• Optical Instruments
  • Vol. 44, Issue 4, 49 (2022)
Jinlei FEI1,2 and Jian LIN1,2,*
Author Affiliations
  • 1Institute of Photonic Chips, University of Shanghai for Science and Technology, Shanghai 200093, China
  • 2School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
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    DOI: 10.3969/j.issn.1005-5630.2022.004.007 Cite this Article
    Jinlei FEI, Jian LIN. Circularly polarized broadband CARS spectroscopy for non-resonant background removal[J]. Optical Instruments, 2022, 44(4): 49 Copy Citation Text show less

    Abstract

    Coherent Anti-Stokes Raman Scattering (CARS) is a stimulated Raman process, which has the non-resonant background (NRB), leading to peak shift and spectral distortion in the spectrum. In this letter, we use a femtosecond laser as the light source and a grating filter system generating narrow-band pump light. The femtosecond laser excites photonic crystal fiber, producing a supercontinuum spectrum as Stokes light. Two beams excite the samples simultaneously after modulated to circular polarized lights to produce CARS spectrums. We illustrate that circularly polarized light can effectively remove the non-resonant background in the CARS spectrum of anisotropic materials by simulation. Thus, the CARS spectrum has a similar spectral line shape to that of spontaneous Raman. The experimental results of CARS spectrums of polystyrene and liquid crystal samples generally agree with the calculations, proving that circularly polarized CARS spectroscopy is an effective method to remove the NRB of CARS spectrum.
    $ Pi(3)(ωout)=jkl(abc)χijkl(3)(ωout;ωa,ωb,ωc)×Ej(ωa)Ek(ωb)El(ωc)$(1)

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    $ {E}_{\mathrm{p}y}={E}_{\mathrm{p}x}{\mathrm{e}}^{\mathrm{i}{\phi }_{\mathrm{p}}} \text{,} {E}_{\mathrm{s}y}^{*}={E}_{\mathrm{s}x}^{*}{\left({\mathrm{e}}^{\mathrm{i}{\phi }_{\mathrm{s}}}\right)}^{*} \tag{2a}$()

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    $ {P}_{x}={3E}_{\mathrm{p}x}^{2}{E}_{\mathrm{s}x}^{*}\left[χ1222(3)eiϕpeiϕp(eiϕs)+χ1111(3)+χ1121(3)eiϕp+χ1122(3)eiϕp(eiϕs)+χ1211(3)eiϕp+χ1212(3)eiϕp(eiϕs)+χ1221(3)eiϕpeiϕp+χ1112(3)(eiϕs)\right] \tag{2b}$()

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    $ {P}_{y}={3E}_{\mathrm{p}x}^{2}{E}_{\mathrm{s}x}^{*}\left[χ2222(3)eiϕpeiϕp(eiϕs)+χ2111(3)+χ2212(3)eiϕp(eiϕs)+χ2112(3)(eiϕs)+χ2122(3)eiϕp(eiϕs)+χ2121(3)eiϕp+χ2221(3)eiϕpeiϕp+χ2211(3)eiϕp\right] \tag{2c}$()

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    $Pxl=3(χ1111(3)+χ1112(3)+χ1121(3)+χ1122(3)+χ1212(3)+χ1211(3)+χ1221(3)+χ1222(3))Epx2Esx \tag{3a} $()

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    $Pyl=3(χ2222(3)+χ2211(3)+χ2212(3)+χ2112(3)+χ2121(3)+χ2122(3)+χ2221(3)+χ2111(3))Epx2Esx \tag{3b}$()

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    $ {P}_{x\mathrm{c}}=\dfrac{\sqrt{2}}{2}{P}_{x} \text{,} {P}_{y\mathrm{c}}=\dfrac{\sqrt{2}}{2}{P}_{y} $()

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    $ Pxc=322Epx2Esx(χ1111(3)+iχ1112(3)+iχ1121(3)χ1122(3)+iχ1212(3)χ1211(3)χ1221(3)iχ1222(3)) \tag{4a}$()

