Hollow hybrid plasmonic waveguide for nanoscale optical confinement with long-range propagation Tarun Sharma and Mukesh Kumar* Department of Electronics and Communication Engineering, Thapar University, Patiala-147004, Punjab, India *Corresponding author: [email protected] Received 7 January 2014; revised 17 February 2014; accepted 17 February 2014; posted 18 February 2014 (Doc. ID 204360); published 19 March 2014
A novel (to our knowledge) hybrid plasmonic (HP) hollow waveguide is proposed for nanoscale optical confinement. The light is guided, with improved propagation characteristics, in an air slice sandwiched between metal and silicon. The optical mode in silicon is dragged toward the metal–dielectric (air) interface to make it a HP mode by optimizing the waveguide dimensions. In comparison to the hybrid mode confined in the dielectrics, the air-confined hybrid mode exhibits a smaller effective mode area Am 0.0685∕μm2 and longer propagation distance Lp 142 μm with a low modal propagation loss of 0.03 dB∕μm at optimized values of the width and height of the air slice. © 2014 Optical Society of America OCIS codes: (230.7370) Waveguides; (250.5403) Plasmonics; (350.4238) Nanophotonics and photonic crystals. http://dx.doi.org/10.1364/AO.53.001954
1. Introduction
To enable device integration on nanoscales, the confinement and controlling light beyond the diffraction limits are crucial problems that can be addressed with plasmonics [1–4]. Various plasmonic waveguides have been proposed as building blocks for integrated circuits [5]. However, a typical challenge for plasmonic waveguides is the trade-off between propagation loss and field confinement. In other words, they can perform either low propagation loss with a diffused field (e.g., long-range surface plasmon polaritons (SPPs) [6]) or compact mode size at the expense of large losses (e.g., metal–insulator–metal waveguides [7,8]). Recently, a new type of plasmonic waveguide called a “hybrid plasmonic waveguide (HPW)” was proposed to attempt both low propagation loss and strong field confinement [9]. Plasmonics as a major part of the emerging field of nanophotonics [10,11] explores how electromagnetic fields can be confined on scales much smaller than 1559-128X/14/091954-04$15.00/0 © 2014 Optical Society of America 1954
APPLIED OPTICS / Vol. 53, No. 9 / 20 March 2014
the wavelength. SPPs are two‐dimensional electromagnetic waves propagating at the flat interface between a conductor and a dielectric. Confinement is achieved because the propagation constant β is greater than the wave vector k in the dielectric, leading to evanescent decay in the perpendicular direction [12,13]. In a dielectric waveguide the guided mode has a long propagation distance, but the light confinement is usually limited to the order of a wavelength in one direction. Nanoscale confinement of light is possible with pure metal surface plasmon waveguides, but they suffer from a limited propagation distance due to the high loss of the metal (ohmic) absorption [14,15]. A hybrid approach, combining the dielectric waveguide mode and surface plasmon mode, has been proposed such that we may achieve both subwavelength confinement and a long propagation distance. In this paper a novel hollow HPW is proposed. Optimization of the width and height of the air slice sandwiched between metal and silicon leads to the confinement of hybrid plasmonic (HP) mode in the air. The simulation of the waveguide is done using the finite element method (FEM) [16]. It is found that the introduction of air to confine
the HP mode in the nanoscale can increase the propagation distance and can reduce the mode area, which are, respectively, because of the reduction in the effective index and in the lateral optical spread. The propagation characteristics reported for the proposed waveguide are improved over other easy-tofabricate HP structures, which include dielectric materials such as SiO2 and Al2 O3 , for application in the realization of nanophotonic devices [17,18]. The presence of air in the waveguide will further enhance its applicability in the guided wave devices [16,19]. Berini [20] studied the perturbation in the performance of waveguiding characteristics of the SPP mode due to the presence of air gaps in proximity to the guiding region. That study was motivated by a fabrication approach based on direct bonding, where various kinds of air gaps may form near the metal stripe due to fabrication imperfections. This feature could be interesting in applications where high-intensity (SPP) fields in nanometric air gaps are sought, but only if coupling and radiation losses are not much of a concern. Our work is focused on intentionally introducing an air gap in the guiding region for the realization of long-range propagation of the HP mode. In our structure we use a thicker metal up to 100 and a 10 nm air gap, keeping in mind the trade-off between optical confinement and propagation loss/propagation length. The introduction of an air gap into the guiding region has important consequences [21]. The fabrication of the HPW will be challenging, and careful inspection of the metal and dielectric surface will be necessary during fabrication. The air gap can be formed by wafer bonding and/or selective wet etching with high selectivity. Multiple steps of selective wet etching can be performed to realize a defect-free and smooth air slice.
