Laser Thermal Tuning by Transient Analytical Analysis of Peltier Device

In any wavelength sensitive application, extensive care should be taken in addressing the wavelength drift issues. In the case in which laser tuning is conducted by using thermoelectric cooler, an accurate expression is needed to describe transient characteristics of the Peltier device to achieve maximum controllability. In addition, thermal tuning issues are of particular relevance to the field of photonic integration. In this paper, the exact solution of the governing equation is presented, considering Joule heating, heat conduction, heat flux of the laser diode, and the thermoelectric effect in one dimension. In addition, the variable separation method and the Sturm-Liouville theorem, along with the completeness features of eigenfunctions, are used to obtain time-dependent electrical potential and temperature distribution of the Peltier device. Additionally, steady-state sensitivity analysis is performed in order to demonstrate the impacts of physical parameters on its thermoelectric characteristics. Transient temperature is also considered that, for a specific case, revealed fast transition to steady-state condition with time constant lower than 400 ms. Lower heat capacity, as well as laser diode heat flux, might lead to faster Peltier response times, such that the effect of heat flux on response time becomes negligible in low heat capacity Peltier.