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Nonlinear Optics with Surface Modes on Smooth Interfaces


Nonlinear Optics with Surface Modes on Smooth Interfaces

Tech Area / Field

  • PHY-OTH/Other/Physics
  • PHY-OPL/Optics and Lasers/Physics

3 Approved without Funding

Registration date

Leading Institute
Institute for Physical Research / Engineering and Physics Laboratory, Armenia, Ashtarak-2


  • American Superlite, Inc., USA, CA, Burbank

Project summary

The proposal aims to fund collaborative work on the non-linear optics of multi-layer structures with smooth interfaces. The main objectives of the project are to develop models of the optical response of surface polaritons on multi-layer structures with smoothly varying dielectric permittivity profiles and to explore, both theoretically and experimentally, the potential for further field optical enhancement and hence stronger non-linear effects on different surface structures. The final outcome will be extension of presently available linear optics models to those involving more elaborate smooth interfaces and structures with several types of nonlinearities.

Motivation for this proposal is that the understanding of the role of processes at interfaces in the enhancement of non-linear optical processes opens up new conceptions as well as a number of perspective applications in integrated and non-linear optics technology.

Interaction of radiation with interface is a very attractive area for research. As an example, let us mention such once-mysterious phenomena as so called Wood's anomalies [1-3] when plane waves of certain wavelengths and incidence angles are fully absorbed by a metallic grating. It is known that these anomalies are caused by excitation of surface plasmon polaritons, localized fields coupled to surface charge density oscillations at the interface.

The surface plasmons, localized at the metal/dielectric boundary, give strongly enhanced electromagnetic fields. For example, in the visible part of the spectrum the surface plasmon on a flat silver/air interface has a field enhancement factor of 10 times the incident field for optimum coupling. This strong field enhancement leads itself to non-linear optical studies. For instance, in experiments on the Raman scattering from molecules adsorbed on a rough metallic surfaces of nanometer scale, an enhancement of the Raman scattering signal up to 106 has been observed [4-5]. Enhancement alone is an interesting object for study but the last achievements in optics suggest there is an even more pressing need to explore this area more carefully. Analogous enhancements have been observed in surface generation of second harmonics [6].

In general, surface polaritons are defined as localized electromagnetic waves propagating along the interfaces of various media [1-3]. A classical example is the above plasmon polariton occurring at a metal-dielectric interface. Exciton-, magnon-, and phonon-polaritons are other important cases. From the point of view of condensed matter physics, surface electromagnetic waves are stipulated by dynamics of respective quasi-particles: plasmons, excitons, magnons, phonons, etc. However, from the point of view of continuous medium electrodynamics, when the light wavelength and the wave-decay distances are much larger than the interatomic distances, such localized waves can be treated phenomenologically via the macroscopic Maxwell equations in terms of dielectric and/or magnetic permittivity tensors. In this case, one should no more consider abrupt transitions from one medium to another as valid approximations.

For time-periodic processes occurring in linear media free from external charges, the macroscopic Maxwell equations are reduced to a system of two coupled equations symmetric with respect to the transposition of pairs (e, E) and (m, H) [7]. The important point then is that if only one of the permittivities is spatially varied this system (i) is split-up, i.e. one of the fields can be determined independently, and (ii) the mentioned symmetry with respect to the transposition is violated. These obvious observations lead to a fundamental difference in behavior of waves with different polarizations. Mathematically, it is expressed in the fact that under such conditions the equations for TE- and TM-modes are essentially different – an additional singularity emerges in one of these equations. For this reason, the abrupt transition approximation (i.e., when the transient layer is assumed vanishingly thin) is conventionally used in the polariton theory. This singularity is actually ignored in the Maxwell equations but is taken into account indirectly via the boundary conditions [1-3]. When this term is discarded the basic equation is reduced to the form of the one-dimensional stationary Schroedinger equation [8], and there of course exists a well-developed theory of special functions based on the hypergeometric type of equations. It’s this term that hinders the mathematically strict theory from development. And the only theory which has presently attained a level satisfying practical requirements is that of the five equations of Heun's class (see [9, 10] and references therein).

The authors of the present project, for the first time, have therefore treated the polariton problem for smooth interfaces via Heun's equation [11-15]. We have constructed the solution to the Heun's equation in a power series form, and derived an approximate solution involving a combination of incomplete beta-functions. Further, we have constructed the exact eigenvalue solution to the polariton problem as a series in terms of incomplete beta-functions or, equivalently, Gauss hypergeometric functions [16].

The present project is to contribute to development of this problem. Such a claim is justified by that some of the theoretical and experimental methods for the solution of some of the proposed tasks are essentially based on the new approaches developed by us for the previous investigations of these problems. The members of the group have sufficiently high qualification and skills in working with both experimental and engineering methods. Specifically, we wish to extend the understanding of the mechanisms for the generation of nonlinear waves (second harmonic generation, etc.), associated with the interaction of electromagnetic waves with smooth interfaces. Three-layer smooth interface profiles are probably the simplest geometric forms to be considered at first.

The proposed project consists of 3 blocks of closely related tasks including 9 particular issues on the above-mentioned problems that include the research work and the dissemination of the results (for details, see further).