is hAu 100 nm. The height of the air slice is denoted as hair , while the width of the air slice is W air . For single-mode operation of the waveguide, the width of the air slice should remain below 240 nm (W air < 240 nm) at an operating wavelength of 1550 nm. For low loss and strong field confinement, the minimum value of hair is 10 nm, below which the rectangular geometry of the air slice will not support the HP mode and the mode will become pure SPP [9]. The electric field is strongly confined within the 10 nm air layer. The optical mode can be dragged toward the metal–dielectric interface to change it to the HP mode to achieve long-range propagation with subwavelength confinement. Further, introduction of an air gap into the guiding region enhances the propagation characteristics [21]. 3. Modal Characteristics
The field distributions Ey of the fundamental TM mode of the HPW, in line graphs and pictorial graphs, are shown in Figs. 2(a) and 2(b). Figure 2(a) shows the HP field confinement when SiO2 is sandwiched between metal (dielectric based) and silicon, while Fig. 2(b) shows the HP field confinement when the air slice is introduced in place of the dielectric between the metal and silicon (hollow). The materialfilled losses will be responsible for field leakage into the bottom Si in the first case, which can be avoided to some extent by introducing an air slice in place of the dielectric. The real part of the effective index neff is 2.75 for a dielectric-based HPW, while it is 2.64 for a hollow HPW, where width W d and height hd of the dielectric/air are, respectively, 200 and 10 nm. Thus
2. Proposed Waveguide Design
The proposed design of the hollow HPW is shown in Fig. 1. It is composed of air, to guide the HP mode, as the dielectric between the top metal layer and silicon. The height of the silicon, as shown in Fig. 1, is hsi 100 nm, and the thickness of the gold layer
Fig. 1. Schematic of the proposed design of the HP hollow waveguide in which an air slice of height hair and width W air is formed in silicon under the top gold layer with a thickness of 100 nm. hair and W air are to be optimized for a long propagation length and singlemode operation.
Fig. 2. Field distributions Ey of the fundamental TM mode of the HPW (a) for a dielectric-based waveguide and (b) for a hollow waveguide. The width and height of the dielectric/air are respectively 200 and 10 nm. The real part of the neff is 2.75 for (a), and it is 2.64 for (b). The field confinement is stronger in (b) than that in (a). 20 March 2014 / Vol. 53, No. 9 / APPLIED OPTICS
1955
1800 Propagation Length (µm)
the field will travel longer in the second case of the hollow HPW. The field distribution is the sum of two exponential functions. When the air slice is very thin (smaller than the evanescent penetration depth), the field at the air-slice layer is enhanced greatly. There is a strong field enhancement in the air slice, which is due to the combination of the surface plasmon at the Au–air interface and the discontinuity in the Ey field at the Si–air interface.
