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Behavioural modelling of Photonic and optronic systems F. Gaffiot(1), G. Jacquemod, P.Bontoux, F.Mieyeville and I.OConnor LEOM UMR CNRS 5512 36 Avenue Guy de Collongue, B.P. 163, 69 131 Ecully Cedex, FRANCE (1) [email protected] Abstract: In order to find the optimal design for a given specification of a lightwave communication link, an integrated simulation of electronic, optoelectronic and optical components of a complete system is required. Models, for optronic and purely photonic components, written in HDL-ATMand providing an accurate time domain simulation of an entire optical communication system in a standard circuit simulator environment, are presented. Introduction The global design of electronic systems through the use of standard hardware description languages from the system specification phase down to final circuit design is being established [1], [2]. The hierarchical character of the language provides a natural way of reducing the gap between system and circuit design. Moreover, it can be used even in a larger system design context, such as that of hardware software codesign or behavioural modelling and simulation of digital signals and systems. VHDL-AMS enlarges this concept to analogue and mixed analogue-digital systems. This paper presents a behavioural modelling approach for optronic systems. The first part presents the main advantages of behavioural modelling for optronic and photonic devices. The second part presents briefly components used in a communication optical link (lasers, detectors, monomode fibres). The third part puts the emphasis on the modelling of a MOEMS. The fourth part deals with devices which may be used for optical interconnects between VLSI chips. 1-CAD tools for optical systems From an industrial point of view, the development of alternative solutions to present methods is possible only if CAD tools exist. Creating such tools for optical systems makes it necessary to insure the compatibility of optronic simulation engines with electronic ones. The main feature for such effective CAD tools is their « multi-domain » and « multi-designer » nature. The wide spectrum of potential applications and users leads to the development of tools capable of providing design capabilities at different levels of abstraction (from systems to devices), i.e. to manage multi-domain analysis and to organise links between specific tools in order to allow top down and bottom up design [3], [4], [5]. In the case of electronic systems, global design through the use of standard hardware description languages from the system specification phase down to final circuit design is being established. The hierarchical character of the language provides a natural way of reducing the gap between system and circuit design. Moreover, it can be used even in a larger system design context, such as that of hardware software co-design or behavioural modelling and simulation of digital signals and systems. Generally speaking, simulation time constraints make it necessary to perform the simulation of systems with high-level abstraction models. In the case of multi-domain systems, the main difficulty is to establish a clear and univocal hierarchy of the different levels of abstraction. This is due to the strong interactions between components arising from non electronic phenomena (for example, the propagation of the optical field in a guide depends not only on its own parameters, but also on the characteristics of the light source). Thus, because of the diversity of component behaviour involved in optronic systems, a unique hierarchy, where each level is associated with a unique simulation engine, is not sufficient. An effective CAD tool should bring together different modelling techniques and simulation algorithms. A standard language must, then, link these tools. Even if VHDL-AMS is essentially dedicated to electronic system design, nonelectronic components and systems can also be described and simulated [6], [7], [8], and thus may be considered as a candidate able to fulfil previous requirements. 2- Communication link devices In this section, we present briefly the models used to simulate an intensity modulated direct detection (IMDD) optical communication link : a laser is directly modulated by a pseudo-random generator, the optical signal is transmitted along a standard monomode fibre, and after optical amplification and filtering, it is detected by a photodiode. Post processing tools allow us to draw the eye diagram, in order to find the optimal decision threshold automatically, and to extract the bit error rate (BER) to estimate the performance of the link. Laser model The MQW DFB laser operates at 1.55 m and is directly modulated at 10 Gb/s using a NRZ pseudo random current signal. The current pulse from the laser driver is directly injected into coupled differential equations (eq.1) which solve the electronphoton balance. The whole laser model has two coupled parts : a purely electrical one and a second one, which describes the electro-optic behaviour. Thus, it becomes possible to include optronic components in a classical electronic CAD tool. The electro-optic conversion is based on the rate equation approach : the behaviour of a single mode semiconductor laser above threshold is described by the following three rate