UV Laser Pulse Trains for Raman Spectroscopy.

The theoretical framework for Raman spectroscopy using a UV probe laser pulse train consisting of multi femtosecond pulses is developed. We show selective excitation of a single Raman mode by tuning the pulse parameters. The use of UV radiation for the probe has a number of advantages for this application. The pulse train consists of multiple pulses of the form, $I_{1} (\tau )=I_{0} \sin^{2}(\pi \tau /\tau_{L} )\left( {\Theta \left( \tau \right)-\Theta \left( {\tau -\tau_{L} } \right)} \right)$, where $\tau_{L} $ is the duration of a single pulse, $\tau_{FWHM} ={\tau_{L} } \mathord{\left/ {\vphantom {{\tau_{L} } 2}} \right. \kern-\nulldelimiterspace} 2,\mbox{\thinspace \thinspace }I_{0} =n_{0} c\varepsilon_{0} {E_{peak}^{2} } \mathord{\left/ {\vphantom {{E_{peak}^{2} } 2}} \right. \kern-\nulldelimiterspace} 2$, is the peak intensity and $\Theta \left( \tau \right)$ is the Heaviside function. The analysis is performed in the group velocity frame, where $\tau =t-z/\mbox{v}_{G} \,\,\mbox{and}\,\,\eta =z$. The reduced propagation equation for the probe pulse field is ${\partial E_{P} (\eta ,\tau )} \mathord{\left/ {\vphantom {{\partial E_{P} (\eta ,\tau )} {\partial \eta }}} \right. \kern-\nulldelimiterspace} {\partial \eta }=i(\mu_{0} \omega_{0}^{2} /2k_{0} )P_{NL} (\eta ,\tau )$ where $P_{NL} $ is the non-linear polarization field. The probe intensity is modulated and grows approximately linearly with the interaction distance. We simulate the detection of the COVID-19 pathogen with a laser pulse train consisting of 10 micro-pulses, each with a duration of $\approx $ 32 fs, peak intensity of 10$^{\mathrm{10\thinspace }}$W/cm$^{\mathrm{2}}$ and central wavelength of 250 nm (frequency tripled Ti:Sapphire). The micro-pulse duration is chosen to match the vibrational period of the smallest Raman shift resonance of the pathogen, $\omega_{V} /(2\pi c)=1032\mbox{cm}^{\mbox{-1}}$. This simulation showed the selective excitation of a single Raman mode.