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Journal of Raman Spectroscopy

A theoretical investigation of super‐resolution CARS imaging via coherent and incoherent saturation of transitions

Willem P. Beeker, Chris Lee, Klaus J. Boller, Petra Groß, Carsten Cleff, Carsten Fallnich, Herman Leonard Offerhaus, Jennifer L. Herek

Published May 3, 2011• 28 citations
Publisher

Abstract

Abstract We review two approaches to achieving sub‐diffraction‐limited resolution coherent anti‐Stokes Raman scattering (CARS) microscopy (Beeker et al., Opt. Express, 2009, 17, 22632 and Beeker et al., J. Herek, Phys. Rev. A, 2010, 81, 012507). We performed a numerical investigation, based on the density matrix model, of the CARS emission process and identified two modified CARS experiments that lead to sub‐diffraction‐limited resolution images. At the heart of both processes is the spatial manipulation of the coherence between the ground state and the vibrational state being probed by the CARS process via a control state and a control laser that is resonant with the ground state to control state transition. We find two possible regimes of operation: in the first regime, the control and vibrational states are coupled via incoherent processes so that the populations of the two states reach equilibrium very quickly compared to the relevant coherence times. Under these conditions, pre‐populating the control state provides a saturable suppression of the coherence between the ground state and the vibrational state, suppressing CARS emission. By using a donut mode to pre‐populate the control state, CARS is suppressed everywhere but the central node, allowing sub‐diffraction‐limited resolution imaging. In the second regime, the control state has a rather long coherence lifetime, and the resonant laser drives Rabi oscillations that periodically deplete the ground state. As a result, the CARS emission process is amplitude‐modulated, which appear as sidebands on the CARS spectrum. By a process of spectral resolution and trilateration, sub‐diffraction‐limited resolution images can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.