1600 1400 1200 1000 800 600 400 200 0
4. Propagation Characteristics
0.1685 0.1485 0.1285 0.1085
20 30 40 Air-slice height (nm)
50
50 nm, the confined mode loses its HP nature, though the propagation length is larger for these values. At hair 10 nm the confined mode shows a strong HP nature, with a moderate value of the propagation length of 142 μm, while it is 28 μm for the SiO2 (dielectric-based) waveguide at wair 100 nm, as shown in Fig. 5. The propagation length further increases with air slice height, but we fix our choice at hair 10 nm, because it shows tight confinement of the HP mode; the effective mode area at this height is 0.068∕μm2 as discussed above. The effect of the width of the dielectric (SiO2 ∕air) on the propagation length is shown in Fig. 5. It is observed that at a constant dielectric height hd of 10 nm the propagation length decreases with an increase in the dielectric width W d . The hollow HPW shows a propagation length larger than that with the dielectric-based (SiO2 here) waveguide. At W d 50 nm the propagation length is largest for both cases, but the confinement of the HP mode will remain poor, as the effective mode area in this case will be larger, as shown in Fig. 3. Our motive is to obtain the optimized structure that can strongly confine the HP mode and can guide it longer. To make the results more complete, the analysis of the modal propagation loss of the proposed hollow 400 350 300 dielectric
250
Air
200 150 100 50 0
0.0885
50 0.0685 50
100 150 200 Width of Air-slice (nm)
250
Fig. 3. Variation in the effective mode area with the width of the air slice at an air slice height of 10 nm. 1956
10
Fig. 4. Effect of the height of the air slice on propagation length at an air slice width of wair 100 nm. The values of the mode area at air slice heights of 10, 20, 30, 40, and 50 nm are, respectively, 0.0685, 0.11, 0.5∕μm2 , 0.61, and 0.11∕μm2 .
Propagation Length (µm)
Effective mode area(/µm2 )
Geometric parameters can significantly control the guiding performance of a waveguide. We analyzed the guiding performance of the HPW by observing the effect of the height hd and width wd of the air slice. The effective index neff of the guided mode rises as w increases or h decreases. The simulation of the guiding characteristics is done using FEM. The waveguide dimensions affect the energy distribution in the waveguide; specifically, for tight confinement in some highindex cores the corresponding neff will be larger. A smaller value of neff will cause the modal propagation loss to be lower. The propagation length for the guided HP mode is give by Lprop μm λ∕4πneff imaginary [19], and the modal propagation loss is given by Lm db∕μm 2K 0 img:neff × 4.34 [16]. The nature of the guided mode can be evidenced by the modal area of the field confinement [9]. The effective mode area of the guided fundamental mode will be a measure of the nature, whether the localized field is optical, pure plasmonic, or HP [10], and it would be the merit for confinement ability, which is given R∞ by Am ∕μm2 −∞ px; ydxdy∕ maxpx; y [16]. Figure 3 shows the effect of a change in the air slice width wair on the effective mode area Am . The value of Am becomes large for wair < 100 nm. It is shown that strong HP mode confinement can be achieved for 100 nm < wair < 250 nm, because the effective mode area remains acceptably small in this range. At wair 100 nm the effective mode area is 0.0685∕μm2, which exhibits the HP nature of the confined mode. Height of the air slice plays a key role in significantly controlling the propagation characteristics of the guided mode. The effect of change in the air slice height on the propagation length is shown in Fig. 4 at wair 100 nm. For values of hair larger than
APPLIED OPTICS / Vol. 53, No. 9 / 20 March 2014
100
150 Width (nm)
200
250
Fig. 5. Variation of propagation length with SiO2 (dielectric) and air width at constant hair ∕hSiO2 10 nm. Values of the effective mode area for air slice widths of 50, 100, 150, 200, and 250 nm are, respectively, 0.08, 0685, 0.11, 0.15, and 0.17∕μm2 .
Modal Propagation Loss(dB/µm)
0.1 0.09
h_10nm
h_20nm
0.08
h_30nm
h_40nm
0.07
h_50nm
of the hollow HPW for low nonlinearity and efficient on-chip tiny sensors. To ease the fabrication process of the proposed waveguide, it is possible to achieve long-range propagation with larger air gaps by further engineering the waveguide structure, which will help in utilizing the waveguide to make functional nanodevices.
