Abstract

The propagation of surface plasmon polaritons on metallic waveguides adjacent to a gain medium is considered. It is shown that the presence of the gain medium can compensate for the absorption losses in the metal. The conditions for existence of a surface plasmon polariton and its lossless propagation and wavefront behavior are derived analytically for a single infinite metal-gain boundary. In addition, the cases of thin slab and stripe geometries are also investigated using finite element simulations. The effect of a finite gain layer and its distance from the SPP waveguide is also investigated. The calculated gain requirements suggest that lossless gain-assisted surface plasmon polariton propagation can be achieved in practice for infrared wavelengths.

© 2004 Optical Society of America

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References

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Appl. Phys. Lett.

N. Hatori, M. Sugawara, K. Mukai, Y. Nakata and H. Ishikawa, �??Room-temperature gain and differential gain characteristics of self-assembled InGaAs/GaAs quantum dots for 1.1-1.3 m semiconductor lasers,�?? Appl. Phys. Lett. 77, 773-775 (2000).
[CrossRef]

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian and N. F. Borrelli, �??Room-temperature gain at 1.3 μm in PbS-doped glasses,�?? Appl. Phys. Lett. 75, 3060-3062 (1999).
[CrossRef]

P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, K. Domen and K. Horino, �??Doping-dependent optical gain in GaN,�?? Appl. Phys. Lett. 76, 2994-2996 (2000).
[CrossRef]

N. Kirstaedter, O. G. Schmidt, N. N. Ledentsov, D. Bimberg, V. M. Ustinov, A. Y. Egorov, A.E. Zhukov, M. V. Maximov, P.S. Kopev and Z. I. Alferov, �??Gain and differential gain of single layer InAs/GaAs quantum dot injection lasers,�?? Appl. Phys. Lett. 69, 1226-1228 (1996).
[CrossRef]

IEEE J. Quant. Elec.

T. Saitoh and T Mukai, �??1.5 μm GaInAsP traveling-wave semiconductor laser amplifier,�?? IEEE J. Quant. Elec. QE-23, 1010-1020 (1987).
[CrossRef]

J. of Appl. Physics

S. Y. Hu, D. B. Young, S. W. Corzine, A.C. Gossard, L. A. Coldren, �??High-efficiency and low-threshold InGaAs/AlGaAs quantum-well lasers,�?? J. of Appl. Physics 76 , 3932-3934 (1994).
[CrossRef]

JETP Lett.

B. Ya Kogan, V. M. Volkov and S. A. Lebedev, �??Superluminescence and generation of stimulated radiation under internal-reflection conditions,�?? JETP Lett. 16, 100 (1972).

JOSA

G. A. Plotz, H. J. Simon, J. M. Tucciarone, �??Enhanced total reflection with surface plasmons,�?? JOSA 69, 419-421 (1979).
[CrossRef]

Nature

W. L. Barnes, A. Dereux and T. W. Ebbesen, �??Surface plasmon subwavelength optics,�?? Nature 424, 824�?? 830 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. B

P. Berini, �??Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,�?? Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Semiconductors

N. A. Pikhtin, S. O. Sliptchenko, Z. N. Sokolova and I. S. Tarasov, �??Analysis of threshold current density and optical gain in InGaAsP quantum well lasers,�?? Semiconductors 36, 344-353 (2002).
[CrossRef]

Solid State Comm.

J. R. Sambles, �??Grain-boundary scattering and surface-plasmon attenuation in noble-metal films,�?? Solid State Comm. 49, 343-345 (1984).
[CrossRef]

Sov. Phys.Tech. Phys

A. N. Sudarkin and P. A. Demkovich, �??Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,�?? Sov. Phys.Tech. Phys. 34, 764-766 (1989).

Other

H. Raether, Surface plasmons on smooth and rough surfaces and on gratings (Springer Verlag, 1988).

E. D. Palik, Handbook of optical constants of solids vol. I (Academic Press, 1985).

C. Vassalo, Optical waveguide concepts (Elsevier, 1991).

F. A. Fernández and Y. Lu, Microwave and optical waveguide analysis by the finite element method, (Wiley, 1996).

L.A. Coldren and S. W. Corzine, Diode lasers and photonic integrated circuits, (Wiley , 1995).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic illustration of various SPP propagation regimes as a function of ε1.

