Abstract

We present a comprehensive analysis for transverse electric (TE) and transverse magnetic (TM) polarized guided Tamm-plasmon polariton (TPP) mode at metal–heterostructure media interface. We explicitly show that the quarter-wavelength stack condition will not be satisfied for TE or TM polarized TPP mode due to the existence of null-point at metal–heterostructure media boundary. Therefore, we propose an alternate route to design TPP waveguide by solving the mode-dispersion relation for different geometrical parameters in a $TiO_2/SiO_2$ bilayer system. The guided TPP-modes (TE and TM) exhibit interesting dispersion characteristics which can be tailored as per the desired application. The group index of TM polarized TPP mode remains constant over a significant wavelength range which results into zero group-velocity dispersion (GVD) at λ ≈ 630 nm wavelength. Also, the propagation length for TM-polarized TPP modes vary between $25\,\mu {m}$ to $50\,\mu {m}$ in a 630–650 nm wavelength range. However, the variation of GVD for TE-modes exhibit a monotonic variation with an exceptionally large ${GVD}\;\approx -3\times 10^{4}\,{ps}/{km $\cdot $ nm}$ around $\lambda =632.8\;{nm}$.

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  1. E. Ozbay (Jan. 2006). Plasmonics: Merging photonics and electronics at nanoscale dimensions. Science [Online]. 311(5758), pp. 189–193. Available: http://www.sciencemag.org/content/311/5758/189.full.html.
  2. F. Liu, Y. Li, R. Wan, H. Yidong, X. Feng, W. Zhang (May 2011). Hybrid coupling between long-range surface plasmon polariton mode and dielectric waveguide mode. J. Lightw. Technol. [Online]. 29(9) , pp. 1265–1273. Available: http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-29-9-1265.
  3. P. Berini (Aug. 2000). Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures. Phys. Rev. B [Online]. 61(15), p. 10484. Available: http://prb.aps.org/abstract/PRB/v61/i15/p10484_1.
  4. J. Homola, S. S. Yee, and G. Gauglitz (Jan. 1999). Surface plasmon resonance sensors: Review. Sens. Actuators B [Online]. 54(1-2), pp. 3–15. Available:: http://www.sciencedirect.com/science/article/pii/S0925400598003219.
  5. E. Kretschmann, H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. 23A, (1968).
  6. R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur (Mar. 2010). Efficient light coupling between dielectric slot waveguide and plasmonic slot waveguide. Opt. Lett. [Online]. 35 (5), pp. 649–651. Available: http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-35-5-649.
  7. V. N. Konopsky and E. V. Alieva (Feb. 2009). Long-range plasmons in lossy metal films on photonic crystal surfaces. Opt. Lett. [Online]. 34(4), pp. 479–481. Available: http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-34-4-479.
  8. T. Srivastava, R. Das, and R. Jha (Nov. 2010). Design considerations and propagation characteristics of channel Bragg-plasmon-coupled-waveguides. Appl. Phys. Lett. [Online]. 97(21), pp. 213104–213106. Available: http://apl.aip.org/resource/1/applab/v97/i21/p213104_s1.
  9. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen and S. I. Bozhevolnyi (Jan. 2005). Integrated optical components utilizing long-range surface plasmon polaritons. J. Lightw. Technol. [Online]. 23(1) , pp. 413–422. Available: http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-29-9-1265.
  10. M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. V. Kavokin, and I. Shelykh (Oct. 2007). Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror. Phys. Rev. B [Online]. 76(16), p. 165415. Available: http://prb.aps.org/abstract/PRB/v76/i16/e165415.
  11. N. Malkova and C. Z. Ning (Jan. 2007). Tamm surface states in a finite chain of defects in a photonic crystal. J. Phys.: Condens. Matter [Online]. 19, p. 056004. Available: http://iopscience.iop.org/0953-8984/19/5/056004.
  12. M. Kaliteevski, S. Brand, R. Abram, I. Iorsh, A. V. Kavokin, and I. A. Shelykh (Dec. 2009). Hybrid states of Tamm plasmons and exciton polaritons. Appl. Phys. Lett. [Online]. 95(25), p. 251108. Available: http://apl.aip.org/resource/1/applab/v95/i25/p251108_s1.
  13. S. Brand, M. Kaliteevski, and R. Abram (Feb. 2009). Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface. Phys. Rev. B [Online]. 79(8), p. 085416. Available: http://prb.aps.org/abstract/PRB/v79/i8/e085416.
