Abstract

In this paper, a kind of surface plasmonic waveguide (SPW) with three circular air cores is presented. Based on the finite-difference frequency-domain (FDFD) method, dependence of the distribution of energy flux density, effective index, propagation length and mode area of the fundamental mode on the geometrical parameters and the working wavelengths is analyzed firstly. Then, comparison with the SPW which was proposed in our previous work has been carried out. Results show that this kind of three cores structure has better propagation properties than the double cores structure. To investigate the relative advantages of this kind of SPW over other previous reported SPWs, comparison with the SPW with a single wedge has been carried out. Results show that this kind of SPW has shorter propagation length and larger mode area. Finally, the possibility to overcome the large propagation loss by using a gain medium as core material is investigated. Since the propagation properties can be adjusted by the geometrical and electromagnetic parameters, this kind of surface plasmonic waveguide can be applied to the field of photonic components in the integrated optical circuits and sensors.

© 2009 Optical Society of America

1. Introduction

Recently, there has been an increase of interest in surface plasmon polaritons (SPPs) [1]. SPPs are electromagnetic wave that are bound to a metal-dielectric interface and are coupled to the oscillations of the free electrons in the metal [2]. Because SPPs have lateral dimensions on the order of subwavelength, it overcomes the diffraction limit that exists in conventional or photonic crystal waveguides, and fulfills the further miniaturization of photonic devices and high integration density of photonic chips. So during the past few years, SPPs-based waveguides have also been a subject of intensive research [36].

Up to now, several kinds of SPWs structures have been proposed, such as nanoparticle SPWs [7,8], film SPWs [9,10], rod SPWs [11,12], gap SPWs [1315], slot SPWs [16,17], wedge SPWs [1821], channel SPWs [2225], heterostructured SPWs [26,27], and mixed SPWs [28].

In our previous work [21], a SPW with double elliptical air cores was proposed and analyzed. Results show that the energy flux density distributes mainly in the two wedged corners which are formed by two elliptical air cores, and the closer to the corners the stronger the longitudinal energy flux density. The effective index and propagation length of the fundamental mode can be adjusted by the centric distance of two ellipses as well as the size of the two semiaxis.

In this paper, an altered SPW with three circular air cores is proposed. The FDFD method is used to study the distribution of energy flux density, effective index, propagation length and mode area of the fundamental mode supported by this SPW structure. Then, comparison with the SPW in our previous work [21] and a SPW with a single wedge have been carried out.

Due to the limitation of the high absorption loss of the metal material, the propagation length of SPPs on SPWs is much shorter than that of the conventional dielectric optical waveguides. There is a tradeoff between modal confinement and propagation length in all SPWs without assisted gain [29]. This shortcoming can be overcome by using optical gain medium [3035]. The possibility to overcome the large propagation loss by using the gain medium as core material is investigated finally.

2. Structure and simulation method

The cross section of our proposed surface plasmonic waveguide in this paper is shown in Fig. 1. It is composed of three circular air cores with the same radius r in the silver cladding, and 2a is the centric distance of the upper two air cores, 2h is the vertical distance from the centre of the nether circular air core to the horizontal line which is passed through the centres of the upper two air cores. Obviously, it can be separated into three cases of 2a>r, 2a=r and 2a<r, when 2h is a fixed value.

Noble metals are usually used to make SPWs. At optical frequencies, the dielectric constants of these metals are complex. In calculation, the dielectric constant of silver εclad is chosen as - 18.0550+0.4776j (λ=632.8 nm), - 23.4046+0.3870j (λ=705.0 nm), and - 31.0784+0.4118j (λ=800.0 nm) [36] respectively. Here, λ is the working wavelength in the vacuum.

In this paper, the 2D full-vectorial FDFD method [3739] is used to study the propagationproperties of our proposed SPW structure. This is a simple and effective numerical simulation approach. Setting the geometrical parameters, electromagnetic parameters and working wavelength, an eigenvalue equation can be obtained. Solving the eigenvalue equation by Arnoldi arithmetic [40], which can deal with large matrix eigenvalue problem with complex coefficient matrix, propagation constant and the distribution of field of each mode at the working wavelength can be obtained. In our calculation, 601×601 Yee’s lattices are adopted to discretize the whole computational domain, and 20 layers of them are perfectly matched layer absorbing boundary layers (APML) that used to truncate the lattices. Spatial discretization distance is Δxy=1.0 nm.

