Phonon dephasing times determined with time-delayed, broadband CARS

TL;DR

The paper addresses the challenge of non-resonant background (NRB) distortion in CARS spectroscopy by introducing time-delayed, broadband CARS (TD-BCARS) with intra-pulse excitation to obtain NRB-free spectra across a broad range ($\sim$0–$1300\,\mathrm{cm}^{-1}$) and to measure phonon dephasing times. The method combines a broadband sub-20 fs Stokes pulse with a narrowband probe, enabling a controllable delay $\Delta t$ that suppresses NRB while retaining resonant phonon signals, albeit with reduced intensity at longer delays. Validation on glass characterizes NRB timescales and response, followed by application to diamond, KTP, and KTA to extract phonon dephasing times $T_{2\nu}$, e.g., $T_{2\nu} = 7.8 \pm 1.3\ \mathrm{ps}$ for diamond and $2.7$–$7.6\ \mathrm{ps}$ for KTP/KTA peaks. The approach offers a fast, broadband, and NRB-free means to probe crystal quality and phonon lifetimes, with potential extensions to imaging and controlled solid-state modulation of material properties.

Abstract

Coherent Raman scattering techniques as coherent anti-Stokes Raman scattering (CARS), offer significant advantages in terms of pixel dwell times and speed as compared to spontaneous Raman scattering for investigations of crystalline materials. However, the spectral information in CARS is often hampered by the presence of a non-resonant contribution to the scattering process that shifts and distorts the Raman peaks. In this work, we apply a method to obtain non-resonant background-free spectra based on time-delayed, broadband CARS (TD-BCARS) using an intra-pulse excitation scheme. In particular, this method can measure the phononic dephasing times across the full phonon spectrum at once. We test the methodology on amorphous SiO2 (glass), which is used to characterize the setup-specific and material-independent response times, and then apply TD-BCARS to the analysis of single crystals of diamond and ferroelectrics of potassium titanyl phosphate (KTP) and potassium titanyl arsenate (KTA). For diamond, we determine a dephasing time of t = 7.81 ps for the single sp3 peak.

Figures (5)

• Figure 1: Jablonski diagrams for a) 2C-BCARS and b) 3C-TD-BCARS schemes. Please note the time-delay $\Delta t$ that can be introduced between the intra-pulse excitation and the probe pulse in the 3C-TD-BCARS setup. The key distinction between the 2C- and 3C-schemes are the uses of a narrowband (NB)-pump pulse in the 2C-scheme, and a broadband (BB) pump pulse in the 3C-scheme. c) Excitation envelope for a sub-20 fs Stokes pulse centered around 1400 nm and a pump laser at 1035 nm. Here, phonons with wavenumbers of up to 1300 cm$^{-1}$ can be probed in the 3C-scheme, while 2C-spectrum is mostly separated from the 3C-region. Using an even lower probe laser wavelength or longer central wavelength for the Stokes pulse could separate the two regions even further. d) Sketch of the experimental setup.
• Figure 2: The zero-time delay 3C-BCARS spectrum (blue) on KTP displays peaks down to 400, necessitating the removal of the NRB contribution for peak shape restoration by perforimg a phase-retrieval in-post processing Camp2016 (orange, 3C-BCARS phase-retr.). The TD-CARS measurement with a delay of 4 ps (red) demonstrates an NRB-free spectrum, eliminating the need for any post-processing. For reference, a SR spectrum of the same crystal is shown (green). Please note, the CARS spectra show a broader peak width of the phonon lines compared to the SR spectrum. This is a result of the spectral bandwidth of the probe laser, which is a 3.7 ps pulse at 1035 nm (approximately 10 cm$^{-1}$ bandwidth). This bandwidth is convoluted with the intrinsic line-width of the phonons. A higher resolution is possible if longer probe pulses are used, see F. Hempel et al., for example Hempel2023ComparingTA. However, using spectrally narrow and longer probe pulses will inevitably limit the temporal resolution for TD-CARS. The Raman shift is given in absolute values to make the anti-Stokes BCARS signal more readily comparable with SR spectra, which are often Stokes-shifted.
• Figure 3: TD-BCARS behavior of the NRB measured on glass: a) The spectral response shows two destinct regions, a 3C-NRB for wavenumbers approximately smaller than <1300 and a 2C-NRB spanning from approximately 1300 to 2500. b) The time-dependent intensity curves can be approximated by the convolution of the 20f Stokes pulse $I_s$ and the 3.8 pump pulse $I_{pu}$, which enters the process quadratically for the 2C-process, but only linearly in the 3C-process.
• Figure 4: TD-BCARS spectra of diamond when varying the probe pulse delay: a) The 3C-NRB and 2C-NRB decay fast, while the strong $sp^3$ diamond peak is measurable even at 10ps delay. b) On a logarithmic scale, both the 3C-NRB and the $sp^3$ signal exhibit a Gaussian-shaped decay region, while the resonant $sp^3$ signal shows an additional, linear decay. c) A symmetric, Lorentz-shaped peak form can be obtained with a time-delay of 3 ps.
• Figure 5: TD-CARS on Z(XXXX)Z KTP and KTA: a) The KTP spectrum at $\Delta t = 0\ps$ shows multiple distorted peaks, while with a delay of $\Delta t = 3\ps$ yields narrow peaks similar to spontaneous Raman scattering. b) The time-delay sweep shows the dephasing of the different peaks. The related material KTA is shown as a comparison in c) and d). Extracted phonon decoherence times are shown in Tab. 1.