Abstract

Coupling of surface plasmon (SP) waves between two metal-dielectric interfaces of a dielectric-metal-dielectric (DMD) waveguide, in which one of the dielectric layers is incorporated with optical gain, is proposed to realize plasmonic lasing. The propagation characteristics of the SP waves supported inside the DMD waveguides are studied by finite-difference time-domain method. It is found that there are optimized thicknesses for the metal film and gain region to obtain minimum propagation loss. Furthermore, a coupled-mode model is developed to analyze the lasing characteristics of the DMD waveguides with coherent optical feedback. The conditions to achieve single-longitudinal-mode lasing from the DMD waveguides are also investigated.

© 2008 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
  2. D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
    [CrossRef] [PubMed]
  3. J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
    [CrossRef] [PubMed]
  4. M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, "Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium," Opt. Express 16, 1385-1392 (2008).
    [CrossRef] [PubMed]
  5. M. P. Nezhad, K. Tetz, and Y. Fainman, "Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides," Opt. Express 12, 4072-4079 (2004).
    [CrossRef] [PubMed]
  6. P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B. 61, 10484-10503 (2000).
    [CrossRef]
  7. S. L. Chuang, Physics of Optoelectronic Devices (John Wiley and Sons, 1995).
  8. H. M. A. Moneim, L. Z. Ismail, G. A. Fatah, and Z. A. Zohdy, "Radiative fluorescence lifetime of rhodamin doped in PVC," Polym. Test. 20, 135-139 (2001).
    [CrossRef]
  9. B. G. Huth and M. R. Kagan, "Dynamics of Flashlamp-pumped Rhodamine 6G Laser," IBM J. Res. Dev. 15, 278 (1971).
    [CrossRef]
  10. Ya. I. Khanin, Fundamentals of Laser Dynamics (Cambridge International Science Publishing, 2005).
  11. L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
    [CrossRef]
  12. S. F. Yu, T. I. Yuk, and P. Shum, "Dynamic analysis of erbium-doped optically pumped waveguide lasers using a time-domain travelling wave model," Opt. Quantum Electron. 29, 683-696 (1997).
    [CrossRef]
  13. R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Elect. 21, 144-150 (1985).
    [CrossRef]

2008

2005

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

2004

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

2001

H. M. A. Moneim, L. Z. Ismail, G. A. Fatah, and Z. A. Zohdy, "Radiative fluorescence lifetime of rhodamin doped in PVC," Polym. Test. 20, 135-139 (2001).
[CrossRef]

2000

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B. 61, 10484-10503 (2000).
[CrossRef]

1997

S. F. Yu, T. I. Yuk, and P. Shum, "Dynamic analysis of erbium-doped optically pumped waveguide lasers using a time-domain travelling wave model," Opt. Quantum Electron. 29, 683-696 (1997).
[CrossRef]

1994

L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
[CrossRef]

1985

R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Elect. 21, 144-150 (1985).
[CrossRef]

1971

B. G. Huth and M. R. Kagan, "Dynamics of Flashlamp-pumped Rhodamine 6G Laser," IBM J. Res. Dev. 15, 278 (1971).
[CrossRef]

Adegoke, J. A.

Bahoura, M.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).

Bergman, D. J.

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Berini, P.

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures," Phys. Rev. B. 61, 10484-10503 (2000).
[CrossRef]

Carroll, J. E.

L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).

Eng, L.

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Fainman, Y.

Fatah, G. A.

H. M. A. Moneim, L. Z. Ismail, G. A. Fatah, and Z. A. Zohdy, "Radiative fluorescence lifetime of rhodamin doped in PVC," Polym. Test. 20, 135-139 (2001).
[CrossRef]

Grafstrom, S.

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Henry, C. H.

R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Elect. 21, 144-150 (1985).
[CrossRef]

Huth, B. G.

B. G. Huth and M. R. Kagan, "Dynamics of Flashlamp-pumped Rhodamine 6G Laser," IBM J. Res. Dev. 15, 278 (1971).
[CrossRef]

Ismail, L. Z.

H. M. A. Moneim, L. Z. Ismail, G. A. Fatah, and Z. A. Zohdy, "Radiative fluorescence lifetime of rhodamin doped in PVC," Polym. Test. 20, 135-139 (2001).
[CrossRef]

Kagan, M. R.

