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Stability plot a versus q for Mathieu functions. The unstable regions correspond to band gaps. Integer order Mathieu functions are found at the borders of the white and gray regions. The points correspond to values of and satisfying Eq. (5).
Magnitude of the damping constant versusdimensionless frequency for a structure with showing the damping constant to be largest at the center of the gaps. As approaches zero, the damping becomes small, and the band gaps narrow and become centered close to integer values of Outside the band gap, where , solutions are periodic and a damping constant is not defined. Inset: Dispersion relation versus as determined by the Mathieu characteristic exponent for
Photoacoustic pressure versus dimensionless frequency for delta function at with For small , the lowest frequency resonances near corresponding to a pressure that varies approximately as either or In order to increase the visibility of the peaks in the plot, a damping term proportional to was added to the factors in brackets in Eq. (9).
Photoacoustic pressure versus dimensionless coordinate z from Eq. (11) with delta function optical excitation at the origin for two values of immediately inside the edge of the first band gap at (a) and (b) .
Photoacoustic pressure versus dimensionless coordinate z from Eq. (11) with delta function optical excitation at the origin for two values of immediately outside the edge of the first band gap at (a) and (b) .
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