Abstract

We analyze the steady-state transmission of high-momentum (high-k) electromagnetic waves through metal-semiconductor multilayer systems with loss and gain in the near-infrared (NIR). Using a semi-classical optical gain model in conjunction with the scattering matrix method (SMM), we study indium gallium arsenide phosphide (InGaAsP) quantum wells as the active semiconductor, in combination with the metals, aluminum-doped zinc oxide (AZO) and silver (Ag). Under moderate external pumping levels, we find that NIR transmission through Ag/InGaAsP systems may be enhanced by several orders of magnitude relative to the unpumped case, over a large angular and frequency bandwidth. Conversely, transmission enhancement through AZO/InGaAsP systems is orders of magnitude smaller, and has a strong frequency dependence. We discuss the relative importance of Purcell enhancement on our results and validate analytical calculations based on the SMM with numerical finite-difference time domain simulations.

© 2015 Optical Society of America

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References

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2015 (2)

C. Duncan, L. Perret, S. Palomba, M. Lapine, B. Kuhlmey, and C. de Sterke, “New avenues for phase matching in nonlinear hyperbolic metamaterials,” Sci. Rep. 5, 8983 (2015).
[Crossref] [PubMed]

T. Galfsky, H. Krishnamoorthy, W. Newman, E. Narimanov, Z. Jacob, and V. Menon, “Active hyperbolic meta-materials: enhanced spontaneous emission and light extraction,” Optica 2, 62–65 (2015).
[Crossref]

2014 (9)

D. Lu, J. Kan, E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nature Nano. 9, 48–53 (2014).
[Crossref]

K. Sreekanth, K. Krishna, A. D. Luca, and G. Strangi, “Large spontaneous emission rate enhancement in grating coupled hyperbolic metamaterials,” Sci. Rep. 4, 6340 (2014).
[Crossref] [PubMed]

T. Xu and H. Lezec, “Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial,” Nature Comm. 5, 4141 (2014).
[Crossref]

J. S. T. Smalley, F. Vallini, B. Kante, and Y. Fainman, “Modal amplification in active waveguides with hyperbolic dispersion at telecommunication frequencies,” Opt. Express 22, 21088–21105 (2014).
[Crossref] [PubMed]

C. Riley, T. Kieu, J. S. T. Smalley, S. Pan, S. Kim, K. Post, A. Kargar, D. Basov, X. Pan, Y. Fainman, D. Wang, and D. Sirbuly, “Plasmonic tuning of aluminum doped zinc oxide nanostructures by atomic layer deposition,” Phys. Stat. Sol. RRL 8, 948–952 (2014).
[Crossref]

J. S. T. Smalley, Q. Gu, and Y. Fainman, “Temperature dependence of the spontaneous emission factor in sub-wavelength semiconductor lasers,” IEEE J. Quantum Electron. 50, 175–185 (2014).
[Crossref]

R. Savelev, I. Shadrivov, and Y. Kivshar, “Wave scattering by metal-dielectric multilayer structures with gain,” J. Exp. Theor. Phys. Lett. 100, 831–836 (2014).

K. Sreekanth, A. De Luca, and G. Strangi, “Excitation of volume plasmon polaritons in metal-dielectric meta-materials using 1D and 2D diffraction gratings,” J. Opt. 16, 105103 (2014).
[Crossref]

L. Ferrari, D. Lu, D. Lepage, and Z. Liu, “Enhanced spontaneous emission inside hyperbolic metamaterials,” Opt. Express 22, 4301–4306 (2014).
[Crossref] [PubMed]

2013 (6)

A. Orlov, I. Iorsh, P. Belov, and Y. Kivshar, “Complex band structure of nanostructured metal-dielectric metamaterials,” Opt. Express 21, 1593–1598 (2013).
[Crossref] [PubMed]

K. Sreekanth, A. De Luca, and G. Strangi, “Experimental demonstration of surface and bulk plasmon polaritons in hypergratings,” Sci. Rep. 3, 3291 (2013).
[Crossref] [PubMed]

G. Naik, V. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: Beyond gold and silver,” Adv. Mat. 25, 3264–3294 (2013).
[Crossref]

S. Zhukovsky, O. Kidwai, and J. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21, 14982–14987 (2013).
[Crossref] [PubMed]

