Multi-dimensional coherent spectroscopy (MDCS) 1,2 is a powerful method for optical spectroscopy that has become an important tool for studying ultrafast dynamics in a wide range of systems. It is an optical analog of multidimensional nuclear magnetic resonance spectroscopy that enables the measurement of homogeneous linewidths in inhomogeneously broadened systems, many-body interactions, and coupling between excited resonances, all of which are not simultaneously accessible by any other linear or non-linear method. Current implementations of MDCS require a bulky apparatus and suffer from resolution and acquisition speed limitations that constrain their applications outside the laboratory 3-5 . Here we propose and demonstrate an approach to nonlinear coherent spectroscopy that utilizes three frequency combs with slightly different repetition rates. Unlike traditional nonlinear methods, tri-comb spectroscopy uses only a single photodetector and no mechanical moving elements to enable faster acquisition times, while also providing comb resolution. As a proof of concept, a multidimensional coherent spectrum with comb cross-diagonal resolution is generated using only 365 ms of data. These improvements make multidimensional coherent spectroscopy relevant for systems with narrow resonances (especially cold atomic and molecular systems). In addition the method has the potential to be field deployable for chemical sensing applications.Rapid, high precision, and sensitive spectroscopic measurements of materials are desirable both in the laboratory and for field applications such as chemical sensing and atmospheric monitoring. The development of frequency comb technology led to a method known as Dual-Comb Spectroscopy (DCS) that emerged as a revolutionary approach to optical spectroscopy 6,7 .
A new method of steering THz pulses radiated from a thin emitter excited by tilted optical pulse-fronts has been developed theoretically and validated in a proof-of-concept experiment. This steering technique is potentially efficient and rapid, and it should benefit from a THz-pulse energy that can scale with optical-beam size and magnitude. Conversely, the method employed for measuring the steered THz pulses is also capable of characterizing the pulse-front tilt of an optical beam.
The determination of the properties (i.e. line center, width, and amplitude) of a spectral line is simulated using a Monte Carlo method. For dual-comb spectroscopy, ideal repetition rates emerge for both the signal and LO combs that do not correspond to the repetition rates that possess the highest signal-to-noise ratio. The determination is even more accurate when the repetition rates have an arbitrary near-harmonic ratio. The simulation results are generalized to allow for the comparison of any two spectroscopic systems (i.e. not just comb-based systems) by performing the simulations as a function of the spectral point spacing and signal-to-noise ratio of the acquired data.
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