Quantum Nanoplasmonics and the Spaser

Transcription

1 Photo Credit: I. Tsukerman, Seefeld, Austria, January, Department 2009 of Physics and Astronomy US Israel Binational Science Foundation Quantum Nanoplasmonics and the Spaser Mark I. Stockman Department of Physics and Astronomy,, Atlanta, GA 30303, USA Donostia, Spain p.1

2 CONTENTS Introduction Quantum theory of spaser Spaser in stationary (CW) mode Spaser as a nanoamplifier Experimental observation of the spaser in qualitative comparison with theory Conclusions Donostia, Spain p.2

3 The original spaser geometry Spaser field per one plasmon in the core Donostia, Spain p.3

4 Spaser is the ultimately smallest quantum nano-generator For small nanoparticles, radiative loss is negligible. Spaser is fully scalable Donostia, Spain p.4

5 These equations of spaser theory are nonlinear to describe non-equilibrium Department second-order of Physics and phase Astronomy transition to spasing arxiv: Journal of Optics, 12, (2010) Quantum Theory of SPASER Nondiagonal element of density matrix (polarization): p) ( p) ( p) ~ ( i ( ) i n a ~ ( p) n 12 ( p) 12 A d n ( p) 12 ( r n p ) / Diagonal elements of density matrix (inversion): n ( p) 12 4 Im ~ ( p) ( p) ( p) ( p) a (1 n ) g(1 n ) n SP field amplitude (semiclassical approximation): ~ )* ( p) ( p a i ( ) a ia n n Spectral width of spaser emission (due to quantum fluctuations of plasmon population number ) D. J. Bergman and M. I. Stockman, Surface Plasmon Amplification by Stimulated Emission of Radiation: 0 Quantum Generation Nanoplasmonics of Coherent and the Surface Spaser, Plasmons in s Donostia, Spain p.5 Nanosystems, Near-Field Phys. Rev. Optics Lett , (2003) 2N 1 p n n 2 n 12 p 12 12, 12

6 arxiv: Journal of Optics, 12, (2010). Donostia, Spain p.6

7 SPASER Threshold h Condition [Consistent t with original i PRL 90, (2003)]: arxiv: Journal of Optics, 12, (2010). The spasing is essentially ill a quantum effect. It is non-relativistic: does not depend on c The spasing condition does not directly contain gain per cm and dthe Purcell llfactor [E. M. Purcell, Phys Rev 69, 681 (1946)] but is related to them Donostia, Spain p.7

8 Gain of bulk Department mediumof Physics required and for Astronomy spasing and for loss compensation by gain: Georgia M. I. State Stockman, University Spaser Action, Loss Compensation, and Stability in Plasmonic Systems with Gain, Phys. Rev. Lett. 106, (2011); Phil. Trans. R. Soc. A 369, 3510 (2011). g g th s( ), g c d ; () d th m d Re s( ) Im m( ) 1 Re s( ) 1 Re s( ) 0 Realistic gain for direct band-gap semiconductors Donostia, Spain p.8

9 Stationary (CW) spaser regime Department of Physics and Astronomy Plasmon number This quasilinear dependence of the number of plasmons per mode N n (g) is a result of the very strong feedback in spaser due to the small modal volume vs. pumping rate Inversion vs. pumping rate Spectral shape of spaser line arxiv: Journal of Optics, 12, (2010). Spectral line width 1/ s N SP g 1 Line width vs. pumping rate Spectral shape of spaser line Spectral shape of spaser line Donostia, Spain p.9

10 This invention changed civilization as we know it This invention is used many more times than all others combined This is the most valuable element of nanotechnology: nanoamplifier, whose pairs in c-mos technology form digital bistable amplifiers and logical gates for information processing MOSFET US Patent Bandwidth ~ GHz Low resistance to ionizing radiation Donostia, Spain p.10

11 Scaling of Spaser 3/2 R MV Field in spaser: E ~ N ~ 3/2 p Np R 10 nm cm Heat per flop: g H N p g, g c Re s( ) Im m( ), s s( ) d th th Threshold: 1 Re ( ) ( ) Switching time: d 10 nm 100 ~ fs R N p 3 Conclusion: Spaser is orders of magnitude more efficient (less heat per flop) and much faster than transistor. It can operate close to the quantum limit. i d m Donostia, Spain p.11

12 The spaser as a Nanoamplifier Major problem: any yquantum amplifier (laser and spaser) in a CW regime possesses exactly zero amplification (it is actually a condition for the CW operation). We have proposed to set the spaser as a nanoamplifier in two ways: 1. In transient mode (before reaching the CW regime), the spaser still possesses non-zero amplification 2. With a saturable absorber, the spaser can be bistable. There are two stable states: with the zero coherent SP population ( logical zero ) and with a high SP population that saturates the absorber ( logical one state). Such a spaser will function as a threshold (digital) amplifier Donostia, Spain p.12

13 Stationary pumping Department of Physics and Astronomy Bandwidth ~ THz Very high resistance to ionizing radiation Amplification in Spaser with a Saturable Absorber (1/3 of the gain chromophores) SP coherent population Population inversion SP coherent population Population inversion Pulse pumping Donostia, Spain p.13

