Abstract

Numerical simulations and an analytic approach based on transmission line theory are used to design splitters for nano-plasmonic signal processing that allow to arbitrarily adjust the ratio of transmission from an input into two different output arms. By adjusting the geometrical parameters of the structure, either a high bandwidth or a sharp transmission resonance is obtained. Switching between the two arms can be achieved by modulating the effective refractive index of the waveguide. Employing the instantaneous Kerr effect, switching rates in the THz regime are potentially feasible. The suggested devices are of interest for future applications in nanoplasmonic information processing.

© 2010 Optical Society of America

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J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance Matching and Emission Properties of Nanoantennas in an Optical Nanocircuit,” Nano Lett. 9, 1897–1902 (2009).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

J. S. Huang, D. V. Voronine, P. Tuchscherer, T. Brixner, and B. Hecht, “Deterministic spatiotemporal control of optical fields in nanoantennas and plasmonic circuits,” Phys. Rev. B 79, 195441 (2009).
[CrossRef]

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nature Photon. 3, 55–58 (2009).
[CrossRef]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A Metal–Oxide–Si Field Effect Plasmonic Modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

W. Cai, J. S. White, and M. L. Brongersma, “Compact, High-Speed and Power-Efficient Electrooptic Plasmonic Modulators,” Nano Lett. 9, 4403–4411 (2009).
[CrossRef] [PubMed]

C. Min and G. Veronis, “Absorption switches in metal–dielectric–metal plasmonic waveguides,” Opt. Express 17, 10757–10766 (2009).
[CrossRef] [PubMed]

P. Tuchscherer, C. Rewitz, D. V. Voronine, F. J. García de Abajo, W. Pfeiffer, and T. Brixner, “Analytic coherent control of plasmon propagation in nanostructures,” Opt. Express 17, 14235–14259 (2009)
[CrossRef] [PubMed]

2008 (10)

S. I. Bozhevolnyi and J. Jung, “Scaling for gap plasmon based waveguides,” Opt. Express 16, 2676–2684 (2008).
[CrossRef] [PubMed]

Z. Kang and G. P. Wang, “Coupled metal gap waveguides as plasmonicwavelength sorters,” Opt. Express 16, 7680–7685 (2008).
[CrossRef] [PubMed]

S. Passinger, A. Seidel, C. Ohrt, C. Reinhardt, A. Stepanov, R. Kiyan, and B. Chichkov, “Novel efficient design of Y-splitter for surface plasmon polariton applications,” Opt. Express 16, 14369–14379 (2008).
[CrossRef] [PubMed]

Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, “Characteristics of gap plasmon waveguide with stub structures,” Opt. Express 16, 16314–16325 (2008).
[CrossRef] [PubMed]

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef] [PubMed]

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of Stimulated Emission of Surface Plasmon Polaritons,” Nano Lett. 8, 3998–4001 (2008).
[CrossRef] [PubMed]

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, 226806 (2008).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nature Photon. 2, 496–500 (2008).
[CrossRef]

E. Verhagen, J. A. Dionne, L. Kuipers, H. A. Atwater, and A. Polman, “Near-Field Visualization of Strongly Confined Surface Plasmon Polaritons in Metal–Insulator–Metal Waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. L. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and Focusing of Electromagnetic Fields with Wedge Plasmon Polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

2007 (4)

M. Sukharev and T. Seideman, “Coherent control of light propagation via nanoparticle arrays,” J. Phys. B 40, 283–298 (2007)
[CrossRef]

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90, 211101 (2007).
[CrossRef]

Z. Han and S. He, “Multimode interference effect in plasmonic subwavelength waveguides and an ultra-compact power splitter,” Opt. Commun. 278, 199–203 (2007).
[CrossRef]

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

2006 (2)

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9 (7-8), 20–27 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511(2006).
[CrossRef] [PubMed]

2005 (1)

G. Veronis and S. Fan, “Bends and splitters in metal–dielectric–metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

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]

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

2002 (1)

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent Control of Femtosecond Energy Localization in Nanosystems,” Phys. Rev. Lett. 88, 067402 (2002).
[CrossRef] [PubMed]

2001 (1)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics-A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

2000 (1)

1998 (2)

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23, 1331–1333 (1998).
[CrossRef]

J. Güdde, J. Hohlfeld, J. G. Müller, and E. Matthias, “Damage threshold dependence on electron-phonon coupling in Au and Ni films,” Appl. Surf. Sci. 127–129, 40–45 (1998).
[CrossRef]

Aeschlimann, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Aggarwal, I. D.