 

Fig. 1. Cross section of the proposed surface plasmonic waveguide with three circular air cores. (a) 2a>r, (b) 2a=r and (c) 2a<r

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To validate our FDFD code, an optical fiber with a finite metallic core [41] is analyzed. The working wavelength is chosen as λ 0=633nm. The relative dielectric constant of the metal and the cladding is taken as εcore=19.00-0.53 j and εclad=4.00 respectively. In the calculation, the radius of the core is assumed from 0.05λ 0 to 0.25λ 0. Here we have taken the notation of the working wavelength in reference [41] as λ 0. In the later text, we will still use λ as the working wavelength in the vacuum. For clarity, we show results in the figure form. As shown in Fig. 2, the analytic [41] and simulated propagation constants for the 0th-order TM mode exhibit good agreement. This fact shows that our FDFD code can be used to simulate plasmonic structures.

 

Fig. 2. Analytic and simulated normalized (a) real part and (b) imaginary part of propagation constant of an optical fiber [41] with a finite metallic core for the 0th-order TM mode. Here, a is the radius of the core, λ 0 is the working wavelength, and k 0=2π/λ 0.

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Yan and Qiu claimed that the corner angle and the corner tip sharpness would affect the modal properties of a Λ -wedge waveguide considerably [42]. Although the FDFD method use orthogonal mesh and corner tips are not rounded in this paper. We find that, in our calculation, the corner angles are not too small and the corner tips are not too sharp. So the situation is in the safe case.

3. Results and discussion

3.1. Modal characteristics

Characteristics of the modes supported by the surface plasmonic waveguide with three circular air cores shown in Fig. 1 are investigated firstly. We find that there is a kind of mode which have longer propagation length among many modes supported by this kind of SPW, and call this mode the fundamental mode. The distribution of field Hx, Hy, and energy flux density Sz in the cases of a=60 nm, h=85 nm, and r=120 nm at λ=705.0 nm is shown in Fig. 3. Here the energy flux density is defined as Sz=Re(ExHy-EyHx), Ex and Ey, Hx and Hy are components of electrical and magnetic field respectively.

 

Fig. 3. The distribution of the field (a) Hx, (b) Hy and (c) Sy on the cross section when a=60 nm, h=85 nm, r=120 nm at λ=705.0 nm. Dashed lines in (a), (b) and (c) indicate the outline of the structure.

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It can be seen from Fig. 3(a) that the component of field x H is symmetric distribution with y axes, however, component of field Hy shown in Fig. 3(b) is antisymmetric distribution with y axes. From Fig. 3(c), we can find that the energy flux density mainly distributes near the left and right wedged corner which are formed by three circular air cores. Among the three cases of 2a>r, 2a=r and 2a<r, the two corner angles are smallest and the two corner tips are sharpest in the case of 2a>r, so the degree of localization of field is the largest.

3.2. Effect of geometrical parameters of the waveguide

Since the effective index Re(neff), propagation length Lprop and mode area Am are the three most important physical quantities that describe the propagation properties of surface plasmonic waveguides, then we investigate the dependence of Re(neff), Lprop and Am of the fundamental mode shown in Fig. 3 on the geometrical parameters. Here Re(neff) is defined as Re(β)λ/2π, Lprop is defined as 1/Im(β), and Am is defined as the area in which the energy flux density Sz descend from 100% to 10% of its maximum value.

The relational graphs of Re(neff), Lprop and Am varied with h in the three cases of r=2a-5 nm, 2a and 2a+5 nm, and 2a=100 nm, 120 nm, 140 nm at λ=705.0 nm are shown in Fig. 4(a–c), Fig. 4(d–f) and Fig. 4(g–i) respectively. It can be seen from these figures that curves can be obviously separated into three groups according to different a. In each group, Re(neff) increases as h increases, however Lprop on the whole lessly varied with h, and Am increases as h decreases. The position of curves is influenced by parameter r. We can also find that curves corresponding to r=2a+5 nm are commonly on the upward side of each group of curves. The above phenomena can be explained by the different field distribution with different geometrical parameters. Because the field is mainly centralized near the left and right wedged corner which are formed by three circular air cores. Relative to the case of r=2a, when r is small, the area of field distribution is small. Namely the degree of localization of field is large. In this instance, the interaction of field and silver is strong. The effective index increases. Then the propagation length and mode area decrease. However, when r is large, the area of field distribution is large. Namely the degree of localization of field is small. In this instance, the interaction of field and silver becomes weak. The effective index decreases. Then the propagation length and mode area increase.

 

Fig. 4. Dependence of (a–c) Re(neff), (d–f) Lprop and (g–i) Am on h when r=2a - 5 nm, 2a and 2a+5 nm at λ=705.0 nm.

