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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 10 — May. 12, 2008
  • pp: 7499–7507
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Feasibility study of nanoscaled optical waveguide based on near-resonant surface plasmon polariton

Min Yan, Lars Thylén, Min Qiu, and Devang Parekh  »View Author Affiliations


Optics Express, Vol. 16, Issue 10, pp. 7499-7507 (2008)
http://dx.doi.org/10.1364/OE.16.007499


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Abstract

Currently subwavelength surface plasmon polariton (SPP) waveguides under intensive theoretical and experimental studies are mostly based on the geometrical singularity property of such waveguides. Typical examples include the metal-insulator-metal based waveguide and the metallic fiber. Both types of waveguides support a mode with divergent propagation constant as the waveguides’ geometry (metal gap distance or fiber radius) shrinks to zero. Here we study an alternative way of achieving subwavelength confinement through deploying two materials with close but opposite epsilon values. The interface between such two materials supports a near-resonant SPP. By examining the relationship between mode propagation loss and the mode field size for both planar and fiber waveguides, we show that waveguides based on near-resonant SPP can be as attractive as those solely based on geometrical tailoring. We then explicitly study a silver and silicon based waveguide with a 25nm core size at 600nm wavelength, in its properties like single-mode condition, mode loss and group velocity. It is shown that loss values of both materials have to be decreased by ~1000 times in order to have 1dB/µm propagation loss. Hence we point out the necessity of novel engineering of low-loss metamaterials, or introducing gain, for practical applications of such waveguides. Due to the relatively simple geometry, the proposed near-resonant SPP waveguides can be a potential candidate for building optical circuits with a density close to the electronic counterpart.

© 2008 Optical Society of America

1. Introduction

The abovementioned subwavelength SPP waveguides are all based on geometrical tailoring. In fact, the peculiar guidance principle of SPP waveguides allows their mode field to be confined in a subwavelength fashion without resorting to geometrical tailoring. For a 1D metal-dielectric interface, the guided SPP mode has its neff value defined as

neff=ε+εε++ε,
(1)

where ε + and ε -(|ε -|>ε +) are permitivities of the dielectric material and metal, respectively. The materials are assumed to be non-permeable. From Eq. 1, it is noticed that n eff can be arbitrarily large, depending on how close (ε ++ε -) is to zero. It follows that the transverse field decay constant in the cladding, kt=k0neff2εclad (ε clad is either ε + or ε -), can also be made arbitrarily large. This gives rise to the possibility of tightly confined field at the interface. A section of the interface can potentially confine light in nanodimensions in 2D. Such a subwavelength waveguide has the obvious advantage of being structurally very simple. A primiary reason for lack of proper study on such waveguide probably is that, in addition to the divergent propagation constant, the propagation loss will also tend to infinity as the operation is near to the ε +=-ε - resonance condition. In fact, the tradeoff between confinement and loss for SPP waveguides has been observed for a wide varieties of guiding structures (e.g. see [4

4. 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. Phy. Lett. 87, 261,114 (2005). [CrossRef]

, 5

5. G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightw. Technol. 25, 2511–2521 (2007). [CrossRef]

, 6

6. E. Feigenbaum and M. Orenstein, “Modeling of complementary (void) plasmon waveguiding,” J. Lightw. Technol. 25, 2547–2562 (2007). [CrossRef]

, 8

8. 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 triangular metal wedges for subwavelength waveguiding,” Appl. Phy. Lett. 87, 061,106 (2005). [CrossRef]

, 9

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

]). In view of many published results on SPP waveguides, it has generally been accepted that some loss reduction technique (rather than merely geometrical optimization) has to be deployed in order to make functioning integrated optical circuits based on SPP.

In this paper, we first compare the confinement-to-loss relationships for two waveguides sharing the same geometry, with one based on the approach of structural tailoring and the other based on the approach of material variation. Waveguides in both planar and fiber shapes are considered. It will be shown that waveguides based on the two approaches experience comarable propagation loss as their mode fields decrease to subwavelength size. Owing to this factor, near-resonant SPP waveguides deserve as much attention as other types of SPP waveguides do in realizing subwavelength light channeling. From the perspective of integrated photonic circuit, we will specifically look into a realistic waveguide design based on a finite section of near-resonant silver-silicon interface.