C. Aryropoulos, N. Estakhri, F. Monticone, and A. Alu, “Negative refraction, gain, and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21, 15037–15047 (2013).
[Crossref]

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B,  87, 115139 (2013).
[Crossref]

2012 (4)

J. Khurgin and G. Sun, “Practicality of compensating the loss in the plasmonic waveguides using semiconductor gain medium,” Appl. Phys. Lett. 100, 011105 (2012).
[Crossref]

K. Ding, Z. C. Liu, M. T. Hill, M. J. H. Marell, P. J. van Veldoven, R. Noetzel, and C. Z. Ning, “Room-temperature continuous wave lasing in deep-subwavelength metallic cavities under electrical injection,” Phys. Rev. B 85, 041301 (2012).
[Crossref]

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14, 063001 (2012).
[Crossref]

2011 (2)

S. Wuestner, A. Pusch, K. Tsakmakidis, J. Hamm, and O. Hess, “Gain and plasmon dynamics in active negative-index metamaterials,” Phil. Trans. Royal Soc. A 369, 3525–3550 (2011).
[Crossref]

X. Ni, S. Ishii, M. Thoreson, V. Shalaev, S. Han, S. Lee, and A. Kildishev, “Loss-compensated and active hyperbolic metamaterials,” Opt Express 19, 25242–25254 (2011).
[Crossref]

2010 (5)

I. D. Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nature Photon. 4, 382–387 (2010).
[Crossref]

S. Xiao, V. Drachev, A. Kildishev, X. Ni, U. Chettiar, H. Yuan, and V. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

F. Krayzel, R. Polles, A. Moreau, M. Mihailovic, and G. Granet, “Simulation and analysis of exotic non-specular phenomena,” J Europ Opt Soc 5, 10025 (2010).
[Crossref]

M. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nature Photon. 4, 395–399 (2010).
[Crossref]

S. Gedney and B. Zhao, “An auxiliary differential equation formulation for the complex-frequency shifted PML,” IEEE Trans. Antennas Propag. 58, 838–847 (2010).
[Crossref]

2008 (3)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[Crossref] [PubMed]

J. Anker, W. Hall, O. Lyandes, N. Shah, J. Zhao, and R. V. Duyne, “Biosensing with plasmonic nanosensors,” Nature Mat. 7, 442–453 (2008).
[Crossref]

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit, Nature Materials 7, 435–441 (2008).
[Crossref] [PubMed]

2007 (2)

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402 (2007).
[Crossref]

M. Hill, Y. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. van Veldhoven, F. van Otten, T. Eijkemans, J. Turkiewicz, H. de Waardt, E. Geluk, S. Kwon, Y. Lee, R. Notzel, and M. Smit, “Lasing in metallic-coated nanocavities,” Nature Photon. 1, 589–594 (2007).
[Crossref]

2006 (5)

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E 74, 046618 (2006).
[Crossref]

B. Wood, J. Pendry, and D. Tsai, “Directed sub-wavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[Crossref]

Z. Jacob, L. Alekseyev, and E. Nariminov, “Optical hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. Panoiu, K. Malloy, R. Osgood, and S. Brueck, “Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks,” Opt. Express 14, 6778–6787 (2006).
[Crossref] [PubMed]

W. Barnes, “Surface plasmon-polariton length scales: a route to sub-wavelength optics,” J. Opt. A: Pure Appl. Opt. 8, S87–S93 (2006).
[Crossref]

2005 (1)

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 (3)

2003 (1)

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[Crossref]

2002 (1)

S. G. Tikhodeev, A. L. Yablonski, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[Crossref]

1999 (1)

J. Homola, S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sensors and Actuators B: Chemical 54, 3–15 (1999).
[Crossref]

1995 (2)

N. Cotter, T. Presit, and J. Sambles, “Scattering-matrix approach to multilayer diffraction,” J. Opt. Soc. Am. A 12, 1097–1103 (1995).
[Crossref]

T. Visser and H. Blok, “Modal analysis of a planar waveguide with gain and loss,” IEEE J. Quantum Electron. 31, 1803–1810 (1995).
[Crossref]

1988 (2)

D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Phys. Rev. B 38, 9945–9951 (1988).
[Crossref]

D. Y. K. Ko and J. Sambles, “Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals,” J. Opt. Soc. Am. A,  51863–1866 (1988).
[Crossref]

1979 (1)

R. Nicholas, J. Portal, C. Houlbert, P. Perrier, and T. Pearsall, “An experimental determination of the effective masses for Gax In1−x Asy P1−y alloys grown on InP,” Appl. Phys. Lett. 34, 492–494 (1979).
[Crossref]

1972 (1)

P. Johnson and R. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370 (1972).
[Crossref]

Alekseyev, L.