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3.3. Effect of working wavelengths

In order to find out the dependence of field distribution of the mode shown in Fig. 3 on the working wavelength, the distribution of field Hx, Hy, and energy flux density Sz in the cases of r=2a=120 nm, h=85 nm at λ=632.8 nm and λ=800.0 nm is calculated respectively. Here we extend the calculation to longer wavelength 800 nm where the vertical-cavity surface-emitting lasers (VCSELs) are available. Results shown that field distribution is similar to the Fig. 3. Relative to the case of λ=705.0 nm, in the case of λ=632.8 nm, the area of field distribution is small. And the field is mainly confined near the left and right wedged corner which are formed by three circular air cores. However, in the case of λ=800.0 nm, the area of field distribution is large, and the field is less confined.

Figure 5(a–c), Fig. 5(d–f) and Fig. 5(g–i) also show the dependence of Re(neff), Lprop and Am on h when radius r=2a=100 nm, 120 nm, 140 nm and λ=632.8 nm, 705.0 nm, 800.0 nm respectively. It can be seen that curves of Re(neff), Lprop and Am could also be separated into three groups according to different λ. And in each group, Re(neff) increases along with the increase of h, however, Lprop has many trends that varied with h, and Am decreases as h increases. Parameter r has effect on the position of curves. It can be seen that curves according to r=2a=140 nm are always on the upward side of each group of curves. The above phenomena can be explained by the different field distribution at different wavelength. Because the field is mainly centralized near the left and right wedged corner which are formed by three circular air cores. Relative to the case of λ=705.0 nm, when λ is small, the area of field distribution is small. Namely the degree of localization of the field is large. In this instance, the interaction of the field and silver is strong. The effective index increases. Then the propagation length and mode area decrease. However, when λ is large, the area of field distribution is large. Namely the degree of localization of field is small. In this instance, the interaction of the field and silver becomes weak. The effective index decreases. Then the propagation length and mode area increase.

 

Fig. 5. Dependence of (a–c) Re(neff), (d–f) Lprop and (g–i) Am on h when r=2a=100 nm, 120 nm and 140 nm at λ=632.8 nm, 705.0 nm, 800.0 nm.

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3.4. Comparation with the SPW with two air cores

It can be found that, under certain conditions, the three circular air cores can be turned into two circular air cores which is similar to a case of the SPW with double elliptical air cores in our previous work [21]. Here, Let’s take the three cores structure and the double cores structure for comparation.

When the centric distance of the upper two air cores 2a (shown in Fig. 1) decreases to zero, the three circular air cores are turned into two circular air cores. In this case, the cross section is similar to the double cores structure in the case of a=b. Here the parameter r of the three cores structure is equal to a and b, and h is equal to c of the double cores structure. Dependence of Re(neff), Lprop and Am on h when a=0 nm, 60 nm, r=120 nm, and λ=632.8 nm, 705.0 nm, 800.0 nm is shown in Fig. 6 respectively. From Fig. 6, we can see that Re(neff) (Fig. 6a and Fig. 6b) increases as h increases, however Lprop (Fig. 6c and Fig. 6d) increases as h increases when λ=800.0 nm, and in the other two cases the propagation length not obviously varied with h. And Am (Fig. 6e and Fig. 6f) increases as h decreases. Parameter λ has effect on the position of the curves in Fig. 6. Results also show that SPW with three circular air cores (Fig. 6b, Fig. 6d and Fig. 6f) has longer propagation length, smaller effective index and mode area compared with the two circular air cores (Fig. 6a, Fig. 6c and Fig. 6e) with the same parameters. In other words, the proposed SPW in this paper has better propagation properties than that of our previous SPW.

 

Fig. 6. Dependence of (a–b) Re(neff), (c–d) Lprop and (e–f) Am on h when a=0 nm, 60 nm, r=120 nm at λ=632.8 nm, 705.0 nm, 800.0 nm.

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3.5. Comparation with the SPW with a single wedge

As shown in subsection 3.4, the three cores structure is an improvement over the double cores structure. To investigate the relative advantages of the double cores structure over other previous reported SPWs, we choose a SPW with a single wedge as shown in Fig. 7(a). It is composed of a single wedged region which is formed by two circular air cores with centric distance 2c on the silver slab. This structure not only can be seen as a representative SPW with a single wedge [1820] but also be comparable to our double cores structure [21]. Here the parameter r and c is equal to r and c of the double cores structure [21]. The corresponding distribution of Hx, Hy and z S of the fundamental mode supported by this single wedge structure is shown in Fig. 7(b), Fig. 7(c) and Fig. 7(d). It can be seen that the energy flux density mainly distributes in the wedged corner. The component of field Hx is symmetric distribution with y axes, however, component of field Hy is antisymmetric distribution with y axes.