2. Comparisons

2.1. Planar case

Fig. 1. (a),(b) Effect of gap distance on the guided SPP mode of a MIM waveguide; (c),(d) Effect of ε + on the guided SPP mode of a MI waveguide. Insets in (b) and (d) depict the guiding structures.

2.2. Fiber case

Fig. 2. (a),(b) Effect of geometrical tailoring on guided fiber SPP mode; (c)–(d) Material effects on guided SPP fiber mode. Inset in (b) depicts the fiber structure.

Here, still, we assess the performances of the waveguides derived from two approaches by examining their loss values when they achieve 100nm MFS. At this particular MFS, the waveguide based on geometrical tailoring experiences a loss of ~1dB/µm [Fig. 2(b)], while the waveguide based on material variation experiences a loss value of ~0.7dB/µm (for both r=100 and r=1000nm situations). Therefore in the case of fiber geometry, electromagnetic field can be more “cost-efficiently” confined to the metal-dielectric interface for the waveguide based on material engineering as compared to the waveguide based on geometrical tailoring.

3. Realistic design

Fig. 3. (a) Schematic diagram of a general near-resonant SPP waveguide. (b) Major mode field (Hx) supported by a sample near-resonant SPP waveguide (ε +=2.1, ε -=-2.3, ε 1,2,3,4=1, w=50nm, λ=600nm). (c) Hx field in the same waveguide but far from the singular condition (ε -=-15).

Although we know from Fig. 2(d) that subwavelength confinement of light can be achieved even when |ε +| is far smaller than |ε -|, however here we purposely choose |ε +|≈|ε -|, i.e., the near-resonant material parameters, in order to realize deep subwavelength MFS. Two materials with close but opposite epsilon values (in their real part ε″) at certain wavelengths do exist in nature, but not without loss. One example is silver (Ag) and silicon (Si). An examination of their dispersion curves tells that their epsilon values meet our requirement around the free-space wavelength of 600nm, at which ε Ag=-16.08+0.4434i and ε Si=15.58+0.2004i [14

14. E. D. Palik, Handbook of Optical Constants of Solids, Part II, Subpart 1 (Academic Press, 1985).

]. The imaginary part of the epsilon values (denoted as ε”) is directly responsible for attenuation of the guided surface mode. A single surface mode formed by the two materials at λ=600nm has a loss value as large as 690.7dB/µm, rendering almost any waveguide built upon such a surface impractical. One of our objectives is to investigate how small the imaginary epsilon values (ε”) of Ag and Si should be for practical applications.

First, to make sure the waveguide is single-mode, we calculate the geometric dispersion as a function of the core width w at λ=600nm (Fig. 4). Mode derivation is done in COMSOL Multiphysics (from COMSOL AB) with an electric-field- and edge-element-based finite element method. The blue curves (with dots) are the first two modes derived with ε”=0 for both Si and Ag materials. The red dots are calculated with ε” values reduced to 1% (compared to their natural values). The mode index changes little when the ε” values change from 0 to 1%. We will show later that when losses are higher, the waveguide is too lossy to be useful. From Fig. 4, it is seen that the waveguide is single-mode when w<27nm. We hence take w=25nm in our following analyses. The n eff value is ~15.6 at w=25nm, which ensures the mode field is highly evanescent in the cladding regions.

Fig. 4. Geometric dispersions of first two modes of the waveguide with respect to w. Loss is assumed to be zero. Red dots: the n eff values when ε” values of both Ag and Si are reduced to their 1%.

Mode supported by the waveguide is depicted in Fig. 5. For this particular mode derivation, material losses of Ag and Si are all reduced to 1% of their natural values. The field does not change appreciably when the material losses vary from 0 to 0.1 (in fractions of their natural values). In the cladding regions, the mode field decreases to its 1/e over a ~6nm distance. Therefore its MFS is approximated to be 37×12nm2. The mode field has a major polarization along y direction. The z-component of the Poynting vector (Sz) shown in Fig. 5(c) confirms the highly confined energy flow in the waveguide. Notice that, although Sz in Ag region is negative, the net energy flow is positive.

