Acoustic waves undetectable by transient reflectivity measurements

A free-standing GaAs membrane is investigated by pump-probe reflectivity measurements with femtosecond laser pulses of 400-nm wavelength. It is found that the detected wide spectrum of laser-generated coherent strain waves in the membrane does not contain a specific hypersonic frequency. Theoretical analysis reveals that this effect is related to zero sensitivity of the acousto-optic detection at a particular frequency defined by the wavelength of the probe laser pulse on the mechanical free surface of the GaAs membrane. We predict that a similar behavior is expected in Si and Au membranes and films, indicating that the presence of zeros in the spectral transformation function of acousto-optic conversion is a rather general phenomenon in picosecond ultrasonics that has so far been neglected.

Figure 1

SEM images of the GaAs membrane. Top: Array of nine membranes. Bottom: Single membrane with two trenches used for underetching of the GaAs film.

Figure 2

(a-i) Transient background contribution to the reflectivity changes, which stems from the relaxation of photoexcited carriers, dynamics of the lattice temperature, and also contributions within the electronic circuit in phase with the repetition rate of the laser. (a-ii) Transient reflectivity change of the GaAs membrane after subtracting the background. The inset shows the first echo. The gray dots are the actual data, while the solid line is the smoothed curve shown for the purpose of better illustration of the pulses. (b) The FFT result of the echo signals and the comparison of the FFT results of the first (solid gray line) and second (dashed gray line) echo.

Figure 3

(a) The dependence of the square of the acoustic frequency, $f_0^2$, on the optical wavelength of probe light from 248 to 620 nm in GaAs. The positive values of $f_0^2$ provide real valued undetectable frequencies $f_0$. The areas shaded in gray correspond to the probe wavelengths at which all acoustic frequencies are detectable. The inset shows the dependence of the positive values of $f_0^2$ on the optical wavelength. (b) The modulus of the spectral transformation function of acousto-optic conversion at the mechanically free surface of GaAs for different wavelengths of probe light, varying from 248 to 620 nm. All the local minima in the modulus of $K_{\text{AO}}\left(\omega \right)$ correspond to undetectable acoustic frequencies. With increasing wavelength of the probe beam the detection sensitivity is progressively concentrating around the Brillouin frequency in backscattering configuration.

Figure 4

(a) The dependence of the square of the acoustic frequency, $f_0^2$, on the optical wavelength of probe light from 317 to 620 nm in Si. The positive values of $f_0^2$ provide real valued undetectable frequencies $f_0$. The areas shaded in gray correspond to the probe wavelengths at which all acoustic frequencies are detectable. The inset shows the dependence of the positive values of $f_0^2$ on the optical wavelength. For the probe wavelength around 440 nm, the undetectable acoustic frequencies could exist (red dot, Ref. [38]) or do not exist (dot shaded by gray square, Ref. [37]) depending on the acousto-optic constants used. (b) The modulus of the spectral transformation function of acousto-optic conversion at the mechanically free surface of Si for different wavelengths of probe light, varying from 317 to 620 nm. All the local minima in the modulus of $K_{\text{AO}}\left(\omega \right)$ correspond to undetectable acoustic frequencies. With increasing wavelength of the probe beam the detection sensitivity is progressively concentrating around the Brillouin frequency in backscattering configuration.

Figure 5

The dependence of the square of the acoustic frequency, $f_0^2$, on the optical wavelength of probe light from 248 to 620 nm in Au. The positive values of $f_0^2$ provide real valued undetectable frequencies $f_0$. The areas shaded in gray correspond to the probe wavelengths at which all acoustic frequencies are detectable.

Figure 6

The dependence of the square of the acoustic frequency, $f_0^2$, on the optical wavelength of probe light in the case of the acousto-optic detection of hypersound in GaAs substrate loaded by the media with different acoustic and electromagnetic properties. Triangles stand for loading by a hypothetical absolutely rigid material with electromagnetic properties of vacuum. Circles correspond to the case where the optical properties of the absolutely rigid material are those of diamond. Squares depict the results for loading of the GaAs surface by air. Undetectable real valued acoustic frequencies $f_0$ exist at such wavelengths of probe light for which $f_0^2$ is positive. The existence or inexistence of the acoustic frequencies undetectable through the acousto-optic effect for a particular wavelength of probe light, incident on the interface between the transparent and opaque media, depends both on the mechanical and electromagnetic boundary conditions at the interface.