  14. C. E. Little, R. Anufriev, I. Iorsh, M. Kaliteevski, R. Abram, and S. Brand (Dec. 2012). Tamm plasmon polaritons in multilayered cylindrical structures. Phys. Rev. B [Online]. 86(23), p. 235425. Available: http://prb.aps.org/abstract/PRB/v86/i23/e235425.
  15. G. Du, H. Jiang, Z. Wang, Y. Yang, and Z. Wang (Sep. 2010). Heterostructure-based optical absorbers. J. Opt. Soc. Amer. B [Online]. 27(9), pp. 1757–1762. Available: http://www.opticsinfobase.org/josab/abstract.cfm?urijosab-27-9-1757.
  16. M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasilev, V. S. Mikhrin, and A. V. Kavokin (Jun. 2008). Tamm plasmon polaritons: Slow and spatially compact light. Appl. Phys. Lett. [Online]. 92(25), p. 251112. Available: http://scitation.aip.org/content/aip/journal/apl/92/25/10.1063/1.2952486.
  17. W. L. Zhang and S. F. Yu (Feb. 2010). Bistable switching using an optical Tamm cavity with a Kerr medium. Opt. Commun. [Online]. 283(12), pp. 2622–2626. Available: http://www.sciencedirect.com/science/article/pii/S0030401810001604.
  18. C. Xue, H. Jiang, H. Lu, G. Du, and H. Chen (Mar. 2013). Efficient third-harmonic generation based on Tamm plasmon polaritons. Opt. lett. [Online]. 38(6), pp. 959–961. Available: http://www.opticsinfobase.org/ol/abstract.cfm?uriōl-38-6-959.
  19. S. H. Tsang, S. Yu, X. F. Li, H. Y. Yang, and H. K. Liang (Dec. 2011). Observation of Tamm plasmon polaritons in visible regime from $ZnO/Al_2 O_3$ distributed Bragg reflector-Ag interface. Opt. Commun. [Online]. 284(7), pp. 1890–1892. Available: http://www.sciencedirect.com/science/article/pii/S0030401810013416.
  20. B. I. Afinogenov, V. O. Bessonov, A. A. Nikulin, and A. A. Fedyanin (Aug. 2013). Observation of hybrid state of Tamm and surface plasmon-polaritons in one-dimensional photonic crystals. Appl. Phys. Lett. [Online]. 103(6) , p. 061112. Available: http://apl.aip.org/resource/1/applab/v103/i6/p061112_s1 .
  21. H. Liu, X. Sun, F. Yao, Y. Pei, F. Huang, H. Yuan and Y. Jiang (Aug. 2012). Optical magnetic field enhancement through coupling magnetic plasmons to Tamm plasmons. Opt. Express [Online]. 20(17), pp. 19160–19167. Available: http://www.opticsinfobase.org/oe/abstract.cfm?uriōe-20-17-19160.
  22. C. Symonds, A. Lemaître, E. Homeyer, J. C. Plenet, and J. Bellessa (Oct. 2009) Emission of Tamm plasmon/exciton polaritons. Appl. Phys. Lett. [Online]. 95(15), p. 151114. Available: http://scitation.aip.org/content/aip/journal/apl/95/15/10.1063/1.3251073.
  23. O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, J. Bloch, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart (Dec. 2011) Evidence for confined Tamm plasmon modes under metallic microdisks and application to the control of spontaneous optical emission. Phys. Rev. Lett. [Online]. 107(24), p. 247402. Avaiable at http://prl.aps.org/abstract/PRL/v107/i24/e247402.
  24. M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev (Jan. 2006). Stability of the photonic band gap in the presence of disorder. Phys. Rev. B [Online]. 73(3), p. 033106. Available: http://prb.aps.org/abstract/PRB/v73/i3/e033106.
  25. P. Yeh, A. Yariv, and C. S. Hong (Apr. 1977). Electromagnetic wave propagation in periodically stratified media: General theory. J. Opt. Soc. Amer. [Online]. 67(4), pp. 423–438. Available: http://authors.library.caltech.edu/7526/.
  26. B. R. West and A. S. Helmy (Jun. 2006). Properties of the quarter-wave Bragg reflection waveguide: Theory. J. Opt. Soc. Amer. B [Online]. 23(6), pp. 1207–1220. Available: http://www.opticsinfobase.org/josab/abstract.cfm?urijosab-23-6-1207.
  27. E. D. Palik, Handbook of Optical Constants of Solids ( Academic, 1985).
  28. T. Toyoda and M. Yabe (Dec. 1983). The temperature dependence of the refractive indices of $SrTiO_3$ and $TiO_2$ . J. Phys. D: Appl. Phys. [Online]. 16(12), pp. L251–L255. Available http://iopscience.iop.org/0022-3727/16/12/002.
  29. G. Ghosh and M. Endo (Aug. 1994). Temperature dependent Sellemeier coefficients and chromatic dispersions for some optical fiber glasses. J. Lightw. Technol. [Online]. 12(8), pp. 1338–1342. Available: http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=317500.
  30. K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal (Nov. 1996). A novel design for dispersion compensating fiber. IEEE Photon. Technol. Lett. [Online]. 8 (11), pp. 1510–1512. Available: http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=541566.