14 Experimental Observations of Spaser Donostia, Spain p.14

15 Donostia, Spain p.15

16 1d plasmonic field confinement Donostia, Spain p.16

17 Donostia, Spain p.17

18 2d plasmonic field confinement Donostia, Spain p.18

19 1d +2d plasmonic field confinement Donostia, Spain p.19

20 Donostia, Spain p.20

21 Plasmonic Green Nanolaser Based on a Metal Oxide Semiconductor Department of Physics and Astronomy Structure, Chen-Ying Georgia State Wu, Cheng-Tai University Kuo, Chun-Yuan Wang, Chieh-Lun He, Meng- Hsien Lin, Hyeyoung Atlanta, GA Ahn, and Shangjr Gwo, Nano Lett. 11, (2011). Donostia, Spain p.21

22 Donostia, Spain p.22

23 For theory of periodic system of spasers see also: E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky, Stationary Behavior of a Chain of Interacting Spasers, Phys. Rev. B 85, (2012). Donostia, Spain p.23

24 Operation of electrically-pumped room-temperature telecom-frequency spaser Donostia, Spain p.24

25 BRIEF CONCLUSIONS 1. Spaser is a nanoscopic quantum generator of coherent and intense local optical fields 2. Spaser can also serve as a nanoscale ultrafast quantum amplifier with a switch time ~100 fs for silver and ~10 fs for gold. It has the same size as MOSFET and can perform the same functions but is ~1000 times faster. 3. Numerous spasers (plasmonic nanolasers) have been designed and observed with 1d, 2d, and 3d confinement 4. Periodic gain-plasmonic i systems (metamaterial) t show pronounced spasing behavior both in theory and experiment 5. The most promising applications of the spasers are an ultrafast nanoamplifier, local optical energy source, active nano-label, and an element of metamaterials with compensated loss 6. Conditions of loss compensation and spasing in a periodic plasmonic metamaterial with gain are identical. Above the threshold, there will be spasing and gain saturation preventing loss compensation. Donostia, Spain p.25

26 END Lecture Donostia, 1 Spain p.26

27 Donostia, Spain p.27

28 This device is very much like a spaser Donostia, Spain p.28

29 CONTENTS Introduction Quantum Q t theory of spaser Spaser in stationary (CW) mode Spaser as a nanoamplifier Experimental observation of the spaser Conclusions on spasers Spasing and loss compensation in plasmonic systems with gain Conclusions on loss compensation Donostia, Spain p.29

30 Donostia, Spain p.30

31 Consider an isotropic i metamaterial that can be described dby complex permittivity and permeability. A known homogenization procedure leads to an exact result for the (effective) )permittivity of the composite Hear E is the macroscopic field and e(r) is the (mesoscopic) local field inside the metamaterial. This local field is expressed as an eigenmode expansion where E n (r) is the eigenmode field. Assume that: there is a resonance with an n-th eigenmode, the metal has a high quality factor, Q>>1, and the metal s fill factor f is not too small, so Qf>>1. Then the local field is Donostia, Spain p.31

32 Then the effective permittivity becomes (where b n >0 is a coefficient): In the case of the full inversion (maximum gain) and in exact resonance, the imaginary part of the host-medium permittivity describes stimulated emission as given by the standard expression Donostia, Spain p.32

33 4 d Department of Physics and Astronomy nc 1 Re s( ) 1 Re s( ) Im ( ) m or g g th, g th c d Re s( ) Im m( ) 1 Re s( ), where g is the required gain This is a criterion for both the loss compensation and spasing, the latter obtained previously in: M. I. Stockman, The Spaser as a Nanoscale Quantum Generator and Ultrafast Amplifier, Journal of Optics 12, (2010) This criterion is analytical and exact, provided that the metamaterials is resonant and dense, and that its eigenmodes are non-uniform in space -- hot spots or reflection from facets -- create a feedback Thus, an attempt at a full compensation of losses will cause spasing instead, which will saturate the gain transition, eliminate the net gain, clamp the inversion, and make the complete loss compensation impossible This criterion does not depend on the geometry of the system or any specific hot spots of local fields, predicated on the gain medium filling all the space left by the metal Donostia, Spain p.33

34 Spasing criterion as a function of optical frequency. The straight line (red on line) represents the threshold for the spasing and full loss compensation, which take place for the curve segments above it. (a) Computations for silver. The chromophore concentration is n c = 6 x10 18 cm -3 for the lower curve (black) and n c = 3x10 19 cm -3 for the upper curve (blue). The magenta solid circle and black diamond show the values of the spasing criterion for the conditions of Refs. 2 and 3, respectively. (b) Computations for gold. The chromophore concentration is n c = 3x10 19 cm -3 for the lower curve (black) and n c =2x10 20 cm -3 for the upper curve (blue). 1. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, Loss-Free and Active Optical Negative-Index Metamaterials, Nature 466, (2010). 2. M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, Stimulated Emission of Surface Plasmon Polaritons, Phys. Rev. Lett. 101, (2008). Donostia, Spain p.34

35 CONTENTS Introduction Quantum Q t theory of spaser Spaser in stationary (CW) mode Spaser as a nanoamplifier Experimental observation of the spaser Conclusions on spasers Spasing and loss compensation in plasmonic systems with gain Conclusions on loss compensation Donostia, Spain p.35

36 BRIEF CONCLUSIONS The same criterion is obtained for both the loss compensation and spasing This criterion is analytical and exact, provided that the metamaterials is resonant and dense, and that its eigenmodes are non-uniform in space (contain hot spots ), which creates an inherent feedback Thus, an attempt at a full compensation of losses will cause spasing instead, which will saturate the gain transition, eliminate the net gain, clamp the inversion, and make the complete loss compensation impossible This criterion does not depend on the geometry of the system or any specific hot spots of local fields, predicated on the gain medium filling all the space left by the metal Donostia, Spain p.36