B. G. Huth and M. R. Kagan, "Dynamics of Flashlamp-pumped Rhodamine 6G Laser," IBM J. Res. Dev. 15, 278 (1971).
[CrossRef]

Kazarinov, R. F.

R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Elect. 21, 144-150 (1985).
[CrossRef]

Marcenac, D. D.

L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
[CrossRef]

Mayy, M.

Moneim, H. M. A.

H. M. A. Moneim, L. Z. Ismail, G. A. Fatah, and Z. A. Zohdy, "Radiative fluorescence lifetime of rhodamin doped in PVC," Polym. Test. 20, 135-139 (2001).
[CrossRef]

Nezhad, M. P.

Noginov, M. A.

Nowell, M. C.

L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
[CrossRef]

Plumb, R. G. S.

L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
[CrossRef]

Podolskiy, V. A.

Reynolds, K.

Ritzo, B. A.

Seidel, J.

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Shum, P.

S. F. Yu, T. I. Yuk, and P. Shum, "Dynamic analysis of erbium-doped optically pumped waveguide lasers using a time-domain travelling wave model," Opt. Quantum Electron. 29, 683-696 (1997).
[CrossRef]

Stockman, M. I.

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Tetz, K.

Yu, S. F.

S. F. Yu, T. I. Yuk, and P. Shum, "Dynamic analysis of erbium-doped optically pumped waveguide lasers using a time-domain travelling wave model," Opt. Quantum Electron. 29, 683-696 (1997).
[CrossRef]

L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
[CrossRef]

Yuk, T. I.

S. F. Yu, T. I. Yuk, and P. Shum, "Dynamic analysis of erbium-doped optically pumped waveguide lasers using a time-domain travelling wave model," Opt. Quantum Electron. 29, 683-696 (1997).
[CrossRef]

Zhang, L. M.

L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
[CrossRef]

Zhu, G.

Zohdy, Z. A.

H. M. A. Moneim, L. Z. Ismail, G. A. Fatah, and Z. A. Zohdy, "Radiative fluorescence lifetime of rhodamin doped in PVC," Polym. Test. 20, 135-139 (2001).
[CrossRef]

IBM J. Res. Dev.

B. G. Huth and M. R. Kagan, "Dynamics of Flashlamp-pumped Rhodamine 6G Laser," IBM J. Res. Dev. 15, 278 (1971).
[CrossRef]

IEEE J. Quantum Elect.

R. F. Kazarinov and C. H. Henry, "Second-order distributed feedback lasers with mode selection provided by first-order radiation loss," IEEE J. Quantum Elect. 21, 144-150 (1985).
[CrossRef]

L. M. Zhang, S. F. Yu, M. C. Nowell, D. D. Marcenac, J. E. Carroll, and R. G. S. Plumb, "Dynamic analysis of radiation and side-mode suppression in a 2nd-order dfb laser using time-domain large-signal traveling-wave model," IEEE J. Quantum Elect. 30, 1389-1395 (1994).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).

Opt. Express

Opt. Quantum Electron.

S. F. Yu, T. I. Yuk, and P. Shum, "Dynamic analysis of erbium-doped optically pumped waveguide lasers using a time-domain travelling wave model," Opt. Quantum Electron. 29, 683-696 (1997).
[CrossRef]

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, 10484-10503 (2000).
[CrossRef]

Phys. Rev. Lett.

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

J. Seidel, S. Grafstrom, and L. Eng, "Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution," Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Polym. Test.

H. M. A. Moneim, L. Z. Ismail, G. A. Fatah, and Z. A. Zohdy, "Radiative fluorescence lifetime of rhodamin doped in PVC," Polym. Test. 20, 135-139 (2001).
[CrossRef]

Other

S. L. Chuang, Physics of Optoelectronic Devices (John Wiley and Sons, 1995).

Ya. I. Khanin, Fundamentals of Laser Dynamics (Cambridge International Science Publishing, 2005).

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Figures (12)

Fig. 1.
Fig. 1.

Instant distribution of |Hz|2 intensity for the coupling SP waves propagating along the two metal interfaces of the DMD waveguide (a) without and (b) with gain at the bottom of the dielectric medium (at y<0). The corresponding schematic diagrams of the DMD waveguides under end-fire coupling to the SP waves are also given.

Fig. 2.
Fig. 2.

Variation of (a) propagation loss, α, and (b) coupling coefficient, M, of the DMD waveguide with different thickness of metal film,

Fig. 3.
Fig. 3.

