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The Journal of Chemical Physics

Three-beam double stimulated Raman scatterings: Cascading configuration

B. Jayachander Rao, Minhaeng Cho

Published Mar 20, 2018• 12 citations
Publisher

Abstract

Two-beam stimulated Raman scattering (SRS) has been used in diverse label-free spectroscopy and imaging applications of live cells, biological tissues, and functional materials. Recently, we developed a theoretical framework for the three-beam double SRS processes that involve pump, Stokes, and depletion beams, where the pump-Stokes and pump-depletion SRS processes compete with each other. It was shown that the net Stokes gain signal can be suppressed by increasing the depletion beam intensity. The theoretical prediction has been experimentally confirmed recently. In the previous scheme for a selective suppression of one SRS by making it compete with another SRS, the two SRS processes occur in a parallel manner. However, there is another possibility of three-beam double SRS scheme that can be of use to suppress either Raman gain of the Stokes beam or Raman loss of the pump beam by depleting the Stokes photons with yet another SRS process induced by the pair of Stokes and another (second) Stokes beam. This three-beam double SRS process resembles a cascading energy transfer process from the pump beam to the first Stokes beam (SRS-1) and subsequently from the first Stokes beam to the second Stokes beam (SRS-2). Here, the two stimulated Raman gain-loss processes are associated with two different Raman-active vibrational modes of solute molecule. In the present theory, both the radiation and the molecules are treated quantum mechanically. We then show that the cascading-type three-beam double SRS can be described by coupled differential equations for the photon numbers of the pump and Stokes beams. From the approximate solutions as well as exact numerical calculation results for the coupled differential equations, a possibility of efficiently suppressing the stimulated Raman loss of the pump beam by increasing the second Stokes beam intensity is shown and discussed. To further prove a potential use of this scheme for developing a super-resolution SRS microscopy, we present a theoretical expression and numerical simulation results for the full-width-at-half-maximum of SRS imaging point spread function, assuming that the pump and Stokes beam profiles are Gaussian and the second Stokes beam has a doughnut-shaped spatial profile. It is clear that the spatial resolution with the present 3-beam cascading SRS method can be enhanced well beyond the diffraction limit. We anticipate that the present work will provide a theoretical framework for a super-resolution stimulated Raman scattering microscopy that is currently under investigation.

DOI
10.1063/1.5022092

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Three-beam double stimulated Raman scatterings

