Polaritons modes

One of the applications of TRXRD is to study complex systems where electric fields couple to multiple degrees of freedom. Though femtosecond laser pulses can generate THz radiation from ferroelectric LiTa03, the corresponding lattice motion remained undetected by optical measurements. Cavalleri and coworkers demonstrated the coherent modulation of the X-ray intensity at 1.5 THz [10], and assigned it as phonon-polariton mode of A symmetry (Fig. 3.3). Nakamura and coworkers detected the coherent LO phonon of CdTe... 

The intriguing properties of devices made by the combination of a film-forming dye and an optical microstructure turn up in the discovery of strong coupling between excited states and photon modes in microcavities, creating Rabi-splitted polariton modes [211]. They occur in materials with narrow absorption bands (e.g., porphyrins and cyanine dyes) and may pave the way to new laser types and fundamental insights into the interaction of matter and light. 

Ions in the lattice of a solid can also partake in a collective oscillation which, when quantized, is called a phonon. Again, as with plasmons, the presence of a boundary can modify the characteristics of such lattice vibrations. Thus, the infrared surface modes that we discussed previously are sometimes called surface phonons. Such surface phonons in ionic crystals have been clearly discussed in a landmark paper by Ruppin and Englman (1970), who distinguish between polariton and pure phonon modes. In the classical language of Chapter 4 a polariton mode is merely a normal mode where no restriction is made on the size of the sphere pure phonon modes come about when the sphere is sufficiently small that retardation effects can be neglected. In the language of elementary excitations a polariton is a kind of hybrid excitation that exhibits mixed photon and phonon behavior. 

In particular, we have only one polariton mode, with an excitonic resonance energy at about cAweA + CgOjeB, which is an average of the energies of the pure excitons A and B. 

We are very much indebted to Professor J. M. Turlet and Dr. J. Bernard for helpful discussions and for providing us with material included in this work. Many stimulating private communications with Dr. M. R. Philpott are acknowledged. Dr. R. Brown has performed very extensive numerical simulations to help explore various extensions of the mean-field theory. One of us (Ph. K.) acknowledges stimulating discussion and correspondence with Professors S. A. Rice and V. M. Agranovitch on the distinction between our monolayer elementary excitations and the usual surface polariton modes investigated by those authors. 

Etchepare I, Grillon G, Antonetti A, Loulergue JC, Fontana MD, Kuge GE. Third-order nonlinear susceptibilities and polariton modes in PbTi03 obtained by temporal measurements. Phys Rev B 1990 41(17) 12362. 

Barker AS, Loudon R. Response functions in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals. Rev Modern Phys 1972 44 18. 

Figure 9. Oscillations of phonon-polariton mode in lithium tantalate crystal excited through inverse electro-optic effect and impulsive stimulated polariton scattering. Time-dependent birefringence measured with probe pulse, which propagated parallel to but not collinear with excitation pulse. (Reprinted with permission from ref. 36.)...

If W denotes the total density operator of the combined atom-cavity system after the writing process, all states W that are identical to W when tracing out the bright polariton modes and 3> /, i.e, for which holds... 

In order to see the effect of the different decoherence processes after tracing out the bright polariton modes, we now express the operators 0/( in terms of polaritons in the limit 6 = tt/2. This yields ... 

Thus the cavity polariton dispersion has a simple interpretation. Let us calculate the electric fields from eqn (10.7) for the modes (10.16). Neglecting small terms of the order of q2 /n2, the fields Ei and Et are related in these modes by Ei = —Et cot (p. Then the y-component of the fields Eu,l is equal to zero. In other words, with accuracy up to small terms (of the order of q2 /k2) the total in-plane electric field in the polaritonic modes is parallel to the dipole moment Pi for any direction of the wavevector q, and the value of the Rabi splitting energy thus does not depend on the wavevector direction. 

As another example, we mention the hybrid plasmon-polariton modes in chains of noncontacting noble metal nanoparticles where the interaction of a photon and nanoparticles leads toe delocalized plasmon-polaritons (see (35) and... 

Mg2Si layers is studied. The asymmetric broadening of the characteristic Mg2Si Raman peaks and the broad features observed in the spectra are interpreted in the framework of the generation of surface and interface polariton modes in both Si and Mg2Si with frequencies, being different in the samples with buried and unburied layers. 

Three branches of phonon polariton modes, two of them in the Mg2Si layer and one in the Si substrate, propagate in the tree-layered structure, as it follows from Fig. 2. In the four-layered structure, additional two branches are generated... 

Silicon has to be considered as an active media when calculating the polariton modes of Si matrix with nanoscaled species within it. The broad features in the Raman spectra of Si, often related with defects, can appear due to the generation of polariton modes. Useful information about nanoobjects and their evolution can be obtained from the Raman scattering. 

Extinction spectra for nanoparticles represented as a silver core covered by a carbon sheath in an insulating matrix (PMMA) will be analyzed in terms of the Mie relationships for sheathed cores [53, 54]. Here, an additional interface for which electrodynamic boundary conditions must be set up arises. Plasmon-polariton modes may be excited in both the core and the sheath. These modes, interacting through the inner interface, are responsible for the resulting extinction spectrum. 

S. A. Maier, P. G. Kik and H. A. Atwater, Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths Estimation of waveguide loss, Appl. Phys. Lett. 81(9), 1714-1716(2002). 

Equation (1.163) represents the dispersion relation of the surface plasmon polariton mode (SPP-mode), i.e. the relationship between the frequency co and the in-plane wavevector for SPPs propagating along the interface between a metal and a dielectric. 

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