Abstract

A new silicon-based sharp waveguide bend in asymmetric metal/multi-insulator configuration is described. TE and TM modes are calculated rigorously electromagnetically from which the general design rules are derived. Numerical simulations show that the respective insertion losses of < 0.085 dB and < 0.229 dB for TE and TM modes can be achieved by introducing a low-index layer between the metal and high-index core. The bending length is determined by the TE mode and has much smaller impacts on the TM that exhibits no resonance-like behavior as does the TE. The combined TE modal and radiation power in the air region is shown to couple back to the Si core through an asymmetric output taper, yielding a high transmission efficiency. Structure-enabled successive photonic-plamsonic mode conversions are shown to increase the TM mode confinement in the high-index core while the plasmonic mode carries up to 42.6% of the input power along the bending section.

© 2011 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).
    [CrossRef] [PubMed]
  2. D. K. Gramotnev, and S. I. Bozhevolnyi, "Plasmonics beyond the diffraction limit," Nat. Photonics 4, 83-91 (2010).
    [CrossRef]
  3. E. A. J. Marcatili, "Bends in optical dielectric waveguides," Bell Syst. Tech. J. 48, 2103-2132 (1969).
  4. I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
    [CrossRef]
  5. D. R. Mason, D. K. Gramotnev, and K. S. Kim, "Wavelength-dependent transmission through sharp 90◦ bends in sub-wavelength metallic slot waveguides," Opt. Express 18, 16139-16145 (2010).
    [CrossRef] [PubMed]
  6. J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, "Beam-propagation analysis of bent step-index slab waveguides," Electron. Lett. 26, 822-824 (1990).
    [CrossRef]
  7. L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
    [CrossRef]
  8. Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, "Integrated waveguide turning mirror in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 68-70 (2002).
    [CrossRef]
  9. M. Popovič, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, "Air trenches for sharp silica waveguide bends," J. Lightwave Technol. 16, 1762-1772 (2008).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
    [CrossRef]
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2011

Y.-J. Chang, and Y.-C. Liu, "A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry," IEEE Photon. Technol. Lett. 23, 121-123 (2011).
[CrossRef]

2010

2009

2008

2007

2006

2005

D. F. P. Pile, and D. K. Gramotnev, "Plasmonic subwavelength waveguides: next to zero losses at sharp bends," Opt. Lett. 30, 1186-1188 (2005).
[CrossRef] [PubMed]

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

J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

2003

2002

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, "Integrated waveguide turning mirror in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 68-70 (2002).
[CrossRef]

G. P. Nordin, S. Kim, J. Cai, and J. Jiang, "Hybrid integration of conventional waveguide and photonic crystal structures," Opt. Express 10, 1334-1341 (2002).
[PubMed]

2001

1999

1995

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
[CrossRef]

1990

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, "Beam-propagation analysis of bent step-index slab waveguides," Electron. Lett. 26, 822-824 (1990).
[CrossRef]

1969

E. A. J. Marcatili, "Bends in optical dielectric waveguides," Bell Syst. Tech. J. 48, 2103-2132 (1969).

Ahmad, R.

Ahmad, R. U.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

Akiyama, S.

M. Popovič, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, "Air trenches for sharp silica waveguide bends," J. Lightwave Technol. 16, 1762-1772 (2008).

Barnes, W. L.

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

Baudrion, A.-L.

J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

Bozhevolnyi, S. I.

Cai, J.

Camarda, G. S.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

Chang, G.-K.

Chang, Y.-J.

Y.-J. Chang, and Y.-C. Liu, "A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry," IEEE Photon. Technol. Lett. 23, 121-123 (2011).
[CrossRef]

Y.-J. Chang, T. K. Gaylord, and G.-K. Chang, "Attenuation in waveguides on FR-4 boards due to periodic substrate undulations," Appl. Opt. 46, 2234-2243 (2007).
[CrossRef] [PubMed]

Chen, Z.

Demeester, P.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
[CrossRef]

Dereus, A.

Dereux, A.

J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

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

Ebbesen, T. W.

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

English, J. M.

Espinola, R.

Espinola, R. L.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

Fan, S.

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

C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "High-density integrated optics," J. Lightwave Technol. 17, 1682-1692 (1999).
[CrossRef]

Gallawa, R. L.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Gaylord, T. K.

