JW3A.53.pdf
Frontiers in Optics 2017 © OSA 2017
Electrically Pumped Spaser Based on Semiconductor Film with Graphene Nanosheet Sergey G. Moiseev1,2,*, Yuliya S. Dadoenkova1,3, Igor O. Zolotovskii1 2
1 Ulyanovsk State University, 42 Leo Tolstoy Str., 432017 Ulyanovsk, Russian Federation Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Ulyanovsk Branch, 48/2 Goncharov Str., 432011 Ulyanovsk, Russian Federation 3 Donetsk Institute for Physics and Technology, 72 Rosa Luxemburg Str., 83114 Donetsk, Ukraine * Corresponding author:
[email protected]
Abstract: We propose a model of slow surface plasmon polariton distributed feedback laser (spaser) with pump by drift currents in graphene. This model is a kind of hybrid of a distributed feedback laser and a travelling-wave tube, well-known in microwave technology. The amplification of surface plasmon polariton wave is created by drift currents in the graphene, and the feedback is realized due to a periodic change of the semiconductor film thickness. OCIS codes: (240.6680) Surface plasmons; (250.5403) Plasmonics; (240.3990) Micro-optical devices
1. Introduction The effective amplification of surface plasmon polaritons (SPPs) is the main problem of the further development of plasmon technologies (SPPs) [1,2]. Obviously, the amplification with provided feedback can lead to the generation of SPP waves. Such structures, called SPP lasers (spasers), can be used for numerous practical applications. A new mechanism of the SPP wave amplification due to the energy transfer from an electric drift current in graphene into a far-infrared surface wave propagating along a semiconductor-dielectric boundary has been proposed in our paper [3]. It has been shown that in the spectral region of high slowing-down of SPP the amplification coefficient can reach values considerably exceeding the SPP damping coefficient. In this Communication, we demonstrate numerically that this approach can be easily expanded to design a plasmon polariton distributed feedback laser with pump by DC current in graphene nanosheet. 2. Generation of SPP in a film structure with pump by DC current We consider a waveguide structure composed of semi-infinite dielectric cladding and substrate with dielectric permittivities 1 and 3 , respectively, and a semiconductor film with dielectric permittivity 2 2 i 2 ( 2 0 ) placed between them. A graphene single-layer is placed on semiconductor-substrate interface as shown in Fig. 1(a). In graphene, an electric current is induced by an applied voltage U 0 , and the direction of electron flux coincides with the SPP propagation direction. The spatial modulationon of the semiconductor film thickness (with period of modulation and modulation depth d ) provides modulation of the SPP wavevector which is necessary for generation conditions. Taking into account the graphene single-layer with the conductivity [4], the dispersion equation for SPP wave in the considered structure has the form: q q q q3 2 i 4 q2 q3 , exp( 2q2 d ) 2 1 1 2 2 3 q21 q1 2 q2 3 q3 2 i 4 q2 q3
(1)
where q j 2 k02 j is the transverse component of SPP wavevector in medium j 1, 2, 3 , i is the longitudinal component of SPP wavevector ( 0 , which corresponds to the SPP damping in the propagation direction), k 0 c and c are the wavevector and speed of light in vacuum, respectively. Note that the phase velocity Vph of the SPP excited in a thin semiconductor film is relatively small in comparison to that of the waves propagating in any media of the waveguiding structure [5]. In this case k 0 , so that Vph c . Such slow surface wave can be amplified by a flux of charged particles in graphene [3]. On the basis of the solutions obtained for the amplitudes of the forward and backward SPP waves, we found the expression for the transmission coefficient T of SPP wave with modulated wavevector ( x ) 1 cos 2 х / :
JW3A.53.pdf
T S exp( L) ( 2 i ) sinh( SL) S cosh( SL) 2
with S
Frontiers in Optics 2017 © OSA 2017 2
(2)
2 2 i , where is the SPP amplification coefficient, d / 2 1 is the 2
2
depth of the SPP wavevector modulation, m is the phase synchronism detuning (m is any integer), and L is the length of graphene film. The calculated transmittivity T is shown in Fig. 1(b) as function of the period of the structure for angular frequency 27.6 s-1. The amplification coefficient of the SPP for the considered frequency is about 100 cm–1, and the loss coefficient is about 2 cm–1. One can see that in the vicinity of two values of the period = 0.327 m and = 0.334 m the transmittivity demonstrates an abrupt increase with T , which corresponds to the conditions of the SPP generation.
(a)
(b)
FIG. 1. (a) Schematic of a plasmonic waveguide structure with spacially modulated semiconductor film thickness with period and modulation depth d . (b) Dependence of the transmission coefficient of SPP wave on period of the structure at frequency 27.6 s-1 and for the depth of the SPP wavevector modulation 0.01 and m 1 . The parameters of the structure: 1 1 , 3 4 , thickness of the film (a p-type semiconductor AlGaAs) is d 0.1μm , the length of graphene film is d 200 μm , and the applied voltage is U 0 10 V . 3. Conclusion We have shown that in the waveguiding system containing a semiconductor film and a graphene single-layer with a DC current it is possible to achieve the SPP generation by the proper selection of the period and depth modulation of semiconductor film thickness. In this kind of spaser the amplification is created by fast drift currents propagating in the graphene, and the feedback is realized due to a periodic change in the thickness of the semiconductor film. 4. Acknowledgments This work was supported by the Ministry of Education and Science of the Russian Federation (Project No. 14.Z50.31.0015, State Contracts Nos. 3.3889.2017, 3.7614.2017/П220 and 3.5698.2017/П220) and the Russian Foundation for Basic Research (Project No. 17-02-01382). 5. References [1] S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Optics Communicstions 258, 295–299 (2006). [2] I. de Leon, P . Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nature Photonics 4, 382–7 (2010). [3] Y. S. Dadoenkova, S. G. Moiseev, A. S. Abramov, A. S. Kadochkin, A. A. Fotiadi, I. O. Zolotovskii, “Surface plasmon polariton amplification in semiconductor–graphene–dielectric structure,” Annalen der Physik (Berlin) 529, 1700037(1-7) (2017). [4] G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” Journal of Applied Physics 103, 064302 (2008). [5] D. Korobko, S. Moiseev, and I. Zolotovskii, “Induced modulation instability of surface plasmon polaritons,” Optics Letters 40, 4619-4622 (2015).