Dependence of Re(neff), Lprop and Am on c when r=100 nm and c=85 nm at λ=705.0 nm is shown in Fig. 8 respectively. From Fig. 8, we can see that Re(neff) increases as c increases, however Lprop and Am decrease as c increase. Results also show that the single wedge SPW has longer propagation length and smaller mode area, but the double cores structure has shorter propagation length and larger mode area. This phenomenon can also be explained by the interactional intensity between the field and metal. For the single wedge SPW, the field is confined only on one single wedge. The interaction of the field and siver is small. So the propagation length is large, but the mode area is small. For the double cores structure, the field is coupled and confined on two wedges. The interaction of the field and siver is large. So the propagation length is short, but the mode area is large. This fact implies that the double cores structure as well as the three cores structure can be used as a key component of a sensor although it is difficult to fabricate than the single wedge SPW.

 

Fig. 7. The cross section of the SPW with a single wedge (a), the distribution of the field (b) Hx, (c) Hy and (d) Sz on the cross section when r=100 nm, c=85 nm, at λ=705.0 nm. Dashed lines in (b), (c) and (d) indicate the outline of the structure.

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Fig. 8. Dependence of (a) Re(neff), (b) Lprop and (c) Am on c (or h) when r=100 nm at λ=705.0 nm.

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Tables Icon

Table 1. The dielectric constants of the SPW.

3.6. Effect of Gain in the Core Dielectric

To investigate the effect of gain in the core dielectric, we fill the whole air cores of the structure shown in Fig. 1(b) with a kind of available gain medium [34,35,43], and the dielectric constants of the SPW are shown in Table 1. Here, the corresponding gain coefficirnt γ=298cm -1 (εcore=11.56-0.025j) and 596cm -1(εcore=11.56-0.050j) [34]. As an example, in the case of λ=1550 nm, a=60 nm, r=120 nm, dependence of Re(neff), Lprop and Am on h and the gain of the core dielectric are shown in Fig. 9. The corresponding distribution of the field z S are shown in Fig. 10.

As shown in Fig. 9(a), Fig. 9(b), and Fig. 9(c), the propagation length can be extended obviously with the help of the gain medium. It demonstrated that the presence of the gain medium result in an increase of the propagation length Lprop. However, the effective index is almost kept invariably with different εcore, here Am not obviously varied with εcore.

 

Fig. 9. Dependence of (a) Re(neff), (b) Lprop and (c) Am on h in the different cases.

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Since the core material has been changed from air to a gain medium with higher dielectric constant, confinement is expected to increase. As shown in Fig. 10, when the core is filled with gain medium (Fig. 10(a), Fig. 10(b) and Fig. 10(c)), the field Sz is more concentrated on the surface of the metal than that with air cores (Fig. 10(d)).

 

Fig. 10. The distribution of the field Sz when λ=1550 nm, a=60 nm, r=120 nm with (a) εcore=11.56-0.000j, (b) εcore=11.56-0.025j, (c) εcore=11.56-0.050j, and (d) εcore=1.00-0.000j.

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The presence of the gain medium to compensate for the absorption loss in propagating [3032] SPPs, although very small, it has been a possible solution, and at the same time localized [33] the surface plasmons. The influence of the gain medium on SPPs propagation has received some attention previously. There are much work to do in later time.

Methods of how to fabricate this kind of SPW and how to couple SPPs efficiently from an external source to this kind of SPW have been suggested in our previous work [21].

4. Conclusions

In this paper, we have designed a kind of surface plasmonic waveguide with three circular air cores. The structure of the waveguide can be separated into three cases of 2a>r, 2a=r and 2a<r. Numerical calculation show that:

(1) The energy flux density distributes mainly in the left and right wedged corner which are formed by three circular air cores, and the closer to the corners the stronger modal energy flux density.

(2) At the certain working wavelength, in the case of 2a<r, the degree of localization of field is the smallest, and the interaction of field and silver becomes small. The effective index decreases. Then the propagation length and mode area become large.

(3) With the certain geometric parameters, in the case of λ=800.0 nm, the area of field distribution is large. Namely, the degree of localization of field is small, and the interaction of field and silver becomes small. The effective index decreases. Then the propagation length and mode area become large.

(4) Comparison with the double air cores structure, this kind of SPW has better propagation properties. Comparison with the SPW with a single wedge, it has shorter propagation length and larger mode area.

(5) The propagation length can be extended obviously with the help of the gain dielectric medium.

Since the effective index, propagation length and the mode area can be adjusted by the geometrical and electromagnetic parameters, this kind of surface plasmonic waveguide can be applied to the field of photonic components in the integrated optical circuits and sensors.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 60878008, 60771052) and the Natural Science Foundation of Shanxi Province (Grant No. 2008012002-1, 2006011029).