DOI
10.1002/jrs.2949

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Abstract We review two approaches to achieving sub‐diffraction‐limited resolution coherent anti‐Stokes Raman scattering (CARS) microscopy (Beeker et al., Opt. Express, 2009, 17, 22632 and Beeker et al., J. Herek, Phys. Rev. A, 2010, 81, 012507). We performed a numerical investigation, based on the density matrix model, of the CARS emission process and identified two modified CARS experiments that lead to sub‐diffraction‐limited resolution images. At the heart of both processes is the spatial manipulation of the coherence between the ground state and the vibrational state being probed by the CARS process via a control state and a control laser that is resonant with the ground state to control state transition. We find two possible regimes of operation: in the first regime, the control and vibrational states are coupled via incoherent processes so that the populations of the two states reach equilibrium very quickly compared to the relevant coherence times. Under these conditions, pre‐populating the control state provides a saturable suppression of the coherence between the ground state and the vibrational state, suppressing CARS emission. By using a donut mode to pre‐populate the control state, CARS is suppressed everywhere but the central node, allowing sub‐diffraction‐limited resolution imaging. In the second regime, the control state has a rather long coherence lifetime, and the resonant laser drives Rabi oscillations that periodically deplete the ground state. As a result, the CARS emission process is amplitude‐modulated, which appear as sidebands on the CARS spectrum. By a process of spectral resolution and trilateration, sub‐diffraction‐limited resolution images can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.
In theoretical investigations, we review several nonlinear optical approaches towards subdiffraction-limited resolution in label-free imaging via coherent anti-Stokes Raman scattering (CARS). Using a density matrix model and numerical integration, we investigate various level schemes and combinations of the light fields that induce CARS along with additional control laser fields. As the key to techniques that gain far-field resolution below the diffraction limit, we identify the inhibition of the buildup of vibrational molecular coherence via saturation or depletion of population (Beeker et al. Opt Express 17:22632–22638, 2009) or the generation of Stark broadening and spatially dependent Rabi sideband generation (Beeker et al. Phys Rev A 81(1), 2010). Depending on the coherence and population decay rates offered by a particular molecular energy level scheme, we identify various different regimes. In the first case, where an additional state (called the control state) and a vibrational state are able to rapidly exchange population via incoherent processes, a prepopulation of the upper vibrational state inhibits the buildup of vibrational coherence. With increasing control laser intensity, this suppresses CARS emission via an incoherent, saturation type of nonlinear process. Using an intense, donut-shaped control laser beam, similar to stimulated emission depletion (STED) microscopy, this can suppress CARS emission from all sample locations except within a subdiffraction-sized range around the central node. Scanning the control beams across the sample provides subdiffraction-limited resolution imaging. An alternative, which does not require a rapid exchange of population with the control state, applies a control beam that only partially depletes the vibrational ground state. Thereby, a CARS point spread function containing a subdiffraction-limited component is generated. Subdiffraction images can then be retrieved through deconvolution. Further approaches are based on the coherent, nonlinear, resonant response of the sample. In this case, CARS signal depletion by Stark splitting of the weakly populated upper vibrational state or the observation of spatially dependent Rabi oscillation may increase the resolution beyond the diffraction limit.
We present a theoretical investigation of stimulated emission pumping to achieve sub-diffraction-limited spatial resolution in coherent anti-Stokes Raman scattering (CARS) microscopy. A pair of control light fields is used to prepopulate the Raman state involved in the CARS process prior to the CARS signal generation. Efficient prepopulation is achieved by employing a path via an electronic or vibrational state. Thereby, the buildup of a coherence between the ground and Raman state during irradiation by the light fields for CARS signal generation is prevented, resulting in the suppression of the CARS intensity by more than 99.8%. Two-dimensional spatial excitation profiles have been calculated using donut-shaped spatial profiles for the control light fields, thus, an intensity-dependent narrowing of the CARS excitation profiles below the diffraction limit. Using computer-generated test images we demonstrate a resolution beyond the diffraction limit for CARS microscopy, which is scalable by the control light field intensity, similar to stimulated emission depletion microscopy.
We theoretically investigate ground-state depletion for subdiffraction-limited spatial resolution in coherent anti-Stokes Raman scattering (CARS) microscopy. We propose a scheme based on ground-state depopulation, which is achieved via a control laser light field incident prior to the CARS excitation light fields. This ground-state depopulation results in a reduced CARS signal generation. With an appropriate choice of spatial beam profiles, the scheme can be used to increase the spatial resolution. Based on the density matrix formalism we calculate the CARS signal generation and find a CARS signal suppression by 75% due to ground-state depletion with a single control light field and by using two control light fields the CARS signal suppression can be enhanced to 94%. Additional control light fields will enhance the CARS suppression even further. In case of a single control light field we calculate resulting CARS images using a computer-generated test image including quantum and detector noise and show that the background from the limited CARS suppression can be removed by calculating difference images, yielding subdiffraction-limited resolution where the resolution achievable depends only on the intensity used.
We present a theoretical investigation of coherent anti-Stokes Raman scattering (CARS) that is modulated by periodically depleting the ground-state population through Rabi oscillations driven by an additional control laser. We find that such a process generates optical sidebands in the CARS spectrum and that the frequency of the sidebands depends on the intensity of the control laser light field. We show that analyzing the sideband frequency upon scanning the beams across the sample allows one to spatially resolve emitter positions where a spatial resolution of 656565 nm, which is well below the diffraction limit, can be obtained.
Coherent anti-Stokes Raman scattering (CARS) microscopy has been a major tool of investigation of biological structures as it contains the vibrational signature of molecules. A quantum control method based on chirped pulse adiabatic passage was recently proposed for selective excitation of a predetermined vibrational mode in CARS microscopy [Malinovskaya and Malinovsky, Opt. Lett. 32, 707 (2007)]. The method utilizes the chirp sign variation at the peak pulse amplitude and gives a robust adiabatic excitation of the desired vibrational mode. Using this method, we investigate the impact of coupling between vibrational modes in molecules on controllability of excitation of the CARS signal. We analyze two models of two coupled two-level systems (TLSs) having slightly different transitional frequencies. The first model, featuring degenerate ground states of the TLSs, gives robust adiabatic excitation and maximum coherence in the resonant TLS for positive value of the chirp. In the second model, implying nondegenerate ground states in the TLSs, a population distribution is observed in both TLSs, resulting in a lack of selectivity of excitation and low coherence. It is shown that the relative phase and coupling between the TLSs play an important role in optimizing coherence in the desired vibrational mode and suppressing unwanted transitions in CARS microscopy.