Ghatak, A. K.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Gonzalez, M. U.

J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

Goyal, I. C.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: A new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Gramotnev, D. K.

Groen, F. H.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
[CrossRef]

Hall, T. J.

Haus, H. A.

M. Popovič, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, "Air trenches for sharp silica waveguide bends," J. Lightwave Technol. 16, 1762-1772 (2008).

C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "High-density integrated optics," J. Lightwave Technol. 17, 1682-1692 (1999).
[CrossRef]

Heider, H. J.

Hirooka, T.

J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, "Beam-propagation analysis of bent step-index slab waveguides," Electron. Lett. 26, 822-824 (1990).
[CrossRef]

Holmgaard, T.

Hu, Y.

Jiang, J.

Joannopoulos, J. D.

Johnson, S. G.

Keuren, E. V.

Kikuchi, S.

J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, "Beam-propagation analysis of bent step-index slab waveguides," Electron. Lett. 26, 822-824 (1990).
[CrossRef]

Kim, K. S.

Kim, S.

Krasavin, A. V.

Li, L.

Li, T.

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, "Integrated waveguide turning mirror in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 68-70 (2002).
[CrossRef]

Li, X.

Liu, Y.-C.

Y.-J. Chang, and Y.-C. Liu, "A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry," IEEE Photon. Technol. Lett. 23, 121-123 (2011).
[CrossRef]

Luo, F.

Ma, C.

Manolatou, C.

Marcatili, E. A. J.

E. A. J. Marcatili, "Bends in optical dielectric waveguides," Bell Syst. Tech. J. 48, 2103-2132 (1969).

Markey, L.

Mason, D. R.

Metaal, E. G.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
[CrossRef]

Michel, J.

M. Popovič, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, "Air trenches for sharp silica waveguide bends," J. Lightwave Technol. 16, 1762-1772 (2008).

Müller, J.

Nakano, H.

J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, "Beam-propagation analysis of bent step-index slab waveguides," Electron. Lett. 26, 822-824 (1990).
[CrossRef]

Nordin, G. P.

Oei, Y. S.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
[CrossRef]

Osgood, R.

Osgood, R. M.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

Pile, D. F. P.

Pizzuto, F.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, "A study of high-index-contrast 90◦ waveguide bend structures," Opt. Express 8, 517-528 (2001).
[CrossRef] [PubMed]

Popovic, M.

M. Popovič, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, "Air trenches for sharp silica waveguide bends," J. Lightwave Technol. 16, 1762-1772 (2008).

Qian, Y.

Rao, H.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

Smit, M. K.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
[CrossRef]

Song, J.

Spiekman, L. H.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
[CrossRef]

Steel, M.

Sun, D.

Tang, Y. Z.

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, "Integrated waveguide turning mirror in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 68-70 (2002).
[CrossRef]

Veronis, G.

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

Villeneuve, P. R.

Wada, K.

M. Popovič, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, "Air trenches for sharp silica waveguide bends," J. Lightwave Technol. 16, 1762-1772 (2008).

Wang, W. H.

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, "Integrated waveguide turning mirror in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 68-70 (2002).
[CrossRef]

Wang, Y. L.

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, "Integrated waveguide turning mirror in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 68-70 (2002).
[CrossRef]

Weeber, J.-C.

J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

Wiechmann, S.

Wong, D.

Yamauchi, J.

J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, "Beam-propagation analysis of bent step-index slab waveguides," Electron. Lett. 26, 822-824 (1990).
[CrossRef]

Zayats, A. V.

Zhang, Q.

Appl. Opt.

Appl. Phys. Lett.

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

J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

Bell Syst. Tech. J.

E. A. J. Marcatili, "Bends in optical dielectric waveguides," Bell Syst. Tech. J. 48, 2103-2132 (1969).

Electron. Lett.

J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, "Beam-propagation analysis of bent step-index slab waveguides," Electron. Lett. 26, 822-824 (1990).
[CrossRef]

IEEE Photon. Technol. Lett.

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, "Integrated waveguide turning mirror in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 68-70 (2002).
[CrossRef]

Y.-J. Chang, and Y.-C. Liu, "A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry," IEEE Photon. Technol. Lett. 23, 121-123 (2011).
[CrossRef]

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002).
[CrossRef]

J. Lightwave Technol.

Nat. Photonics

D. K. Gramotnev, and S. I. Bozhevolnyi, "Plasmonics beyond the diffraction limit," Nat. Photonics 4, 83-91 (2010).
[CrossRef]

Nature

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

Opt. Express

Opt. Lett.