1968 (1)

E. Kretschmann, H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. 23A, (1968).

Z. Naturforsch. (1)

E. Kretschmann, H. Raether, "Radiative decay of non-radiative surface plasmons excited by light," Z. Naturforsch. 23A, (1968).

Other (29)

R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur (Mar. 2010). Efficient light coupling between dielectric slot waveguide and plasmonic slot waveguide. Opt. Lett. [Online]. 35 (5), pp. 649–651. Available: http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-35-5-649.

V. N. Konopsky and E. V. Alieva (Feb. 2009). Long-range plasmons in lossy metal films on photonic crystal surfaces. Opt. Lett. [Online]. 34(4), pp. 479–481. Available: http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-34-4-479.

T. Srivastava, R. Das, and R. Jha (Nov. 2010). Design considerations and propagation characteristics of channel Bragg-plasmon-coupled-waveguides. Appl. Phys. Lett. [Online]. 97(21), pp. 213104–213106. Available: http://apl.aip.org/resource/1/applab/v97/i21/p213104_s1.

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen and S. I. Bozhevolnyi (Jan. 2005). Integrated optical components utilizing long-range surface plasmon polaritons. J. Lightw. Technol. [Online]. 23(1) , pp. 413–422. Available: http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-29-9-1265.

M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. V. Kavokin, and I. Shelykh (Oct. 2007). Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror. Phys. Rev. B [Online]. 76(16), p. 165415. Available: http://prb.aps.org/abstract/PRB/v76/i16/e165415.

N. Malkova and C. Z. Ning (Jan. 2007). Tamm surface states in a finite chain of defects in a photonic crystal. J. Phys.: Condens. Matter [Online]. 19, p. 056004. Available: http://iopscience.iop.org/0953-8984/19/5/056004.

M. Kaliteevski, S. Brand, R. Abram, I. Iorsh, A. V. Kavokin, and I. A. Shelykh (Dec. 2009). Hybrid states of Tamm plasmons and exciton polaritons. Appl. Phys. Lett. [Online]. 95(25), p. 251108. Available: http://apl.aip.org/resource/1/applab/v95/i25/p251108_s1.

S. Brand, M. Kaliteevski, and R. Abram (Feb. 2009). Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface. Phys. Rev. B [Online]. 79(8), p. 085416. Available: http://prb.aps.org/abstract/PRB/v79/i8/e085416.

C. E. Little, R. Anufriev, I. Iorsh, M. Kaliteevski, R. Abram, and S. Brand (Dec. 2012). Tamm plasmon polaritons in multilayered cylindrical structures. Phys. Rev. B [Online]. 86(23), p. 235425. Available: http://prb.aps.org/abstract/PRB/v86/i23/e235425.

G. Du, H. Jiang, Z. Wang, Y. Yang, and Z. Wang (Sep. 2010). Heterostructure-based optical absorbers. J. Opt. Soc. Amer. B [Online]. 27(9), pp. 1757–1762. Available: http://www.opticsinfobase.org/josab/abstract.cfm?urijosab-27-9-1757.

M. E. Sasin, R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Yu. Egorov, A. P. Vasilev, V. S. Mikhrin, and A. V. Kavokin (Jun. 2008). Tamm plasmon polaritons: Slow and spatially compact light. Appl. Phys. Lett. [Online]. 92(25), p. 251112. Available: http://scitation.aip.org/content/aip/journal/apl/92/25/10.1063/1.2952486.

W. L. Zhang and S. F. Yu (Feb. 2010). Bistable switching using an optical Tamm cavity with a Kerr medium. Opt. Commun. [Online]. 283(12), pp. 2622–2626. Available: http://www.sciencedirect.com/science/article/pii/S0030401810001604.

C. Xue, H. Jiang, H. Lu, G. Du, and H. Chen (Mar. 2013). Efficient third-harmonic generation based on Tamm plasmon polaritons. Opt. lett. [Online]. 38(6), pp. 959–961. Available: http://www.opticsinfobase.org/ol/abstract.cfm?uriōl-38-6-959.