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References

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  1. H. A. Atwater, “The promise of plasmonics,” Science 296, 56–63 (2007).
  2. H. Rather, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, Berlin, 1988).
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [CrossRef]
  4. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
    [CrossRef]
  5. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
    [CrossRef]
  6. S. A. Maier, “Plasmonics: The promise of highly integrated optical devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1671–1677 (2006).
  7. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
    [CrossRef]
  8. H. X. Zhang, Y. Gu, and Q. H. Gong, “A visible-near infrared tunable waveguide based on plasmonic gold nanoshell,” Chinese Physics B 17(7), 2567–2573 (2008).
  9. E. N. Economou, “Surface plasmon in thin films,” Phys. Rev. 182(2), 539–554 (1969).
    [CrossRef]
  10. P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24(15), 1011–1013 (1999).
    [CrossRef]
  11. J. Jung, T. Sondergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76(3), 035434 (2007).
    [CrossRef]
  12. J. Guo and R. Adato, “Control of 2D plasmon-polariton mode with dielectric nanolayers,” Opt. Express 16(2), 1232–1237 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-2-1232.
    [CrossRef]
  13. K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
    [CrossRef]
  14. F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86(21), 211101 (2005).
    [CrossRef]
  15. R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13(6), 1933–1938 (2005), http://www.opticsexpress.org/abstract.cfm?uri=oe-13-6-1933.
    [CrossRef]
  16. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
    [CrossRef]
  17. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005), http://www.opticsexpress.org/abstract.cfm?uri=oe-13-17-6645.
    [CrossRef]
  18. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
    [CrossRef]
  19. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
    [CrossRef]
  20. A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-8-5252.
    [CrossRef]
  21. W. R. Xue, Y. N. Guo, P. Li, and W. M. Zhang, “Propagation Properties of a Surface Plasmonic Waveguide with double elliptical air cores,” Opt. Express 16(14), 10710–10720 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-14-10710.
    [CrossRef]
  22. J. Q. Lu and A. A. Maradudin, “Channel plasmons,” Phys. Rev. B 42(17), 11159–11165 (1990).
    [CrossRef]
  23. L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31(14), 2133–2135 (2006).
    [CrossRef]
  24. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29(10), 1069–1071 (2004).
    [CrossRef]
  25. I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15(25), 16596–16603 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-25-16596.
    [CrossRef]
  26. G. P. Wang and B. Wang, “Metal heterostructure-based nanophotonic devices: finite-difference time-domain numerical simulations,” J. Opt. Soc. Am. B 23(8), 1660–1665 (2006).
    [CrossRef]
  27. B. Wang and G. P. Wang, “Planar metal heterostructures for nanoplasmonic waveguides,” Appl. Phys. Lett. 90(1), 013114 (2007).
    [CrossRef]
  28. D. Arbel and M. Orenstein, “Plasmonic modes in W-shaped metal-coated silicon grooves,” Opt. Express 16(5), 3114–3119 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-5-3114.
    [CrossRef]
  29. 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(12), 2442–2446 (2004).
    [CrossRef]
  30. A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34, 764–766 (1989).
  31. M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-17-4072.
    [CrossRef]
  32. I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B 70(15), 155416 (2004).
    [CrossRef]
  33. N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85(21), 5040–5042 (2004).
    [CrossRef]
  34. S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).
    [CrossRef]
  35. D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31(1), 98–100 (2006).
    [CrossRef]
  36. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  37. Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002), http://www.opticsexpress.org/abstract.cfm?uri=oe-10-17-853.
  38. S. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express 12(15), 3341–3352 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-15-3341.
    [CrossRef]
  39. C. P. Yu and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express 12(25), 6165–6177 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-25-6165.
    [CrossRef]
  40. W. E. Arnoldi, “The principle of minimized iteration in the solution of matrix eigenvalue problems,” Q. Appl. Math. 9, 17–29 (1951).
  41. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997).
    [CrossRef]
  42. M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal coners,” J. Opt. Soc. Am. B 24(9), 2333–2342 (2007).
    [CrossRef]
  43. E. D. Palik, Handbook of Optical Constants of Solids(Academic, New York, 1985).

2008 (6)

H. X. Zhang, Y. Gu, and Q. H. Gong, “A visible-near infrared tunable waveguide based on plasmonic gold nanoshell,” Chinese Physics B 17(7), 2567–2573 (2008).