equations for the electron density N(t), the photon density S(t) and the instantaneous phase (t) [9] : g n g ( N N 0 ) dN I AN BN 2 CN 3 S dt eV 1 S (1a) dS g n g ( N N 0 ) 1 R S dt 1 S p V d 1 g n g ( N N th ) dt 2 (1b) (1c). The optical power and the complex envelope of the electric field at the input of the fibre may then be expressed by : Vh P( t ) S( t ) (2a) 2 p and E in ( t ) P( t ) e j( t ) (2b). and Pout ( t ) A Ein ( t ) h( t) with h( t ) 1 j 42 L 12 2 (3b) 2 exp jt 2 L 2 (4). A, L, D= 2c2 20 are the attenuation, the length and the group velocity dispersion parameter of the fibre, respectively ; c, 2 and 0 are the speed of light, the dispersion and the central wavelength of the optical signal. In order to calculate Eout in the time domain, the infinite impulse response h(t) is approximated by a FIR numerical filter and a digital process block samples Ein and computes the convolution numerically : E out kTs N 1 a ( n) E in k n Ts (5) n0 (Ts is the sampling period and N the FIR filter order). To obtain the filter coefficients a(n), h(t) is truncated and smoothed by the classical time window function hW(t). p h W ( t ) 0.54 0.46 cos t NTs (6). A comparison between this time domain model and a classical BPM algorithm has been carried out for different values of the order of the filter N. For N=200, the simulation results of the two methods are closer than 5% and computation times are analogous (about 1 minute for a pseudo random frame of 64 bits on a Sparc20 workstation). The main advantage of the time domain method is its full compatibility with transient analysis, which makes on line simulation possible, whereas BPM method needs the knowledge of the whole frame before the simulation may be performed. Detection The detector is considered as purely quadratic : the generated signal is proportional to the output optical power. The electrical signal is then filtered. The decision circuit is modelled by an ideal sampler, of which the threshold and decision instants are adjustable. Simulation results Fibre model The fibre model takes into account only linear propagation phenomena (the injected power remaining weak, the Kerr effect may be neglected), so the field at the output of the fibre is computed as the convolution of its impulse response h(t) and the input field Ein(t) : Eout ( t ) Ein ( t ) h( t ) (3a) The parameters of the laser, the fibre and the detector, used in the models, are given in [10]. Figure 1 shows typical simulation results for a point to point link. In this example, the fibre impulse response has been approximated with N=1000 (see § 2.3). The sampling criteria is largely satisfied since the sampling frequency is 500 GHz and much higher than the laser signal bandwidth (10 GHz). Top Bragg Reflector p InP Air InP Air InP Resonant Cavity i Air Bottom Bragg Reflector n InP Air InP Air InP n Additional air InP substrat n+ Figure 2 : Schematic structure of the micromachined filter Modelling of the MOEMS Figure 1 : Typical simulation results: generator signal, drive current, frequency chirp, optical power at the fibre input and after a 50 km propagation in the fibre The behavioural model of the optical tunable filter is shown in figure 3 : electrically, it behaves like a reversed biased pin diode. The internal tuning voltage (V) induces an electrostatic force, which reduces the thickness of the cavity (d). Thus, for each optical channel (Chi), the transfer function (Hi) is modified depending on the channel wavelength (i). Electrical 3- MOEMS modelling WDM is highly promising for a wide range of optical communication applications (for example, increase of data rate of existing optical networks, computer interconnections). Such systems need highly selective and tunable optical filters. MOEMS (microopto-electro-mechanical systems) technology is suitable for the realisation of such filters [11]. From a system designer's point of view, it is highly desirable to be able to simulate, in the same environment, the physical layer and the high level layer. It then becomes possible to relate the physical design parameters to system performance. MOEMS design The filter is essentially made up of a Fabry-Perot air gap resonant cavity and two high reflectance Bragg mirrors based on InP/air-gap pairs. Due to the high index contrast between the air and the InP quarterwave layers, reflectivity as high as 99.9 % is achieved with only 2.5 pairs (Fig. 2). Selective micromachining of InGaAs sacrificial layers allows the fabrication of the reflectors and the cavity air gap. The layers of the top mirror are p-doped, the cavity ones are non-intentionally doped and the bottom mirror ones are n-doped, thus, a p-i-n junction is formed. A reverse voltage applied to the junction induces an electrostatic force, which reduces the Fabry-Perot cavity thickness and tunes the resonant wavelength. Mechanical V ~ d Ch0 Ch1 ... ChN Hi(lambdai,d) ChiHi Optical Figure 3 : Opto-electro-mechanical behavioural model The electrical behaviour of the MOEMS is analogous to a PIN, depending on the geometrical parameters of the bridge. The paddle-shaped bridge is designed in such a way that the arms support the whole mechanical effort and the two platforms adjacent to the cavity stay parallel without deformation. The structure has several mechanical resonance modes, but a reasonable approximation of the displacement is obtained by considering only the first mode. Thus, the dynamics of the beam is described by a simple second order motion equation : M d 2x dt 2 dx kx F (9) dt where t is time, x is the displacement, M the mass of the platform, F the electrostatic force, is the damping coefficient and k the spring constant. The electrostatic force is related to the voltage V [12] : F 0AV 2 0b a l a V2 2 d d x 2 d x (10) The optical behaviour of the MOEMS is determined by the transfer matrix method [13]. The global transfer matrix [T] of a MOEMS, including N successive layers, is a product of N transfer matrices [Tk], taking into account the interface i,i+1, the thickness di and the wave vector ki of each individual layer. T11 T12 [T] = [T1 ][T2 ]...