Polaritonics in nanowires made from dispersive materials Mahi R. Singh Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, Canada N6A 3K7 Received 19 May 2009; revised manuscript received 15 July 2009; published 3 November 2009 We have studied the optoelectronics of a polaritonic nanowire which is fabricated by embedding a polari- tonic crystal into another polaritonic crystal. It is considered that the band gap of the embedded crystal lies within the band gap of the host crystal. This band-gap engineering is satisfied by GaP and MgO crystals where MgO is the host crystal. Polaritons in the nanowire are confined within the embedded crystal. Bound states of the confined polaritons are calculated using the transfer-matrix method. The bound polariton energies are evaluated for a GaP-MgO nanowire. It is found that the number of bound states in the wire depends on its size, well depth, and the barrier height. The absorption coefficient of the system has also been calculated by using the time-dependent Schrödinger equation method. Numerical simulations for the GaP-MgO nanowire show that when the resonant energy of a quantum dot lies near the bound states the spectrum has several transparent states. The nanowire can be switched among the transparent or absorbing states by tuning the resonant state of the quantum dot. The present findings can be used to make types of polaritonic devices such as polaritonic switches and transistors. DOI: 10.1103/PhysRevB.80.195303 PACS numbers: 73.21.-b I. INTRODUCTION Recently there has been considerable interest in studying the properties of polaritonic materials. 1–11 Examples of these materials include semiconductors i.e., GaP, GaAs, and SiC, oxide crystals i.e., MgO, and salts. They are also called dispersive materials. 1–3 Polaritonic materials have energy gaps in their dispersion relation due to the coupling between optical phonons and photons. 1–4 In this paper we study the optoelectronic properties of nanowires made from polari- tonic materials. In polaritonic materials the radiation signals are carried out by an admixture of photons and optical phonons rather than electrons or photons. An admixture of photons and op- tical phonons create a new quantum particle called polari- tons. The study of characterizations and applications of these materials is called “polaritonics.” Polaritons propagate with frequencies in the range of hundreds of gigahertz to several terahertz THz. Therefore, polaritonics lies in an intermedi- ate regime between photonics and electronics. The new field of polaritonics is going to be useful because electronics suffers technological and physical barriers to in- crease speed whereas photonics requires lossy integration of a light source and guiding structures. 5,6 Therefore, it bridges the gap between electronics and photonics. It has a wide range of applications, including high bandwidth signal pro- cessing, THz imaging, and THz spectroscopy. 5,6 Rupasov and Singh 1 have shown that there is the suppres- sion of spontaneous emission when a quantum dot is placed within polaritonic materials. We found a polariton-dot bound state in which the polaritons are localized in the vicinity of the dot. We have also shown that bound polariton BP soli- tons can be created in these materials. 1 Lau and Singh 2 have studied the spontaneous emission rate of polaritons in III-V semiconductors when two two-level atoms are doped. It is found that when the two atoms are very close to each other the degenerate states split into a symmetric and an antisym- metric states. The system in the symmetric state can radiate a polariton with a probability that is twice that of the indepen- dent dot case. This is known as super-radiance. Nonlinear two-polariton absorption has also been studied in polaritonic materials doped with an ensemble of three- level quantum dots. 3 It was considered that the quantum dots are interacting with each other via the dipole-dipole interac- tion. It has been found that two-photon absorption can be turned on and off when the decay resonance energy of the three-level quantum dots is moved within the lower energy band. The inhibition of two-polariton absorption can also be achieved by controlling the strength of the dipole-dipole in- teraction. Polaritonic waveguides and resonators are also fabricated through the femtosecond laser machining of holes or trenches which are carved through LiNbO 3 or LiTaO 3 host crystals. 5–7 Infrared and optical 111 polaritons propagation have also been investigated in a polaritonic wire made from an isotropic dielectric material coated with metal. 8 The wire contains surface bound modes which did not exist previously in the dielectric material. Polaritons have also been studied in periodic and quasip- eriodic multilayers made up of both positive SiO 2  and negative refractive index materials. 9 Polaritonic band gaps have been found in these structures. The reflection and ab- sorption measurements for polaritons have been performed in ferroelectric crystals in the terahertz region. 10 Photonic crystals have also been fabricated by using polaritonic materials. 11 In the present paper polaritonic nanowires are fabricated by embedding a polaritonic material into another. A sche- matic diagram for the nanowire is shown in Fig. 1. It is considered that the embedded polaritonic material has a smaller band gap than the host material. For example, the semiconductor GaP has a smaller band gap than that of MgO see Fig. 2. Therefore, a nanowire can be fabricated by em- bedding GaP into MgO. Because of this band-gap engineer- ing, the polaritons are confined in the embedded materials and have bound states. The radius of the wire is taken in the order of several hundred nanometers. PHYSICAL REVIEW B 80, 195303 2009 1098-0121/2009/8019/1953038 ©2009 The American Physical Society 195303-1