Dr Paul Kinsler. [Acknowledgements & Feedback]

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Continuum theories of optical phonons and polaritons in superlattices

*copied*

<>   JN: PHYSICAL REVIEW B-CONDENSED MATTER, 1991, Vol.43, No.11, pp.9096-9101
<>   AB: The controversy concerning the confinement of optical modes in       
<>       superlattices concerns the use of electromagnetic (EM) or           
<>       hydrodynamic (HD) boundary conditions and the roles of dispersion and
<>       retardation in continuum theories, and how continuum theories relate
<>       to microscopic models. In this paper we describe EM and HD continuum
<>       models and discuss recent attempts to reconcile the EM model with
<>       microscopic theory. We conclude that the lack of retardation and     
<>       dispersion in the EM model results in a confusion between LO modes
<>       and polaritons. In particular, we question the attribution of a LO-  
<>       type Frohlich scalar potential to Fuchs-Kliewer interface polaritons.

The introduction has some good comment.

p9096: All microscopic models (4-6: Molinari-FK-1986, Kanellis-1987, Yip-C-1984) agree that relative ionic displacement u must be zero at or very close to the interface.

GaAs - AlGaAs; disparity of frequency bands for optical phonon modes is total

LO-phonon modes in disparate heterostructures are confined to layers (as u_z~=0 across boundary) -- interface -like modes (IP-phonons) in such must be phonon-polaritons

p9099: The phonon-polaritons ... epsilon(omega)!=0 -- no scalar potential and so no Frohlich -like (e phi) interaction -- instead the interaction term is A.p. These phonon-polaritons transversely polarized, and have a photon - TO (TO-phonon) -like character, and become increasingly photon -like as omega approaches omega_T(q). However, polaritons near omega_T(q) may interact with electrons via a (presumably approximate) deformation potential. (+unclear TO-limit remarks, and electron and hole difference).

This paper uses LO-phonon boundary-conditions of:
Continuity of strain: S_z = ... = that of u_z
Continuity of pressure: pi = ... = rhobar v_L^2 (grad . u)
claim that these are the same as those in Babiker-1986, barring rho normalisation, I assume)
Implies the existence of similar or related TO-phonon boundary conditions. "It seems that the use of EM boundary conditions (DC-model) for LO-phonon modes is not warranted on these grounds."

p9100: "Thus the use of EM boundary conditions (DC-model) for the Fuchs Kliewer interface (FK-phonon) modes and for guided polaritons is justified only provided the mechanical energy component can be neglected." ... "the use of EM boundary-conditions cannot be justified on the grounds of energy conservation (except for very long wavelength polaritons)."

p9100: "For example, in the Al(x)Ga(1-x)As -- GaAs with x not too large, the mismatch between the elastic properties of the two media is small enough for u_z to be appreciable such that a guided mode in GaAs penetrates into the Al(x)Ga(1-x)As layer. An interface mode is then possible for finite q_par, and being a true LO-phonon mode it will interact strongly with electrons via its scalar potential (Ridley-1989). Clearly such an interface mode has to be distinguished from the FK-phonon interface modes, which will also be present." (IP-phonon).

XINDEX: log-file, boundary-condition, Ridley-1993, LO-phonon, Babiker-1992, Babiker-1986, index-file, log-file.

19971127 1211

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