Ambati, M.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of Stimulated Emission of Surface Plasmon Polaritons,” Nano Lett. 8, 3998–4001 (2008).
[CrossRef] [PubMed]

Atwater, H. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A Metal–Oxide–Si Field Effect Plasmonic Modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

E. Verhagen, J. A. Dionne, L. Kuipers, H. A. Atwater, and A. Polman, “Near-Field Visualization of Strongly Confined Surface Plasmon Polaritons in Metal–Insulator–Metal Waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics-A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Aussenegg, F. R.

Barnes, W. L.

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

Bartal, G.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of Stimulated Emission of Surface Plasmon Polaritons,” Nano Lett. 8, 3998–4001 (2008).
[CrossRef] [PubMed]

Bauer, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Bayer, D.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

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]

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent Control of Femtosecond Energy Localization in Nanosystems,” Phys. Rev. Lett. 88, 067402 (2002).
[CrossRef] [PubMed]

Biagioni, P.

J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance Matching and Emission Properties of Nanoantennas in an Optical Nanocircuit,” Nano Lett. 9, 1897–1902 (2009).
[CrossRef] [PubMed]

Borghs, G.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nature Photon. 3, 283–286 (2009).
[CrossRef]

Bouhelier, A.

J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi and J. Jung, “Scaling for gap plasmon based waveguides,” Opt. Express 16, 2676–2684 (2008).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511(2006).
[CrossRef] [PubMed]

Bozhevolnyi, S. L.

E. Moreno, S. G. Rodrigo, S. L. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, “Guiding and Focusing of Electromagnetic Fields with Wedge Plasmon Polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

Brixner, T.

J. S. Huang, D. V. Voronine, P. Tuchscherer, T. Brixner, and B. Hecht, “Deterministic spatiotemporal control of optical fields in nanoantennas and plasmonic circuits,” Phys. Rev. B 79, 195441 (2009).
[CrossRef]

P. Tuchscherer, C. Rewitz, D. V. Voronine, F. J. García de Abajo, W. Pfeiffer, and T. Brixner, “Analytic coherent control of plasmon propagation in nanostructures,” Opt. Express 17, 14235–14259 (2009)
[CrossRef] [PubMed]

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007).
[CrossRef] [PubMed]

Brongersma, M. L.

W. Cai, J. S. White, and M. L. Brongersma, “Compact, High-Speed and Power-Efficient Electrooptic Plasmonic Modulators,” Nano Lett. 9, 4403–4411 (2009).
[CrossRef] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9 (7-8), 20–27 (2006).
[CrossRef]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics-A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
[CrossRef]

Cai, W.

W. Cai, J. S. White, and M. L. Brongersma, “Compact, High-Speed and Power-Efficient Electrooptic Plasmonic Modulators,” Nano Lett. 9, 4403–4411 (2009).
[CrossRef] [PubMed]

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9 (7-8), 20–27 (2006).
[CrossRef]

Cheong, S.-W.

Chichkov, B.

Ciarlet, P. G.

W. H. A. Schilders, P. G. Ciarlet, J. Lions, and E. J. W. T. Maten, Numerical Methods in Electromagnetics (Elsevier, 2005).

De Vlaminck, I.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nature Photon. 3, 283–286 (2009).
[CrossRef]

Dereux, A.

J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

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

des Francs, G. C.

J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511(2006).
[CrossRef] [PubMed]

Diest, K.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A Metal–Oxide–Si Field Effect Plasmonic Modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

Dionne, J. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A Metal–Oxide–Si Field Effect Plasmonic Modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef] [PubMed]

E. Verhagen, J. A. Dionne, L. Kuipers, H. A. Atwater, and A. Polman, “Near-Field Visualization of Strongly Confined Surface Plasmon Polaritons in Metal–Insulator–Metal Waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef] [PubMed]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511(2006).
[CrossRef] [PubMed]

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

Faleev, S. V.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent Control of Femtosecond Energy Localization in Nanosystems,” Phys. Rev. Lett. 88, 067402 (2002).
[CrossRef] [PubMed]

Fan, S.

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M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of Stimulated Emission of Surface Plasmon Polaritons,” Nano Lett. 8, 3998–4001 (2008).
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Adv. Mater. (1)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics-A Route to Nanoscale Optical Devices,” Adv. Mater. 13, 1501–1505 (2001).
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Appl. Phys. Lett. (2)

G. Veronis and S. Fan, “Bends and splitters in metal–dielectric–metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005).
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Appl. Surf. Sci. (1)

J. Güdde, J. Hohlfeld, J. G. Müller, and E. Matthias, “Damage threshold dependence on electron-phonon coupling in Au and Ni films,” Appl. Surf. Sci. 127–129, 40–45 (1998).
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J. Phys. B (1)

M. Sukharev and T. Seideman, “Coherent control of light propagation via nanoparticle arrays,” J. Phys. B 40, 283–298 (2007)
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[CrossRef]

