Modelling Optical Devices and Systems in MAPP

In this technical report, we illustrate how optical devices and systems are formulated and implemented in the Berkeley Model and Algorithm Prototyping Platform (MAPP). With examples and their code snapshots, this report documents the current structure and capabilities of MAPP’s optical modules. It is also useful as a quick-start guide for new users working with optical modelling and simulation in MAPP. I. Concepts behind Optical Modelling in MAPP Similar to electrical circuits, an optical system is modelled as a set of optical devices interacting with each other through node connections. One simple example is shown in Fig. 1 (from [1]) — a communication link where an optical fiber connects a laser diode and a photodiode. Fig. 1. A simple intensity-modulated optical fiber communication link, adapted from Fig 1.1 in [1]. The link has connections to electrical circuits around it, which is typical for most practical optical systems. But to illustrate our ideas on optical modelling, we consider only the optical parts in this report. We can then abstract the laser diode as an ideal light source and photodiode an ideal light sink which doesn’t emit or reflect any light. The abstracted system diagram of the communication link is shown in Fig. 2. Fig. 2. System diagram for the purely optical parts in the simple optical fiber communication link in Fig. 1. While the block diagram in Fig. 2 seems straightforward, with optical devices represented by blocks and connections drawn as line segments in between, several questions need to be answered before the system is fully defined. For example, what does an optical connection mean? Is such a connection directional? Furthermore, what is inside of the blocks? In the remainder of this section, we answer these questions by clarifying a few concepts related to optical modelling. A. Optical Connection To begin with, the modelling of an optical connection should not be confused with the physical device of an optical fiber connector. Proper modelling of a physical optical connector requires taking into account a lot of factors. Its performance depends on the alignment of the centers of the connected fibers, the angle between them, as well as the quality of the assembly and polishing operations. All these factors affect the attenuation and reflection of light. Moreover, different models have to be deployed in the cases of multimode and singlemode fibers, or in the context of long-haul communication and nano-scale silicon photonics. Therefore, it becomes clear to us that a physical optical connection, e.g., a fiber connector, is better modelled as a device rather than an optical connection used in diagrams like Fig. 2. Instead, we define a simpler, artificial connection to use in system diagrams. We define that when two optical ports are connected with each other, all the optical properties on one side of the connection are equal to the corresponding properties on the other side. Under this definition, an optical port can be thought of as the left or right side of a crosssection of a fiber or waveguide, and an optical connection of two ports merely describes the continuation of light through the media. Note that this definition of an optical connection allows only two optical ports to be connected. In the case of connecting three fibers, a three-port device like a splitter or a joiner is needed and all the physical factors are considered in the modelling of such devices. B. Optical IOs at an Optical Port In this subsection, we define the optical quantities modelled at an optical connection of two ports, and explain our reasons. In electrical circuits, the consensus is that the inputs/outputs (IOs) at an electrical port are voltages and currents; Kirchhoff’s current law and voltage law (KCL and KVL) is used to write the system-level equations. However, no such standard is agreed upon for optical modelling at this moment. Instead, people often use different optical quantities in their models for different applications. In laser modelling, people often use only the intensity of light as the IO to model at the optical port of a laser. But it quickly becomes insufficient for applications in optical communication, where the phase of light is also required for the model to be meaningful. Moreover, in cases like WavelengthDivision Multiplexing (WDM) fiber-optic communication, intensities and phases of light with multiple frequencies or spatial modes all need to be taken into consideration. But even all these may still not be sufficient. While in optical