0.06 0.05 0.04 0.03
References
0.02
1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). 2. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). 3. M. Mansuripur, A. R. Zakharian, A. Lesuffleur, S.-H. Oh, R. J. Jones, N. C. Lindquist, H. Im, A. Kobyakov, and J. V. Moloney, “Plasmonic nano-structures for optical data storage,” Opt. Express 17, 14001–14014 (2009). 4. Q. Min, C. Chen, P. Berini, and R. Gordon, “Long range surface plasmons on asymmetric suspended thin film structures for biosensing applications,” Opt. Express 18, 19009–19019 (2010). 5. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010). 6. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005). 7. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005). 8. G. Veronis and S. H. Fan, “Bends and splitters in metaldielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005). 9. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008). 10. D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17, 16646–16653 (2009). 11. P. D. Flammer, J. M. Banks, T. E. Furtak, C. G. Durfee, R. E. Hollingsworth, and R. T. Collins, “Hybrid plasmon/dielectric waveguide for integrated silicon-on-insulator optical elements,” Opt. Express 18, 21013–21023 (2010). 12. I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18, 348–363 (2010). 13. M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express 18, 11728–11736 (2010). 14. I. Goykhman, B. Desiatov, and U. Levy, “Experimental demonstration of locally oxidized hybrid silicon plasmonic waveguide,” Appl. Phys. Lett. 97, 141106 (2010). 15. S. A. Maier, “Plasmon waveguides,” in Plasmonics: Fundamentals and Applications (Springer, 2007), pp. 107–129. 16. L. Gao, L. Tang, F. Hu, R. Guo, X. Wang, and Z. Zhou, “Active metal strip hybrid plasmonic waveguide with low critical material gain,” Opt. Express 20, 11487–11495 (2012). 17. J. T. Robinson, K. Preston, O. Painter, and M. Lipson, “First-principle derivation of gain in high-index-contrast waveguides,” Opt. Express 16, 16659–16669 (2008). 18. P. Muellner, M. Wellenzohn, and R. Hainberger, “Nonlinearity of optimized silicon photonic slot waveguides,” Opt. Express 17, 9282–9287 (2009). 19. Y. Kou, F. Ye, and X. Chen, “Low-loss hybrid plasmonic waveguide for compact and high-efficient photonic integration,” Opt. Express 19, 11746–11752 (2011). 20. P. Berini, “Air gap in metal strip waveguides supporting longrange surface plasmon polaritons,” J. Appl. Phys. 102, 033112 (2007). 21. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11, 321–328 (2011).
0.01 0 50
100
150 200 Air - sliceWidth (nm)
250
Fig. 6. Change in modal propagation loss of the hollow HP waveguide with the width of air slice for different heights of the air slice.
HPW is carried out, which is shown in Fig. 6. The variation in the propagation loss with the air slice width is shown at different values of the height of the air slice. The propagation loss decreases with decreasing wair , and the loss increases with decreasing hair . As discussed above, the optimized values of wair and hair are, respectively, 100 and 10 nm. The propagation at these values is 0.03 dB∕μm. For low loss and strong field confinement, the minimum value of hair is 10 nm, below which the rectangular geometry of the air slice will not support the HP mode and the mode will become pure SPP [9], which will be seen as a smaller propagation length in the waveguide. To further increase the propagation length with tight confinement at smaller heights of the air slice, a circular air slice may be a potential candidate for long-range propagation. 5. Conclusion
A novel (to our knowledge) design of a hollow HPW for nanoscale optical confinement and long-range propagation is proposed. The propagation characteristics of the proposed waveguide are improved over other easy-to-fabricate HP structures. Optimized width and height of the air slice sandwiched between metal and silicon lead to a strong confinement of the HP mode in the air, with a small mode area. The introduction of air into the HPW can increase the propagation distance with acceptably small propagation loss. As compared to the hybrid mode confined in the dielectrics, the air-confined hybrid mode exhibits a smaller effective mode area Am 0.0685∕μm2 and longer propagation distance Lp 142 μm, with a low modal propagation loss of 0.03 dB∕μm at optimized values of the width and height of the air slice. The proposed easy-to-fabricate design of the waveguide will be useful for the realization of integrated nanophotonic devices with acceptably small losses. To further enhance the guiding performance, a circular air slice can be formed into the HPW for longer propagation and stronger field confinement. The presence of air in the guiding region may enable the application
20 March 2014 / Vol. 53, No. 9 / APPLIED OPTICS
1957
