Abstract

A plasmon wave is perfectly split to 4 identical waves when encountering nano intersection. This is substantially different from the dielectric waveguides case where power coupling to vertical segments is negligible. When larger multimode plasmonic junction is realized — beating and retardation come into effect. The analysis of the plasmonic coupling in this device is helpful also in understanding plasmonic assisted enhanced transmission.

©2007 Optical Society of America

1. Introduction

Nanoplasmonic circuitry was studied extensively in recent years. Favorable scheme for realization of such nano circuits is based on plasmonic gap structures, where the plasmonic wave (Surface Plasmonic Polariton mode) is essentially propagating in the dielectric gap between two metal plates [1,2]. While the metal plates eliminate outgoing radiation and reduce inter-device coupling, the modal size inside the gap can be reduced below the “diffraction limit” and down to few nanometers. In addition, the dielectric medium in the gap exhibits in-plane “reduced diffraction” which allows the implementation of a variety of nano circuit elements [3]. Although the losses of the metal cladding limit the plasmonic wave propagation length — within the framework of nano-circuitry this attenuation is manageable. The dispersion characteristic of gap TM modes is illustrated in Fig. 1. Differently from the TM0, which is a slow plasmonic mode propagating also for vanishing gap width, the higher TM modes are not slow waves and do exhibit cutoff.

 figure: Fig. 1.

Fig. 1. Plasmonic gap; “Modal dispersion” over gap size: (a) real and (b) imaginary parts of effective index. Inset: structure schematics. ngap=1, λ0=1.55µm.

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Multiple plasmonic gap based devices were analyzed and some were experimentally realized including Febry-Perot resonators [4], nano-sized cavities [4], negative index [5], 2D-waveguides [6,7,8], couplers [9,10,11], multilayer devices [12], interferometers [13], bends and T-splitters [14]. Many of these devices are designed by mimicking the concepts of similar dielectric photonic devices (a detailed review in [15]).

Here we study a 4-arm cross-junction (“X-junction”) comprised of plasmonic gap waveguides. Not only that this device is a key component for the realization of high density plasmonic interconnects, its performance exemplifies the unique features of plasmonic circuitry emphasizing different characteristics of nano photonic devices — compared to regular (micro) photonic integrated circuits. Furthermore, the peculiar and very efficient sideways coupling of plasmons, is a key ingredient in other scenarios of interest — e.g. the “sideway” coupling of surface plasmonic waves into slits and holes typical to the field of extraordinary transmission [16].

We show here that a simple nano sized plasmonic X-junction is a “memoryless” device in the sense that launching an input signal via an arbitrary port — the output is comprised of 4 equal (carry the same power) plasmonic waves in the 4 arms. Achieving such merit with dielectric waveguides requires complex structure of the junction [17]). We validate this characteristic with full wave simulations and interpret the embedded mechanisms. Then we examine more elaborated field interactions taking place as the gap width is enhanced towards and above the “diffraction limit” where multiple mode beating is dominating.

2. Cross junction performance — full wave simulations

The conceptual device under study is an X junction between plasmonic gap waveguides, formed by vertical intersection of two identical infinite air slabs cladded by plasmonic metal boundaries as illustrated in Fig. 2 inset (the invariant direction is the y-axis). The metallic interfaces consist of thick (» skin depth) Au layers, modeled by the Drude model fitted to experimental permittivity at the wavelength of interest [18]. The modeling was done by Finite Difference Time Domain (FDTD) solution of Maxwell’s equation. Uniform TM excitation field (E field normal to the input gap waveguide walls) is applied, to accommodate with the plasmonic TM0 gap mode. Although our basic interest is steady state solutions, we employed also excitation by very short pulses, consisting of several optical cycles, centered at λ=1.5µm (for all figures), in order to visually observe the splitting dynamics (mainly for resolving the back reflected plasmon from the input one). It is important to note that the perfect splitting is exhibited also for these short pulses propagating within the cross junction which is a very dispersive scheme, as an indication for the usability of this circuit element for ultra fast plasmonic interconnects. The H-field distribution and the total power flow in all 4 arms were temporally monitored at the same distance from the junction point.

