Ultracompact vibrometry measurement with nanometric accuracy using optical feedback

The nonlinear dynamics of a semiconductor laser with optical feedback (OF) combined with direct current modulation of the laser is demonstrated to suffice for the measurement of subwavelength changes in the position of a vibrating object. So far, classical Optical Feedback Interferometry (OFI) has been used to measure the vibration of an object given its amplitude is greater than half the wavelength of emission, and the resolution of the measurement limited to some tenths of the wavelength after processing. We present here a methodology which takes advantage of the combination of two different phenomena: continuous wave frequency modulation (CWFM), induced by direct modulation of the laser, and non-linear dynamics inside of the laser cavity subject to optical self-injection (OSI). The methodology we propose shows how to detect vibration amplitudes smaller than half the emission wavelength with resolutions way beyond λ/2, extending the typical performance of OFI setups to very small amplitudes. A detailed mathematical model and simulation results are presented to support the proposed methodology, showing its ability to perform such displacement measurements of frequencies in the MHz range, depending upon the modulation frequency. Such approach makes the technique a suitable candidate, among other applications, to economic laser-based ultrasound measurements, with applications in nondestructive testing of materials (thickness, flaws, density, stresses), among others. The results of simulations of the proposed approach confirm the merit of the figures as detection of amplitudes of vibration below λ/2) with resolutions in the nanometer range.