Surface-Plasmon-Assisted Guiding of Broadband Slow and Subwavelength Light in Air Aristeidis Karalis, * E. Lidorikis, Mihai Ibanescu, J. D. Joannopoulos, and Marin Soljac ˇic ´ Center for Materials Science and Engineering and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 23 April 2005; published 2 August 2005) A class of axially uniform waveguides is introduced, employing a new mechanism to guide light inside a low-index dielectric material without the use of photonic band gap, and simultaneously exhibiting subwavelength modal size and very slow group velocity over an unusually large frequency bandwidth. Their basis is the presence of plasmonic modes on the interfaces between dielectric regions and the flat unpatterned surface of a bulk metallic substrate. These novel waveguides allow for easy broadband coupling and exhibit absorption losses limited only by the intrinsic loss of the metal. DOI: 10.1103/PhysRevLett.95.063901 PACS numbers: 42.82.Et, 73.20.Mf, 78.20.Ci, 78.68.+m Precise control of the properties of light propagation along linear waveguides has always been of great impor- tance in the world of optics. One challenging goal has been to guide light through air in the presence of higher-refrac- tive-index dielectric media, since light tends to localize itself mostly in these high-index regions. So far, photonic band gaps [1] and other index-guiding based mechanisms [2] have been ways to address this issue. Another very desirable attribute for modern nanophotonics is the trans- verse confinement of guided light in subwavelength-size regions. Such compact guidance has been accomplished by exploring surface-plasmon modes [3] into designing wave- guides, by using conductors of a finite cross section [4 –8], combinations of surface plasmons with band gaps [9], or coupled-metallic-nanoparticle chains [10]. Finally, great effort has been focused recently on slowing down light [11], but so far the proposed systems have the undesirable characteristic of a fairly small frequency bandwidth, which is often described as a fundamental limit to the achievable delay-bandwidth product [12]. In this Letter, we introduce a new class of axially uniform waveguides that simulta- neously accomplish all the desired properties discussed above. They are implemented on a simple flat conducting surface of a large extent and rely on a nonperiodic dielec- tric distribution on top of this substrate to generate trans- versely confined guided modes. The new mechanism for confining much more field in the low-index region rather than in the adjacent high-index region is based on the relative dispersive characteristics of different surface- plasmon modes present in these structures and is appli- cable within a finite but wide frequency regime that abides by certain cutoff conditions. Supporting subwavelength modal sizes is a common property of all surface-plasmon structures. Similarly, supporting very slow group velocities over unusually large frequency bandwidths is a unique physical property inherent to most layered plasmonic structures, that is, to our knowledge, pointed out here for the first time and extended to linear waveguides. The promises of the proposed systems in the field of nano- photonics are exciting, including a significant reduction in all (spatial, temporal, and operational energy) device scales. These novel waveguides can easily be coupled to other systems and exhibit propagation losses minimized to the limit set by the intrinsic loss of the metallic substrate. Surface plasmons (SP) are well known [3] electromag- netic waves that propagate along the interface between a dielectric material and a metal of permittivities  and  p . The conditions for the existence of a SP are TM polariza- tion (magnetic field parallel to the interface) and  p < < 0. For example, with  p ! 1  ! 2 p =! 2 , where ! p is the bulk plasma frequency, these conditions lead to a high frequency cutoff at ! c  ! p =  1   p . The disper- sion relation k  !=c     p !=   p ! q is shown by curves A and B in Fig. 1 for two different dielectric materials ( hi > low in insets A and B). Several extensions of this simple structure in the form of planar layers have been examined in the past [13,14]. As 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 k/k p ω/ω p A D B ε hi ε low ω c (ε hi )/ω p ω c (ε low )/ω p d decreases ε p ε p ε hi d ε low A D ε low ε p ε p ε hi ε hi ε low d y x z C C B FIG. 1. !-k diagrams (solid curves) for conventional layered surface-plasmon structures (insets A–D) with  hi  4 and  low  1 (air). Layer thicknesses d= p  0:015, 0.02, and 0.025 are used for C and D (solid  dotted curves). The light lines !=! p    p k=k p (‘‘vertical’’ dashed lines) and the cutoff fre- quencies ! c =! p  1=   1   p (horizontal dashed lines) are shown. PRL 95, 063901 (2005) PHYSICAL REVIEW LETTERS week ending 5 AUGUST 2005 0031-9007= 05=95(6)=063901(4)$23.00 063901-1  2005 The American Physical Society