Learning semiconductor laser characteristics using virtual analogue simulation

International Journal of Electrical Engineering Education, Jan 1998 by Cheung, W N

Abstract This article describes a simple method for simulating typical characteristics of semiconductor lasers based on the rate equations of the device. The method being implemented in PSpice may be used to demonstrate the light-current characteristics, charge number clamping, modulation response, transient and nonlinear behaviour of semiconductor laser diodes.

1 INTRODUCTION

Analogue or digital intensity modulation of semiconductor lasers are being used increasingly in communication systems. Short-haul optical fibre links between satellite dish and receiving terminals has accelerated the use of direct microwave modulation on semiconductor lasers. Modern high speed data links are mostly implemented using fibre optics. In such applications, the system designer has a need to model the laser characteristics both in the electronic and optical domains. A common approach is to apply various equivalent circuits of the semiconductor laser to suit separately the need of small- or large-signal conditions1-2.

Equivalent circuits are useful to describe specific aspects of a device. They are dependent on the bias point and are usually derived from the rate equations under the condition of small-signal perturbation about the bias point. Because of the nonlinear interaction between electrons and photons, equivalent circuits of the semiconductor laser are usually approximate and restricted in their applications. A single equivalent circuit is generally not accurate enough for the purpose of describing both large-signal intensity switching and small-signal operation.

It is shown in this paper that an easily implemented simulation program based on the rate equations will enable us to find the d.c., a.c., and transient characteristics of semiconductor lasers. All such characteristics are obtainable within a simulation program based on PSpice3. Moreover, the program allows us to monitor nonlinear distortion which may be present in the modulation product.

2 SIMULATION PROGRAM

3 SEMICONDUCTOR LASER CHARACTERISTICS

For a set of device parameters as given in Table 1, the light-current characteristics can be obtained by a d.c. sweep and the result is as shown in Fig. 2. All voltage scales in our simulation should be interpreted as the analogue of currents, i.e., there is a conversion scale of 1 mA per mV reading. VBIAS stands for the bias or injection current. Curve (a) shows the normalised light output (y) versus bias current, and curve (b) shows the normalised charge numbers (x) in the cavity. It is clear that the light output is very small when the injection current is below the threshold value Ith, which is equal to 30 mA in this case, and over this range of injection current, the electron population builds up linearly as the input current increases. Once operating above threshold, stimulated emission increases. The electron number is then clamped at an almost constant level, with any additional injection current converted to light. Curve (c) denotes the injection current I and it is very close to the sum of the steadystate values of electrons (x) and photons (y). The threshold current depends on the device parameters4, and it can be adjusted on the simulation program.

The light intensity of the laser can be modulated by adding a signal component to the bias current. Both frequency response for small-signal modulation and transient response for digital modulation are easily obtainable from the model. For the above device biased at 21^sub th^, a 1 mA input signal produces a frequency response as shown in Fig. 3, which clearly shows the resonance characteristics in the laser. Curve (a) shows the low-pass characteristics of the light modulation, which agrees with theoretical calculation using small-signal equivalent circuits'. Curve (b) indicates the band-pass nature of electron numbers in the cavity in response to bias modulation, and its response is very much less than that of photons because the electron number is basically clamped to the threshold value. One can easily demonstrate that the resonant frequency increases as the bias current is increased.

If a digital signal is used instead of a sinusoid, we obtain the transient response of the laser diode as shown in Fig. 4. Curve (a) is the input digital signal with pulse amplitude equal to I^sub th^. Curve (b) shows the light output, displaying the characteristic ringings at pulse transitions with high oscillating frequency at the upward transition and low frequency at the downward transition. Curve (c) shows the transient variation of electron number in the laser with the average value remaining largely unchanged.

When two signals at closely spaced frequencies f^sub 1^ and f^sub 2^ are modulating the laser, nonlinearities in the device will cause second- and third-order products to be generated. Second-order products (2f^sub 1^, 2f^sub 2^,f^sub 1^ f^sub 2^) are of concern in broadband systems, whereas third-order products (2f^sub 1^ f^sub 2^, 2f^sub 2^ f^sub 1^) may generate in-band intermodulation distortion in narrow band systems. Fig. 5(a) shows the sum of two signals, one at 1.2 GHz and the other at 1.4 GHz. The bias is at 2I^sub th^, and each signal amplitude is equal to 0.53I^sub th^. The signals may represent two nearby TV channels within the bandwidth of a satellite transponder, which, when down-converted, fall within the frequency range of 0.9 to 1.6 GHz. Fig. 5(b) shows the corresponding light output. In this case the negative swing of the modulation is hardly deep enough to turn off the laser. Fig. 6 shows the frequency spectrum of the light output in which both second harmonics at 2.4 and 2.8 GHz, and intermodulation products at 1.0 and 1.6 GHz are clearly seen. If the overall transponder signal has a large enough negative peak as to cause the laser to turn off momentarily, there will be an additional amount of `ringing noise' accompanying the light output as shown in Fig. 7.