A novel (to our knowledge) hybrid plasmonic (HP) hollow waveguide is proposed for nanoscale optical confinement. The light is guided, with improved propagation characteristics, in an air slice sandwiched between metal and silicon. The optical mode in silicon is dragged toward the metal–dielectric (air) interface to make it a HP mode by optimizing the waveguide dimensions. In comparison to the hybrid mode confined in the dielectrics, the air-confined hybrid mode exhibits a smaller effective mode area Am 0.0685∕μm2 and longer propagation distance Lp 142 μm with a low modal propagation loss of 0.03 dB∕μm at optimized values of the width and height of the air slice. © 2014 Optical Society of America OCIS codes: (230.7370) Waveguides; (250.5403) Plasmonics; (350.4238) Nanophotonics and photonic crystals. http://dx.doi.org/10.1364/AO.53.001954
1. Introduction
To enable device integration on nanoscales, the confinement and controlling light beyond the diffraction limits are crucial problems that can be addressed with plasmonics [1–4]. Various plasmonic waveguides have been proposed as building blocks for integrated circuits [5]. However, a typical challenge for plasmonic waveguides is the trade-off between propagation loss and field confinement. In other words, they can perform either low propagation loss with a diffused field (e.g., long-range surface plasmon polaritons (SPPs) [6]) or compact mode size at the expense of large losses (e.g., metal–insulator–metal waveguides [7,8]). Recently, a new type of plasmonic waveguide called a “hybrid plasmonic waveguide (HPW)” was proposed to attempt both low propagation loss and strong field confinement [9]. Plasmonics as a major part of the emerging field of nanophotonics [10,11] explores how electromagnetic fields can be confined on scales much smaller than 1559-128X/14/091954-04$15.00/0 © 2014 Optical Society of America 1954
APPLIED OPTICS / Vol. 53, No. 9 / 20 March 2014
the wavelength. SPPs are two‐dimensional electromagnetic waves propagating at the flat interface between a conductor and a dielectric. Confinement is achieved because the propagation constant β is greater than the wave vector k in the dielectric, leading to evanescent decay in the perpendicular direction [12,13]. In a dielectric waveguide the guided mode has a long propagation distance, but the light confinement is usually limited to the order of a wavelength in one direction. Nanoscale confinement of light is possible with pure metal surface plasmon waveguides, but they suffer from a limited propagation distance due to the high loss of the metal (ohmic) absorption [14,15]. A hybrid approach, combining the dielectric waveguide mode and surface plasmon mode, has been proposed such that we may achieve both subwavelength confinement and a long propagation distance. In this paper a novel hollow HPW is proposed. Optimization of the width and height of the air slice sandwiched between metal and silicon leads to the confinement of hybrid plasmonic (HP) mode in the air. The simulation of the waveguide is done using the finite element method (FEM) [16]. It is found that the introduction of air to confine
the HP mode in the nanoscale can increase the propagation distance and can reduce the mode area, which are, respectively, because of the reduction in the effective index and in the lateral optical spread. The propagation characteristics reported for the proposed waveguide are improved over other easy-tofabricate HP structures, which include dielectric materials such as SiO2 and Al2 O3 , for application in the realization of nanophotonic devices [17,18]. The presence of air in the waveguide will further enhance its applicability in the guided wave devices [16,19]. Berini [20] studied the perturbation in the performance of waveguiding characteristics of the SPP mode due to the presence of air gaps in proximity to the guiding region. That study was motivated by a fabrication approach based on direct bonding, where various kinds of air gaps may form near the metal stripe due to fabrication imperfections. This feature could be interesting in applications where high-intensity (SPP) fields in nanometric air gaps are sought, but only if coupling and radiation losses are not much of a concern. Our work is focused on intentionally introducing an air gap in the guiding region for the realization of long-range propagation of the HP mode. In our structure we use a thicker metal up to 100 and a 10 nm air gap, keeping in mind the trade-off between optical confinement and propagation loss/propagation length. The introduction of an air gap into the guiding region has important consequences [21]. The fabrication of the HPW will be challenging, and careful inspection of the metal and dielectric surface will be necessary during fabrication. The air gap can be formed by wafer bonding and/or selective wet etching with high selectivity. Multiple steps of selective wet etching can be performed to realize a defect-free and smooth air slice.