Nano Lett. (6)

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of Stimulated Emission of Surface Plasmon Polaritons,” Nano Lett. 8, 3998–4001 (2008).
[CrossRef] [PubMed]

J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance Matching and Emission Properties of Nanoantennas in an Optical Nanocircuit,” Nano Lett. 9, 1897–1902 (2009).
[CrossRef] [PubMed]

E. Verhagen, J. A. Dionne, L. Kuipers, H. A. Atwater, and A. Polman, “Near-Field Visualization of Strongly Confined Surface Plasmon Polaritons in Metal–Insulator–Metal Waveguides,” Nano Lett. 8, 2925–2929 (2008).
[CrossRef] [PubMed]

J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, “Gain-Assisted Propagation in a Plasmonic Waveguide at Telecom Wavelength,” Nano Lett. 9, 2935–2939 (2009).
[CrossRef] [PubMed]

W. Cai, J. S. White, and M. L. Brongersma, “Compact, High-Speed and Power-Efficient Electrooptic Plasmonic Modulators,” Nano Lett. 9, 4403–4411 (2009).
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Figures (7)

Fig. 1.
Fig. 1.

Basic geometry of a 2D splitter structure. Waveguide modes are injected into the top arm (input). The electromagnetic fields are recorded in spectral and temporal domain by appropriate monitors in the left and right output arm. The frequency-dependent transmission and reflection are investigated for varying stub length l and distance d using a waveguide of gap width b.

Fig. 2.
Fig. 2.

Geometry for a series of simulations, where a stub of varying width b and length l is attached to a 30nm wide waveguide.

Fig. 3.
Fig. 3.

FDTD (a) and TLT (b) reflection of a waveguide of 30nm width with an attached stub of varying width and length. The width of the reflection minima and maxima depends on the relative stub width.

Fig. 4.
Fig. 4.

Transmission to the right arm (a: TLT, b: FDTD), left arm (c), and reflection (d) of the splitter structure shown in Fig. 1. All data are shown as a function of the stub length and its distance from the intersection.

Fig. 5.
Fig. 5.

TLT (dashed) and FDTD (solid) reflection (thick, light blue) and transmission to the left (red) and right (black) arm of a splitter structure consisting of 30nm wide waveguides. Two examples are depicted: (a) l = 170nm, d = 320nm, T right T left ≃ 2.5. (b) l = 240nm, d = 350nm, T right T left ≃ 1.2.

Fig. 6.
Fig. 6.

(a) Geometry of the proposed switch. Plasmons are injected by a mode source in the upper arm (input). The electromagnetic fields are recorded in the input, left and right output arm. (b) Electic field amplitude of a 200 fs Gaussian-envelope plasmonic signal before (black) and after (red) the switch. No significant phase-related pulse broadening can be observed.

Fig. 7.
Fig. 7.

(a) Transmission to the left (red) and right (black) arm of a splitter structure upon variation of the refractive index from n = 1 (solid) to n = 1.05 (dashed). (b) Spectral intensity at the left (red) and right (black) output when a Gaussian plasmon pulse of 5nm FWHM impinges on the splitter. Most of the intensity is transmitted to the right arm in the case n = 1 (black solid), while it is transmitted to the left arm for n = 1.05 (red dashed).

Equations (9)

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Z 0 ( b , ω ) Re [ γ ( b , ω ) ] ω ε 0 b .
R = Z load Z 0 Z load + Z 0 2 .
Z i n = Z 0 Z load + Z 0 tanh ( γ l W G ) Z 0 + Z load tanh ( γ l W G ) .
Z in , stub = Z 0 , stub tanh ( γ l ) .
Z 0 , stub tanh ( γ l ) = i Z 0 , stub tan ( I m [ γ ] l ) ,
Z i n , splitter = 1 + tanh ( γ d ) + tanh ( γ l ) 1 + tanh ( γ d ) [ 1 + tanh ( γ l ) ] Z 0 .
R splitter = 1 + tanh ( γ d ) + tanh ( γ l ) 3 + tanh ( γ l ) + tanh ( γ d ) [ 3 + 2 tanh ( γ l ) ] 2 .
T rightarm = ( 1 R splitter ) R e { 1 + tanh ( γ d ) [ 1 + tanh ( γ l ) ] [ 2 + tanh ( γ l ) [ 1 + tanh ( γ d ) ] } .
T leftarm = ( 1 R splitter ) R e { 1 + tanh ( γ d ) + tanh ( γ l ) [ 2 + tanh ( γ l ) ] [ 1 + tanh ( γ d ) ] } e R e [ γ ] d R e { 1 1 + tanh ( γ l ) } .

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