The loss of the waveguide with w=25nm is then computed as ε” values of both Ag and Si are varied. The result is shown in a contour map in Fig. 6. ε” values of both materials are varied from 10-6 to 10-1, in fractions of their natural values. It is observed that the waveguide loss is almost equally sensitive to variations in each of the two ε” values. In practice, the requirement of propagation length depends on the application. Here, given such a tiny circuit cross-section, a loss level of 1dB/µm (corresponding to a propagation length of a few micrometers) could be suitable for a wide range of purposes. A circuit with over 100 length-to-crosssection aspect ratio permits necessary waveguide bends for forming basic components (coupler, interferometer etc) and inter-connecting various ports in a high-density fashion. From Fig. 6, it is shown that both ε” values (or equivalently, conductivities of the two materials) have to be decreased by ~1000 times in order to have 1dB/µm propagation loss. It should be noted that keeping the desired negative ε′ and decreasing ε” will, as dictated by the Kramers-Krönig relations, require either other (meta)materials than the materials employed here, or possibly low temperature operation.

Fig. 5. Field plots of the SPP-based waveguide with a 25nm-sized core. Three panels share the same color scale. (a) Hx field (min:0, max:1.27); (b) Hy field (min:-5.02e-2, max:5.02e- 2); and (c) z-component Poynting vector Sz (min:-6.0e2, max:6.2e2). Axis unit: nm.
Fig. 6. Contour plot of the loss values in dB/µm when the ε” values of both Ag and Si are varied in fractions of their natural values at room temperature.

It’s understood that near-resonant 1D SPP exhibits an interesting property of slow group velocity (GV) [15

15. A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063,901 (2005). [CrossRef]

]. However, explicit studies on GV and also the group velocity dispersion (or GVD, which is reposnible for pulse broadening in digital communication links) for 2D SPP waveguides are often ignored in most published works. Here we numerically derive GV and GVD of the particular waveguide depicted in Fig. 5. Results obtained are shown in Table 1. Frequency-dependent ε Ag and ε Si values are taken from [11

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

] and [14

14. E. D. Palik, Handbook of Optical Constants of Solids, Part II, Subpart 1 (Academic Press, 1985).

] respectively, except that the imaginary parts are kept at their 1%. The result show that the group velocity in this particular waveguide can be slowed down by over 1700 times at the near-resonant operation condition. The huge negative GVD value (notice the propagation length unit is in mm) at 600nm wavelength suggests that such waveguide may be promising for dispersion compensation applications. Further GV and GVD tailoring can be realized by using a multilayer dielectric material, in replacement of the homogeneous region denoted by ε + in Fig. 3 [15

15. A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063,901 (2005). [CrossRef]

].

Table 1. Group velocity and group velocity dispersion

table-icon
View This Table

4. Conclusion

In conclusion, we have shown that apart from solely relying on geometrical tailoring, choosing appropriate materials can be an equally compelling approach for achieving small mode field size for an SPP waveguide. We systematically studied a nanoscaled optical waveguide based on the phenomenon of near-resonant SPP confined at a silver-silicon interface at 600nm wavelength. In particular, we show that the material losses for both silver and silicon have to be reduced by ~1000 times in order for the waveguide to achieve practical propagation length. Therefore we point out the urgency of material loss reduction for such waveguides. Decreasing environment temperature [15

15. A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063,901 (2005). [CrossRef]

] and using quantum-dot-based metamaterials [17

17. D. Parekh, L. Thylén, and C. Chang-Hasnain, “Metal nanoparticle metamaterials for engineering dielectric constants and their applications to near resonant surface plasmon waveguides,” in Frontiers in Optics, OSA Technical Digest Series, p. FThF6 (Optical Society of America, 2007).

] could be two viable ways to achieving the goal. Such SPP waveguides can be potentially useful for constructing exotic miniature optical devices once the metamaterial or loss reduction/compensation technology matures.

Acknowledgement

This work is supported by the Swedish Foundation for Strategic Research (SSF) through the INGVAR program, the SSF Strategic Research Center in Photonics, and the Swedish Research Council (VR).

References and links

1.

A. E. Craig, G. A. Olson, and D. Sarid, “Experimental observation of the long-range surface-plasmon polariton,” Opt. Lett. 8, 380 (1983). [CrossRef] [PubMed]

2.

Y. Kuwamura, M. Fukui, and O. Tada, “Experimental observation of long-range surface plasmon polaritons,” J. Phys. Soc. Jpn. 52, 2350–2355 (1983). [CrossRef]

3.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B 44, 13,556–13,572 (1991). [CrossRef]

4.

