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Strong Coupling Between Surface Plasmon Polaritons and Emitters: a Review Home Search Collections Journals About Contact us My IOPscience Strong coupling between surface plasmon polaritons and emitters: a review This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Rep. Prog. Phys. 78 013901 (http://iopscience.iop.org/0034-4885/78/1/013901) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 129.132.227.98 This content was downloaded on 13/01/2015 at 14:21 Please note that terms and conditions apply. IOP Reports on Progress in Physics Reports on Progress in Physics Rep. Prog. Phys. Rep. Prog. Phys. 78 (2015) 013901 (34pp) doi:10.1088/0034-4885/78/1/013901 78 Report on Progress 2015 Strong coupling between surface plasmon © 2015 IOP Publishing Ltd polaritons and emitters: a review RPP P Törmä1 and W L Barnes2,3 013901 1 Department of Applied Physics, COMP Centre of Excellence, Aalto University, FI-00076 Aalto, Finland 2 School of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, Devon EX4 4QL, UK Report on Progress 3 Complex Photonic Systems (COPS), MESA + Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands Strong coupling between surface plasmon polaritons and emitters E-mail: [email protected] and [email protected] Received 14 April 2014, revised 8 September 2014 Printed in the UK Accepted for publication 17 October 2014 Published 23 December 2014 ROP Abstract In this review we look at the concepts and state-of-the-art concerning the strong coupling of 10.1088/0034-4885/78/1/013901 surface plasmon-polariton modes to states associated with quantum emitters such as excitons in J-aggregates, dye molecules and quantum dots. We explore the phenomenon of strong coupling with reference to a number of examples involving electromagnetic fields and matter. 0034-4885 We then provide a concise description of the relevant background physics of surface plasmon polaritons. An extensive overview of the historical background and a detailed discussion of 1 more recent relevant experimental advances concerning strong coupling between surface plasmon polaritons and quantum emitters is then presented. Three conceptual frameworks are then discussed and compared in depth: classical, semi-classical and fully quantum mechanical; these theoretical frameworks will have relevance to strong coupling beyond that involving surface plasmon polaritons. We conclude our review with a perspective on the future of this rapidly emerging field, one we are sure will grow to encompass more intriguing physics and will develop in scope to be of relevance to other areas of science. Keywords: surface plasmon polariton, strong coupling, normal mode splitting, vacuum Rabi splitting (Some figures may appear in colour only in the online journal) 1. Introduction the local optical environment. If this happens the energy lev- els of this hybrid system may be very different from those of Many sources of light involve transitions between the elec- the emitter or the optical system individually. This situation is tronic energy levels of a well-defined quantum system, for known as strong coupling and is the subject of this review. Not example dye molecules and quantum dots. It is now widely only do these new hybrid systems offer an exciting arena in known that the rate of the emission process can be modified by which to explore light-matter interactions, they also offer the placing the emitter in a structured environment, e.g. in front of prospect of exploiting nano-fabrication techniques to design a mirror [1]. Usually the interaction between the emitter and quantum optical systems. its local optical environment is such that only the spontaneous The paradigm model of strong coupling is that of two cou- emission rate is modified, the emission frequency remaining pled harmonic oscillators, they may become coupled if there unaltered. However, if the interaction is strong enough then is some way for them to exchange energy. The dynamics of the energy levels responsible for the emission are also altered, the coupled system is influenced not only by the original fre- they become inextricably linked with the levels (modes) of quencies of the oscillators but also by the exchange process 0034-4885/15/013901+34$33.00 1 © 2015 IOP Publishing Ltd Printed in the UK Rep. Prog. Phys. 78 (2015) 013901 Report on Progress involved in the coupling. The energy spectrum of the system which we refer to by the labels 1 and 2. These differential is modified: indeed, one obtains new modes whose frequen- equations can be solved to give the time evolution for the posi- cies are different from those of the original oscillator modes, tions of the oscillators: the difference between the original and the new frequencies xt1 () Atsin(ωωCB)sin ()tD, (3) depends on the strength of the coupling. If the coupling is very =++−++ small compared to other relevant energy scales, the modifica- xt2 ()=−Atsin(ωω++CB)sin ()tD+ . (4) tion of the original energies due to the coupling is negligible: +− this is the weak coupling regime. On the other hand if the cou- The constants A, B, C and D may be determined from the ini- pling is large compared to other energies, the coupling modi- tial conditions. The new frequencies that appear here are, fies the energy spectrum of the total system qualitatively: this 222 ωω=+c Ω (5) is the strong coupling regime. The new energies in the strong + coupling regime correspond to modes that are hybrids of the 222 ωω− =−c Ω (6) original modes of the two oscillators [2]. Strong coupling phenomena are observed in and are of 222 ωωc =+Ω . (7) importance to several fields of physics and technology. A 2 large variety of strong coupling phenomena are observed in Here ωc is the frequency that one of the oscillators would have case of the light-matter interaction: the light field of a certain if the other one was held fixed. The new frequenciesω + and frequency is one of the oscillators and a material (atom, mol- ω− are the normal modes of the coupled oscillator system. Let ecule, semiconductor, etc) with a well-defined optical transi- us now assume that we want to find the frequenciesω + and tion provides the other oscillator. The phenomenon has been ω− by observing the dynamics of the system. From (3)–(4) realized also for systems where the field frequency is not in one obtains the optical domain. 1 sin(ω tC+=) ((xt12)(− xt)), (8) One of the attractions of the combination of having exci- + 2A tons as one of the oscillators and plasmon modes as the other is the very extensive control we have over the plasmon modes 1 supported by metallic nanostructures. This control derives sin(ω tC+=) ((xt12)(+ xt)). (9) − 2B from a combination of impressive nano-fabrication techniques [3] and a very good understanding of the relationship between We see that the normal modes ω+ and ω− are not related to the details of the nanostructure and the nature of the associ- the motion (position) of either of the single oscillators alone, ated plasmon modes [4]. instead, to find the normal modes one needs to examine the We will now discuss the basics of the strong coupling time evolution of the motion of both oscillators. In other phenomenology with the aid of a simple example, that of words, the normal modes are hybrid modes of the two origi- two coupled classical harmonic oscillators. More elaborate nal oscillators. As a result it is no longer adequate to describe descriptions, in the specific context of this review article, are the system in terms of the original oscillators, rather one given in sections 3 and 5. should use the normal, hybrid modes. Note that the energy (frequency) separation of the normal modes depends on the coupling Ω. 1.1. Strong coupling basics: two coupled harmonic oscillators One can show, as will be done in sections 3 and 5, that the Let us consider two harmonic oscillators that are coupled. effect of the coupling becomes smaller the further away one is Examples of such systems include: two coupled pendula from the resonance condition. Let us say the oscillators have (oscillating at small frequencies), an optical field coupled to a different frequencies, ω1 and ω2; their difference is defined as dipolar two-level transition of an atom/molecule and a micro- δ = ω1 − ω2 and is called the detuning. Assume now that one of wave field coupled to a resonating circuit. Here, for simplicity, the original oscillator frequencies is not tuneable: for instance we set the resonance condition, that is, the frequencies of the in the case of an atom interacting with a light field it would oscillators, to be the same. The treatment can be easily gen- be natural to have the energy of the electronic transition fixed, eralized to the case of the individual oscillators having differ- the other frequency can be varied. In the atom + light example, ent frequencies. Using the theory of simple harmonic motion it would be possible to tune the frequency of the light field. the dynamics of the coupled system is described by (see also Naturally, when one of the frequencies changes, the detun- figure 1) [5], ing δ changes. The behaviour of the energies (frequencies) of the coupled system is now shown in figure 2. The data show 2 d x1 2 2 the avoided crossing of an excitonic transition associated with ++ωΩxx1 ()12−=x 0, (1) dt2 J-aggregated dye molecules and a surface plasmon-polariton mode taken from the work of Bellessa et al and discussed in 2 section 4.1 below. The behaviour expected if there were no d x2 2 2 ++ωΩxx2 ()21−=x 0.
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