The summary of the quantitative performance of the plasmonic X junction is depicted in Fig. 2(a). We observe clearly 3 regions of operation: For gap width much smaller than λ/2 (e.g. below 100nm) the input optical pulse is perfectly split with almost equal powers into the 4 arms. As the gap size is increased, approaching a half-wavelength size, the forward transmitted power becomes the dominant portion, and the general performance is becoming similar to that of regular photonic counterpart. For gap width larger than λ/2 the emergence of higher modes enrich the cross-junction dynamics and beating effects are evident. Furthermore in the latter case the junction serves as a resonator (junction capacity), which is manifested by the nonmonotonous characteristics (and sees movie of Fig. 3(b)). This relatively low Q resonator is formed at the prescribed wavelength for junction (an effective cavity with partially reflecting mirrors) size of integer multiples of ~λ/2.

 figure: Fig. 2.

Fig. 2. Plasmonic gap X-junction.; 2D-FDTD calculated power transmission of pulses in different arms vs. gap size: (a) Pulse energy ratio of reflection to forward transmission (red) and sideways to forward transmission (green), (b) The imaginary part of the effective index is extracted from the energy ratio of all outgoing pulses to the incoming one (dots). (Calculated values for gap TM modes are given as reference in red). The inset shows the structure schematics. ngap=1, λ0=1.55µm, εM=-96+11i, spatial resolution is 30nm (only for 100nm gap the resolution was 15nm).

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The total loss in the cross-junction, translated into imaginary part of effective index using the relation Im{neff}=-ln(Wout/Win)/(2k0L), is depicted in Fig. 2(b), where L is distance between the monitoring points, k0 is the free-space wave-number, Win and Wout are the incoming pulse energy and outgoing pulses total energy. The imaginary part of the effective index of TM0, TM1, TM2 modes at the different gap sizes are brought as a reference on the graph (red). Below λ/2 (TM0 mode) the junction loss is enhanced with reducing gap size. For wider gaps higher TM modes are supported, and the loss depends on the specific weighting between the modes.

Figure 3 depicts the plasmonic cross junction operation at the two extreme situations: the nano regime (Fig. 3(a)) where a “memoryless” perfect split of the input pulse is exhibited and the micro regime Fig. 3(b), where additional modes contribute to interferences, resonances and beating. It should be noted that in most of the ‘extraordinary transmission’ scenarios the slits or holes are of dimensions ~λ/2 [19] — thus related phenomena to these of Fig. 3(b) are expected there as will be further discussed. Note (movie of Fig. 3(b)) that residual outgoing power is evacuating the relatively large junction long after the passage of the main pulse elucidating the capacitance effects in the large X-junction.

 figure: Fig. 3.

Fig. 3. Plasmonic gap X- junction (a) “perfect” split for gap width smaller than λ/2 (0.3µm), (255kb) [Media 1], (b) multimode effects for gap width >λ/2 (0.9µm), (423kb) [Media 2]. λ at pulse center=1.5µm.

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3. Mechanism

The basic mechanism of equal 4-way power splitting as observed in nano sized x-junctions is discussed here. The incoming wave (TM polarized), when encountering a junction discontinuity (in Fig. 4(a,b) a discontinuity between input gap waveguide and free space is exemplified), is diffracted as a semi-cylindrical wave, propagating radially from the junction point. It should be noted that the approximated description of a single semi cylindrical wave (point source) is valid for small enough gaps (<100nm). The semi cylindrical wave is angularly polarized (Eθ, Hy with radial propagation) (Fig. 4), which is exactly the required polarization to be coupled efficiently to the plasmonic modes of the forward and side gap waveguides (TM0 of each). This simple description is thus providing an explanation for equal power coupling to the forward and side arms, as well as to the surprisingly efficient side coupling which may seem naively counterintuitive due to the orthogonal polarizations of the input and output waves (major polarization Ex and Ez respectively). It should be noted that in Fig 4(a) some power is coupled from the discontinuity source also to side-going surface waves on the horizontal metal surfaces (surface plasmons [19], CDEW [20]), but the details of these waves are not important for the complete X-junction analysis.

