltage-size figure-of-merit enhancement provided by the new electrode geometry. A 1cm-long device with a conventional push-pull metal electrode design requires an EO material having a large r33 = 600pm/V to achieve Vπ = 0.5V. However, if the EO layer is directly modulated by transparent electrodes as in Fig. 1(c), the r33 required for Vπ = 0.5V is only 75pm/V. Furthermore, for sub-milliwatt operation (e.g., 200µW for a 1 cm active length push-pull design), a conventional modulator structure requires an EO material having a currently unattainable r33 = 3000pm/V, while the TCO-based modulator requires only r33 = 375pm/V, which is currently possible [4–9].
3. Modulator fabrication and evaluation results
New Device Structure. To demonstrate the low VπL 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 . 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) . 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 . 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  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.
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 VπL 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 VπL 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 VπL 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 Vπ = 2.8V with in an 8mm straight waveguide device or VπL = 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 VπL (0.56V-cm/2μm versus 0.75V-cm/1.5μm).
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 ГTTCO than the top TCO layer (from Fig. 2, ГBTCO = 0.71% and ГTTCO = 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 αTCO and ГTCO, it can be reduced by engineering the TCO material to have a lower αTCO, or by inserting thin buffer layers between the EO and TCO layers to reduce ГTCO. The first method requires TCO materials development, and a systematic study of how to reduce the αTCO while keeping a high σTCO 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 Vπ, 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 nEO 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: dcor = 1.3μm and wcor = 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 ГEO = 83%. If r33 = 150pm/V and a dual drive structure are assumed (which means the effective EO coefficient r = 2r33 = 300pm/V), then VπL = (λdel-sep)/(n3rГEO) = 0.205V-cm for λ = 1.55μm, and 0.173V-cm for λ = 1.31μm, and an L = 5mm long active length yields Vπ = 0.41V for λ = 1.55μm operation and 0.34V for λ = 1.31μm operation. At this point we assume that del-sep = dcor 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 αTCO and ГTCO, an effective way to reduce the optical insertion loss is by reducing ГTCO. Later we show that, by inserting thin buffer layers between the TCO electrodes and the EO waveguide core, ГTCO can be reduced significantly, and this strategy allows the TCO electrodes to have much higher electrical conductivity without significantly increasing the VπL 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.
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: Iout/Iin = TTCO × TMet × Toth, where TTC is the optical power transmission coefficient accounting for the optical loss caused by the TCO layer alone, which can be further described by: TTCO = exp(-αTCoptΓTCL), where L is the length of TCO layer in the device (it is also the modulator interaction length) and ΓTCO is the percentage of optical mode energy overlapping with the TCO layer (the TCO optical-mode overlapping factor). TMet 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 TMet = exp(-αMetL). As mentioned above, for an optimal design, we can let TMet = TTCO. 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), Toth 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 (TTCO × TMet) > 0.6 (less than 2.2dB) or TTCO > 0.775 (less than 1.1dB) assuming TTCO = TMet, so that (Toth × TTCO × TMet) 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 TTCO will be > 0.8 if αTCoptΓTC < ln(0.8)/L = 0.22/L (for L in cm) which requires αTCopt ΓTCO < 0.44/cm when L = 0.5cm. Table 3 summarizes the optical loss caused by each part of the TCO electrode-based EO modulator.