J. Guo and R. Adato, “Control of 2D plasmon-polariton mode with dielectric nanolayers,” Opt. Express 16(2), 1232–1237 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-2-1232.
[CrossRef]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
[CrossRef]

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-8-5252.
[CrossRef]

W. R. Xue, Y. N. Guo, P. Li, and W. M. Zhang, “Propagation Properties of a Surface Plasmonic Waveguide with double elliptical air cores,” Opt. Express 16(14), 10710–10720 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-14-10710.
[CrossRef]

D. Arbel and M. Orenstein, “Plasmonic modes in W-shaped metal-coated silicon grooves,” Opt. Express 16(5), 3114–3119 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-5-3114.
[CrossRef]

2007 (5)

B. Wang and G. P. Wang, “Planar metal heterostructures for nanoplasmonic waveguides,” Appl. Phys. Lett. 90(1), 013114 (2007).
[CrossRef]

I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15(25), 16596–16603 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-25-16596.
[CrossRef]

J. Jung, T. Sondergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76(3), 035434 (2007).
[CrossRef]

H. A. Atwater, “The promise of plasmonics,” Science 296, 56–63 (2007).

M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal coners,” J. Opt. Soc. Am. B 24(9), 2333–2342 (2007).
[CrossRef]

2006 (7)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef]

S. A. Maier, “Plasmonics: The promise of highly integrated optical devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1671–1677 (2006).

G. P. Wang and B. Wang, “Metal heterostructure-based nanophotonic devices: finite-difference time-domain numerical simulations,” J. Opt. Soc. Am. B 23(8), 1660–1665 (2006).
[CrossRef]

L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31(14), 2133–2135 (2006).
[CrossRef]

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).
[CrossRef]

D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31(1), 98–100 (2006).
[CrossRef]

2005 (5)

F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86(21), 211101 (2005).
[CrossRef]

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13(6), 1933–1938 (2005), http://www.opticsexpress.org/abstract.cfm?uri=oe-13-6-1933.
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005), http://www.opticsexpress.org/abstract.cfm?uri=oe-13-17-6645.
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
[CrossRef]

2004 (7)

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(12), 2442–2446 (2004).
[CrossRef]

M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-17-4072.
[CrossRef]

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B 70(15), 155416 (2004).
[CrossRef]

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85(21), 5040–5042 (2004).
[CrossRef]

D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29(10), 1069–1071 (2004).
[CrossRef]

S. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express 12(15), 3341–3352 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-15-3341.
[CrossRef]

C. P. Yu and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express 12(25), 6165–6177 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-25-6165.
[CrossRef]

2003 (3)

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef]

2002 (1)

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002), http://www.opticsexpress.org/abstract.cfm?uri=oe-10-17-853.

1999 (1)

P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24(15), 1011–1013 (1999).
[CrossRef]

1997 (1)

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997).
[CrossRef]

1990 (1)

J. Q. Lu and A. A. Maradudin, “Channel plasmons,” Phys. Rev. B 42(17), 11159–11165 (1990).
[CrossRef]

1989 (1)

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34, 764–766 (1989).

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1969 (1)

E. N. Economou, “Surface plasmon in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

1951 (1)

W. E. Arnoldi, “The principle of minimized iteration in the solution of matrix eigenvalue problems,” Q. Appl. Math. 9, 17–29 (1951).

Adato, R.

J. Guo and R. Adato, “Control of 2D plasmon-polariton mode with dielectric nanolayers,” Opt. Express 16(2), 1232–1237 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-2-1232.
[CrossRef]

Albin, S.

S. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express 12(15), 3341–3352 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-15-3341.
[CrossRef]

Arbel, D.

D. Arbel and M. Orenstein, “Plasmonic modes in W-shaped metal-coated silicon grooves,” Opt. Express 16(5), 3114–3119 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-5-3114.
[CrossRef]

Arnoldi, W. E.

W. E. Arnoldi, “The principle of minimized iteration in the solution of matrix eigenvalue problems,” Q. Appl. Math. 9, 17–29 (1951).

Atwater, H. A.

H. A. Atwater, “The promise of plasmonics,” Science 296, 56–63 (2007).

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef]

Avrutsky, I.

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B 70(15), 155416 (2004).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef]

Berini, P.

P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24(15), 1011–1013 (1999).
[CrossRef]

Boltasseva, A.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-8-5252.
[CrossRef]

Bozhevolnyi, S. I.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-8-5252.
[CrossRef]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
[CrossRef]

J. Jung, T. Sondergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76(3), 035434 (2007).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef]

Brolo, A. G.

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13(6), 1933–1938 (2005), http://www.opticsexpress.org/abstract.cfm?uri=oe-13-6-1933.
[CrossRef]

Brongersma, M. L.

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(12), 2442–2446 (2004).
[CrossRef]

Brown, T. G.

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002), http://www.opticsexpress.org/abstract.cfm?uri=oe-10-17-853.

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(12), 2442–2446 (2004).
[CrossRef]

Chang, H. C.