The last ingredient; interpretation of the power equality of the back reflected wave (to the input port) is assisted by Fig. 4(c). Here a “3/4 junction” is analyzed — showing that the same power is coupled to the side arm and back reflected (for nano dimensions). For vanishingly small junctions — the discontinuity points of the junction can be considered as a single point source located equivalently at the center point of the junction. Furthermore, since the input transverse field size is also shrinking with the gap width, it completely overlaps with this discontinuity, thus all the cross section of the input field excites the source. Since the junction is completely symmetric for to the input and side arm - the scattered power to each should be the identical. The same idea is valid for the complete nano x-junction (Fig. 3(a)) where the 4 arms structure is symmetrical in respect to the junction center, thus memoryless power splitting is exhibited. Due to the angular polarization of the source waves — it is clear that in each pair of opposing arms, the plasmonic waves will be in antiphase — as actually evident from the simulations (Fig. 5).

To summarize the operation of nano plasmonic X-junction — the unique memoryless power splitting performance originates from the shrinkage of the effective waveguide junction discontinuity to a source point at the cross center. What enables this shrinkage is the plasmonic effect which supports mode size of vanishing dimensions. This is also the reason why one cannot expect to observe such a characteristic from dielectric waveguides which cannot support modes smaller than ~λ/2 in dimensions.

 figure: Fig. 4.

Fig. 4. Step by step assembly of the X-junction: two lower metal quadrants (a) H-field (363kb) [Media 3] and (b) E-field, and (c) three metal quadrant, for gap size smaller than λ/2 (GAP=0.3µm), (284kb) [Media 4]. X-junction for gap size ~λ/2: (d) GAP=0.6µm (363kb) [Media 5].

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As the plasmonic gap width is enhanced towards λ/2, the two ingredients described above are not valid. First the discontinuity source is not generating a cylindrical wave, but a power distribution with a more pronounced central lobe — meaning more power will be launched forward than sideways, as can be directly calculated from the azimuthal spectrum of the junction aperture. Second — the source term is not collapsing to the center of the now larger junction but rather has memory for the direction of arrival of the excitation field — namely retardation effects in the junction cannot be neglected. Thus the symmetry between forward and back reflected waves is broken. (see results for gap size~λ/2 in Fig. 4(d))

 figure: Fig. 5.

Fig. 5. E-field components in X-junction with gap size smaller than λ/2 (GAP=0.3µm): (a) Ex (229kb) [Media 6], (b) Ez (217kb) [Media 7].

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For even wider plasmonic gaps, multimode effects are dominant. In the range between λ/2 and λ, two modes are supported: TM0 and TM1, (TE1 is not excited in our scheme due to the orthogonal excitation), while a basic single mode input excitation (TM0) is preserved. In the forward arm only the TM0 is launched due to the symmetrical junction. In the sideways arms a TM0+TM1 combination is exited, exhibiting mode beating and the anti-phase excitation into sideways arms is apparent. The vertical asymmetry of the source at the junction is apparent yielding much less back power reflection. To resolve the TM1 at the sideway arm we monitor the Ex component (the TM0 has negligible Ex component) revealing the non plasmonic nature of this mode (maximal field value at the center) (Fig. 6(b)). The mode beating is apparent by monitoring the Ez component — which has similar magnitudes for both modes. (Fig. 6(b)). The lingering temporal tail to sideways arms is also apparent, indicating a junction capacitance. The Q factor of the equivalent junction cavity is ~15 for the conditions of Fig. 6.

 figure: Fig. 6.

Fig. 6. E-field components in X junction with gap size between λ/2 and λ (GAP=0.9µm): (a) Ex (379kb) [Media 8], (b) Ez (356kb) [Media 9].

