Compound semiconductor quantum dot (QD) materials show a large electro-optic (EO) effect due to the quantum-confined Stark effect (QCSE) [1]. Recent reports have shown that the QDs can be vertically and laterally aligned forming QD chains along the $[01\overline{1}]$ direction [2–5]. Because of high QD density induced by strain and intense inter-dot coupling along QD chains, the EO effect can be further increased along QD chains. These QD chains can the enable development of EO modulators with very low drive voltage and ultra-wide bandwidth operation.

In this Letter, two types of EO phase modulators were designed and fabricated: (a) modulators with waveguide along the $[011]$ direction and (b) modulators with waveguide along the $[01\overline{1}]$ direction. We call the first type the $[011]$ modulator and the second type the $[01\overline{1}]$ modulator. The linear EO coefficients were measured as $24.3\mathrm{pm}/\mathrm{V}$ along the $[011]$ direction and $30.6\mathrm{pm}/\mathrm{V}$ along the $[01\overline{1}]$ direction at 1.55 μm operational wavelength. Similar measurement was done at 1.32 μm, and the linear EO coefficients are $33.8\mathrm{pm}/\mathrm{V}$ along the $[011]$ direction and $40.3\mathrm{pm}/\mathrm{V}$ along the $[01\overline{1}]$ direction. To the best of our knowledge, this is the first report of the anisotropic EO effect on semiconductor QD materials. The EO anisotropy can be increased by growing long and uniform QD chains. These devices can be used in low-bias high-bandwidth photonic links.

The QD chain wafers were grown on the n-GaAs (100) substrate followed by an n-GaAs buffer layer, an $\mathrm{n}-{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ cladding layer, a QD chain active region, a $\mathrm{p}$-${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ cladding layer and a thin $\mathrm{p}+-\mathrm{GaAs}$ contact layer by a solid source molecular beam epitaxy (MBE) reactor. The active region consists of 16 stacked ${\mathrm{In}}_{0.45}{\mathrm{Ga}}_{0.55}\mathrm{As}$ QD layers cladded by the GaAs separate confinement heterostructures (SCHs). The growth temperature of the QD chain multilayers was 540°C. Detailed information about the QD chain growth and formation can be found in [4,5]. Figure 1(a) shows the atomic force microscopy (AFM) image of the grown epilayer wafer. The image shows that the QD chains with $\sim 5\mathrm{QDs}$ per chain in average are formed along $[01\overline{1}]$ direction. Figure 1(b) shows the photoluminescence (PL) spectrum with $[011]$ and $[01\overline{1}]$ polarizations. The PL peaks were designed at $\sim 1025\mathrm{nm}$ to reduce the absorption loss for operational wavelength from 1.3 to 1.6 μm. The PL intensity of the $[01\overline{1}]$ polarization is $\sim 21\%$ higher than that of the $[011]$ polarization at the PL peak. The polarized luminescence is a fingerprint of the anisotropic properties of the grown QD chains.

 

Fig. 1. (a) AFM image of the QD chain wafer after 16 stacks of QD growth. (b) PL spectrum of the grown wafer with $[011]$ and $[01\overline{1}]$ polarizations.

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The QD phase modulators were fabricated with p-contact metal deposition, waveguide dry-etching, n-contact metal deposition, Benzocyclobutene (BCB) coating, BCB dry-etching, and gold electrode plating. Standard optical ridge waveguide structures were fabricated. The lengths of the active modulation regions vary from 0.5 to 2 mm. The ridge width was 4 μm.

The modulation efficiency at a certain device length is measured by the half-wave voltage ($\mathrm{V}\pi$). It is defined as the voltage required for introducing an optical phase difference of $\pi$. The $\mathrm{V}\pi \mathrm{s}$ were measured using a polarizer and an analyzer. Detailed information about the experiment is in [1]. At 1.55 μm wavelength, $\mathrm{V}\pi$ is 4.65 V for the 1.5 mm long $[011]$ modulator and 5.35 V for the $[01\overline{1}]$ modulator. Similarly, we measured $\mathrm{V}\pi \mathrm{s}$ at 1.32 μm. At 1.32 μm wavelength, $\mathrm{V}\pi$ is 3.86 V for the $[011]$ modulator and 4.35 V for the $[01\overline{1}]$ modulator. Note that the polarization of light is perpendicular to the light traveling direction, so the $[011]$ modulator represents the EO effect along $[01\overline{1}]$ direction, and the $[01\overline{1}]$ modulator represents the EO effect along $[011]$ direction. The experimental results indicate that the EO effect is $\sim 15\%$ higher along the $[01\overline{1}]$ direction than the $[011]$ direction at 1.55 μm, and $\sim 12\%$ higher at 1.32 μm.

The phase variation as a function of reverse bias voltage for the 1.5 mm long modulators are shown in Fig. 2. These data also confirm the $\mathrm{V}\pi$ measurements. Assuming the electrical field fully drop across the undoped region (GaAs SCH and the QD layers), we obtain the QD EO coefficient by fitting the data in Fig. 2 to the equation:

 

Fig. 2. Phase change as a function of bias at (a) 1.55 μm wavelength and (b) 1.32 μm wavelength. The blue and red dots are data from measurement results. The dash lines are linear fits of experimental results.