C. P. Yu and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt. Express 12(25), 6165–6177 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-25-6165.
[CrossRef]

Chen, L.

L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31(14), 2133–2135 (2006).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Citrin, D. S.

D. S. Citrin, “Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium,” Opt. Lett. 31(1), 98–100 (2006).
[CrossRef]

Demkovich, P. A.

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34, 764–766 (1989).

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef]

Economou, E. N.

E. N. Economou, “Surface plasmon in thin films,” Phys. Rev. 182(2), 539–554 (1969).
[CrossRef]

Fainman, Y.

M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-17-4072.
[CrossRef]

Fukui, M.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
[CrossRef]

García-Vidal, F. J.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
[CrossRef]

Gong, Q. H.

H. X. Zhang, Y. Gu, and Q. H. Gong, “A visible-near infrared tunable waveguide based on plasmonic gold nanoshell,” Chinese Physics B 17(7), 2567–2573 (2008).

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D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
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D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29(10), 1069–1071 (2004).
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H. X. Zhang, Y. Gu, and Q. H. Gong, “A visible-near infrared tunable waveguide based on plasmonic gold nanoshell,” Chinese Physics B 17(7), 2567–2573 (2008).

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Guo, Y. N.

W. R. Xue, Y. N. Guo, P. Li, and W. M. Zhang, “Propagation Properties of a Surface Plasmonic Waveguide with double elliptical air cores,” Opt. Express 16(14), 10710–10720 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-14-10710.
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L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005), http://www.opticsexpress.org/abstract.cfm?uri=oe-13-17-6645.
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D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
[CrossRef]

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He, S.

L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13(17), 6645–6650 (2005), http://www.opticsexpress.org/abstract.cfm?uri=oe-13-17-6645.
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I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15(25), 16596–16603 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-25-16596.
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Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
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I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15(25), 16596–16603 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-25-16596.
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Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
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F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86(21), 211101 (2005).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
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N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85(21), 5040–5042 (2004).
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I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15(25), 16596–16603 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-25-16596.
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I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15(25), 16596–16603 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-25-16596.
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Li, P.

W. R. Xue, Y. N. Guo, P. Li, and W. M. Zhang, “Propagation Properties of a Surface Plasmonic Waveguide with double elliptical air cores,” Opt. Express 16(14), 10710–10720 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-14-10710.
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S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
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Matsuo, S.

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[CrossRef]

Matsuzaki, Y.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
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Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
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Moreno, E.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
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A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-8-5252.
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M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-17-4072.
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Nielsen, R. B.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-8-5252.
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Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
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D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
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Okamoto, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
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D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
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Park, J.

I. Lee, J. Jung, J. Park, H. Kim, and B. Lee, “Dispersion characteristics of channel plasmon polariton waveguides with step-trench-type grooves,” Opt. Express 15(25), 16596–16603 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-25-16596.
[CrossRef]

Pile, D. F. P.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
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D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
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D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29(10), 1069–1071 (2004).
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M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal coners,” J. Opt. Soc. Am. B 24(9), 2333–2342 (2007).
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S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2(4), 229–232 (2003).
[CrossRef]

Rodrigo, S. G.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100(2), 023901 (2008).
[CrossRef]

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-8-5252.
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Rogowski, R. S.

S. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express 12(15), 3341–3352 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-15-3341.
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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(12), 2442–2446 (2004).
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Shakya, J.

L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31(14), 2133–2135 (2006).
[CrossRef]

Sondergaard, T.

J. Jung, T. Sondergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76(3), 035434 (2007).
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S. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express 12(15), 3341–3352 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-15-3341.
[CrossRef]

Takahara, J.

F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86(21), 211101 (2005).
[CrossRef]

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997).
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Taki, H.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997).
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K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
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Tanaka, M.

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

Tetz, K.

M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-17-4072.
[CrossRef]

Vernon, K. C.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Volkov, V. S.

A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16(8), 5252–5260 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-8-5252.
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[CrossRef]

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B. Wang and G. P. Wang, “Planar metal heterostructures for nanoplasmonic waveguides,” Appl. Phys. Lett. 90(1), 013114 (2007).
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Wang, G. P.

B. Wang and G. P. Wang, “Planar metal heterostructures for nanoplasmonic waveguides,” Appl. Phys. Lett. 90(1), 013114 (2007).
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G. P. Wang and B. Wang, “Metal heterostructure-based nanophotonic devices: finite-difference time-domain numerical simulations,” J. Opt. Soc. Am. B 23(8), 1660–1665 (2006).
[CrossRef]

Wu, F.

S. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express 12(15), 3341–3352 (2004), http://www.opticsexpress.org/abstract.cfm?uri=oe-12-15-3341.
[CrossRef]

Xue, W. R.