Proc. Inst. Elect. Eng.-Optoelectronics

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, "Ultrasmall waveguide bends: The corner mirrors of the future?" Proc. Inst. Elect. Eng.-Optoelectronics 142, 61-65 (1995).
[CrossRef]

Other

D. L. Lee, Electromagnetic Principles of Integrated Optics (John Wiley & Sons, Inc., 1986).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the proposed sharp waveguide bend in metal/multi-insulator configuration, where δoffset,inx1xin and δoffset,outy2yout.

Fig. 2
Fig. 2

Schematic of a general metal/multi-insulator waveguiding structure.

Fig. 3
Fig. 3

Transmission coefficient of (a) TE and (b) TM modes with varying input taper length lin and input lateral offset δoffset,inx1xin (Fig. 1). The highest transmissions for TE and TM modes are 88.24% and 96.36% at (lin,δoffset,in) = (700, 30) and (lin,δoffset,in) = (900, 5) nm, respectively.

Fig. 4
Fig. 4

Phase plots of the y-directed complex Poynting vector along the input taper followed by the linear section of length l1 for (a) TE and (b) TM excitations.

Fig. 5
Fig. 5

Bending efficiency as a function of the bending length for differing bending widths from 290 nm to 350 nm for (a) TE and (b) TM modes. The Ez field component in the case of (wbend, lbend) = (350, 250) nm is shown as an inset in (a).

Fig. 6
Fig. 6

Time average power flow of the optimized sharp waveguide bend for (a) TE and (b) TM modes with structure parameters wgap = 80, lin = 700, δoffset,in = 45, l1 = l2 = 364, wbend = 330, lbend = 450, lout = 660, and δoffset,out = −85. All figures are in units of nm.

Fig. 7
Fig. 7

Power interchange of a straight silver-silica-Si waveguide for (a) TE and (b) TM modes with input/output tapers identical to those used in the optimized waveguide bend.

Fig. 8
Fig. 8

Power interchange of the optimized sharp waveguide bend for (a) TE and (b) TM modes.

Tables (2)

Tables Icon

Table 1 Effective refractive index Neff and the corresponding guided wavelength λg at the operating wavelength of 1550 nm for differing bending widths wbend. wbend and λg are in units of nm

Tables Icon

Table 2 General design rules for the proposed waveguide bend

Equations (18)

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Z up + Z dn = 0 ,
Z i = { ω μ 0 / κ i TE mode κ i / ( ω ɛ 0 ɛ i ) TM mode ,
Z in , i = Z i ( 1 + Γ i , i + 1 e j 2 κ i h i 1 Γ i , i + 1 e j 2 κ i h i ) ,
Γ i , i + 1 = Z in , i + 1 Z i Z in , i + 1 + Z i
κ 1 S + κ m T = 0.
ɛ 1 κ m S + κ 1 ɛ m T = 0 ,
S = ( Z i n , 2 + Z 1 ) ( Z i n , 2 Z 1 ) e j 2 κ 1 h 1
T = ( Z i n , 2 + Z 1 ) + ( Z i n , 2 Z 1 ) e j 2 κ 1 h 1 .
κ 1 ( A B e j 2 κ 1 h 1 ) + κ m ( A + B e j 2 κ 1 h 1 ) = 0
ɛ 1 κ m ( Ψ Ω e j 2 κ 1 h 1 ) + ɛ m κ 1 ( Ψ + Ω e j 2 κ 1 h 1 ) = 0
A = 1 κ 2 P Q + 1 κ 1
B = 1 κ 2 P Q 1 κ 1
Ψ = κ 2 ɛ 2 P Q + κ 1 ɛ 1
Ω = κ 2 ɛ 2 P Q κ 1 ɛ 1
P = ( Z 0 + Z 2 ) + ( Z 0 Z 2 ) e j 2 κ 2 h 2
Q = ( Z 0 + Z 2 ) ( Z 0 Z 2 ) e j 2 κ 2 h 2 .
η = T | bend T | straight ,
ϕ θ c , 12 sin 1 ( n 0 n 2 ) ,

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