PLU for monitoring of GHz – sub-THz surface Rayleigh waves

In laser ultrasonics (LU) I was always interested not only in bulk acoustic waves, but, perhaps, even more, in surface acoustic waves (as well as interface waves and Lamb waves). Starting from Moscow State University (MSU), I either initiated or supported theoretically, or both, LU projects related to surface and guided acoustic waves in Heidelberg, in Leuven and in Sapporo. For the picosecond laser ultrasonics, I had for a long time an idea (a theory published in 1990 and 1992) to efficiently generate by ultrafast lasers GHz frequency SAWs in normally cut superlattices (SLs). The idea was to grow the semiconductor/dielectric SL of alternating light-absorbing and transparent layers and, then, to cleave it along the growth direction to get a periodically structured surface for monitoring of GHz SAWs. When working on this theory (for the future, with no chances at that time to be supported in MSU) I was excited by two things. First of all, the carriers photo-generated by the inter-band pump light absorption would be confined laterally in the light-absorbing semiconductor layers, their lateral diffusion would be suppressed, leading to enhanced generation efficiency of SAWs. Second, by using the SLs with a period of single-digit nanometers it could be possible to monitor the SAWs at sub-THz and even THz frequencies. We have started the realization of the project on “cleaved SLs” in Le Mans only in 2020, when we received Post-Doctoral Fellowships, first, from the Institute of Acoustics of Le Mans University (LMU) and, then, the Marie-Sklodowska-Curie Fellowship of the European Commission. However, before this, I accumulated an experience with GHz SAWs all-optical monitoring with the nanostructures of sub-optical periodicity, by initiating, designing and theoretically supporting in 2011-2015 the project on surface metal gratings in the Laboratory of Prof. Thomas Dekorsy in Konstanz University. To my knowledge, the records, resulted from the realization of this project (optical monitoring about 90 GHz generalized Rayleigh waves [see ref.], and 197 GHz generalized Lamb waves [see ref.] are not bitten in journal publications until now.

Although applications of metal gratings to SAWs had been reported earlier, we managed to increase the efficiency of SAWs laser generation, by combining in phase thermoelastic expansion of metallic lines with contraction of Si substrate (irradiated between the metal lines) due to deformation-potential mechanism. We were able to detect higher order generalized Rayleigh and Lambs modes in these phononic structures/samples and achieve the detection of quasi-monochromatic GHz SAWs generated in a periodic nanostructure at a sharp edge of a metal film (non-periodic detector, however, providing an access to large wave vectors of SAWs) deposited several micrometers aside. The end of these investigations was close to the time of Prof. Thomas Dekorsy departure from Konstanz University. Therefore, the experiments on the monitoring GHz surface CAPs (and not quasi-periodic wave packets) were shifted to Hokkaido University (Prof. O. B. Wright and DR. Osamu Matsuda). The experiments on all-optical monitoring of SAWs, generated at one nanometers-width and micrometers-length metal line and propagating to another spatially-separated one, were started around 2017 [see ref.]. The lines were either additionally periodically structured along their length (to get profit from the plasmon resonances) or not. However, because of the limitations with metal nano-patterning in Hokkaido University the frequencies of the monitored SAWs were up to 15 GHz only and in most of the experiments the frequency spectra were strongly structured because of significant role of the strong mechanical resonances of gold wires deposited on Si, which were influencing both spectral transformation functions (optoacoustic in generation and acousto-optic in detection). Therefore, we designed new nanostructures with aluminum wires of optimal height, deposited in the grooves on Si surface, to suppress acoustic resonances. We have preliminary experimental results in Hokkaido University, confirming that we are moving in the right direction for monitoring Rayleigh CAPs with broad and smooth frequency-spectrum, but still in the frequency range around or below 10 GHz, because of technical difficulties in structures preparation.

