Abstract
A novel electronically tunable optical delay line based on InGaAs quantum well microresonators is proposed for high frequency RF transmission. The device utilizes the charge-controlled blue shift of the absorption edge in InGaAs quantum wells to change the effective refractive indices of the resonators and couplers, therefore, provides an efficient way to produce variable time delay. A theoretical model based on measurements is used to analyze the device performance. Simulation results for five 3 × 27 μm2 cascaded resonators with bias voltages <0.7 V show a continuous tuning range of 7~68 ps, a ripple delay <1.5 ps, and a useable bandwidth of 39.3 GHz.
1. Introduction
Optical delay is a valuable concept for a multitude of microwave and millimeter wave applications. However to be useful, the value of this delay should be controlled electronically, and this has remained a challenging problem for the various implementations. This problem falls under the general classification of slow light which refers to the ability to decrease the group velocity of an optical medium in order to control the delay. Various approaches have been reported such as SOI ring resonators [1], SOI gratings [2], and LPCVD ring resonator [3]. But the most interest has centered on semiconductor waveguides because of the prospect of a high degree of device integration and room temperature operation as described recently [4]. The potential applications lie in the areas of information processing, communications, and the generalized RF area of Microwave Photonics (MWP). However, in all of these areas the intrinsic limitations of slow light have prevented its incorporation in high bit rate applications. All the proposed and reported tunable optical delay lines utilize the thermo-optic effect and, therefore, require high operating voltages and large footprints. For example, in the MWP area, silicon-on-insulator (SOI) microring resonators have been used to achieve full phase tuning over 40 GHz but the implementation employs temperature variations with microheaters to control the resonant frequency of the ring. The thermal response time in the ms range and the associated power dissipation are clearly limitations for the device applications.
In this paper, we introduce a new concept for the microresonator which enables direct electrical control of slow light. This is implemented by the field effect control of charge in the input waveguide and the resonator separately, which shifts the absorption edge, resulting in index changes predicted by Kramers-Kronig relations, and provides coupling and resonance control as discussed later. The microresonator has been reported previously as a high-speed modulator in the form of a rectangle which utilized corner reflectors and straight waveguides [5, 6]. A top view and cross-sectional view of the resonator through A-A′ are shown in Figure 1. The input-output waveguide is implemented with a unique zig-zag configuration that realizes layout symmetry between the input waveguide and the resonator waveguide resulting in optimum coupling. It has the added advantage of supporting the fundamental mode of the resonator and rejecting higher order modes. In addition to these desirable properties, the input waveguide, by running parallel to the resonator waveguide, creates a directional coupler with the special capability that the charge may be injected into the input channel by electrical injection. This is indicated in Figure 1(b) by the coupler bias terminals and this enables the unique capability of voltage control of the coupling coefficient into the resonator [7]. Since the differential group delay of the resonator is controlled by the coupling coefficient, high-speed electrical control of slow light is, therefore, possible.
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2. Optical Time Delay Based on Microresonator Interactions
The transfer characteristics of microresonators have been studied intensively [8, 9]. The field transmission of the rectangular resonator is where is the amplitude loss of the coupler, is the overall power coupling coefficient, and is the amplitude loss per round trip in the resonator, where is the circumference of the resonator, is the confinement factor, is the absorption coefficient in the quantum wells, is the phase shift per round trip, and is the effective index at input wavelength . When a modulated optical carrier passes through a waveguide and interacts with the microresonator, a differential group delay is produced which is defined as where is the phase angle of the field transmission in (1). Effectively the light has been delayed, thereby, creating slow light. It has also been well established [9] that when the loss is included the result is where is the resonator transit time, is the free space light velocity, and the functions , , , all depend on the power coupling parameter . For a lossless resonator, that is, , (3) is reduced to
The dependence of on coupling coefficient is illustrated in Figure 2 for μm, , , and nm, and it shows that as power coupling parameter is reduced very large values of delay are possible. The maximum delay is obtained near the minimum normalized transmission which is the condition of critical coupling in the resonator. It is also noted that large values of delay result from large values of and, therefore, a very narrow frequency range over which the delay is realized. The group delay frequency response for single resonator with is shown in Figure 3(a), which is centered at the resonant frequency of the resonator.
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Clearly this is not the best choice because the narrow bandwidth of the ring resonator limits the transmitted frequencies. A natural solution is to use multiple resonators with different resonant frequencies so that the bandwidth of the time delay spectrum can be extended over a wider frequency range [10], as shown by the solid line in Figure 3(b) with individual resonator response shown by dotted lines. Note that for delay units consisting of multiple resonators, an inherent tradeoff exists between peak delay, bandwidth, delay ripple, and number of resonators. The time delay obtained with the three resonator contributions can still achieve a flattened bandpass region by optimizing the resonant frequency of each resonator and its power coupling to the waveguide. By comparison, the dotted line shows the result of using multiple resonators without proper adjustment. Since the top of the spectrum has larger ripples, RF transmission will suffer significant distortion.
