Superradiance, Amplification, and Lasing of Terahertz Radiation in an Array

of Graphene Plasmonic Nanocavities

V. V. Popov,1 O. V. Polischuk,1 A. R. Davoyan,1 V. Ryzhii,2 T. Otsuji,2 and M.S. Shur3

1Kotelnikov Institute of Radio Engineering and Electronics (Saratov Branch),Saratov 410019, Russia

2Research Institute for Electrical Communication, Tohoku University,Sendai 980-8577, Japan

3Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute,

Troy, New York 12180, USA

Outline

Optical conductivity of pumped graphene

Terahertz photonics vs terahertz plasmonics

Array of graphene nanocavities - electromagnetic approach

Terahertz amplification and plasmonic lasing condition

Confinement and superradiance of plasmon modes

Conclusions

Bound- and Free-carrier Oscillations at THz

1 THz 4 meV 50 K

1 ps 0.64 meV 8 K

B 24 meV @300 Kk T THz

Bk T

quantum transitions

free carrier oscillations

THz/

/ 2 pump,D E j E

0Re , 0 THz energy gainE

Carrier Relaxation Dynamics in Graphene

J.M. Dawlaty et al.APL 92 (2008) 042116

P.A. George et al.Nano Lett. 8 (2008) 4248

J.H. Strait et al.Nano Lett. 11 (2011) 4902

Evolution of the carrier distribution function

Quasi-equilibration via carrier-carrier scattering

Energy relaxation and Recombination via opticalphonons and carrier-carrierinteraction

Population inversion!

after 20~200 fs after a few ps

－

＋

Complex-Valued Sheet Conductivity of Pumped Graphene

2B F F F F

2 2B B 0

8 2 ( , ) ( / 2, )4( ) ln 1 exp tanh 4 (1 ) 4 ( ) 4

k T G Ge di k T k T i

B

B B

sinh( / )( , )cosh( / ) cosh( / )

k TGk T k T

intraband processes interband transitions

L.A. Falkovsky, S.S. Pershoguba,Phys. Rev. B 76, 153410 (2007)G.W. Hanson, J. Appl. Phys. 103, 064302 (2008)A.A. Dubinov, V.Ya. Aleshkin, V. Mitin, T. Otsuji, and V. Ryzhii, J. Phys.: Condens. Matter 23, 145302 (2011)

2F F/ eV

μ 250000 cm2/V∙s (1 ps) for 40 meV M. Orlita et al, Phys. Rev. Lett. 101, 267601 (2008)M. Sprinkle et al, Phys. Rev. Lett. 103, 226803 (2009)J.M. Dawlaty et al, Appl. Phys. Lett. 92, 042116 (2008)T. Otsuji et al, J. Phys. D: Appl. Phys. 45, 303001 (2012)

( )F F ( )n pn pV N N N E

Gain and Loss Regimes

=1 ps =0.1 ps

B 24 meV @300 Kk T

3 THz 12 meV 150 K

THz photonics vs THz plasmonics

A. Satou et al. F.T. Vasko, V. Ryzhii, Phys. Rev. B 78, 115431 (2008)

V. Ryzhii et al. J. Appl. Phys. 110,094503 (2011)

S. Boubanga-Tombet et al. Phys. Rev. B 85 (2012) 035443

T. Li et al. Phys. Rev. Lett. 108 (2012)167401

F. Rana, IEEE Trans. Nanotechnol. 7, 91 (2008)

A.A. Dubinov et al. J. Phys.: Condens. Matter 23, 145302 (2011)

A. Bostwick et al. Nature Physics 3, 36 (200

F. Rana et al. Phys. Rev. B 84 (2011) 045437

Stimulated emission of THz plasmons in graphene

Stimulated emission of IR and THzphotons in graphene

high quality factor – weak dephasingsmall active volume – small gain

strong confinement – large gainstrong dephasing – low quality factor

Graphene photonic THz laser ? Graphene plasmonic THz laser

Planar Array of Graphene Nanocavities

Me Me Me Me Gr Me 0Me Gr

2( ) ( , ) ( ) ( , ) ( )1

j x K x x j x dx K x x j x dx E

Gr Gr Gr Gr Me Gr 0Gr Me

2( ) ( ) ( , ) ( ) ( ) ( , ) ( ) ( )1

j x K x x j x dx K x x j x dx E

Electromagnetic Approach

D.V. Fateev, V.V. Popov, and M.S. Shur, Semiconductors 44, 1406 (2010)

Me Gr are the electric current densities in the graphene nanocavity and metal contact( ) and ( ) j x j x

Electromagnetic approach treats the plasmon radiative damping self-consistently,which is important for describing the lasing process

The system of the integral equations for the array of graphene microcavities over the structure period, 0 < x < L, is

Plasmon Resonances in Graphene Microcavities

00.5(1- )RmaxresA

maxresA

=1 ps, a=2m, L=4m

absorption

Fano-like

amplification

Self-Excitation Regime

rad scg

300 K blackbody radiation amplified above the mW/cm2

rad scg

Plasmon Lasing Condition

(s-e) (s-e)F Frad sc, ,g E E

At lasing condition,the plasmon coherence in strongly non-equilibrium grapheneis restored due to constructive balance of the plasmon gain and plasmon radiative damping:

THz Apmplification in Plasmonic Nanocavities

a=200 nm, L=400 nm

=1 ps =0.1 ps

Re[Gr(ω)]>0

Re[Gr(ω)]<0Re[Gr(ω)]<0

Re[Gr(ω)]>0

Plasmonic Confinement and Superradiance

lasingTHz 100 m

graphene nanocavities

2 2F2 /e q E

2 /q a

number of cavities / unit lengh of the arrayrad

Superradiance:

Giant amplification (exceeding 103) and lasing of THz radiation due to stimulated generation of plasmons in the array of graphene resonant micro/nanocavities is predicted.

The amplification of THz wave at the plasmon resonance frequencies is several orders of magnitude stronger than away from the resonances.

THz lasing is possible for strong coupling between plasmons and THz radiation due to constructive balance of the plasmon gain and plasmon radiative damping. The lasing at the plasmon resonance is achieved when the plasmon gain balances the dissipative and radiative plasmon damping.

Giant THz wave amplification is ensured due to strong plasmon confinement, plasmon local-field enhancement, and superradiant nature of THz emission by the array of plasmonic micro/nanocavities.

Conclusions