Opto-electronic Circuit Simulation and Microwave Photonics
The ongoing convergence of electrical, solid state photonic and optical technologies has produced a wave of experimental results, new devices and novel applications - with Microwave Photonics (MWP) being a particularly exciting field. Roughly speaking, microwave photonics involves the optical generation, distribution and processing of microwave frequency (40 to 200 GHz) signals imposed on an optical carrier as a modulated envelope.
Although simple distribution of RF or microwave signals over optical fiber is an attractive feature of MWP there are, in addition, a very wide range of more complex applications. Optical devices can be used to generate microwave signals (by beating two optical signals differing slightly in frequency) and also to split, manipulate, delay and add signals. The primary goal of MPW is to exploit optical effects such as phase delay and interference, in order to generate and manipulate the microwave signal present on the optical carrier.
The combination of two mature and powerful technologies with innovative device and application engineering has produced a wealth of experimental results; varying from optical pulse generation circuits to complex hybrid circuits such as optical phase locked loops. However, a considerable challenge in the industrial exploitation of all this work is the immaturity of the computer aided design (CAD) environment needed for the efficient development of applications.
The Challenge for Computer Aided Design
Microwave photonics applications offer some very significant challenges to CAD. Although individually, electrical (microwave) and optical simulation tools are quite mature, the integration of the approaches used in the two areas is not straightforward. A primary complication is the need to perform a coupled self-consistent simulation of the opto-electronic circuit, when a dramatic difference in frequency exists between the optical carrier (~200 THz) and the microwave signal (10 GHz to 100 GHz). Other complicating issues are: strong non-linearities present in electrical and electro-optic devices, the need to model the phase of optical carrier and optical interference; use of multiple optical carriers, and the interaction of other physical processes such as heat flow and noise.
Circuit Level Time Domain Simulation
Although there are a variety of approaches possible for coupled simulation at the circuit level (10 to 100s of devices), it is instructive to look at electrical CAD where the use of time domain analysis tools has been very successful. These tools formulate the system in terms of a set of 1st order non-linear differential equations; essentially linking voltage nodes, using compact models of devices such as resistors, capacitors and transistors. The simulator solves for the circuit voltages, currents and stored charges by integrating the equations in time and iterating at each time-step to account for non-linear elements.
The extension of such a scheme to an opto-electronic circuit requires first the definition of an “optical signal”. The most practical definition is that of a complex envelope of the optical carrier. The use of the envelope removes the high frequency optical oscillation, and its complex nature allows for the retention of the phase of the optical signal. This combination allows for efficient time domain simulation of optical effects such as interference, reflection and resonance. The formulation requires an explicit delineation of all optical signals in a device. A waveguide, for example, may have a number of optical modes present, travelling in both directions and possibly multiple optical carriers. Each of these signals would be explicitly represented in the simulator. Within this framework, optical devices are defined using compact models that capture the physical effects present and link the optical “nodes” at the inputs and outputs. As an example, a waveguide element would be represented by a set of signals - each subject to attenuation, time and phase delays and possibly reflections at either end of the waveguide.
Two Examples – Signal Modulation and Pulse Generation
Figure 1. Ring resonator based WDM system.
An example of a simulator based on such principles is OptiSPICE; a flexible CAD tool incorporating a full suite of optical and electrical devices and also possessing sophisticated thermal models. Figure 1 shows an example opto-electronic circuit consisting of a multi-channel optical link with a modulated signal placed on each channel and configurable filter used to select the channel to be output. Each channel is generated by an integrated solid-state laser source powered by an electrical driver consisting of a bipolar junction transistor and a biasing network (only the first channel is presented). A ring modulator is then used to impose a bit stream on the laser source. All the channels are then joined together by an optical multiplexer producing the multi-channel optical signal that is distributed using an optical fiber. At the output of the fiber a configurable filter can be used to select a particular channel that is then converted to electrical current by a photo-diode; which in turn is converted to an output voltage by a trans-impedance amplifier.
Figure 2. Ring circuit transient response. Top plot presents the change in the ring index. Second plot presents the optical field magnitude at the ring filter input. Third plot presents the two optical outputs at the through (solid line) and drop (dotted line) ports. The final plot shows the two output voltages.
Results from the simulation of this circuit are shown in Figure 2; where the switching of a bit stream from the drop port to the through port is presented. For this simulation a bit stream was produced using the first ring (R-1) to modulate the CW laser. The second ring (R-2) was initially configured by the application of a voltage such that the bit stream was passed to the drop port and then converted to a voltage by the photodiode and TIA. During the transient, the index of the second ring was linearly dropped and the filter became transparent at the channel wavelength; routing the bit stream to the through port and its detector. The results from the simulation can be seen in Figure 2; the first plot presents the change in the ring index. The optical bit stream present at the input of R-2 produced by the modulator is shown in the second graph. The optical outputs at the through and drop ports and the two output voltages are presented in the third and fourth plots respectively. It can be seen in these plots that when the filter is configured to route the bit stream to the through port, the high Q of the ring filter results in low pass filtering of the bit stream being passed to the drop port and some high frequency components of the signal being routed to the through port. It can also be seen that the photo-diode and TIA also produce some filtering of the bit stream.
Figure 3. Waveguide based pulse generator.
A second circuit example is presented in Figure 3 - a thermally tunable pulse generation device that is used to generate a 40 GHz encoded pulse stream from a 10 GHz input. The circuit consists of 6 stages each incorporating an interferometer where the length difference between the arms specifies a time delay equivalent to 40 GHz. At the input of each stage is an optical cross-coupler which splits the input signal between the two arms of the interferometer. Multiple pathways with different delays for signals traveling though the interferometers produce a train of 40 GHz pulses from a 10 GHz excitation. Thermally tunable phase delays in the interferometers are used to determine amplitude or phase encoding - each stage incorporates an electrically driven heater to allow for thermal tuning of the phase delay in one arm of the interferometer. The final figure shows two cases of pulse encoding one for amplitude coding the other phase.
Figure 4. Waveguide based pulse generator results: a) Amplitude and b) phase coding.
To conclude, microwave photonics is a rapidly developing and exciting field; however, as was the case with microelectronics and optical telecom, industrial uptake of fundamental technology will require the development and use of powerful and sophisticated CAD tools.
Posted by Janine E. Mooney, Editor
November 17, 2011