Abstract

This work examines vertical coupling between gap plasmon waveguides for use in high confinement power transfer and power splitting applications at 1.55 µm free space wavelength. The supermode interference method is used to obtain key coupler performance parameters such as coupling length, extinction ratio, net coupled output power, radiated power, and reflected power as a function of waveguide center-to-center spacing, core refractive index, and gap width. The initial power distribution among the two coupler supermodes is obtained via the mode matching method for a single input waveguide feed. Excellent agreement with three-dimensional finite difference time domain simulations is observed for the case of square 50 nm gaps with core refractive indices of 2.50 and a center-to-center spacing of 112 nm. Local maxima in the net coupled output power are found to coincide with local minima in the coupling length. An increase in the core refractive index from 1.00 to 2.5 increases the local maximum net coupled output power from 6.4% to 49% but decreases the extinction ratio from 12.7 to 6.94. A sweep of the width of the core from 25 to 100 nm increases the net coupled output power from 43.7% to 52.0%, but increases the coupling length from 1.58 to 3.19 µm and decreases the extinction ratio from 7.39 to 6.57.

© 2008 Optical Society of America

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2008 (1)

2007 (7)

2006 (4)

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 13101 (2006).
[CrossRef]

L. Chen, J. Shakya, and M. Lipson, "Subwavelength confinement in an integrated metal slot waveguide on silicon," Opt. Lett. 31, 2133 - 2135 (2006).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9, 20 - 27 (2006).
[CrossRef]

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

2005 (4)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 46802 (2005).
[CrossRef]

D. Gramotnev, "Adiabatic nanofocusing of plasmons by sharp metallic grooves: Geometrical optics approach," J. Appl. Phys. 98, 104302 (2005).
[CrossRef]

G. Veronis and S. Fan, "Guided subwavelength plasmonic mode supported by a slot in a thin metal film," Opt. Lett. 30, 3359 - 3361 (2005).
[CrossRef]

R. M. Reano and S. W. Pang, "Sealed three-dimensional nanochannels," J. Vac. Sci. Technol. B 23, 2995 - 2999 (2005).
[CrossRef]

2004 (1)

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A. 21, 2442 - 2446 (2004).
[CrossRef]

2003 (1)

J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D full-wave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331 - 335 (2003).
[CrossRef]

2000 (1)

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]

1975 (1)

Berini, P.

P. Berini, "Air gaps in metal stripe waveguides supporting long-range surface plasmon polaritons," J. Appl. Phys. 102, 33112 (2007).
[CrossRef]

R. Buckley and P. Berini, "Figures of merit for 2D surface plasmon waveguides and application to metal stripes," Opt. Express 15, 12174 - 12182 (2007).
[CrossRef] [PubMed]

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]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 46802 (2005).
[CrossRef]

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9, 20 - 27 (2006).
[CrossRef]

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A. 21, 2442 - 2446 (2004).
[CrossRef]

Buckley, R.

Catrysse, P. B.

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A. 21, 2442 - 2446 (2004).
[CrossRef]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9, 20 - 27 (2006).
[CrossRef]

Chen, L.

Collin, S.

Conway, J. A.

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 46802 (2005).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 46802 (2005).
[CrossRef]

Fan, S.

Fukui, M.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 13101 (2006).
[CrossRef]

Gramotnev, D.

D. Gramotnev, "Adiabatic nanofocusing of plasmons by sharp metallic grooves: Geometrical optics approach," J. Appl. Phys. 98, 104302 (2005).
[CrossRef]

Gramotnev, D. K.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 13101 (2006).
[CrossRef]

Gudat, W.

Hagemann, H. J.

Haraguchi, M.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 13101 (2006).
[CrossRef]

Jung, K.

K. Jung, F. L. Teixeira, and R. M. Reano, "Au/SiO2 nanoring plasmon waveguides at optical communication band," IEEE J. Lightwave Tech. 25, 2757 - 2765 (2007).
[CrossRef]

Kim, K. C.

