# Integrated IR Modulator with a Quantum Cascade Laser
## 3 Simulations  
The pulse operation performances of the laser modulator were analyzed using SPICE (Simulation Program with Integrated Circuit Emulation) models of the switching module and the prepared electrical model of the QC laser (LTSpice XVII software ver.17.0.27.0, Analog Devices, Norwood, MA, USA). During the simulations, no parameters for the PCB technology were included. Such assumptions simplify the scope of simulations but should be considered in actual conditions [28]. Its manufacturer delivered the SPICE description of the switching module. For the QC laser, the SPICE model was prepared using data from Alpes Lasers (St Blaise, Switzerland) for the lasing structure, and IXYS Corporation (Milpitas, CA, USA) for the inductance of the laser package [29, 30]. In Figure 2, an electrical  
Figure 1: Optical power and voltage vs. current of the mounted QC laser (**a**) and a picture of the integrated IR modulator (**b**).  
schematic of the IR lighting device is presented. The Alpes laser model combines a resistor (\(R_{\text{L}}\)) and two capacitors (C\({}_{1}\), C\({}_{2}\)). The \(R_{\text{L}}\) values depend on the laser operation point (e.g., for a low current: 10-20 \(\Omega\), and for the lasing current: 1-3 \(\Omega\)). The C\({}_{1}\) (\(\sim\)100 pF) and C\({}_{2}\) (below 100 pF) are mainly determined by bonding pads and laser mounting technologies, respectively. IXYS Corporation determines the inductance level (\(L\)) for various signal interface technologies applied in laser housings. For example, a connection of two points at a distance of 0.2 mm, with a copper wire 0.014 mm in diameter and a height of 0.06 mm, gives an inductance of 3.6 nH.  
A simulation of the light device was performed for different lasing structure electrical parameters (Figure 3). The reactance parts of load impedance did not influence the pulse amplitude (Figure 3a,b). The capacitances generate some oscillations at the pulse rising edge caused by feedback signals conditions. Growing these capacitances, the response time constant also increases. The most critical issue is load inductance, considering pulse shape and its oscillations. We observed a slower modulator response and current high-level changes for both biasing ranges. A current-voltage dependence for the inductor and signal resonance conditions defined these effects. Even at the rising and falling parts of the pulse, these signal fluctuations can be the critical point for the current amplitude, causing, e.g., laser structure damage. The bonding pad capacitance is an almost ideal plate capacitor with a PTFE dielectric [31]. For inductance, the bonding wire generally is 1 nH/mm. However, all of these parameters vary from laser to laser. To reduce pulse degradation, i.e., overshoot and ringing, any unnecessary hardware between the switching unit and the laser must be avoided. That is why the laser's direct and short connection to the electronics is preferable [32].  
The load resistance has a direct influence on current amplitude and response time constant (Figure 3c). High resistance attenuates signal fluctuations at the pulse rising edge and increases its fall time. The current level is inversely proportional to this resistance. This is a crucial issue with regard to QCL's switching with dynamic resistance. There is a need to supply lasing structure to ensure population inversion (high resistance--low current--no light) and to emit photons (low resistance--high current--light) [33].  
Figure 2: Electrical scheme of the IR modulator (\(V_{\text{DD}}\)—voltage supply of the module, \(VI\) (\(CI\))—voltage control of output current, \(EF\)-\(EN\)—differential triggering signals).