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4. Conclusion

Nano size plasmonic X-junctions exhibit memoryless perfect split of an input plasmonic wave to 4 equal waves at the arms of the cross. This is a virtue of the nano dimensions leading to the generation of a perfect memoryless “point source like” at the junction center — and by applying symmetry considerations — the perfect split becomes apparent. Larger cross junction — cannot be treated as a memoryless single source — and the structured discontinuity exhibits forward directed emission as well as retardation effect (and multimode effects where applicable). The side coupling into slits with ~λ/2 width is also the generic scenario of the enhanced transmission experiments.

References and Links

1. E. N. Economou, “Surface Plasmons in thin films,” Phys. Rev. 182, 539 (1969). [CrossRef]  

2. B. Prade, J.Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B 44, 13556 (1991). [CrossRef]  

3. E. Feigenbaum and M. Orenstein, “Optical 3D cavity modes below the diffraction-limit using slow-wave surface-plasmon-polaritons,” Opt. Express 15, 2607 (2007). [CrossRef]   [PubMed]  

4. H.T. Miyazaki and Y. Kurokawa, “Squeezing Visible LightWaves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006) [CrossRef]   [PubMed]  

5. H.J. Lezec, J.A. Dionne, and H.A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430 (2007). [CrossRef]   [PubMed]  

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

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

8. B. Wang and G.P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85, 3599 (2004) [CrossRef]  

9. P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett. 31, 3288 (2006). [CrossRef]   [PubMed]  

10. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15, 1211 (2007) [CrossRef]   [PubMed]  

11. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: From micro to nano scale lambda/4 impedance matching”, the 2007 1st European Topical Meeting on Nanophotonics and Metamaterials, Austria. Paper WED4f.60.

12. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. A 21, 2442 (2006). [CrossRef]  

13. B. Wang and G.P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992 (2004) [CrossRef]   [PubMed]  

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

15. E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol. 25, 2547 (2007). [CrossRef]  

16. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998). [CrossRef]  

17. C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999). [CrossRef]  

18. E. D. Palik, Handbook of optical constants of solids, 2’nd Ed., (San-Diego: Academic, 1998).

19. C. Genet and T.W. Ebbesen, “Light in tiny holes,” Nature 445, 39 (2007). [CrossRef]   [PubMed]  

20. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006). [CrossRef]  

References

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  1. E. N. Economou, “Surface Plasmons in thin films,” Phys. Rev. 182, 539 (1969).
    [Crossref]
  2. B. Prade, J.Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B 44, 13556 (1991).
    [Crossref]
  3. E. Feigenbaum and M. Orenstein, “Optical 3D cavity modes below the diffraction-limit using slow-wave surface-plasmon-polaritons,” Opt. Express 15, 2607 (2007).
    [Crossref] [PubMed]
  4. H.T. Miyazaki and Y. Kurokawa, “Squeezing Visible LightWaves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006)
    [Crossref] [PubMed]
  5. H.J. Lezec, J.A. Dionne, and H.A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430 (2007).
    [Crossref] [PubMed]
  6. K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158 (2003)
    [Crossref]
  7. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475 (1997)
    [Crossref] [PubMed]
  8. B. Wang and G.P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85, 3599 (2004)
    [Crossref]
  9. P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett. 31, 3288 (2006).
    [Crossref] [PubMed]
  10. G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15, 1211 (2007)
    [Crossref] [PubMed]
  11. P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: From micro to nano scale lambda/4 impedance matching”, the 2007 1st European Topical Meeting on Nanophotonics and Metamaterials, Austria. Paper WED4f.60.
  12. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. A 21, 2442 (2006).
    [Crossref]
  13. B. Wang and G.P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992 (2004)
    [Crossref] [PubMed]
  14. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102, (2005).
    [Crossref]
  15. E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol. 25, 2547 (2007).
    [Crossref]
  16. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998).
    [Crossref]
  17. C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
    [Crossref]
  18. E. D. Palik, Handbook of optical constants of solids, 2’nd Ed., (San-Diego: Academic, 1998).
  19. C. Genet and T.W. Ebbesen, “Light in tiny holes,” Nature 445, 39 (2007).
    [Crossref] [PubMed]
  20. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
    [Crossref]

