Theoretical investigation of metal–metal waveguides for terahertz quantum-cascade lasers

Optical and Quantum Electronics, Sep 2014

We report our theoretical investigations of metal–metal waveguides for terahertz quantum-cascade lasers. The device is considered as a planar, multilayer structure. The optical properties of constituent materials are calculated according to Drude–Lorenz model. The Helmholtz equation is solved numerically using transfer matrix method. We concentrate on selecting the proper metallic material for claddings to minimize the waveguide losses. In addition, we analyze the consequences of inserting Ti separation layers between claddings and semiconductor core for blocking the destructive diffusion of metals into the active layer and improving the adhesion.

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Theoretical investigation of metal–metal waveguides for terahertz quantum-cascade lasers

Micha Szyma nski Anna Szerling Kamil Kosiel We report our theoretical investigations of metal-metal waveguides for terahertz quantum-cascade lasers. The device is considered as a planar, multilayer structure. The optical properties of constituent materials are calculated according to Drude-Lorenz model. The Helmholtz equation is solved numerically using transfer matrix method. We concentrate on selecting the proper metallic material for claddings to minimize the waveguide losses. In addition, we analyze the consequences of inserting Ti separation layers between claddings and semiconductor core for blocking the destructive diffusion of metals into the active layer and improving the adhesion. The terahertz region of the electromagnetic spectrum proves its usability in number of applications including security screening, (bio)chemical detection, remote sensing, nondestructive materials evaluation, communications, astronomy, biology and medicine (Williams 2007; Belkin 2009). Therefore the development of compact, cheap, high-power and convenient continuous-wave radiation sources in this range is strongly desired. The terahertzemitting quantum-cascade lasers (THz QCLs) seem to be an excellent response for these needs. The first THz QCL was demonstrated in 2002 as a cryogenic device. Obviously, for most practical applications, such feature is not acceptable. A lot of efforts are made to fabricate - Table 1 List of symbols used in the paper = n2 Thickness (subscript in the text denote layer numbers or materials) Free space wavevector Confinement factor Background dielectric constant Dielectric constant (subscripts in the text denote materials) Free space wavelength devices able to lase in higher, at least TEC-controlled, temperatures. Here, it is useful to recall the formula for threshold gain, valid for any semiconductor laser: gth = List of symbols can be found in Table 1. All the parameters on the right side of Eq. (1) are determined by the passive waveguide structure, while the material gain depends on the carrier transport and radiative properties of the quantum-well gain medium. Minimizing the threshold gain generally results in reduced threshold current densities and increased operating temperatures (Kohen 2005). Therefore two ways leading to improvements of THz QCL can be distinguished: (i) designing new lasing schemes with higher gain and (ii) lowering the waveguide loss. For example, present temperature performance record of 200 K has been achieved mainly due to approach (i), namely by optimizing the lasing transition oscillator strength of the resonant phonon based three-well design (Fathololoumi 2012). In this theoretical work, we explore the path (ii). Our investigations deal with metal metal waveguides commonly used for THz QCLs. Our goal is to select the proper metallic material for claddings and thus to minimize the waveguide losses wg . In addition, we analyze the consequences of inserting separation layers between claddings and semiconductor core for blocking the destructive diffusion of metals into the active layer and improving the adhesion. Fig. 1 Geometry of the planar waveguide. Coordinates x, y, z indicate the directions: across the epitaxial layers, lateral and of wave propagation, respectively. To the right one can see the field components 2 The model THz QCLs can be considered as planar waveguides. Schematic view of such a structure is shown in Fig. 1. It is well known that QCLs support TM modes only (Sirtori 2002). The further analysis will be based on these two facts. 2.1 Modes of the laser waveguide The total electromagnetic field of TM mode can be determined by Hy , which satisfies the Helmholtz equation (Marcuse 1974): Hy (x ) = 0, According to the transfer matrix method and boundary conditions imposed on the layer interfaces we get the following dispersion equation (Chilwell and Hodgkinson 1984): where m pq are elements of the transfer matrix defined as () = M+1m11 + M+10m12 + m21 + 0m22 = 0, M = Mm = In Eqs. (3) and (4) m = n2mmk0 0/ 0, m = (k02n 2m 2) and m = m dm . Numerical solution of Eq. (3) provides the propagation constant = n e f f k0. The waveguide loss can be calculated as: 2.2 Material parameters The optical properties of metals as well as highly doped semiconductors are determined by the behaviour of free carriers, which exhibit well known collective charge oscillations, i.e. plasmons. Introducing the volume plasma frequency and using the classical DrudeLorenz model, it is possible to calculate the refractive index as (Lu 2009): where = 1 + 1/( )2 and = me f f e/e is the relaxation time. For calculating n Ga As with different doping levels, we created our own software. We assumed me f f = 0.063 me (http://www.ioffe.ru/SVA/NSM/), e = 0.85 m2/(Vs) for low doping (http://www.ioffe.ru/SVA/NSM/), e = 0.2 m2/(Vs) for highly doped contact lay2 ers (Zivanov and Zivanov 1995) and b = n Ga As , where n Ga As = 2.99 is the value measured for 0 = 100 m by trans (...truncated)


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Michał Szymański, Anna Szerling, Kamil Kosiel. Theoretical investigation of metal–metal waveguides for terahertz quantum-cascade lasers, Optical and Quantum Electronics, 2015, pp. 843-849, Volume 47, Issue 4, DOI: 10.1007/s11082-014-0007-z