## Abstract

Standing wave effect of applied electrical field on optical modulation in multiple-cascaded integration (CI) electroabsorption modulator (EAM) and high-impedance transmission line (HITL) has been investigated in this paper. As modulation frequency is increased to the scale that electrical wavelength is in the order of optical modulator length, multiple electrical reflection and self-interference on impedance-mismatch boundaries becomes significant, leading to strong position-dependent field distribution and degrading modulation bandwidth. Sharp bandwidth roll of electrical-optical (EO) conversion by standing wave has been found experimentally in CI structure, consistent with simulation results. By comparing different segment number and length of CI- structure, larger section number of design can overcome such problem to get more flatten bandwidth response. Such simple CI for 300μm long EAM has been demonstrated with flat EO response of −3dB drop 45GHz and −10dB microwave reflection (up to 65GHz) in 6-segement device, suggesting this scheme design is quite useful for efficient broad band modulation.

© 2012 OSA

## 1. Introduction

High-speed optical modulators have been the main components for research and development recently since the 40Gb/s and 100Gb/s Ethernets (40GBE and 100GBE) were issued as standards of optical fiber communications. III-V semiconductor Electroabsorption modulator (EAM) is one of the most promising solutions due to high efficiency, low frequency chirp, broad bandwidth, and compatibility for integration and feasibility design operation wavelength in O (1300nm) and C (1550nm) band, which can match the requirements of 40GBASEE-FR and VSR2000-3R2 specification by IEEE 802.3 bg and ITU-T G.693. Even though the cost issue for 40Gb/s operation is under argument, there are still lots of motivation for fundamental research in high-speed high-efficient EAM, including the innate compatibility with network and further promotion in the future [1–6].

To pursue high-speed high-efficiency optical modulators, distributive electrical-to-optical (EO) interaction along waveguide is a necessary fact to be considered in design. As modulation frequency is set as a scale that the microwave wavelength is close to the device length, phase and amplitude of electrical field should be taken into account for optimization [7–10], suggesting the importance of design issues in electrical- and optical- distributive interaction. Typically, EAM waveguides are made of p-i-n heterogeneous material in order to attain highly confined electric field for low-power operation. High capacitance, however, simultaneously brings out large charging time, which is so-called slow waveguide property, i.e. low electrical impedance (typically ~20Ω), low electrical phase velocity, and high electrical loss [7–11]. At high-frequency regimes, impedance mismatch between EAM waveguide with surrounding electrical connections (low capacitance loaded line and 50Ω) will lead to multiple electrical reflections, forming electrical standing wave behavior. Therefore, the strongly position-dependent field and phase distribution inside waveguide will be formed, seriously affecting broadband EO conversion. Several approaches through impedance engineering have been proposed [8–9, 12–15]. Even though standing wave problem can be solved by utilizing short waveguide device, the price will be on modulation extinction ratio and efficiency from short EO interaction, and thus low tolerance on material design [5]. The extra microwave circuits can be used to tune the circuit inductance-capacitance (L-C) resonance for improving impedance matching [8, 12], but the EO conversion still suffer strong degradation when the frequency higher than resonance frequency due to the standing wave effect. Constructive field interference could lead to low driving power through standing wave property, but, narrow band operation cannot be avoided [13,14]. In order to attain broadband, the segmented EAM structure with different length of EAMs can match different resonance conditions at different frequency component [15]. However, the precise design on segment length is needed. In previous works, structure named as cascaded integration (CI) of EAM and semiconductor optical amplifier (SOA) with by-pass High Impedance Transmission Line (HITL) has been proposed for reducing impedance- and velocity- mismatch and compensating optical insertion loss, by which 40Gb/s performance has been demonstrated [10,12,16]. Inherent difference of characteristic impedance between EAM and HITL could still face multiple reflections during high frequency. In this work, distributed field distribution is proposed to investigate EO response of multiple CIs. Through large segmental section, CI could be used to reduce standing wave property for flap-band response.

## 2. Device design and fabrication

The schematic plot of CI structure is shown in Fig. 1(a) . Segmental SOAs are periodically cascaded with segmental EAMs for compensating optical propagation loss and also offering optical phase delay between each EAM. By wiring each EAM through HITLs (microwave strip waveguide), low impedance and slow electrical velocity in EAM can be improved by HITL for high-speed optical modulation [10, 12]. However, the intrinsic impedance contrast between low-impedance EAM and HITL will inherently result in high electrical reflection in the boundaries. Therefore, as approaching higher frequency modulation, the shorter electrical wavelength property induces significant multi-electrical reflections and interference inside waveguide (namely standing wave effect), causing strong dependence on space-distributed electrical power and thus frequency-dependent modulation. In order to attain broadband low-power driving optical modulation, reducing standing wave effect becomes a crucial task, where not only impedance, phase, and loss, but also multi-reflection inside microwave cavity is needed to be taken into account.