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. Phy. Lett. 87, 261,114 (2005). [CrossRef]

5.

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightw. Technol. 25, 2511–2521 (2007). [CrossRef]

6.

E. Feigenbaum and M. Orenstein, “Modeling of complementary (void) plasmon waveguiding,” J. Lightw. Technol. 25, 2547–2562 (2007). [CrossRef]

7.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95, 046,802 (2005). [CrossRef]

8.

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 triangular metal wedges for subwavelength waveguiding,” Appl. Phy. Lett. 87, 061,106 (2005). [CrossRef]

9.

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

10.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137,404 (2004). [CrossRef]

11.

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

12.

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14, 13,030–13,042 (2006). [CrossRef]

13.

B. Prade and J. Y. Vinet, “Guided optical waves in fibers with negative dielectric constant,” J. Lightwave Technol. 12, 6–18 (1994). [CrossRef]

14.

E. D. Palik, Handbook of Optical Constants of Solids, Part II, Subpart 1 (Academic Press, 1985).

15.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063,901 (2005). [CrossRef]

16.

B. Wang and G. P. Wang, “Planar metal heterostructures for nanoplasmonic waveguides,” Appl. Phy. Lett. 90, 013,114 (2007).

17.

D. Parekh, L. Thylén, and C. Chang-Hasnain, “Metal nanoparticle metamaterials for engineering dielectric constants and their applications to near resonant surface plasmon waveguides,” in Frontiers in Optics, OSA Technical Digest Series, p. FThF6 (Optical Society of America, 2007).

OCIS Codes
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 12, 2008
Revised Manuscript: April 3, 2008
Manuscript Accepted: April 30, 2008
Published: May 9, 2008

Citation
Min Yan, Lars Thylén, Min Qiu, and Devang Parekh, "Feasibility study of nanoscaled optical waveguide based on near-resonant surface plasmon polariton," Opt. Express 16, 7499-7507 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7499


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References

  1. A. E. Craig, G. A. Olson, and D. Sarid, "Experimental observation of the long-range surface-plasmon polariton," Opt. Lett. 8, 380 (1983). [CrossRef] [PubMed]
  2. Y. Kuwamura, M. Fukui, and O. Tada, "Experimental observation of long-range surface plasmon polaritons," J. Phys. Soc. Jpn. 52, 2350-2355 (1983). [CrossRef]
  3. B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 556-572 (1991). [CrossRef]
  4. 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. Phy. Lett. 87, 114 (2005). [CrossRef]
  5. G. Veronis and S. Fan, "Modes of subwavelength plasmonic slot waveguides," J. Lightw. Technol. 25, 2511-2521 (2007). [CrossRef]
  6. E. Feigenbaum and M. Orenstein, "Modeling of complementary (void) plasmon waveguiding," J. Lightw. Technol. 25, 2547-2562 (2007). [CrossRef]
  7. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett. 95, 802 (2005). [CrossRef]
  8. 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 triangular metal wedges for subwavelength waveguiding," Appl. Phy. Lett. 87, 106 (2005). [CrossRef]
  9. M. Yan and M. Qiu, "Guided plasmon polariton at 2D metal corners," J. Opt. Soc. Am. B 24, 2333-2342 (2007). [CrossRef]
  10. M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 404 (2004). [CrossRef]
  11. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972). [CrossRef]
  12. P. Berini, "Figures of merit for surface plasmon waveguides," Opt. Express 14, 13030-13042 (2006). [CrossRef]
  13. B. Prade and J. Y. Vinet, "Guided optical waves in fibers with negative dielectric constant," J. Lightwave Technol. 12, 6-18 (1994). [CrossRef]
  14. E. D. Palik, Handbook of Optical Constants of Solids, Part II, Subpart 1 (Academic Press, 1985).
  15. A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 901 (2005). [CrossRef]
  16. B. Wang and G. P. Wang, "Planar metal heterostructures for nanoplasmonic waveguides," Appl. Phy. Lett. 90, 114 (2007).
  17. D. Parekh, L. Thylén, and C. Chang-Hasnain, "Metal nanoparticle metamaterials for engineering dielectric constants and their applications to near resonant surface plasmon waveguides," in Frontiers in Optics, OSA Technical Digest Series, p. FThF6 (Optical Society of America, 2007).

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