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

Kim, P. S.

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

Kim, S.

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

Kunz, C.

Lipson, M.

Oh, C.

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

Okamoto, T.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 13101 (2006).
[CrossRef]

Pang, S. W.

R. M. Reano and S. W. Pang, "Sealed three-dimensional nanochannels," J. Vac. Sci. Technol. B 23, 2995 - 2999 (2005).
[CrossRef]

Pardo, F.

Park, S.

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

Pelouard, J.

Pereda, J. A.

J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D full-wave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331 - 335 (2003).
[CrossRef]

Pile, D. F. P.

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 13101 (2006).
[CrossRef]

Prieto, A.

J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D full-wave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331 - 335 (2003).
[CrossRef]

Qiu, M.

Reano, R. M.

K. Jung, F. L. Teixeira, and R. M. Reano, "Au/SiO2 nanoring plasmon waveguides at optical communication band," IEEE J. Lightwave Tech. 25, 2757 - 2765 (2007).
[CrossRef]

R. M. Reano and S. W. Pang, "Sealed three-dimensional nanochannels," J. Vac. Sci. Technol. B 23, 2995 - 2999 (2005).
[CrossRef]

Sahni, S.

Schuller, J. A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9, 20 - 27 (2006).
[CrossRef]

Selker, M. D.

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A. 21, 2442 - 2446 (2004).
[CrossRef]

Shakya, J.

Song, S. H.

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

Szkopek, T.

Teixeira, F. L.

K. Jung, F. L. Teixeira, and R. M. Reano, "Au/SiO2 nanoring plasmon waveguides at optical communication band," IEEE J. Lightwave Tech. 25, 2757 - 2765 (2007).
[CrossRef]

Vegas, A.

J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D full-wave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331 - 335 (2003).
[CrossRef]

Veronis, G.

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 46802 (2005).
[CrossRef]

Won, H. S.

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

Yan, M.

Zia, R.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9, 20 - 27 (2006).
[CrossRef]

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A. 21, 2442 - 2446 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

H. S. Won, K. C. Kim, S. H. Song, C. Oh, P. S. Kim, S. Park, and S. Kim, "Vertical coupling of long-range surface plasmon polaritons," Appl. Phys. Lett. 88, 11110 (2006).
[CrossRef]

IEEE J. Lightwave Tech. (2)

G. Veronis and S. Fan, "Modes of subwavelength plasmonic slot waveguides," IEEE J. Lightwave Tech. 25, 2511 - 2521 (2007).
[CrossRef]

K. Jung, F. L. Teixeira, and R. M. Reano, "Au/SiO2 nanoring plasmon waveguides at optical communication band," IEEE J. Lightwave Tech. 25, 2757 - 2765 (2007).
[CrossRef]

J. Appl. Phys. (3)

P. Berini, "Air gaps in metal stripe waveguides supporting long-range surface plasmon polaritons," J. Appl. Phys. 102, 33112 (2007).
[CrossRef]

D. Gramotnev, "Adiabatic nanofocusing of plasmons by sharp metallic grooves: Geometrical optics approach," J. Appl. Phys. 98, 104302 (2005).
[CrossRef]

D. F. P. Pile, D. K. Gramotnev, M. Haraguchi, T. Okamoto, and M. Fukui, "Numerical analysis of coupled wedge plasmons in a structure of two metal wedges separated by a gap," J. Appl. Phys. 100, 13101 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A. (1)

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A. 21, 2442 - 2446 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Vac. Sci. Technol. B (1)

R. M. Reano and S. W. Pang, "Sealed three-dimensional nanochannels," J. Vac. Sci. Technol. B 23, 2995 - 2999 (2005).
[CrossRef]

Mat. Today (1)

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next chip-scale technology," Mat. Today 9, 20 - 27 (2006).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D full-wave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331 - 335 (2003).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. B (1)

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. (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 46802 (2005).
[CrossRef]