Fig. 2.
Fig. 2.

Plots of: (a) Im(kx ), (b) propagation length, (c) wavefront tilt angle and (d) Im( k z 1 ) versus gain. The points corresponding to lossless propagation, zero wavefront tilt and bound surface wave limit, respectively, are also shown.

Fig. 3.
Fig. 3.

FEA simulations of total electric field for SPPs propagating on a silver interface embedded in an InGaAsP-based gain medium: (a) Symmetric mode in slab configuration without gain, kx =14.06+i0.0197 µm-1. (b) Symmetric mode in slab configuration with gain, kx =14.06 µm-1. (c) Symmetric mode in stripe configuration without gain, kx =13.76+i0.0094 µm -1. (d) Symmetric mode in stripe configuration with gain, kx =13.76 µm-1.

Fig. 4.
Fig. 4.

(a) Metallic stripe waveguide of Fig. 3 in proximity to a gain layer with finite thickness. (b) FEA generated results showing variation of gain required for lossless propagation as the gap d increases. Each curve corresponds to a different value of gain layer thickness h.

Equations (12)

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{ E j = ( E x , 0 , E z j ) exp ( i ( k x x + k z j z ω t ) ) H j = ( 0 , H y , 0 ) exp ( i ( k x x + k z j z ω t ) ) , j = 1 , 2
{ ε 1 k z 1 = ε 2 k z 2 k z 2 + k z i 2 = ε i k 0 2 E x = k z i ω ε i H y , E z i = k x ω ε i H y i = 1 , 2
{ k x 2 = k 0 2 ε 1 ε 2 ε 1 + ε 2 ( a ) k z i 2 = k 0 2 ε i 2 ε 1 + ε 2 ( b )
{ k x 2 = k 0 2 ( ε 1 + i ε 1 ) ( ε 2 + i ε 2 ) ( ε 1 + ε 2 ) + i ( ε 1 + ε 2 ) ( a ) k z i 2 = k 0 2 ( ε i + i ε i ) 2 ( ε 1 + ε 2 ) + i ( ε 1 + ε 2 ) ( b )
k z 1 k 0 ε 1 + ε 2 ( ε 1 + ε 2 ) 2 + ( ε 1 + ε 2 ) 2 ( ε 1 + i ε 1 ) ( 1 i ( ε 1 + ε 2 ) 2 ( ε 1 + ε 2 ) )
( ε 1 ) 2 + ε 2 ε 1 + 2 ε 1 ( ε 1 + ε 2 ) < 0
ε 2 ( ε 2 ) 2 8 ε 1 ( ε 1 + ε 2 ) 2 < ε 1 < ε 2 + ( ε 2 ) 2 8 ε 1 ( ε 1 + ε 2 ) 2
k x 2 = k 0 2 ( ε 1 + ε 2 ) 2 + ( ε 1 + ε 2 ) 2 [ ε 1 ( ( ε 2 ) 2 + ε 1 2 ε 1 ε 2 + ( ε 2 ) 2 ) + i ε 2 ( ( ε 1 ) 2 + ε 2 2 ε 2 ε 1 + ( ε 1 ) 2 ) ]
ε 1 = ε 2 2 2 ε 2 ( 1 ± 1 4 ( ε 1 ε 2 ) 2 ε 2 4 ) { ε 2 2 ε 2 + ( ε 1 ) 2 ε 2 ε 2 2 ( a ) ( ε 1 ) 2 ε 2 ε 2 2 ( b )
γ 0 = 2 π λ 0 ε 2 ( ε 1 ) 3 2 ( ε 2 ) 2 + ( ε 2 ) 2
P = 1 2 Re ( E 1 × H * ) = H y 2 2 ω [ Re ( k x ε 1 ) x ̂ + Re ( k z 1 ε 1 ) z ̂ ]
Re ( k z 1 ε 1 ) = Re ( k 0 ε 1 + ε 2 + i ( ε 1 + ε 2 ) ) k 0 ( ε 1 + ε 2 ) 2 ( ε 1 + ε 2 ) 3 2

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