S. H. Tsang, S. Yu, X. F. Li, H. Y. Yang, and H. K. Liang (Dec. 2011). Observation of Tamm plasmon polaritons in visible regime from $ZnO/Al_2 O_3$ distributed Bragg reflector-Ag interface. Opt. Commun. [Online]. 284(7), pp. 1890–1892. Available: http://www.sciencedirect.com/science/article/pii/S0030401810013416.

B. I. Afinogenov, V. O. Bessonov, A. A. Nikulin, and A. A. Fedyanin (Aug. 2013). Observation of hybrid state of Tamm and surface plasmon-polaritons in one-dimensional photonic crystals. Appl. Phys. Lett. [Online]. 103(6) , p. 061112. Available: http://apl.aip.org/resource/1/applab/v103/i6/p061112_s1 .

H. Liu, X. Sun, F. Yao, Y. Pei, F. Huang, H. Yuan and Y. Jiang (Aug. 2012). Optical magnetic field enhancement through coupling magnetic plasmons to Tamm plasmons. Opt. Express [Online]. 20(17), pp. 19160–19167. Available: http://www.opticsinfobase.org/oe/abstract.cfm?uriōe-20-17-19160.

C. Symonds, A. Lemaître, E. Homeyer, J. C. Plenet, and J. Bellessa (Oct. 2009) Emission of Tamm plasmon/exciton polaritons. Appl. Phys. Lett. [Online]. 95(15), p. 151114. Available: http://scitation.aip.org/content/aip/journal/apl/95/15/10.1063/1.3251073.

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, J. Bloch, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart (Dec. 2011) Evidence for confined Tamm plasmon modes under metallic microdisks and application to the control of spontaneous optical emission. Phys. Rev. Lett. [Online]. 107(24), p. 247402. Avaiable at http://prl.aps.org/abstract/PRL/v107/i24/e247402.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev (Jan. 2006). Stability of the photonic band gap in the presence of disorder. Phys. Rev. B [Online]. 73(3), p. 033106. Available: http://prb.aps.org/abstract/PRB/v73/i3/e033106.

P. Yeh, A. Yariv, and C. S. Hong (Apr. 1977). Electromagnetic wave propagation in periodically stratified media: General theory. J. Opt. Soc. Amer. [Online]. 67(4), pp. 423–438. Available: http://authors.library.caltech.edu/7526/.

B. R. West and A. S. Helmy (Jun. 2006). Properties of the quarter-wave Bragg reflection waveguide: Theory. J. Opt. Soc. Amer. B [Online]. 23(6), pp. 1207–1220. Available: http://www.opticsinfobase.org/josab/abstract.cfm?urijosab-23-6-1207.

E. D. Palik, Handbook of Optical Constants of Solids ( Academic, 1985).

T. Toyoda and M. Yabe (Dec. 1983). The temperature dependence of the refractive indices of $SrTiO_3$ and $TiO_2$ . J. Phys. D: Appl. Phys. [Online]. 16(12), pp. L251–L255. Available http://iopscience.iop.org/0022-3727/16/12/002.

G. Ghosh and M. Endo (Aug. 1994). Temperature dependent Sellemeier coefficients and chromatic dispersions for some optical fiber glasses. J. Lightw. Technol. [Online]. 12(8), pp. 1338–1342. Available: http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=317500.

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal (Nov. 1996). A novel design for dispersion compensating fiber. IEEE Photon. Technol. Lett. [Online]. 8 (11), pp. 1510–1512. Available: http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=541566.

E. Ozbay (Jan. 2006). Plasmonics: Merging photonics and electronics at nanoscale dimensions. Science [Online]. 311(5758), pp. 189–193. Available: http://www.sciencemag.org/content/311/5758/189.full.html.

F. Liu, Y. Li, R. Wan, H. Yidong, X. Feng, W. Zhang (May 2011). Hybrid coupling between long-range surface plasmon polariton mode and dielectric waveguide mode. J. Lightw. Technol. [Online]. 29(9) , pp. 1265–1273. Available: http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-29-9-1265.

P. Berini (Aug. 2000). Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures. Phys. Rev. B [Online]. 61(15), p. 10484. Available: http://prb.aps.org/abstract/PRB/v61/i15/p10484_1.

J. Homola, S. S. Yee, and G. Gauglitz (Jan. 1999). Surface plasmon resonance sensors: Review. Sens. Actuators B [Online]. 54(1-2), pp. 3–15. Available:: http://www.sciencedirect.com/science/article/pii/S0925400598003219.

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