In order to investigate these effects, voltage distribution formed in microwave transmission lines (EAMs and HITLs) is simulated for design and characterization, including distributed amplitude and phase of electrical field along EAM and HITL. The simulation tool is based on the transfer matrix and the equivalent circuit model of EAM and HITL. A 3µm wide EAM waveguide with dielectric constant of 12.25 and characteristic impedance of 19Ω is used as EAM regions. And a low dielectric constant material of 2.3 with 10µm thickness and characteristic impedance of 60Ω is defined as material for microwave strip waveguide in HITL region. Six structures with different segments and different HITL lengths are calculated for comparison. Modulation frequencies are set as 0.04, 20, 40, and 60GHz. The total EAM length of 300µm is used as controlling parameter for all structures. The distributive EO conversion can be modeled by Eq. (1) [7, 17]:

*C*is coupling loss at each facet, ${V}_{b}$ is bias voltage, ${V}_{ac}(z,t)$ is the distributed voltage at position “z” and time “t”, $\mathrm{exp}(-{\alpha}_{0}{l}_{0})$and $\mathrm{exp}(-\Gamma {\alpha}_{b}{l}_{0})$are propagation loss and absorption loss at bias point, $\Gamma $is optical confinement factor of active region, and $d{\alpha}_{b}/d{V}_{b}$is modulation efficiency. After feeding electrical power, the distributed voltage, ${V}_{ac}(z,t)$, is generated and loaded in EAM regions, performing distributive EO conversion. Amplitude and phase of voltage along EAM region are thus the main factors attributing to output response. Thus, ${V}_{ac}(z,t)$ distribution along propagating trace (“z”) is then used for analysis, where Fig. 2 is calculated results by tracing EAM- and HITL- regions for different CI structures. Output and input ends are terminated by 50Ω loads and the input AC voltage is set as 0.2 V

_{pp}. As shown in Fig. 2(a), the controlled factor for comparison is the single EAM. And, Fig. 2(b), 2(c), and 2(d) show CI results for conditions with total HITL lengths of 600µm, 800µm and 1200µm. And Fig. 2(d), 2(e), and 2(f) plot the 3, 4, and 6 segments of EAMs with 1200µm HITL. Voltage in EAM regions is marked within dash lines. As modulation frequency is increased to mid frequency range (40GHz), the loaded voltage in single EAM exhibits a significant reduction, while in CI structures (Fig. 2(b)–2(f)) higher voltage is obtained. Although voltage distribution exhibits a relatively smoother curve in single EAM, inherent impedance mismatch from 50Ω in either input or output port of feed lines restrict modulation capability. Consequently, longer HITL device, as shown from Fig. 2(a) to 2(d), is allowed to get higher effective impedance to enhancing the loaded voltage within EAM regions. On the other hand, as frequency is higher than 40GHz that cavity length is compatible with microwave wavelength, electrical multi-reflection inside cavity becomes significant to get self-interference, leading to strong-position dependence on voltage distribution. This can be confirmed that the half electrical wavelength at the frequency of 40GHz is estimated as 1500µm, which is the same order of magnitude with device length. That is, by self interference, voltage applied on EAM doesn’t increase or reduce by increasing HITL length (or impedance), exhibiting different trend on frequency dependence as compared to frequency regime of <40GHz and suggesting standing wave effect could dominates at such high frequency. For lowering such effect, one way is to increase the section number of cascaded structure to reduce the size of segmental EAM and HITL, while keeping the total length. As a result, phase shift of wave propagation in each segmental element is kept small so as to reducing multi-reflection in the boundaries. As from Fig. 2(d), 2(e), and 2(f), EAM segment is increased from 3 to 6, standing wave effect can be diminished for high-frequency (>40GHz) voltage distribution, showing same frequency dependence. Therefore, by such configuration, other factors in design, such as velocity mismatch and electrical loss could be reduced with higher tolerance for broadband EO conversion.

