Lasing Dynamics of A Novel Silicon Photonic Crystal Cavity

Abstract

In this paper we proposed novel silicon laser design based on the dispersion engi- neered photonic crystals. With the unique self-collimation property, we design an optical cavity with a Q factor of 2000. The strong mode conflnement in the low index active material ofiers an opportunity to realize a lasing mechanism. To investigate the lasing dynamics we introduce the rate equations of atomic system into the electromagnetic polarization. With these auxil- iary difierential equations we solve the time evolutions of the electromagnetic waves and atomic populations by using the FDTD method. DOI: 10.2529/PIERS060907132027 Silicon, the leading material in microelectronics during the last four decades, also promises to be the key material in the future. Recent activities have focused on the achieving active functionalities, mostly light ampliflcation and generation. However, due to the fundamental limitation related to the indirect bandgap of the bulk Si, the development of silicon gain and laser becomes one of most challenging goal in the silicon photonics and optoelectronics. Many difierent approaches have been taken to achieve this goal. Recently stimulated Raman scattering efiect has been used to demonstrate the light ampliflcation and lasing in the silicon both in pulse and continuous-wave operation. (1,_ 2)In the presented work, we attempt to design a novel silicon laser. To this end, we will design a novel optical cavity based on the dispersion engineered photonic crystals (PhCs). To observe the lasing dynamics, we will incorporate the rate equations of a four level atomic system into the device to simulate the gain and absorption of the active material. By solving the Maxwell's equations with these auxiliary difierential equations with the Finite-difierence Time-domain (FDTD) method, we will track the time evolutions of the electromagnetic waves and atomic populations. 2. DISPERSION BASED PHOTONIC CRYSTAL CAVITY The light propagation in a PhC is most appropriately interpreted through a dispersion diagram, which characterizes the relationship between the frequency of the wave, !, and its associated wavevector, k. Dispersion surfaces provide the spatial variation of the spectral properties of a certain band within the photonic crystal structure. Electromagnetic wave vectors propagate at directions normal to the dispersion surface as shown in Fig. 1, which stems from the relation vg = rk!(k). The equil frequency contour (EFC) can lead to beam divergence or convergence as shown in the flgure. The ability to shape the EFCs, and thereby engineer the dispersion properties of the PhC, opens up a new paradigm for the design of optical devices. (3{5) For self-collimation, we desire a ∞at EFC, in which case the wave is only allowed to propagate along those directions normal to the sides of the straight curvatures. As such, it is possible to vary the incident wavevector over a wide range of angles and yet maintain a narrow range of propagating angles within the PhC. Consider silicon photonic crystals perforated by a square lattice with holes back-fllled by the gain medium, i.e., Er-doped glasses, as shown in the inset of Fig. 2(a). The hole has radius of 0.3a, where a is the lattice constant. The silicon and glass have refractive indices of 3.5 and 1.5, respectively. The dispersion surface of flrst band diagram is plotted in Fig. 1(a). By carefully selecting the frequency, one can obtain a ∞at curvature within certain angular range at specifled frequency, i.e., 0.18c/a, as depicted in Fig. 1(b), where the blue curvature is the dispersion contour in the free space with frequency of 0.18a. Such ∞atness of the curvature ofiers self-collimation along iM direction within a wide incident angular range. Self-collimation efiect has been widely used in the applications of optical routing, sensors, vari- able beam splitters, self collimated optical emitters to enhance the emission from a light emitting diode. In the presented paper we propose a novel design of silicon laser based on the self-collimation phenomena. Fig. 2 depicts the schematic chart of our design. A photonic crystal cavity consists of