5.2. Diffraction on 2D Spheres Monolayer in Water
A monolayer of spheres (d
~λ) deposited on the fiber end face gives a 2D system of laser jets which interfere in the medium and act as a diffraction grating [20
] generating a 3D periodical laser field pattern with spatial periodicity on the order of λ. Finite difference time domain (FDTD) calculations of the laser field distribution generated by the monolayer of polysterene spheres deposited on a glass surface and immersed in the water medium were performed. The effects of the aperture and possible defects in the monolayer packing were neglected. Thus, the periodicity of the monolayer was taken into account to minimize the volume of the calculation cell [20
]. The calculated distribution of the enhancement of the electric field square with respect to the incident beam value is shown in Figure 7
. The parameters of the calculations matched our experimental conditions. Namely, the wavelength of the incident light (in vacuum) is λ = 1.064 µm, the sphere diameter is d
= 0.96 μm, the refractive indices of the spheres, glass fiber and water are n1
= 1.58, nfib
= 1.46, and n0
= 1.33, respectively. The light absorption length in water is much larger than the cuvette size, thus the absorption can be also neglected in the FDTD calculations. However, according to the estimations, а thermal microstructure of laser heated pellets (LHP) with characteristic size on the order of λ, with temperature rise up to 10−2
degree is created in water by a short laser pulse of 0.005 J energy.
5.3. Generation of Ultrasound
The excitation of ultrasound in a liquid using a fiber with converter is accompanied with a number of features that are worth considering. When the radiating end of a fiber is immersed into a liquid, surface waves on the liquid can be excluded from consideration. Sound waves generated in the beam may hit the fiber end. However, this is a second-order effect; therefore, the emission of sound waves in this case can be considered as the emission from a lumped source in the free space of a liquid. The spatial parameters of the emitter without spheres are determined by the fiber diameter and the length of beam absorption in liquid, whereas in the case of a coated fiber, they also depend on the parameters of the beams focused by the spheres. In this study (pure, weakly absorbing water), in the absence of spheres the emitting region within the experimental cuvette L >> λus (λus is the wavelength of the ultrasound) can be considered as a rod with a fiber diameter and light intensity decreasing as e−αx (x is beam length).
In the presence of spheres, the emitting rod is divided into individual LHP areas. The diameter d0 of these LHP in the waist is fractions of a micron, and their length is of the order of a micron (at a wavelength of λus ~1 mm), and their power drops down as e−αx. The radiation from LHP can be considered as the radiation of a point sources with dimensions d0 << λus.
Three main features can be distinguished in the experimental results on the excitation of ultrasound (Figure 4
and Figure 5
A significant increase in the level of ultrasound intensity (up to 20 dB) in the range of 0.5–4 MHz.
In experiments without coating, radiation with peaks of 0.25 and 0.75 MHz prevails. The same radiation is present in experiments with the coating too.
When applying coatings, there appears an OA response with peaks in the 1–4 MHz range and with the amplitude comparable to that of the radiation in the region up to 1 MHz.
It is clear that both effects, i.e., the observed overall enhancement of the OA response and the appearance of an OA response in the 1–4 MHz, are associated with the colloidal coating of the fiber tip.
The observed amplification can be related to the specific features of the experiments, when the diameter of the fiber and, therefore, of the beam in the liquid is of order of the wavelength of the generated ultrasound (~0.35–5 mm). In this case, the interference of waves generated in the beam volume, “blocks” the radiation in the direction of ~90°, which leads to sound channeling in the laser beam [22
]. When a pellet structure is formed in the heated region, this prohibition is removed, which leads to the appearance of directional pattern petals in the direction close to normal and to amplification of the received ultrasound.
Comparison of the spectral-temporal composition of the laser pulse with the spectrum of the optoacoustic response allows determining the generation mechanism at different frequencies and linking them to different areas in the structure of the laser radiation. The case of ultrasound generation “without spheres” is quite clear. The maximum of the observed US spectrum lies in the 0.7–1.5 MHz region, which corresponds to the “classical” generation mechanism [3
] with a characteristic frequency ν1
~1.5 × 106
Hz related to the ultrasound run time through the beam diameter. The frequency-time structure of the laser pulse also meets with the optimal conditions for the excitation of ultrasound in this frequency range.
The case of 2D coating is more interesting as the ultrasound spectrum is enriched in the 1–4 MHz frequency range. This generation region is obviously related to the coating of the fiber end with PS spheres of ~1 μm in diameter, which create a regular structure in the transmitted laser beam with regions of increased intensity and LHP regions in the liquid. The diameter of these LHP structures is 0.5–1 μm. If we assume that the ultrasonic response in this case also corresponds to the “classical” generation mechanism [10
], then its maximum response spectrum should be in the frequency band of ~(1–5) GHz, which does not correspond to the considered spectral region. Therefore, the results of the coating experiment show that additional studies are required.
Interestingly, the frequency range of ultrasound radiation in this case is in a good agreement with the LHP cooling time τ2
is the LHP diameter, χ is thermal diffusivity), which is ~(0.1–0.5) × 10−6
Preliminary examination shows that 1–4 MHz ultrasound may be associated with cooling an array of heated “pellets” with a characteristic time τ2. It is interesting that the integrated intensity of such an ultrasound is of the same order of magnitude as the sound associated with heating the area of the laser beam as a whole at the same frequency. The advantage of this generation of ultrasound are both a higher frequency and a higher local heating of the tablets, which can make it possible to obtain and study the effects associated with supercritical liquid overheating with an increase in the laser radiation power and an increase in the optical absorption of the liquid.