We hope to establish analytical and efficient numerical techniques that have a wide range of applicability in problems related to the linear and nonlinear optics with surface electromagnetic modes on smooth interfaces. In view of present developments in integrated optics technology and the desire for ever-faster switching for optical signals, the possible technical developments from this work may be quite substantial. To this end we have been collaborating with very experienced western groups that have a wide range of facilities and who will be able to fabricate some test structures to establish the experimental validity of some of the theoretical predictions. Since the work is original then all the research work will be presented at international conferences and written up and published in the open scientific literature. With the present paper production rate of the groups it is likely that a final outcome of the project will be at least 6 research publications in the leading referee journals. Furthermore, more importantly, we are going to apply for US and International patents for the technology arising from the research and development within the framework of this project. It is supposed that at least 3 international patent applications will be developed during the course of the project.

The proposed project will promote the constant increasing of the professional level and the intimacy of the scientists, collaboration in their scientific activity efforts. It will promote complete integration of the members of the group into the international scientific community. The project will assist to form a new research team from scientists and engineers, working at the Engineering Center, who were previously engaged in different defense programs of the former USSR. The influx of a new thinking that comes with collaborations will undoubtedly steer the Armenian side into the allocation of resources. This is further endorsed by appreciating the ages of the junior members involved in the Armenian group. Also, the collaborators will benefit from the contact with high-level and highly-skilled Armenian scientists and engineers as well as from the early access to results.

The collaboration will lead to long-term cooperation in science and technology and, we hope, will find deepening continuation in the future under internationally funded projects.

American Superlite, Inc. concerns itself with investigations and development of various industrial lighting systems. It designs bring LED vehicle lights into the future of vehicle lighting and beyond. The research group has analyzed, tested existing LED lights and enhanced them with optical lens- and reflector system producing a wider viewing angle. As a result, the company has developed a large family of unique vehicle safety markers and brake lights, which greatly exceed the existing filament bulbs in reliability and efficiency. The patented lens and reflector designs produce LED lights that surpass all others in quality and brightness. Test results on company’s LED lighting systems demonstrate a failure rate of less than 0.01 percent that allows American Superlite, Inc. to offer a lifetime guarantee on their product. The company continues today the research in several other fields, such as, various thin film coatings on display glass doors for the refrigeration industry, conductive coatings on automotive lighting systems using LEDs, optical sensors for the petroleum industry, etc. American Superlite, Inc., has been involved in research, development and design of optical lenses used in conjunction with light sources using LEDs (light emitting diodes) and fiber optics. 13 years experience also expands into the effects of lasers and radiation on plastic and glass materials. The research has lead to several US and international Patents in the field of optics. Extensive research and innovation in the field of optics have played a vital role in making American Superlite, Inc. into one of the leading and recognized firms in the specialty lighting industry.

The collaborators to this project will participate in various ways (for details, see further).

Since the current research interests of the involved groups substantially overlap, it is our clear intention to coordinate closely the work of the teams by means of intensive information exchange. Communication between the groups has been established already and can be continued via electronic means.


1. A.D. Boardman, (ed.), Electromagnetic Surface Modes (Wiley, London, 1982).
2. H. Raether, Surface Plasmons (Berlin, Springer-Verlag, 1988).
3. V.M. Agranovich and D.L. Mills, (ed.), Surface Polaritons (North-Holland, Amsterdam, 1982).
4. M. Fleischmann et al., Chem. Phys. Lett. 26, 163 (1974).
5. A. Otto et al., J. Phys. C4, 1143 (1992).
6. Y.R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
7. A.W. Snyder and J.D. Love, Optical Waveguide Theory (Chapman and Hall, London, 2000).
8. L.D. Landau and E.M. Lifshitc, Quantum Mechanics (Nauka, Moscow, 1989).
9. A. Ronveaux, Heun’s Differential Equations (Oxford University Press, London, (1995).
10. S.Yu.Slavyanov and W.Lay. Special functions (Oxford University Press, Oxford, 2000); E.Kamke. Handbook of Ordinary Differential Equations (Dover, New York, 1976).
11. A.M. Ishkhanyan, "Analytic solution of the polariton problem for a smooth boundary", Reports (Armenian Nat’l Ac. Sci.), 101(3), 245 (2001).
12. A.M. Ishkhanyan and K.-A. Suominen, "Analytic treatment of the polariton problem for a smooth interface", J. Phys. A: Math. Gen. 34, L591 (2001).
13. A.M. Ishkhanyan and G.P. Chernikov, "Polariton problem for a model symmetric three-layer structure", J. Contemporary Physics (Armenian Nat’l Ac. Sci.), 36(6), 1 (2001).
14. G.P. Chernikov and A.M. Ishkhanyan, "Surface polaritons in symmetric non-uniform three-layer structures with losses", Laser Physics 13(7), xxx (2003).
15. A.M. Ishkhanyan and G.P. Chernikov, "Polariton spectra for two specific symmetric structures", Reports (Armenian Nat’l Ac. Sci.), 102(2), 127 (2002); A.M. Ishkhanyan, G.P. Chernikov, and A.M. Manukyan, "Polaritons in three-layer structures with losses", Proc. Int’l Conf. Laser Physics-2001, Ashtarak, 55 (2001).
16. M. Abramovitz and I.A.Stegun, (ed.), Handbook of Mathematical Functions (Dover, New York, 1965).


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