3. Device Structure and Characteristics
As discussed, the key to a practical implementation of slow light is electrical control of both resonance frequency and value of the resonators. This control is possible with the input waveguide and resonator combination shown in Figure 1. The structure is fabricated in the GaAs/InGaAs/AlGaAs system with a quantum well core in the waveguides as indicated in Figure 1. The quantum well is modulation doped with type doping just above the well. For the coupling control, we now consider the cross-section through B-B′ in Figure 1(a) and this is shown in Figure 4(a). It is first noted that the waveguide is formed as a ridge with ion implants on either side. These implants are multifunctional. First, in the passive regions away from the resonator on both the input and output sides, they provide lateral optical confinement. However in the section B-B′ that runs parallel to the resonator waveguide, the input waveguide is covered with a refractory metallization that masks the ion implant and creates the transistor structure. To appreciate this, the transistor structure with source and drain contacts and a completely metalized gate region is shown in Figure 4(b). In Figure 4(a), since the surface is doped, then the gate voltage is still effectively applied when the optical aperture is formed by metal removal. Also, without the drain terminal the channel charge continues to respond to the changes in gate-to-source voltage.
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The device shown in Figure 1 with μm, μm, μm, μm, and an input wavelength of 1026.5 nm has been described [5] in terms of an analytical absorption model based upon the blue shift of the absorption edge. The absorption model has been combined with an electrical model for the transistor. Thus, when a bias voltage is applied to the resonator indicated in Figure 1(a), the absorption coefficient changes (and also ) as shown in Figure 5(a) with the associated effective index change in the resonator via Kramers-Kronig relations. Thus, the resonant frequency is modified. In addition, the absorption edge shift causes changes in the value of the resonator. Simultaneously, another bias voltage (see Figure 1(a)) is applied to the waveguide arm of the coupler which realizes corresponding absorption and index changes in the input guide. Using RSOFT the decreases in coupling between the waveguide and the resonator are determined and plotted in Figure 5(b). The combined changes of and reduce the value of the resonator and, therefore, expand the bandwidth of the spectrum, while the change adjusts the frequency of the resonance. Both of these dependences are important and in Figure 6, the combined effect of both bias voltages on the time delay spectrum of the resonator-coupler combination is shown (calculated using the design tool in Agilent's Advanced Design System).
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It shows that combinations of and may be used to control the resonator characteristic and realize a wider possible time delay spectrum by trading off time delay amplitude for bandwidth. Then to maintain larger time delay amplitude together with enhanced bandwidth, multiple resonators are combined as discussed next.
4. Optimization of Bandwidth and Time Delay
To make use of slow light in a practical MWP application, the combined effects of resonator and coupler bias are used to adjust the parameters of multiple resonators in unique ways. A typical situation in which five resonators with μm, μm, μm, μm, and is arranged on one side of the waveguide in series with an optical amplifier which can also be integrated in the same circuit. Using the integrated format for the microresonators, there are unavoidable losses due to the minimum values of , such as the resonator corner loss and the coupler loss (typical values are 2.6 dB/resonator), and so it is expected that signal restoration will be required by the appropriate positioning of in-waveguide optical amplifiers. By individually adjusting the bias voltages on each resonator and coupler, a composite time delay spectrum with 38 ps delay and about 70 GHz useable bandwidth is realizable as shown in Figure 7(a). The corresponding transmission spectrum is shown in Figure 7(b).
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One important application of this multiple resonator system is the generation of time delay for beam steering in a phased array system. A schematic of a (periodic phased array) PAA delay unit is shown in Figure 8(a). For an RF carrier of 35 GHz (Ka band), a time delay difference between elements (i.e., variable delay unit of three resonators) of 0.7 ps at a minimum and 14 ps at a maximum would allow continuous beam steering over an angle of 0°~90° with a time spectrum width of >40 GHz. With proper adjustment of and , a variable delay unit consisting of five resonators can provide a time delay ranging from 7 ps to ~68 ps with a ripple <1.5 ps and can allow transmission of RF signals up to 39.3 GHz, as shown in Figure 8(b). With the aid of a fixed delay unit and optical switches as shown in Figure 8(a), a 180° steering angle can be achieved which would require a bidirectional optical feed as shown. It is evident that an optoelectronic circuit that provides electronics to perform the adjustment of, (by the use of optical amplifiers) and on a per resonator basis would be an ideal approach to achieve electronic scanning in both and directions.
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5. Conclusion
In this paper, we have described a novel electronically tunable optical delay line based on InGaAs quantum well microresonators. Time delay units are comprised of multiple rectangular microresonators cascaded on one side of the waveguide. The resonant frequency of each resonator and the coupling between the resonators and the waveguide can be adjusted by electronically controlling the effective index of the resonators and couplers. The performance of time delay units consisting of five series resonators is evaluated in FDTD, MATLAB, and ADS software. A time delay ranging from 7 ps to ~68 ps with a ripple <1.5 ps and enabling transmission of RF signals up to 39.3 GHz is obtained. For RF signals with frequencies as high as 70 GHz, a time delay up to 40 ps can be provided. Finally, a time delay unit appropriate for application in a PAA is presented as an example of the device.