$\mu$-GLANCE: A Novel Technique to Detect Chromatically and Achromatically Lensed Gravitational Wave Signals

Gravitational microlensing in the wave-optics (WO) regime occurs when the Schwarzschild radius of a lensing object is comparable to or smaller than the wavelength of incoming gravitational waves (GWs), producing chromatic amplitude and phase modulations. In contrary, geometric optics effects happen when wavelength is much smaller than the lensing object leading to frequency independent amplifications and phase shifts. GWs can undergo both effects of lensing due to interactions with objects of different scales. To detect and characterize the wave-optics features from a lensed GW, we have developed a novel method \texttt{$\mu$-GLANCE} (Micro-Gravitational Lensing Authenticator using Non-modelled Cross-correlation Exploration). In this technique, we calculate the cross-correlation between the residuals from different detectors. We assign a false alarm rate to each potential WO microlensed candidate from a statistical viewpoint, depending on how many times the noise cross-correlation matches the strength of the residual cross-correlation of the candidate over a certain period of time. We show that for an event with a matched-filtering signal-to-noise ratio (SNR) close to thirty, a residual due to wave-optics lensing with an amplitude about $10\%$ of magnification $\mu\approx 3.2$ will start to show deviation from noise distribution at more than $68\%$ Confidence interval with the LIGO-Virgo-KAGRA sensitivity for the fourth observation run. This method provides the first technique to detect geometric optics and wave-optics effects from a WO microlensed GW without assuming any specific lensing model, and its application on the current and future GW data can identify events with both chromatic and achromatic lensed scenarios.