A Gaussian beam is an asymptotic solution to Maxwell's equations that propagate along a curve; at each time instant its energy is concentrated around one point on the curve. Such a solution is of the form
2. Bossavit, A., "On the notion of anisotropy of constitutive laws. Some implications of the 'Hodge implies metric' result," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 20, No. 1, 233-239, 2001.
3. Kravtsov, Y. A. and Y. I. Orlov, Geometrical Optics of Inhomogeneous Media, Springer-Verlag, 1990.
4. Kachalov, A. and M. Lassas, "Gaussian beams and inverse boundary spectral problems," New Analytic and Geometric Methods in Inverse Problems, 127-163, 2004.
5. Kachalov, A., Y. Kurylev, and M. Lassas, Inverse Boundary Spectral Problems, Chapman & Hall/CRC, 2001.
6. Ralston, J., "Gaussian beams and the propagation of singularities," Studies in Partial Differential Equations, Vol. 23, 206-248, 1982.
7. Kachalov, A. P., "Gaussian beams, Hamilton-Jacobi equations, and Finsler geometry," Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), Vol. 297, 2003.
8. Kachalov, A. P., "Gaussian beams for Maxwell equations on a manifold," Journal of Mathematical Sciences, Vol. 122, No. 5, 2004.
9. Kachalov, A. P., "Nonstationary electromagnetic Gaussian beams in inhomogeneous anisotropic media," Journal of Mathematical Sciences, Vol. 111, No. 4, 2002.
10. Shen, Z., Lectures on Finsler Geometry, World Scientific, 2001.
11. Kozma, L. and L. Tamassy, "Finsler geometry without line elements faced to applications," Reports on Mathematical Physics, Vol. 51, 2003.
12. Antonelli, P. L., R. S. Insgarden, and M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluwer Academic Publishers, 1993.
13. Miron, R. and M. Anastasiei, The Geometry of Lagrange Spaces: Theory and applications, Kluwer Academic Publishers, 1994.
14. Miron, R. and M. Radivoiovici-Tatoiu, Extended Lagrangian Theory of Electromagnetism, Vol. 27, No. 2, Reports on Mathematical Physics, 1989.
15. Asanov, G. S., Finsler Geometry, Relativity and Gauge Theories, D. Reidel Publishing Company, 1985.
16. Bellman, R., Introduction to Matrix Analysis, McGraw-Hill book company, 1960.
17. Naulin, R. and C. Pabst, "The roots of a polynomial depend continuously on its coefficients," Revista Colombiana de Matematicas, Vol. 28, 35-37, 1994.
18. Guillemin, V. and S. Sternberg, "Geometric asymptotics," Mathematical Surveys, No. 14, 1977.
19. Dahl, M., "Propagation of electromagnetic Gaussian beams using Riemann-Finsler geometry," Licentiate thesis, 2006.
20. Abraham, R. and J. E. Mardsen, Foundations of Mechanics, 2nd ed., Perseus Books, Cambridge..