is hAu 100 nm. The height of the air slice is denoted as hair , while the width of the air slice is W air . For single-mode operation of the waveguide, the width of the air slice should remain below 240 nm (W air < 240 nm) at an operating wavelength of 1550 nm. For low loss and strong field confinement, the minimum value of hair is 10 nm, below which the rectangular geometry of the air slice will not support the HP mode and the mode will become pure SPP [9]. The electric field is strongly confined within the 10 nm air layer. The optical mode can be dragged toward the metal–dielectric interface to change it to the HP mode to achieve long-range propagation with subwavelength confinement. Further, introduction of an air gap into the guiding region enhances the propagation characteristics [21]. 3. Modal Characteristics
The field distributions Ey of the fundamental TM mode of the HPW, in line graphs and pictorial graphs, are shown in Figs. 2(a) and 2(b). Figure 2(a) shows the HP field confinement when SiO2 is sandwiched between metal (dielectric based) and silicon, while Fig. 2(b) shows the HP field confinement when the air slice is introduced in place of the dielectric between the metal and silicon (hollow). The materialfilled losses will be responsible for field leakage into the bottom Si in the first case, which can be avoided to some extent by introducing an air slice in place of the dielectric. The real part of the effective index neff is 2.75 for a dielectric-based HPW, while it is 2.64 for a hollow HPW, where width W d and height hd of the dielectric/air are, respectively, 200 and 10 nm. Thus
2. Proposed Waveguide Design
The proposed design of the hollow HPW is shown in Fig. 1. It is composed of air, to guide the HP mode, as the dielectric between the top metal layer and silicon. The height of the silicon, as shown in Fig. 1, is hsi 100 nm, and the thickness of the gold layer
Fig. 1. Schematic of the proposed design of the HP hollow waveguide in which an air slice of height hair and width W air is formed in silicon under the top gold layer with a thickness of 100 nm. hair and W air are to be optimized for a long propagation length and singlemode operation.
Fig. 2. Field distributions Ey of the fundamental TM mode of the HPW (a) for a dielectric-based waveguide and (b) for a hollow waveguide. The width and height of the dielectric/air are respectively 200 and 10 nm. The real part of the neff is 2.75 for (a), and it is 2.64 for (b). The field confinement is stronger in (b) than that in (a). 20 March 2014 / Vol. 53, No. 9 / APPLIED OPTICS
1955
1800 Propagation Length (µm)
the field will travel longer in the second case of the hollow HPW. The field distribution is the sum of two exponential functions. When the air slice is very thin (smaller than the evanescent penetration depth), the field at the air-slice layer is enhanced greatly. There is a strong field enhancement in the air slice, which is due to the combination of the surface plasmon at the Au–air interface and the discontinuity in the Ey field at the Si–air interface.
