Non-Linear Synthesis of Spectra

This chapter turns away from the linear world of the Fourier transform and introduces the concepts related to non-linear operations as a means of spectral modification through waveshaping. The idea of non-linear functions applied to simple sinusoidal signals is explored from various perspectives. Closed-form summation formulae are first shown as examples of non-linear techniques. This is followed by a thorough discussion of phase and frequency modulation methods, themselves also shown to be based on the application of non-linear waveshaping methods. This is complemented by the techniques of phase distortion and the more general vector phase shaping algorithm. A look into adaptive forms of frequency modulation is followed by a complete study of polynomial and other forms of waveshaping.

Degenerate Four-Wave Mixing in Phycoerythrin Dye-Doped Nanoparticles

We have generated a phase-conjugate (PC) wave from nanoparticles with a new microscopic system proposed. The microscope includes a confocal system with a degenerate four-wave mixing (DFWM) system, which plays a major role in generating the phase-conjugate wave to compensate phase distortion in the optical path toward targets. The proposed optical system detects feeble PC wave and imagines 3D particles while improving the inplane contrast resolution of the microscopic image.

Acoustic properties across the human skull

Transcranial ultrasound is emerging as a noninvasive tool for targeted treatments of brain disorders. Transcranial ultrasound has been used for remotely mediated surgeries, transient opening of the blood-brain barrier, local drug delivery, and neuromodulation. However, all applications have been limited by the severe attenuation and phase distortion of ultrasound by the skull. Here, we characterized the dependence of the aberrations on specific anatomical segments of the skull. In particular, we measured ultrasound propagation properties throughout the perimeter of intact human skulls at 500 kHz. We found that the parietal bone provides substantially higher transmission (average pressure transmission 31±7%) and smaller phase distortion (242±44 degrees) than frontal (13±2%, 425±47 degrees) and occipital bone regions (16±4%, 416±35 degrees). In addition, we found that across skull regions, transmission strongly anti-correlated (R = −0.79) and phase distortion correlated (R = 0.85) with skull thickness. This information guides the design, positioning, and skull correction functionality of next-generation devices for effective, safe, and reproducible transcranial focused ultrasound therapies.