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 αTCO. Besides the low loss requirement, an electrode TCO material must have a sufficiently high electrical conductivity, σTCO, to drive the modulator at high speed. While doping TCO materials with additional carriers increases σTCO, it also increases free carrier absorption at longer wavelengths, increasing αTCO [17–24]. The electrical conductivity to optical absorption coefficient ratio, FTCO = σTCO/αTCO, is an intrinsic materials property at a given wavelength and an important TCO modulator figure-of-merit. As discussed before, the acceptable αTCO is inversely proportional to ΓTCO through the relationship αTCoptΓTCO < 0.44 when L = 0.5cm, while σTCO is proportional to αTCO when a certain FTCO is assumed. Therefore, the optical mode overlapping factor ΓTCO must be as small as possible to obtain as large a σTCO 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 ΓTCO and the thicknesses of the TCO and buffer layers. The results are given by COMSOL, which is an FEM method based mode solver . Here we define the optical mode overlapping factor in the bottom TCO layer to be ΓBTCO and the optical mode overlapping factor in the top TCO layer to be ΓTTCO. The total mode overlapping factor in the TCO layers is ΓTCO = ΓBTCO + ΓTTCO. Note that if the TCO layers directly contact the EO layer, ΓTCO is 2.9% and the corresponding αTCopt = 15 /cm. ΓBTCO is larger than ΓTTCO 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, ΓTCO will be reduced to 0.77%, and the corresponding αTCopt becomes 57 /cm . Here we make dBBuff > dTBuff to assure that ΓBTCO ≈ΓTTCO (i.e. separate bottom TCO layer away from the EO layer further than the top TCO layer). The thickness of the two TCO layers TTCO is set here to 100nm. Assuming FTCO = 1S, the corresponding σTCO = 57S/cm. Note that the 400nm thick buffer layer will only increase the Vπ 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 dBbuff = 300 nm and dTbuff = 100nm. In Table 4 we also list the overlap integral ηoverlap 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 . Here ηoverlap is defined as
Note in Table 4 that the values of ηoverlap 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 neff and ngopt at different optical wavelengths for the modulator structure with dBbuff = 300 nm and dTbuff = 100nm. Here ngopt = nopt – λ0dnopt/dλ. The group index optical waveguide ngopt is found to be 1.642 at λ = 1.31μm and 1.643 at λ = 1.55μm–slightly higher than neff. Later in the RF simulation, ngopt will be used to calculate the velocity mis-match. Figure 5(c) shows the relationship between ГEO, ГTCO, and λ. Note that ГTCO at λ = 1.31μm is smaller than ГTCO at λ = 1.55μm and therefore will allow the TCO layers to have a larger αTCO. Figure 5(d) shows the relationship between αMet (calculated from the extinction coefficient к) and Wgap. As discussed above, the metal-induced optical insertion loss is required to be <1dB. This requires that we find a Wgap at which TMet = exp(-αMetL) > 0.775, or αMet < 0.44/cm when L = 5mm. In order to minimize Wgap, we first choose a large refractive index difference between the EO waveguide core (nEO = 1.6) and the side cladding layer (nscl = 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 Wgap because the TM mode has a better horizontal confinement in the EO waveguide core, compared with the TE mode case. In the numerical simulation, αMet is found through the extinction coefficient к which is the imaginary part of the complex effective refractive index of a mode (nc = n + iк) using the relationship: к = αMetλ/(4π). We see from Fig. 5(d) that when Wgap > 1.6μm, αMet is small enough (below 0.44/cm for both λ = 1.31μm and λ = 1.55μm).
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 αRF and TCO-RC voltage drop coefficient rRC. 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 Zs = 50Ω feeding transmission line. A ZL = 50Ω termination is assumed at the end of the active region.
Assuming the voltage applied to the feeding transmission line is Vappl, then the instantaneous RF voltage seen by the optical packet along the active region is given by:
Here γRF = αRF + jβRF is the complex propagation constant of the RF wave and ω = 2πf is the angular frequency. αRF is the microwave attenuation coefficient which accounts for the RF loss in the TCO loaded active region. βRF 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 Zm is not equal to Zs and ZL, and this is accounted for by Гs = (Zs-Zm)/ (Zs + Zm), which is the RF reflection coefficient at the entrance of the active region, and ГL = (ZL-Zm)/(ZL + Zm), which is the RF reflection coefficient at the termination of the active region. T = 1- Гs 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: rRC = VEO/Vmetal. The average switching voltage applied to the optical packet after it leaves the active region, is found by integrating Veff(x,ω) along 0 to L:
Here γFW and γBW are given by γFW = αRF + j (ω/c)(nRF-ngopt) and γBW = αRF + j (ω/c)(nRF + ngopt).
