Abstract
The generation of thermal waves in a one-dimensional structure with a sinusoidal variation in thermal diffusivity can be described by an inhomogeneous Mathieu equation. An exact solution to the frequency-domain Mathieu equation can be found by using a variation of parameters method to give the alternating component of the temperature along the structure. From the theory of Mathieu functions a dispersion relation for the thermal waves is found, which does not display band gaps, but which shows damping that departs from that for thermal waves in a uniform medium.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Mandelis, Diffusion Wave Fields (Springer, New York, 2001)
A. Mandelis (ed.), Photoacoustic and Thermal Wave Phenomena in Semiconductors (North Holland, New York, 1987)
A. Mandelis (ed.), Progress in Photothermal and Photoacoustic Science and Technology, vol. 1 (Elsevier, New York, 1992)
J.A. Sell (ed.), Photothermal Investigations of Solids and Fluids (Academic Press, Boston, 1989)
S.E. Bialkowski (ed.), Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, New York, 1996)
A. Mandelis, J. Math. Phys. 26, 2676 (1985)
L. Liu, C. Wang, X. Yuan, A. Mandelis, J. Phys. D, Appl. Phys. 43, 285403/1 (2010)
A. Hellen, A. Mandelis, Y. Finer, J. Phys. Conf. Ser. 214, 012024/1 (2010)
M.C. Larciprete, C. Sibilia, S. Paoloni, G. Leahu, R. Li Voti, M. Bertolotti, K. Panajotov, Rev. Sci. Instrum. 24, 860 (2003)
N.W. McLachlan, Theory and Application of Mathieu Functions (Dover, New York, 1964)
E.T. Whittaker, G.N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1958)
L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1946)
B. Wu, G.J. Diebold, Photoacoustic effect in a periodically modulated structure. To be published
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, B., Diebold, G.J. Photothermal waves in a periodically modulated structure. Appl. Phys. B 105, 619–622 (2011). https://doi.org/10.1007/s00340-011-4501-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00340-011-4501-8