Why could hybridization of the symmetric and antisymmetric SPP modes be important in hybrid thin film structures? Cesar Herreno · Universidad Distrital Francisco José de Caldas

We are studying the enhancement of the T-MOKE signal in hybrid thin films (Au/Co/Au) with an overall thickness of 25nm. We would like to understand why hybridization of the symmetric and antisymmetric SPP modes could be important in such hybrid structures. Is there any reference to check this?

• Kai Fauth · 117.59 · 201.39 · University of Wuerzburg

I guess SPP refers to surface plasmon polariton and symmetric/antisymmetric modes refer to charge oscillations in the gold layers (or at the interfaces) in phase or with relative phases shifted by pi. Am I guessing right?

If these oscillations mix (hybridize) then there must be some interaction producing some coupling between these (then idealized) modes. Any ideas about the nature of such interactions?

The question of the importance of SPP modes for T-MOKE through interaction with the magnetic material might be one to address separately in a first step (unless this has already been done in the literature, which I haven't checked).

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• Ertuğrul Karademir · 8.89 · 10.43 · Bilkent University

I don't know any references on this particular subject, however, in any physical context, symmetric and anti-symmetric modes differ in their energy levels and also ease of coupling to these modes. This is also related to the energy transfer and quality factor. My answer might be too superficial but it might give you an idea.

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• Cesar Herreno Thanks for your helpful and enlightening answers.

Kai Fauth: Your guess is right. The point is that I don't know if such symmetric (s) and anti-symmetric (a) modes can exist together in the same interface. What do you think? As far as I have seen, these modes appear in the case of lateral confinement of the SPP (waveguides), and in the case of excitation on different neighbor layers. None of above is our case. The system under consideration is glass/Au/Co/Au/air illuminated in total reflection condition by a p-polarized laser from the glass side (Kretschmann configuration) such that the SPP are excited only in the Au/air interface. The other interfaces do not fulfil the coupling conditions for SPP excitation. The overall thickness of the trilayer is 25 nm (Au:14.1nm/Co:10.1nm/Au:0.5nm).
You are right, our interest is on the effect of these s and a modes when interacting with the magnetic material. Up to my knowledge, this remains unexplored. The problem of magneto-optics in structures exhibiting plasmonic resonances is currently one of the two main lines of research in magnetoplasmonics.

Ertuğrul Karademir: According to you, it could be still possible to excite these s and a modes at the same time in our system given that we use a monochromatic light source (green laser)? I guess no, unless the light undergone a kind of Stokes shift (inelastic scattering). Could it be possible for such overall thickness? If so, I think that the effect could not be even measurable. Our study is based on the change of reflectivity of the system under magnetization inversion (transversal magneto-optic Kerr effect) as a function of the incident angle.

1 day ago

• Scott Joseph Maddox · 10.73 · 9.7 · University of Texas at Austin

The theory for non-magnetic material is treated quite thoroughly in [1]. I'm not sure if anyone has considered the case of a magnetic material in the waveguide, but it should not affect the properties at optical frequencies, as long as there are no resonant nano-structures (magnetic responses in traditional materials are limited to <~THz frequencies).

I also recommend [2], as a good overview of plasmonics.

[1] B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric constant,” Phys. Rev. B, vol. 44, no. 24, pp. 13556–13572, Dec. 1991.

[2] S. A. Maier, Plasmonics: Fundamentals and Applications. Springer, 2007.

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• Ertuğrul Karademir

Well as Maier's book is popular, I find the text quite obscure for a review on plasmonics. Sure, it touches many aspects of the field, however, it is not as clear and as comprehensible as its title suggests to be.

I recommend Raether's book (Surface plasmons on smooth surfaces) for a better physical description. Also, the review by Knoll is much clear (http://dx.doi.org/10.1146/annurev.physchem.49.1.569 ). Additionally the review by Berini is a quite good text on long range plasmons (http://dx.doi.org/10.1364/AOP.1.000484 )

Regarding the question, I am not an expert on magnetoplasmonics, however, one example of coupled symmetric and anti-symmetric modes is the Rabi oscillation problem. In this case, the energy can oscillate between s and as modes. What affects the coupling between them should depend on the particular appplication of the model.