To further confirm standing-wave behaviors of EO response, CI structures of EAM, SOA, and HITL based on p-i-n heterogeneous material are designed and fabricated, where identical InGaAsP multiple quantum well (MQWs, 6wells and 7 barriers) is used as active region sandwiched by top p-InP and bottom n-InP cladding layers. The whole processing is following the steps reported in [10, 12], except different CI structures. The optical waveguide is 7 degree relative to the cleaved faces for decreasing optical reflection in facets. Based on the design discussed in previous section, 3μm wide optical EAM waveguide with total length of 300μm using selective undercut wet-etching was used [18]. Electrical isolation region between EAM and SOA was defined by H^{+}-ion implantation. Low dielectric material PMGI was used for defining microwave stripe line in HITL region and also planarization. The final electrical transmission line was formed by hybrid combination of coplanar waveguide (EAM, low impedance) and micro-strip line (HITL). According to the simulation in the previous section, three different lengths of HITL (800, 1000 and 1200μm) with 3 segments structures and three different segments (3, 4 and 6 segments) with same HITL (1200μm) were used for characterization. Two top-views of finished devices are shown in Fig. 1.

## 3. Experimental results and discussion

To show the advantages of long EO interaction, DC optical transmission for different lengths of EAM is first fabricated to characterize extinction ratio, where two tapered fibers are used coupling into waveguide. The normalized optical transmission against with bias for EAM lengths of 100μm, 150μm and 300μm is shown in Fig. 3 , showing that the extinction ratio can be improved form 12dB to 35dB up to 5V of biasing. It indicates that high modulation efficiency can be beneficial from increasing long EO conversion, while reducing the dependence on material design.

As for characterizing high-speed field distribution, small-signal microwave reflection, microwave transmission and EO response measurements based upon 50Ω load are performed. First, same-segment devices with different lengths of HITL are measured. Dash lines of Fig. 4 show the experimental results, where the solid lines are the fitting curves derived from fabricated waveguides, where the simulation exhibits quite consistent results with experiments. As mentioned in previous section, at the frequency lower than 40 GHz, longer HITL gives higher effective impedance, thus reducing electrical reflection and improving transmission. More loaded voltage overlapping in EAM region can be achieved by increasing HITL length and also the phase adjustment in HITL [10], improving EO response. But, due to frequency-dependent phase propagation, electrical field suffers from standing wave problem as frequency higher than 40GHz, revealing the opposite trend with HITL length and thus the faster drop with frequency. According to phenomenon of standing wave, strong reflection on abrupt index change boundaries can be eliminated by increasing the section number of CI structure (i.e. reducing size of segmental EAM and HITL). Therefore, in second part, experiment results from different segments of EAM and HITL are extracted, as shown in Fig. 5 , while total HITL length is kept at 1200μm. Microwave reflections show almost same results below mid frequency regime, implying impedance matching effect still applies. Otherwise, in high frequency regime, quite different behavior is observed. By increasing frequency, smaller section number of devices has larger microwave reflection and lower transmission, leading to faster bandwidth drop in EO response. Same total length of EAM and HITL with different high-frequency EO response implies standing wave behavior affects distributive EO interaction. As shown, increasing the segments of CI suppresses standing wave property to not only reduce microwave reflection and transmission, but also lead to more flatten EO response. In 6-segement device, flat EO frequency response with −3dB bandwidth of 45GHz and low than −10dB in microwave reflection from DC to 65GHz are obtained. In the further, though optimizing microwave loss and velocity mismatch, enhanced and flatten EO response will be expected.

## 4. Conclusion

The electrical field distribution in multiple-cascaded integration (CI) EAM and SOA with HITL has been investigated in this work. Multiple electrical reflections on impedance-mismatch boundaries become more significant as increasing frequency. As a result, standing wave effect will dominate to get strong position-dependent field distribution, thus degrading optical modulation bandwidth. It is found experimentally and theoretically that through increasing HITL length and increasing segment number, device impedance mismatch and standing wave effect can be suppressed simultaneously up to 65GHz. Through such CI structure, the loaded voltage inside EAM can thus be enhanced to get an efficiency EO modulation. Microwave reflection of lower than −10dB from DC to 65GHz and flatten response with 45GHz of −3dB bandwidth is demonstrated in this work. Using such CI structure, small design tolerance and complicated microwave circuit design can be avoided to suppress the frequency dependence field distribution, suitable for design and fabrication of broadband operation in optical modulation.

## Acknowledgments

The authors would like to thank the financial supports from the National Science Council, Taiwan (NSC99-2221-E-110-029-MY3), and “Aim for the Top University Plan Taiwan” (98C030133). Also, the authors would like to thank the wafer growth from Land Mark Optoelectronic Corporation. Contact information for the authors is as follows: Tel: 886-7-5252000 ext 4460, Fax: 886-7-5254499.

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