Other (8)

http://www.comsol.com

Bruce McConnel, "Using self-assembly to create airgap microprocessors" (IBM, 2007), http://www-03.ibm.com/press/us/en/presskit/21463.wss, Accessed 10-30-07.

http://www.rsoftdesign.com

K. Okamoto, Fundamentals of Optical Waveguides, (Academic Press, 2006).

C. Pollock, Fundamentals of Optoelectronics, (Ceramic Book and Literature Service, 2003), Chap. 11.

W. C. Chew, Waves and Fields in Inhomogeneous Media, (IEEE Press, 1995), Chap. 6.

D. Marcuse, Light Transmission Optics, (Van Norstrand Reinhold Company, 1972), pp. 322-326.

G. Strang, Linear Algebra and Its Applications 3rd Ed., (Thomson Learning, 1988), pp. 448 - 449.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic cross-section of the (a) gap plasmon waveguide (GPW) and (b) vertical gap plasmon coupler (VGPC).

Fig. 2.
Fig. 2.

(a) Effective propagation index obtained by different mode solvers for the fundamental mode of the gap plasmon waveguide with h=w=50 nm, λ 0=1.55 µm, nclad =ncore =nsub =nsilica =1.44, nmetal =(-143-10i)0.5. b) Corresponding propagation length.

Fig. 3.
Fig. 3.

Side-view schematic of our excitation condition for the VGPC along the yz-plane at x=0. The input mode of the single GPW (Ei ) is used to excite the coupler.

Fig. 4.
Fig. 4.

(a) The computed transverse electric field vector (arrow plot) and time average power density, Savgz (surface plot) for the input mode, Ei , of a square silica-filled 50 nm gap, b) the symmetric supermode, Es , of the corresponding coupler, and c) the asymmetric supermode, Ea .

Fig. 5.
Fig. 5.

a) Real part of the effective propagation indices (neff ’s) for MIM-TM0, Es , Ea , and Ei for w=h=50 nm and ncore =1.44 in the target materials-geometry-excitation system note that the effective indices of the supermodes cross each other at s≈110 nm b) coupling length, Lc , versus vertical CTC gap spacing, s.

Fig. 6.
Fig. 6.

Performance parameters for the VGPC versus ncore and s: in Figs. (a)–(e), the thick solid line is for ncore =1.00, the thin solid line is for ncore =1.44, the thick dotted line is for ncore =2.00, and the thin dotted line is for ncore =2.50. a) Coupling Length, Lc , which tends to decrease with increasing ncore and decreasing s, but reaches a singularity where the supermode phase constants cross each other b) Extinction Ratio, ER, which increases when either ncore or s is increased c) Radiated power, Prad , which monotonically decreases with increasing s, d) Net coupled output power, Pnet , which is large where Lc is small, and reaches a maximum where s=112 nm for ncore =2.5 e) Average supermode propagation length, Lp-avg , which is a weak function of s, f) Comparison of supermode interference with the mode matching method (SI-MMM) and FDTD in predicting the power oscillations along the coupler for the case where ncore =2.50. Excellent agreement is observed.

Tables (1)

Tables Icon

Table 1. Performance parameters for ncore =2.50 for different core widths, w.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

E i t ( 1 + r ) = t s E s t + t a E a t
H i t ( 1 r ) = t s H s t + t a H a t
E n t × H m t dxdy = E m t × H n t dxdy = δ nm
[ ξ is 1 0 ξ ia 0 1 ξ si 1 0 ξ ai 0 1 ] [ r t s t a ] = [ ξ is ξ ia ξ si ξ ai ]
ξ nm = E n t × H m t dxdy
P rad = 1 ( P refl + t s 2 + t a 2 )
P refl = r 2 .
S avgz tot = 1 2 · Re { E tot t × H tot t * } = 1 2 · Re { S avgz ss e 2 α s z + S avgz aa e 2 α a z + S avgz sa e 2 α z · e j β Δ z + S avgz as e 2 α z . e j β Δ z } .
S avgz nm = 1 2 · Re { E n t × H m t * } .

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