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Two-beam stimulated Raman scattering (SRS) has been used in diverse label-free spectroscopy and imaging applications of live cells, biological tissues, and functional materials. Recently, we developed a theoretical framework for the three-beam double SRS processes that involve pump, Stokes, and depletion beams, where the pump-Stokes and pump-depletion SRS processes compete with each other. It was shown that the net Stokes gain signal can be suppressed by increasing the depletion beam intensity. The theoretical prediction has been experimentally confirmed recently. In the previous scheme for a selective suppression of one SRS by making it compete with another SRS, the two SRS processes occur in a parallel manner. However, there is another possibility of three-beam double SRS scheme that can be of use to suppress either Raman gain of the Stokes beam or Raman loss of the pump beam by depleting the Stokes photons with yet another SRS process induced by the pair of Stokes and another (second) Stokes beam. This three-beam double SRS process resembles a cascading energy transfer process from the pump beam to the first Stokes beam (SRS-1) and subsequently from the first Stokes beam to the second Stokes beam (SRS-2). Here, the two stimulated Raman gain-loss processes are associated with two different Raman-active vibrational modes of solute molecule. In the present theory, both the radiation and the molecules are treated quantum mechanically. We then show that the cascading-type three-beam double SRS can be described by coupled differential equations for the photon numbers of the pump and Stokes beams. From the approximate solutions as well as exact numerical calculation results for the coupled differential equations, a possibility of efficiently suppressing the stimulated Raman loss of the pump beam by increasing the second Stokes beam intensity is shown and discussed. To further prove a potential use of this scheme for developing a super-resolution SRS microscopy, we present a theoretical expression and numerical simulation results for the full-width-at-half-maximum of SRS imaging point spread function, assuming that the pump and Stokes beam profiles are Gaussian and the second Stokes beam has a doughnut-shaped spatial profile. It is clear that the spatial resolution with the present 3-beam cascading SRS method can be enhanced well beyond the diffraction limit. We anticipate that the present work will provide a theoretical framework for a super-resolution stimulated Raman scattering microscopy that is currently under investigation.
Two-beam stimulated Raman scattering with pump and Stokes beams is manifest in both the Raman loss of the pump beam and the Raman gain of the Stokes beam, and it has been used in various label-free bioimaging applications. Here, a three-beam stimulated Raman scattering that involves pump, Stokes, and depletion beams is considered, where two stimulated Raman gain-loss processes are deliberately made to compete with each other. It is shown that the three-beam Raman scattering process can be described by coupled differential equations for the increased numbers of Stokes and depletion beam photons. From approximate solutions of the coupled differential equations and numerical calculation results, it is shown that a highly efficient suppression of the Stokes Raman gain is possible by using an intense depletion beam whose frequency difference from that of the pump beam is identical to another acceptor Raman mode frequency. I anticipate that the present work will provide a theoretical framework for super-resolution stimulated Raman scattering microscopy.
Summary form only given. Sub-diffraction limited imaging schemes have become widely used in fluorescence microscopy [1]. Howaever, the need for labeling with fluorescent dyes remains a major downside of fluorescence microscopy. The size, availability, toxicity as well as photo-bleaching of the used dyes can complicate measurements [2]. In contrast, Raman imaging is inherently label-free. Unfortunately, the super-resolution schemes used in fluorescence microscopy are currently not transferable to Raman microscopy. This paper presents the development of a scheme for the suppression of coherent Raman scattering through the depletion of probe photons, inspired by the work of M. Cho et al. [3, 4], who showed the suppression of coherent Raman scattering using laser pulses at three different wavelengths and two Raman resonances. In our case, probe depletion is achieved through saturated stimulated Raman scattering in a three-beam setup with only two colors involved. Fig. 1 (a) describes the working principle: in the unsuppressed case, the combination of pump and probe pulse induces stimulated Raman scattering at the Raman resonances, leading to stimulated Raman loss (SRL) of the probe and and stimulated Raman gain (SRG) of the pump. The Raman spectrum then results from the difference between two spectra, recorded with pump on and off, respectively. In the suppressed case a second strong pump pulse, working as a depletion pulse, depletes the probe pulse via stimulated Raman scattering (SRLD) and induces a shortage of the probe photons at the Raman resonances, saturating the stimulated Raman scattering. Thus, only a small amount of additional SRLSup is induced by the original pump. If SRL is detected in addition to the spectral change, induced by the depletion pulse, the SRL will be reduced resulting in SRLSup<; SRL.
We theoretically investigate a scheme in which stimulated Raman scattering (SRS) can be suppressed by coherently controlling the coupling between molecular states. In conventional SRS, two laser beams at different frequencies interact resonantly with molecular vibration to induce a gain and a loss for the two beams, respectively. In our scheme, a third beam is introduced to couple the vibrational state to another coupling state. As a result, SRS is suppressed in a way analogous to electromagnetically induced transparency. We calculated the SRS signal analytically by the density matrix approach, and investigated the feasibility of this scheme for real molecular imaging. In SRS microscopy, a donut-shaped coupling laser can be used to suppress the SRS signal from the rim part of the focal spot, leading to super-resolution. Based on our numerical studies, the lateral resolution starts to be enhanced when the coupling laser intensity exceeds 0.1TW/cm20.1\phantom{\rule{0.16em}{0ex}}\mathrm{TW}/\mathrm{c}{\mathrm{m}}^{2}0.1TW/cm2 at picosecond pulse duration.
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 present a three-dimensional theory of stimulated Raman scattering (SRS) or super-radiance. In particular we address how the spatial and temporal properties of the generated SRS beam or Stokes beam of radiation depends on the spatial properties of the gain medium. Maxwell equations for the Stokes field operators and of the atomic operators are solved analytically and a correlation function for the Stokes field is derived. In the analysis we identify a super-radiating part of the Stokes radiation that exhibit beam characteristics. We show how the intensity in this beam builds up in time and at some point largely dominates the total Stokes radiation of the gain medium. We show how the SRS depends on the Fresnel number and the optical depth and that in fact these two factors are the only factors describing the coherent radiation.
The nonlinear regime of stimulated Raman scattering (SRS) may be reached in two ways. The best known is that of depletion of the pump laser as a large number of photons are scattered into the Stokes field. There is, however, another way in which gain saturation can occur, that is, by depletion of the atomic population while the laser remains undepleted. The equations which describe SRS, including damping and population inversion,1 are remarkably similar to those of well-known theories of two-level superfluorescence, and it is possible by analogy to define a delay time τ D for cooperative Raman scattering (CRS). This delay time is inversely proportional to the spontaneous scattering rate, which depends on the pump laser intensity. A sufficient condition for CRS is that the spontaneous Stokes linewidth Γ is very much greater than τ D − 1 . The only other requirement is that there be more laser photons than scatterers, so that τ D is independent of the number of scatterers. The S(1) transition in molecular hydrogen, when excited by a short (≅ 100-ps) laser pulse, provides a possible system for observing pure CRS. Similar studies have been carried out previously2 for Γ ≅ τ D − 1 .