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  because here we add the TCO-RC drop factor rRC 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 αRF) and the voltage drop along the TCO bridge electrodes (denoted by rRC). 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 Zm = Zs = ZL. and βRF = ω/vRF = ω/vgopt (which means ngRF = ngopt). Later we will show that this can be achieved by carefully selecting the dielectric materials and tuning the transmission line dimensions. Then, (ω/vgRF) − βgRF = 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 αRF(f)L is given by:
The solution of Eq. (7) is:
Here W(x) is the Lumbert W function . Assuming rRC(fBW) = 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 αRF is defined as the microwave attenuation coefficient of the electric field amplitude of the RF wave, therefore 3.2/cm corresponds to 20log(e3.2L)/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 rRC is taken into consideration, then the upper limit of αRF(fBW) will be reduced to a lower value. Figure 7 shows the theoretical upper limit of αRF(fBW) under different rRC 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 rRC(f) ~0.5), there is little room for the RF loss, and a small αRF(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 αRF when rRC = 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.
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 del-sep = 9μm (6x larger than a TCO-based structure), the required active length L becomes 3cm, and the acceptable αRF(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 (f3dBo > 40GHz) because it can be made short (<5mm active length) while still achieving low switching voltages (Vπ < 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.
The structure is modeled using HFSS, which is a commercial finite element method (FEM) solver . 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 rRC, the characteristic impedance Z0, and the RF transmission line effective group index ngRF. Figure 9(a) and 9(b) show that the structure is optimized so that Z0 is tuned to match 50Ω and the ngRF also matches ngopt (~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 αRF and rRC depend on the electrical conductivity of the TCO electrodes which is in turn dependent on the TCO material figure of merit FTCO = σTCO/αTCO where αTCO = 57/cm is determined by the optical insertion loss requirement discussed before. We explored the FTCO = 0S, 0.2S, 0.5S and 1S cases and the corresponding σTCO = 0S/cm, 11.4S/cm, 28.5S/cm and 57S/cm, cases, respectively. The curve with σTCO = 0S/cm represents the case in which only pure copper coplanar slot transmission lines are present. Note that αRF in this case can be quite small. At 40GHz, the predicted αRF 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, αRF will increase significantly. Note from Fig. 9(c) that when σTCO = 11.4S/cm or FTCO = 0.2S, αRF 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 αRF 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 rRC = 0.81718 [Fig. 9(d)] and from Fig. 7 we find that the corresponding theoretical upper limit of αRF 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 FTCO values (0.5S or 1S), σTCO can be increased to 28.5S/cm or 57S/cm. In these cases, at 40GHz, αRF will fall to 0.58/cm (5.3dB/cm) for FTCO = 0.5S, or 0.37/cm (3.21dB/cm) for FTCO = 1S. And at the same time, rRC increases to 0.956 for FTCO = 0.5S, and 0.984 for FTCO = 1.0S, which can be seen from Fig. 9(d). This result shows the importance of the TCO figure of merit because a larger FTCO will allow higher σTCO values, which in turn lead to lower αRF and higher rRC. 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), αTCO 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 ГTCO and this in turn leads to larger αTCO (as shown in Table 4). When FTCO is fixed, larger αTCO values mean larger σTCO.
Note that the size of TCO overlapping area has a significant impact on the microwave attenuation coefficient αRF. Figure 10 shows the value of αRF under different overlapping widths Woverlap. When the TCO overlapping area width drops from 3.2μm to −0.8μm, αRF drops from 0.445/cm or 3.86dB/cm to 0.195/cm or 1.69dB/cm. Here the σTCO is set to be 57S/cm (FTCO = 1S case). This is because the two overlapped TCO bridge electrodes act as a loading capacitor with two series resistors. Increasing Woverlap 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 Woverlap ≥ Wcor 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 Wcor of the EO waveguide core. The overall frequency response of the average applied voltage Vav is found by plugging the results in Fig. 9(a)–9(d) into Eq. (4), and the final result of Vav 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.
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.
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