Alu, A.

Anker, J.

J. Anker, W. Hall, O. Lyandes, N. Shah, J. Zhao, and R. V. Duyne, “Biosensing with plasmonic nanosensors,” Nature Mat. 7, 442–453 (2008).
[Crossref]

Arnold, J.

G. Slavcheva, J. Arnold, and R. Ziolkowski, “FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities,” IEEE. J. Sel. Top. Quantum Electron. 10, 1052–1062 (2004).
[Crossref]

Aryropoulos, C.

Avrutsky, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402 (2007).
[Crossref]

Barnes, W.

W. Barnes, “Surface plasmon-polariton length scales: a route to sub-wavelength optics,” J. Opt. A: Pure Appl. Opt. 8, S87–S93 (2006).
[Crossref]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[Crossref] [PubMed]

Basov, D.

C. Riley, T. Kieu, J. S. T. Smalley, S. Pan, S. Kim, K. Post, A. Kargar, D. Basov, X. Pan, Y. Fainman, D. Wang, and D. Sirbuly, “Plasmonic tuning of aluminum doped zinc oxide nanostructures by atomic layer deposition,” Phys. Stat. Sol. RRL 8, 948–952 (2014).
[Crossref]

Belov, P.

Belov, P. A.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B,  87, 115139 (2013).
[Crossref]

Berini, P.

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Figures (7)

Fig. 1
Fig. 1

Schematic of multilayer metal-InGaAsP MQW system. The heterostructure, with twell=10nm and tbarrier=20nm is grown in the x-direction and TM-polarized light propagates in the z-direction.

Fig. 2
Fig. 2

Wave-vector diagrams for 30/30nm (a) AZO/InGaAsP and (b) Ag/InGaAsP systems at 1500nm with losses omitted. (solid blue line=real part of Bloch vector, dotted blue line=imaginary part of Bloch vector, dashed red line=effective medium theory prediction of real part of Bloch vector) The transmission windows in (a) and (b) extend from 0≤kx≤2.83k0 and 4.91k0≤kx≤6.56k0, respectively.

Fig. 3
Fig. 3

(a,c) Transmission and (b,d) reflection for TM-polarized light of wavelength 1500nm, incident on 10-period (a,b) AZO/InGaAsP and (c,d) Ag/InGaAsP multilayer with 30nm layers, coupled via prism with εP=64. (Abs: N=1×1016cm−3; Tra: εD”=0; Inv: N=5×1018cm−3; [0]: εM”=εD”=0)

Fig. 4
Fig. 4

Transmission enhancement factor (TEF) for TM-polarized light incident on 10-period (a) AZO/InGaAsP and (b) Ag/InGaAsP multilayer with 30nm layers, coupled via prism with εP=64. (c) Angular-averaged TEF for the Ag/InGaAsP system with 30nm layers and wavelength of 1500nm as a function of number of periods.

Fig. 5
Fig. 5

(a,b) Transmission and (c,d) TEF through prism-coupled 10-period 30/30nm Ag/InGaAsP system under inversion at λ0= (a,c) 1500nm and (b,d) 1550nm (SMM=scattering matrix method, FDTD=finite-difference time-domain).

Fig. 6
Fig. 6

Transmission as a function of wavelength and in-plane wavenumber for 10-period 30/30nm (a) AZO/InGaAsP and (b) Ag/InGaAsP systems with losses and gain omitted. The greater-than-unity transmission in the absence of gain is an unphysical result that motivates the use of the SMM.

Fig. 7
Fig. 7

Transmission through prism-coupled 10-period 30/30nm Ag/InGaAsP system under inversion at (a) λ0=1500nm and (b) λ0=1550nm (SMM=scattering matrix method, FDTD=finite-difference time-domain). In (b) the center wavelength, λC, used for the FDTD source is varied from 1500nm to 1550nm to show that results between SMM and FDTD most closely match for λ0 = λC.

Equations (1)

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T E F T ( 5 × 10 18 cm 3 ) / T ( 1 × 10 16 cm 3 ) ,

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