1600 1400 1200 1000 800 600 400 200 0
4. Propagation Characteristics
0.1685 0.1485 0.1285 0.1085
20 30 40 Air-slice height (nm)
50
50 nm, the confined mode loses its HP nature, though the propagation length is larger for these values. At hair 10 nm the confined mode shows a strong HP nature, with a moderate value of the propagation length of 142 μm, while it is 28 μm for the SiO2 (dielectric-based) waveguide at wair 100 nm, as shown in Fig. 5. The propagation length further increases with air slice height, but we fix our choice at hair 10 nm, because it shows tight confinement of the HP mode; the effective mode area at this height is 0.068∕μm2 as discussed above. The effect of the width of the dielectric (SiO2 ∕air) on the propagation length is shown in Fig. 5. It is observed that at a constant dielectric height hd of 10 nm the propagation length decreases with an increase in the dielectric width W d . The hollow HPW shows a propagation length larger than that with the dielectric-based (SiO2 here) waveguide. At W d 50 nm the propagation length is largest for both cases, but the confinement of the HP mode will remain poor, as the effective mode area in this case will be larger, as shown in Fig. 3. Our motive is to obtain the optimized structure that can strongly confine the HP mode and can guide it longer. To make the results more complete, the analysis of the modal propagation loss of the proposed hollow 400 350 300 dielectric
250
Air
200 150 100 50 0
0.0885
50 0.0685 50
100 150 200 Width of Air-slice (nm)
250
Fig. 3. Variation in the effective mode area with the width of the air slice at an air slice height of 10 nm. 1956
10
Fig. 4. Effect of the height of the air slice on propagation length at an air slice width of wair 100 nm. The values of the mode area at air slice heights of 10, 20, 30, 40, and 50 nm are, respectively, 0.0685, 0.11, 0.5∕μm2 , 0.61, and 0.11∕μm2 .
Propagation Length (µm)
Effective mode area(/µm2 )
Geometric parameters can significantly control the guiding performance of a waveguide. We analyzed the guiding performance of the HPW by observing the effect of the height hd and width wd of the air slice. The effective index neff of the guided mode rises as w increases or h decreases. The simulation of the guiding characteristics is done using FEM. The waveguide dimensions affect the energy distribution in the waveguide; specifically, for tight confinement in some highindex cores the corresponding neff will be larger. A smaller value of neff will cause the modal propagation loss to be lower. The propagation length for the guided HP mode is give by Lprop μm λ∕4πneff imaginary [19], and the modal propagation loss is given by Lm db∕μm 2K 0 img:neff × 4.34 [16]. The nature of the guided mode can be evidenced by the modal area of the field confinement [9]. The effective mode area of the guided fundamental mode will be a measure of the nature, whether the localized field is optical, pure plasmonic, or HP [10], and it would be the merit for confinement ability, which is given R∞ by Am ∕μm2 −∞ px; ydxdy∕ maxpx; y [16]. Figure 3 shows the effect of a change in the air slice width wair on the effective mode area Am . The value of Am becomes large for wair < 100 nm. It is shown that strong HP mode confinement can be achieved for 100 nm < wair < 250 nm, because the effective mode area remains acceptably small in this range. At wair 100 nm the effective mode area is 0.0685∕μm2, which exhibits the HP nature of the confined mode. Height of the air slice plays a key role in significantly controlling the propagation characteristics of the guided mode. The effect of change in the air slice height on the propagation length is shown in Fig. 4 at wair 100 nm. For values of hair larger than
APPLIED OPTICS / Vol. 53, No. 9 / 20 March 2014
100
150 Width (nm)
200
250
Fig. 5. Variation of propagation length with SiO2 (dielectric) and air width at constant hair ∕hSiO2 10 nm. Values of the effective mode area for air slice widths of 50, 100, 150, 200, and 250 nm are, respectively, 0.08, 0685, 0.11, 0.15, and 0.17∕μm2 .
Modal Propagation Loss(dB/µm)
0.1 0.09
h_10nm
h_20nm
0.08
h_30nm
h_40nm
0.07
h_50nm
of the hollow HPW for low nonlinearity and efficient on-chip tiny sensors. To ease the fabrication process of the proposed waveguide, it is possible to achieve long-range propagation with larger air gaps by further engineering the waveguide structure, which will help in utilizing the waveguide to make functional nanodevices.
