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Volumn 78, Issue 2, 2008, Pages

Optical excitation and detection of picosecond acoustic pulses in liquid mercury

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EID: 48749109568     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.024303     Document Type: Article
Times cited : (32)

References (83)
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    • The maximum transient temperature rise can be estimated using the expression Q (1-R) /AC ζ′, where Q is the energy of a single incident optical pump pulse, R≈0.7 is the optical reflectance of the pump beam from the sample (including the front face of the sapphire), A=π w2 /2 is the pump beam-spot area, C is the specific heat per unit volume of liquid Hg, and ζ′ is the effective penetration depth of the pump beam into the Hg, taken to be ∼20 nm (as explained in Sec. 3). The spot radius w=17.5 μm is obtained from the pump beam lateral intensity profile, given by I (r) =exp (-2 r2 / w2). There is a simple relation between w and the full intensity width at half maximum D in this case: w≈0.85D. In our case Q (1-R) is equal to 0.7 nJ
    • The maximum transient temperature rise can be estimated using the expression Q (1-R) /AC ζ′, where Q is the energy of a single incident optical pump pulse, R≈0.7 is the optical reflectance of the pump beam from the sample (including the front face of the sapphire), A=π w2 /2 is the pump beam-spot area, C is the specific heat per unit volume of liquid Hg, and ζ′ is the effective penetration depth of the pump beam into the Hg, taken to be ∼20 nm (as explained in Sec. 3). The spot radius w=17.5 μm is obtained from the pump beam lateral intensity profile, given by I (r) =exp (-2 r2 / w2). There is a simple relation between w and the full intensity width at half maximum D in this case: w≈0.85D. In our case Q (1-R) is equal to 0.7 nJ. The steady-state temperature rise of the sample at the center of the optical pump spot can be estimated from the expression P (1-R) / (2π) 1/2 w κS, where P is the average power of the (chopped) optical pump beam and κS is the thermal conductivity of the sapphire substrate. The presence of the Hg has a negligible effect on this steady-state temperature rise. In our case P (1-R) is equal to 27 mW
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    • For the transparent sapphire, the exponential term in the integral of Eq. 5 ensures that only acoustic waves at frequency 2 ns v1′ /λ are detected.
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    • We have estimated the effect of the frequency-dependent sound velocity and ultrasonic attenuation on the acoustic reflection coefficient rac (ω) using the simple models of relaxational processes described in Sec. 5. We find that the contribution to the apparent velocity dispersion and ultrasonic attenuation in the measured data from this source in our case is negligible.
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    • The accuracy of the analysis for the determination of the dispersion in velocity and attenuation was checked using synthesized acoustic pulses with dispersion and attenuation similar to that of Hg. The numerical error in this process is negligible compared to the scatter in the data for different Hg films.
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    • Strictly speaking, an independent measurement of z′ is required to determine the dispersion. However, if the velocity dispersion is small, as is expected to be the case for liquid Hg below 10 GHz, it is a good approximation to estimate z′ from the time between the maxima of the first and second echoes and from the known low-frequency sound velocity.
    • Strictly speaking, an independent measurement of z′ is required to determine the dispersion. However, if the velocity dispersion is small, as is expected to be the case for liquid Hg below 10 GHz, it is a good approximation to estimate z′ from the time between the maxima of the first and second echoes and from the known low-frequency sound velocity.
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    • This estimate is based on a Gaussian distribution of surface heights for the two sapphire surfaces.
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    • The gradient of the positive dispersion dv/dω is known to an accuracy ∼50%.
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