2007 (5)

2006 (4)

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
[Crossref]

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. A 21, 2442 (2006).
[Crossref]

P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett. 31, 3288 (2006).
[Crossref] [PubMed]

H.T. Miyazaki and Y. Kurokawa, “Squeezing Visible LightWaves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006)
[Crossref] [PubMed]

2005 (1)

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

2004 (2)

B. Wang and G.P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992 (2004)
[Crossref] [PubMed]

B. Wang and G.P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85, 3599 (2004)
[Crossref]

2003 (1)

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

1999 (1)

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
[Crossref]

1998 (1)

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998).
[Crossref]

1997 (1)

1991 (1)

B. Prade, J.Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B 44, 13556 (1991).
[Crossref]

1969 (1)

E. N. Economou, “Surface Plasmons in thin films,” Phys. Rev. 182, 539 (1969).
[Crossref]

Alloschery, O.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
[Crossref]

Arbel, D.

Atwater, H.A.

H.J. Lezec, J.A. Dionne, and H.A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430 (2007).
[Crossref] [PubMed]

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. A 21, 2442 (2006).
[Crossref]

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. A 21, 2442 (2006).
[Crossref]

Dionne, J.A.

H.J. Lezec, J.A. Dionne, and H.A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430 (2007).
[Crossref] [PubMed]

Ebbesen, T.W.

C. Genet and T.W. Ebbesen, “Light in tiny holes,” Nature 445, 39 (2007).
[Crossref] [PubMed]

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998).
[Crossref]

Economou, E. N.

E. N. Economou, “Surface Plasmons in thin films,” Phys. Rev. 182, 539 (1969).
[Crossref]

Fan, S.

G. Veronis and S. Fan, “Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15, 1211 (2007)
[Crossref] [PubMed]

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

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
[Crossref]

Feigenbaum, E.

Gay, G.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
[Crossref]

Genet, C.

C. Genet and T.W. Ebbesen, “Light in tiny holes,” Nature 445, 39 (2007).
[Crossref] [PubMed]

Ghaemi, H.F.

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998).
[Crossref]

Ginzburg, P.

P. Ginzburg, D. Arbel, and M. Orenstein, “Gap plasmon polariton structure for very efficient microscale-to-nanoscale interfacing,” Opt. Lett. 31, 3288 (2006).
[Crossref] [PubMed]

P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: From micro to nano scale lambda/4 impedance matching”, the 2007 1st European Topical Meeting on Nanophotonics and Metamaterials, Austria. Paper WED4f.60.

Haus, H.A.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
[Crossref]

Joannopoulos, J.D.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
[Crossref]

Johnson, S.G.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
[Crossref]

Kobayashi, T.

Kurokawa, Y.

H.T. Miyazaki and Y. Kurokawa, “Squeezing Visible LightWaves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006)
[Crossref] [PubMed]

Lezec, H.J.

H.J. Lezec, J.A. Dionne, and H.A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430 (2007).
[Crossref] [PubMed]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
[Crossref]

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998).
[Crossref]

Manolatou, C.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
[Crossref]

Miyazaki, H.T.

H.T. Miyazaki and Y. Kurokawa, “Squeezing Visible LightWaves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006)
[Crossref] [PubMed]

Morimoto, A.

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O’Dwyer, C.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
[Crossref]

Orenstein, M.

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids, 2’nd Ed., (San-Diego: Academic, 1998).

Prade, B.

B. Prade, J.Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B 44, 13556 (1991).
[Crossref]

Selker, M. D.

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. A 21, 2442 (2006).
[Crossref]

Takahara, J.

Taki, H.

Tanaka, K.

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158 (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, 1158 (2003)
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Thio, T.

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998).
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Viaris de Lesegno, B.

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Villeneuve, P.R.

C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
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B. Prade, J.Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B 44, 13556 (1991).
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B. Wang and G.P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85, 3599 (2004)
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B. Wang and G.P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992 (2004)
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B. Wang and G.P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85, 3599 (2004)
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Weiner, J.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
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Wolff, P.A.