In our first experiments in Le Mans on the SLs, grown, characterized and cleaved by Prof. Hong Lu in Nanjing University [see ref.] we monitored the generalized Rayleigh SAW at 40 GHz (generation, detection, ballistic propagation from one SLs to another). We think that we have preliminary experimental results, demonstrating diffusive propagation of these SAWs in these structures, i.e., due to a parabolic and not a linear relation between their frequencies and wave numbers in the vicinity of the Brillouin zone center (k=0) of the periodic nanostructure (where they are monitored). We presented the diffusive SAWs at the conferences, but decided not to include in the first journal publication before confirming their observation in SLs with other (shorter) periodicity. For supporting the above described experiments, I developed a theory of the generation and detection in cleaved SLs of the generalized Rayleigh waves, which explicitly takes into account that the latters contain laterally homogeneous (non-periodic component) in their mode structure. The theory predicts that laterally averaged part of laser excitation contributes to their generation, while their detection can be dominated by a laterally averaged response of the SLs to their propagation and can be detected by heterodyning acoustically-scattered light in the direction normal to the surface. Speaking, differently we are optically monitoring k=0 (near k=0) motions in a vicinity of the Brillouin zone center. For example, the homogeneous component of the SAW is detectable due to laterally averaged homogeneous component of the photoelastic parameter. Additionally, the interaction of periodic component of SAW with periodic component of photoelastic parameter, also contributes to k=0 detection, because of k-k=0. The theory, describing the expected different dominant contributions to the generation and detection processes is available in the Supplementary Information to [see ref.].

Recently the developed theory suggested opportunity of a detection of sub-optical wavelength SAWs by the evanescent components of the diffracted probe laser field under the sub-optical metal grating [see ref.].

In our next series of the experiments with shorter (about 20 nm) period SLs (grown, characterized and cleaved by Dr. Aristide Lemaitre, Dr. Martina Morassi and Prof., Daniel Lanzillotti-Kimura in University Paris-Sacley), we monitored at sub-THz frequencies all acoustical waves, which were accessible by our probe light incident on the cleaved surface (the generalized Rayleigh waves at 160 GHz, shear and longitudinal waves carrying energy along the surface at frequencies 180-200 GHz and 300 GHz, respectively) [see ref.]. We also conducted the experiments with the cleaved SLs, on which ~2 nm thick transparent films were deposited immediately after the cleavage to protect surface from possible oxidation processes, which are potentially increasing the surface roughness. We are rather close to submit these experimental results, presented only at the conferences, for journal publication: we have drafted experimental part of the manuscript and currently approaching a confident theoretical explanation for the broad band 180-200 GHz of the detected quasi-shear waves both analytically and through numerical modelling of their generation and propagation/focusing in an elastically anisotropic (cubic) medium. COMSOL modelling of acoustic waves propagation in the cleaved SLs and also in the non-periodic cleaved structures, containing individual layers for the generation and detection of CAPs, is conducted for about 5 years already by my collaborator Dr. Serhii Kukhtaruk in V.E. Lashkaryov Institute of Semiconductor Physics in Kyiv.

Of course, by extending the project on surface Rayleigh CAPs monitoring with metallic lines (rods) in Hokkaido, we tried to achieve generation and detection of GHz Rayleigh CAPs using the cleaved nanostructures. After epitaxial growth on the substrate of a designed non-periodic sequence of transparent and opaque nanometers-thick layers with hundreds of nanometers separation between them, a cleavage along the direction of growth produces the nanostructured surface for all-optical experiments with GHz CAPs. The samples were grown and characterized by Dr. Jerome Wolfman and Dr. Beatrice Negulecu in University of Tours. In these experiments we used structures prepared from oxides to avoid oxidation of the cleaved (or cut by ion-beam) surface. With a single layer of a metallic oxide (SRO, LSMO) for CAPs generation, which is confined between two layers of transparent oxides (STO, BSTO), we managed to rise a record in laser-based wide-frequency-band Rayleigh CAPs from below 10 GHz (controlled by laser focusing) to 40 GHz (controlled by the thickness of light absorbing layer). Additional advantage of the oxides, for the substrate and the layers, are very tiny differences in their acoustic impedances. Therefore, the photo-generated CAPs are reflected only on the edge of the sample (which in our experiments is either mechanically free or loaded by non-oxide material). In both cases, in the absence of the reflection at the interfaces of oxides, it is rather easy to identify the monitored longitudinal and Rayleigh CAPs via their arrival times. We drafted the manuscript based on CAPs identification through their arrivals times and the durations (suggested by analytical theory and numerical modelling), presented the results at the conferences [see ref. 1, ref. 2], but we are delaying its submission, because our current theories of their detection are not reproducing the detected signals close-enough. We are currently continuing to work on this topic with our collaborators.