[TN ] T21 T22 (11) When a time domain simulation of the entire component including electrical, mechanical and optical behaviour is required, modifications of the thickness of the air cavity as well as the two air gaps next to the cavity, due to applied electrostatic force, are updated to the global transfer matrix [T] at each simulator time step. We have assumed that the information channel bandwidth BI is small compared to the optical filter bandwidth BF. Thus, the optical output O of the model is the sum of the contributions of each individual channel, calculated by multiplying the channel contents chi(i,t) by its transfer function Hi{[T(i,x(t))])} at i, where x(t) is the displacement of the beam center (relation 12). O = H i T(i , x(t)) chi (i ,t) (12) i Simulation results The comparison between measured and simulated spectra shows good agreement (fig. 4), concerning the resonance wavelength shift versus tuning voltage. Such a behavioural model allows to link naturally the physical design parameters of the MOEMS, and system specifications : the hierarchical structure of the language allows, in one hand, the transfer of system specifications to technological parameters of the devices and, on the other hand, an effective measurement of the influence of the devices on the performance of the system. The global optimisation of the whole system (including its elementary components) is then made possible. As an example, a WDM network has been modelled in a mixed-signal environment. The optical and optoelectronic components are described by HDLA models and the network controller with VHDLlike models[14],[15]. 4-Optical interconnects In the short term, interconnects will be a severe bottleneck in the evolution of electronic systems performances. According to the SIA roadmap, next generation technologies will lead to specifications that metallic interconnects will not be able to reach [16]. Table 1 shows such constraints for the near-2010 50nm technology. Table 1: predictive performances of VLSI circuits in the early 2010 Technology generation Transistors/chip (microprocessor) Chip size Number of package pins On-chip clock Chip to chip buses Supply voltage Maximum dissipated power <50nm >500 M 600 mm2 >2000 >1GHz >1GHz <1V >150W Optical solutions are potentially available to alleviate some of these constraints, essentially because they offer a better bandwidth/power compromise comparing to electrical interconnects as soon as the length of the link exceeds some millimeters. Since they do not withstand exactly the same constraints, and, then, do not address the same optical alternative, it is usual to distinguish on-chip and chipto-chip interconnects. On-chip optical interconnects Figure 4: Comparison between experimental and simulated tuning characteristics The increase of the integration density will allow one to realise VLSI’s with tenths of millions of transistors working at some gigahertz clock frequencies. Such potential will certainly lead to improve the functionality of the chips in two concurrent ways: the design of new architectures and/or the integration of present discrete VLSIs in a unique one. In such a context, it is possible to mention, from now on, some improvements that optical interconnects may provide: the increase of high frequency connectivity between functional blocks and the relative simplicity of the clock distribution. Guided optics is certainly most suited for high density connectivity and technological compatibility requirements that on-chip interconnects demand, although integrated microsources are not yet available. Modelling and simulation of guided optics use different methods and algorithms. In the case of integrated guides, coupled wave phenomena impose to solve Maxwell’s equations, moreover the constraint of simulating photonic systems in the time domain lead to use a FDTD (finite difference - time domain) method [17], [18]. Unfortunately, FDTD is drastically time consuming since the discretisation step has to be smaller than the wavelength. We are investigating, at the present time, the transfer of FDTD simulation files to HDL models. Chip-to-chip interconnects On chip-to-chip scale, optical alternatives have been investigated from several years and solutions have been prototyped, they aim to increase the global throughput of chips and/or to give new solutions to the problem of massive reconfigurable links needed for multiprocessor systems. In most cases, proposed solutions use VCSEL’s and fibre or free-space propagation; some investigate integrated photonics. 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