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998).
[Crossref]

Yamagishi, S.

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. A 21, 2442 (2006).
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Appl. Phys. Lett. (3)

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158 (2003)
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B. Wang and G.P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85, 3599 (2004)
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G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102, (2005).
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E. Feigenbaum and M. Orenstein, “Modeling of Complementary (Void) Plasmon Waveguiding,” J. Lightwave Technol. 25, 2547 (2007).
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C. Manolatou, S.G. Johnson, S. Fan, P.R. Villeneuve, H.A. Haus, and J.D. Joannopoulos, “High-Density Integrated Optics,” J. Lightwave Technol. 17 (9), 1682 (1999).
[Crossref]

J. Opt. Soc. 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. A 21, 2442 (2006).
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Nature (2)

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667 (1998).
[Crossref]

C. Genet and T.W. Ebbesen, “Light in tiny holes,” Nature 445, 39 (2007).
[Crossref] [PubMed]

Nature Physics (1)

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H.J. Lezec, “ The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
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Opt. Express (2)

Opt. Lett. (3)

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Phys. Rev. B (1)

B. Prade, J.Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B 44, 13556 (1991).
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Phys. Rev. Lett. (1)

H.T. Miyazaki and Y. Kurokawa, “Squeezing Visible LightWaves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006)
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H.J. Lezec, J.A. Dionne, and H.A. Atwater, “Negative Refraction at Visible Frequencies,” Science 316, 430 (2007).
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Other (2)

P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: From micro to nano scale lambda/4 impedance matching”, the 2007 1st European Topical Meeting on Nanophotonics and Metamaterials, Austria. Paper WED4f.60.

E. D. Palik, Handbook of optical constants of solids, 2’nd Ed., (San-Diego: Academic, 1998).

Supplementary Material (9)

» Media 1: MOV (255 KB)     
» Media 2: MOV (423 KB)     
» Media 3: MOV (362 KB)     
» Media 4: MOV (284 KB)     
» Media 5: MOV (362 KB)     
» Media 6: MOV (229 KB)     
» Media 7: MOV (217 KB)     
» Media 8: MOV (379 KB)     
» Media 9: MOV (356 KB)     

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Figures (6)

Fig. 1.
Fig. 1. Plasmonic gap; “Modal dispersion” over gap size: (a) real and (b) imaginary parts of effective index. Inset: structure schematics. ngap=1, λ0=1.55µm.
Fig. 2.
Fig. 2. Plasmonic gap X-junction.; 2D-FDTD calculated power transmission of pulses in different arms vs. gap size: (a) Pulse energy ratio of reflection to forward transmission (red) and sideways to forward transmission (green), (b) The imaginary part of the effective index is extracted from the energy ratio of all outgoing pulses to the incoming one (dots). (Calculated values for gap TM modes are given as reference in red). The inset shows the structure schematics. ngap=1, λ0=1.55µm, εM=-96+11i, spatial resolution is 30nm (only for 100nm gap the resolution was 15nm).
Fig. 3.
Fig. 3. Plasmonic gap X- junction (a) “perfect” split for gap width smaller than λ/2 (0.3µm), (255kb) [Media 1], (b) multimode effects for gap width >λ/2 (0.9µm), (423kb) [Media 2]. λ at pulse center=1.5µm.
Fig. 4.
Fig. 4. Step by step assembly of the X-junction: two lower metal quadrants (a) H-field (363kb) [Media 3] and (b) E-field, and (c) three metal quadrant, for gap size smaller than λ/2 (GAP=0.3µm), (284kb) [Media 4]. X-junction for gap size ~λ/2: (d) GAP=0.6µm (363kb) [Media 5].
Fig. 5.
Fig. 5. E-field components in X-junction with gap size smaller than λ/2 (GAP=0.3µm): (a) Ex (229kb) [Media 6], (b) Ez (217kb) [Media 7].
Fig. 6.
Fig. 6. E-field components in X junction with gap size between λ/2 and λ (GAP=0.9µm): (a) Ex (379kb) [Media 8], (b) Ez (356kb) [Media 9].

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