Variation of (a) propagation loss, α, and (b) coupling coefficient, M, of the DMD waveguide with different thickness of gain region, tg .

Fig. 4.
Fig. 4.

Plot of (a) propagation coefficient, α, and (b) coupling coefficient, M, of a waveguide with the variation of real part of refractive index of the gain region, nreal .

Fig. 5.
Fig. 5.

Transition stats in R6G dye doped polymer.

Fig. 6.
Fig. 6.

Schematic diagram of a SP laser with cladding layer, gain medium and substrate of same refractive index.

Fig. 7.
Fig. 7.

Transient response of (a) SA and SC and (b) N 2 for DMD waveguide with coated facets r L=r R=0.92 pumped at Pext =1.03 times threshold. (c) Steady-state lasing spectra of SA for the facet coated DMD laser with Pext equals to P 1 (1.03×threshold), P 1 (2.0×threshold) and P 3 (3×threshold).

Fig. 8.
Fig. 8.

(a). Plot of spatial distribution of SA (black) and SC (red). (b) Calculated steady-state lasing spectra without (top) and with (bottom) plasmonic coupling taken into consideration.

Fig. 9.
Fig. 9.

Schematic diagram of a DMD waveguide with periodic grating.

Fig. 10.
Fig. 10.

Transient response of (a) SA and SC and (b) N 2 for the AR coating (i.e., r L=rR =0) DMD waveguide with grating κ=80 cm-1 and Pext =1.03 times its threshold.

Fig. 11.
Fig. 11.

Spatial distribution of (a) SA , (b) SC , (c) N 2 and (d) steady-state lasing spectra of SA for the AR coated DMD laser with κ=80 cm-1 and Pext equals to P 1 (1.03×threshold), P1 (2.0.threshold) and P 3 (3×threshold).

Fig. 12.
Fig. 12.

Spatial distribution of (a) SA , (b) SC , (c) N 2 and (d) steady-state lasing spectra of SA for the cleaved facets DMD laser with κ=80 cm-1 and Pext equals to P 1 (1.03×threshold), P 1 (2.0×threshold) and P 3 (3×threshold)..

Equations (20)

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d N 2 ( x , t ) d t = [ R 13 ( x , t ) + W a ] N 1 ( x , t ) [ W e + τ R 2 1 ] N 2 ( x , t ) ,
N 1 ( x , t ) + N 2 ( x , t ) N dye ,
R 13 ( x , t , λ P ) = A eff 1 σ P 13 ( λ P ) h v P P pump ,
W a ( x , t , λ S ) = A eff 1 σ S a ( λ S ) P S 0 ( λ s ) h v S S A ( x , t ) ,
W e ( x , t , λ S ) = A eff 1 σ S e ( λ S ) P S 0 ( λ s ) h v S S A ( x , t ) ,
[ 1 V g d d t ± d d x ] S C ± = [ α + j δ β ] S C ± + j M S A ±
[ 1 v g d d t ± d d x ] S A ± = [ ( Γ g S α ) + j δ β ] S A ± + j M S C ± + χ A ±
g S = σ S e N 2 σ S a N 1
S A = S A + 2 + S A 2
S C = S C + 2 + S C 2
S A + ( x = 0 , t ) = r L S A ( x = 0 , t ) and S A ( x = L , t ) = r R S A + ( x = L , t )
S C + ( x = 0 , t ) = r L S C ( x = 0 , t ) and S C ( x = L , t ) = r R S C + ( x = L , t )
χ A ( z , t ) χ A * ( z ' , t ' ) = P spont δ ( z z ' ) δ ( t t ' ) ,
χ A ( z , t ) χ A ( z ' , t ' ) = 0 ,
P spont = β s v g σ S e τ R 2 1 N 2 ,
P pump ( t ) = { 0 t < 0 P ext t 0 ,
H ( ω ) 2 = ( 1 b ) 2 1 + b 2 2 b cos ( ( ω ω p ) Δ t ) ,
S A + ( t + Δ t , x + Δ x ) = B · S A + ( t , x + Δ x ) + ( 1 B ) · S A + ( t , x ) ,
[ 1 v g d d t ± d d x ] S C ± = [ α + j δ β ] S A ± + j M S A ± + j κ S C
κ Δ n λ S Γ g sin ( 2 π b Λ )

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