W. R. Xue, Y. N. Guo, P. Li, and W. M. Zhang, “Propagation Properties of a Surface Plasmonic Waveguide with double elliptical air cores,” Opt. Express 16(14), 10710–10720 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-14-10710.
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J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22(7), 475–477 (1997).
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D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

Yan, M.

M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal coners,” J. Opt. Soc. Am. B 24(9), 2333–2342 (2007).
[CrossRef]

Yotsuya, T.

F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86(21), 211101 (2005).
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Zhang, H. X.

H. X. Zhang, Y. Gu, and Q. H. Gong, “A visible-near infrared tunable waveguide based on plasmonic gold nanoshell,” Chinese Physics B 17(7), 2567–2573 (2008).

Zhang, W. M.

W. R. Xue, Y. N. Guo, P. Li, and W. M. Zhang, “Propagation Properties of a Surface Plasmonic Waveguide with double elliptical air cores,” Opt. Express 16(14), 10710–10720 (2008), http://www.opticsexpress.org/abstract.cfm?uri=oe-16-14-10710.
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Zia, R.

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(12), 2442–2446 (2004).
[CrossRef]

Appl. Phys. Lett. (6)

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, “Propagation properties of guided waves in index-guided two-dimensional optical waveguides,” Appl. Phys. Lett. 86(21), 211101 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two- dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on riangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87(6), 061106 (2005).
[CrossRef]

B. Wang and G. P. Wang, “Planar metal heterostructures for nanoplasmonic waveguides,” Appl. Phys. Lett. 90(1), 013114 (2007).
[CrossRef]

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85(21), 5040–5042 (2004).
[CrossRef]

Chinese Physics B (1)

H. X. Zhang, Y. Gu, and Q. H. Gong, “A visible-near infrared tunable waveguide based on plasmonic gold nanoshell,” Chinese Physics B 17(7), 2567–2573 (2008).

IEEE J. Sel. Top. Quantum Electron. (1)

S. A. Maier, “Plasmonics: The promise of highly integrated optical devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1671–1677 (2006).

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(12), 2442–2446 (2004).
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J. Opt. Soc. Am. B (2)

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Figures (10)

Fig. 1.
Fig. 1.

Cross section of the proposed surface plasmonic waveguide with three circular air cores. (a) 2a>r, (b) 2a=r and (c) 2a<r

Fig. 2.
Fig. 2.

Analytic and simulated normalized (a) real part and (b) imaginary part of propagation constant of an optical fiber [41] with a finite metallic core for the 0th-order TM mode. Here, a is the radius of the core, λ 0 is the working wavelength, and k 0=2π/λ 0.

Fig. 3.
Fig. 3.

The distribution of the field (a) Hx , (b) Hy and (c) Sy on the cross section when a=60 nm, h=85 nm, r=120 nm at λ=705.0 nm. Dashed lines in (a), (b) and (c) indicate the outline of the structure.

Fig. 4.
Fig. 4.

Dependence of (a–c) Re(neff ), (d–f) Lprop and (g–i) Am on h when r=2a - 5 nm, 2a and 2a+5 nm at λ=705.0 nm.

Fig. 5.
Fig. 5.

Dependence of (a–c) Re(neff ), (d–f) Lprop and (g–i) Am on h when r=2a=100 nm, 120 nm and 140 nm at λ=632.8 nm, 705.0 nm, 800.0 nm.

Fig. 6.
Fig. 6.

Dependence of (a–b) Re(neff ), (c–d) Lprop and (e–f) Am on h when a=0 nm, 60 nm, r=120 nm at λ=632.8 nm, 705.0 nm, 800.0 nm.

Fig. 7.
Fig. 7.

The cross section of the SPW with a single wedge (a), the distribution of the field (b) Hx , (c) Hy and (d) Sz on the cross section when r=100 nm, c=85 nm, at λ=705.0 nm. Dashed lines in (b), (c) and (d) indicate the outline of the structure.

Fig. 8.
Fig. 8.

Dependence of (a) Re(neff ), (b) Lprop and (c) Am on c (or h) when r=100 nm at λ=705.0 nm.

Fig. 9.
Fig. 9.

Dependence of (a) Re(neff ), (b) Lprop and (c) Am on h in the different cases.

Fig. 10.
Fig. 10.

The distribution of the field Sz when λ=1550 nm, a=60 nm, r=120 nm with (a) εcore =11.56-0.000j, (b) εcore =11.56-0.025j, (c) εcore =11.56-0.050j, and (d) εcore =1.00-0.000j.

Tables (1)

Tables Icon

Table 1. The dielectric constants of the SPW.

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