# What is the difference between a Surface Acoustic Wave (SAW) (Rayleigh Wave) and a Leaky SAW?

I have come across leaky SAWs and I'm not sure what the difference is, and why some substrate cuts are listed as leaky SAW design.

Trying to search for diagrams so I could see what the differences maybe, I typically find this one where a SAW reaches a fluid/gas medium in contact with the surface of the substrate and this it appears to dampen, while transferring energy to fluid/gas. Generally anything in contact with the substrate of a SAW will dampen it and absorb energy. So I do not see any difference, it just appears to be a SAW.

I am hoping someone could enlighten me as to what a Leaky SAW is and why certain crystal cuts appear better at promoting them.

While I know next to nothing about piezoelectrics and crystal cuts, I hope that I can help you a bit with the difference between non-leaky and leaky waves.

The basic solutions that you'll find in textbooks for Rayleigh waves assume that your solid medium is bounded by a vacuum on one side. That way, the boundary conditions are simpler, as the moving surface is not pushing against anything. Now, let's consider what happens if the other medium is not a vacuum but a fluid (i.e., a liquid or gas). The boundary conditions then require that the motion and mechanical stresses are the same at the boundary for both the solid and the adjacent fluid. In other words, the motion of the solid surface causes a motion in the fluid medium.

Now, even if you have a fluid medium adjacent to the solid, you don't necessarily have a leaky Rayleigh wave. For that to happen, the speed of the Rayleigh wave must be higher than the sound speed in the fluid medium. In that case, the fluid motion will be a plane wave propagating away from the solid, carrying some of the Rayleigh wave's energy away into the fluid. If the speed of the Rayleigh wave is lower than the speed of sound in the fluid, however, the fluid motion will be an evanescent wave that does not leak energy into the fluid. (As the Rayleigh wave has a frequency-dependent speed, this also means that there is a critical frequency at which the Rayleigh wave becomes leaky.)

Now, back to your crystal cuts. At a guess, I'd say that different crystal cuts give different Rayleigh wave speeds, and that the Rayleigh wave speeds for some cuts are higher than the speed of sound in a typical fluid medium (whatever "typical" means for your application), thus meaning that these cuts will more easily give you leaky surface waves.

• Thank you for this explanation, going back over the wave speeds for the cuts listed as Leaky SAW, I saw that they were higher by 800-1500 m/s compared with the what was listed as the SAW cuts. From your explanation this means that depending on the fluid medium and the relative acoustic velocity, any of the substrate cuts could theoretically be suitable for leaky waves. But the cuts chosen are likely chosen because of their higher velocities.
– Dave
Aug 20, 2019 at 10:17

Sorry I did not see your post sooner, but this interpretation is incorrect. Leaky SAW devices suffer from radiation of energy into other wave modes within the substrate material - typically slow shear bulk acoustic waves. This leakage can be controlled on certain substrates through control of electrode thicknesses. See:. Plessky, J. Koskela and R. Hammond, "Leaky SAW Devices with Beryllium Electrodes," 2018 IEEE International Ultrasonics Symposium (IUS), 2018, pp. 1-5, doi: 10.1109/ULTSYM.2018.8580172.