0.06 0.05 0.04 0.03
References
0.02
1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). 2. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006). 3. M. Mansuripur, A. R. Zakharian, A. Lesuffleur, S.-H. Oh, R. J. Jones, N. C. Lindquist, H. Im, A. Kobyakov, and J. V. Moloney, “Plasmonic nano-structures for optical data storage,” Opt. Express 17, 14001–14014 (2009). 4. Q. Min, C. Chen, P. Berini, and R. Gordon, “Long range surface plasmons on asymmetric suspended thin film structures for biosensing applications,” Opt. Express 18, 19009–19019 (2010). 5. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010). 6. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005). 7. L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express 13, 6645–6650 (2005). 8. G. Veronis and S. H. Fan, “Bends and splitters in metaldielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005). 9. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008). 10. D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17, 16646–16653 (2009). 11. P. D. Flammer, J. M. Banks, T. E. Furtak, C. G. Durfee, R. E. Hollingsworth, and R. T. Collins, “Hybrid plasmon/dielectric waveguide for integrated silicon-on-insulator optical elements,” Opt. Express 18, 21013–21023 (2010). 12. I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18, 348–363 (2010). 13. M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express 18, 11728–11736 (2010). 14. I. Goykhman, B. Desiatov, and U. Levy, “Experimental demonstration of locally oxidized hybrid silicon plasmonic waveguide,” Appl. Phys. Lett. 97, 141106 (2010). 15. S. A. Maier, “Plasmon waveguides,” in Plasmonics: Fundamentals and Applications (Springer, 2007), pp. 107–129. 16. L. Gao, L. Tang, F. Hu, R. Guo, X. Wang, and Z. Zhou, “Active metal strip hybrid plasmonic waveguide with low critical material gain,” Opt. Express 20, 11487–11495 (2012). 17. J. T. Robinson, K. Preston, O. Painter, and M. Lipson, “First-principle derivation of gain in high-index-contrast waveguides,” Opt. Express 16, 16659–16669 (2008). 18. P. Muellner, M. Wellenzohn, and R. Hainberger, “Nonlinearity of optimized silicon photonic slot waveguides,” Opt. Express 17, 9282–9287 (2009). 19. Y. Kou, F. Ye, and X. Chen, “Low-loss hybrid plasmonic waveguide for compact and high-efficient photonic integration,” Opt. Express 19, 11746–11752 (2011). 20. P. Berini, “Air gap in metal strip waveguides supporting longrange surface plasmon polaritons,” J. Appl. Phys. 102, 033112 (2007). 21. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11, 321–328 (2011).
0.01 0 50
100
150 200 Air - sliceWidth (nm)
250
Fig. 6. Change in modal propagation loss of the hollow HP waveguide with the width of air slice for different heights of the air slice.
HPW is carried out, which is shown in Fig. 6. The variation in the propagation loss with the air slice width is shown at different values of the height of the air slice. The propagation loss decreases with decreasing wair , and the loss increases with decreasing hair . As discussed above, the optimized values of wair and hair are, respectively, 100 and 10 nm. The propagation at these values is 0.03 dB∕μm. For low loss and strong field confinement, the minimum value of hair is 10 nm, below which the rectangular geometry of the air slice will not support the HP mode and the mode will become pure SPP [9], which will be seen as a smaller propagation length in the waveguide. To further increase the propagation length with tight confinement at smaller heights of the air slice, a circular air slice may be a potential candidate for long-range propagation. 5. Conclusion
A novel (to our knowledge) design of a hollow HPW for nanoscale optical confinement and long-range propagation is proposed. The propagation characteristics of the proposed waveguide are improved over other easy-to-fabricate HP structures. Optimized width and height of the air slice sandwiched between metal and silicon lead to a strong confinement of the HP mode in the air, with a small mode area. The introduction of air into the HPW can increase the propagation distance with acceptably small propagation loss. As compared to the hybrid mode confined in the dielectrics, the air-confined hybrid mode exhibits a smaller effective mode area Am 0.0685∕μm2 and longer propagation distance Lp 142 μm, with a low modal propagation loss of 0.03 dB∕μm at optimized values of the width and height of the air slice. The proposed easy-to-fabricate design of the waveguide will be useful for the realization of integrated nanophotonic devices with acceptably small losses. To further enhance the guiding performance, a circular air slice can be formed into the HPW for longer propagation and stronger field confinement. The presence of air in the guiding region may enable the application
20 March 2014 / Vol. 53, No. 9 / APPLIED OPTICS
1957