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Compared with the EO coefficient from bulk GaAs, which is $\sim 1.3\mathrm{pm}/\mathrm{V}$, the EO coefficients of these QDs are greatly increased. From these results, the $[011]$ devices, in which the light is polarized along $[01\overline{1}]$, are preferable for low drive applications due to their high EO effect. To further reduce drive voltage, long and uniform QD chains are favorable. This requires optimization of the MBE growth condition. From Fig. 2, the phase change is linearly proportional to the bias voltage, which indicates the first-order EO effect (Pockels effect) dominates, and the high-order EO effects are negligible in our QD chain structures. This linear property can be used in highly linear optical systems, such as optical phase arrays and optical switches. The EO coefficients are 30%–40% greater at 1.32 μm than at 1.55 μm because the QCSE is stronger when the photon energy is closer to the QD bandgap.

The high-frequency response was characterized by a network analyzer (HP 8720ES), a high-speed photodetector ($>30\mathrm{GHz}$), and low-noise amplifiers. The RF response of the RF amplifiers, SMA cables, and the GSG probe were calibrated out from the measurement. The results are shown in Fig. 3. The simulation results were done by the high-frequency structure simulation software (HFSS) from Ansys, Inc. We obtain a 3 dB bandwidth of 12.3 GHz for the 0.8 mm long device, and 10 GHz for the 1.5 mm long device. The frequency responses of these modulators are mainly limited by the resistance and capacitance (RC) time constant and not the actual EO effect. The speed limited by the fundamental QD EO response should be significantly higher. The contact resistance is $\sim 6\mathrm{\Omega }$ for the 1.5 mm long modulator and $\sim 11.3\mathrm{\Omega }$ for the 0.8 mm long modulator. The results indicate a length-dependent junction capacitance (156 fF for the 1.5 mm long modulator and 83 fF for the 0.8 mm long modulator) and a constant parasitic capacitance ($\sim 127\mathrm{fF}$) generated by the metal pads. The junction capacitance can be reduced by optimizing the epilayer design, and the parasitic capacitance can be reduced by removing the n-contact layers below the signal pads.

 

Fig. 3. (a) Experiment setup and (b) experimental and simulation results for frequency roll-off.

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Optical loss is another important parameter for optical modulators. The insertion losses for these devices were obtained by measuring devices with different lengths. No significant anisotropy was found between the $[011]$ modulators and the $[01\overline{1}]$ modulators in terms of optical loss. Figure 4 shows the measured total loss as a function of device length for 4 μm ridge wide $[011]$ modulator waveguides. The insertion loss is $4.4\mathrm{dB}/\mathrm{mm}$ at operational wavelength of 1.55 μm and is $4.5\mathrm{dB}/\mathrm{mm}$ at operational wavelength of 1.32 μm. Material absorption is slightly higher at 1.32 μm than at 1.55 μm. Since operational wavelengths are more than 100 nm away from the material absorption edge ($\sim 1.2\mathrm{\mu m}$), the material absorption loss is small. Therefore, most of the optical loss is the aggregation loss from sidewall scattering and QD scattering. Scattering loss can be minimized by optimizing the QD growth and the device fabrication processes. Coupling loss can be obtained from the intercepts from the linear fit curves from Fig. 3. The coupling loss between the lensed fiber and the modulator waveguide is $\sim 2.4\mathrm{dB}$ assuming that the output and input coupling losses are the same. Because there are no antireflection coatings on the modulator facets, the coupling loss (2.4 dB) includes the back-reflection loss of $\sim 1.5\mathrm{dB}$ between the lensed fiber and the modulator facet.

 

Fig. 4. Waveguide loss measurement data for different waveguide lengths.

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In conclusion, we designed, fabricated, and characterized QD chained-based EO modulators. The $[011]$ modulators with 1.5 mm long waveguides show $\mathrm{V}\pi \mathrm{s}$ of 4.65 V at 1.55 μm and 3.86 V at 1.32 μm, and the $[01\overline{1}]$ modulators have $\mathrm{V}\pi \mathrm{s}$ of 5.35 V at 1.55 μm and 4.35 V at 1.32 μm. The QD chains reduced $\mathrm{V}\pi$ by 15% at 1.55 μm and $\sim 12\%$ at 1.32 μm. The QD linear EO coefficients are calculated to be $30.6\mathrm{pm}/\mathrm{V}$ along $[01\overline{1}]$ direction and $24.3\mathrm{pm}/\mathrm{V}$ along $[011]$ direction at 1.55 μm wavelength. These numbers are $40.3\mathrm{pm}/\mathrm{V}$ along the $[01\overline{1}]$ direction and $33.8\mathrm{pm}/\mathrm{V}$ along the $[011]$ direction at 1.32 μm. The EO effects can be increased by optimizing the QD chain growth, forming long chains and increasing the QD overall density. The insertion loss for these QD chain modulators is $4.5\mathrm{dB}/\mathrm{mm}$ at 1.55 μm and $4.6\mathrm{dB}/\mathrm{mm}$ at 1.32 μm. The optical loss is mainly due to sidewall scattering and QD scattering. The 3 dB bandwidths are 12.3 GHz for 0.8 mm long devices and 10 GHz for 1.5 mm long devices. The bandwidths of our modulators are limited by the RC time constant. These devices have great potential in applications for analog and digital optical links.