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    $ Pyc=322Epx2Esx(iχ2211(3)iχ2222(3)χ2212(3)+iχ2112(3)χ2121(3)+iχ2122(3)χ2221(3)+χ2111(3))\tag{4b} $()

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    $ Pxc=322Epx2Esx(χ1111(3)iχ1112(3)+iχ1121(3)+χ1122(3)+iχ1212(3)+χ1211(3)χ1221(3)+iχ1222(3))\tag{5a}$()

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    $ Pyc=322Epx2Esx(iχ2222(3)+iχ2211(3)+χ2212(3)iχ2112(3)+χ2121(3)+iχ2122(3)χ2221(3)+χ2111(3)) \tag{5b}$()

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    $ {P}_{x\mathrm{l}}=3\left({\chi }_{1111}^{\left(3\right)}+{\chi }_{1122}^{\left(3\right)}+{\chi }_{1221}^{\left(3\right)}{+\chi }_{1212}^{\left(3\right)}\right){E}_{\mathrm{p}x}^{2}{E}_{\mathrm{s}x}^{*}\tag{6a} $()

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    $ {P}_{y\mathrm{l}}=3\left({\chi }_{2222}^{\left(3\right)}+{\chi }_{2211}^{\left(3\right)}+{\chi }_{2112}^{\left(3\right)}{+\chi }_{2121}^{\left(3\right)}\right){E}_{\mathrm{p}x}^{2}{E}_{\mathrm{s}x}^{*} \tag{6b}$()

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    $ {P}_{x\mathrm{c}}=\frac{3\sqrt{2}}{2}\left({\chi }_{1111}^{\left(3\right)}-{\chi }_{1122}^{\left(3\right)}-{\chi }_{1221}^{\left(3\right)}{-\chi }_{1212}^{\left(3\right)}\right){E}_{\mathrm{p}x}^{2}{E}_{\mathrm{s}x}^{\mathrm{*}} \tag{7a}$()

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    $ {P}_{y\mathrm{c}}=\frac{3\sqrt{2}}{2}\left({\chi }_{2222}^{\left(3\right)}-{\chi }_{2211}^{\left(3\right)}-{\chi }_{2112}^{\left(3\right)}{-\chi }_{2121}^{\left(3\right)}\right){E}_{\mathrm{p}x}^{2}{E}_{\mathrm{s}x}^{*} \tag{7b}$()

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    $ {P}_{x\mathrm{c}}=\frac{3\sqrt{2}}{2}\left({\chi }_{1111}^{\left(3\right)}+{\chi }_{1122}^{\left(3\right)}-{\chi }_{1221}^{\left(3\right)}{+\chi }_{1212}^{\left(3\right)}\right){E}_{\mathrm{p}x}^{2}{E}_{\mathrm{s}x}^{*} \tag{8a}$()

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    $ {P}_{y\mathrm{c}}=\frac{3\sqrt{2}}{2}\mathrm{i}\left({\chi }_{2222}^{\left(3\right)}+{\chi }_{2211}^{\left(3\right)}-{\chi }_{2112}^{\left(3\right)}{+\chi }_{2121}^{\left(3\right)}\right){E}_{\mathrm{p}x}^{2}{E}_{\mathrm{s}x}^{*} \tag{8b}$()

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    $ {\chi }_{1122}^{\left(3\right)}={\chi }_{1221}^{\left(3\right)}={\chi }_{1212}^{\left(3\right)}=\dfrac{1}{3}{\chi }_{1111}^{\left(3\right)} \tag{9a}$()

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    $ {\chi }_{2211}^{\left(3\right)}+{\chi }_{2112}^{\left(3\right)}+{\chi }_{2121}^{\left(3\right)}=\dfrac{1}{3}{\chi }_{2222}^{\left(3\right)} \tag{9b}$()

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    Jinlei FEI, Jian LIN. Circularly polarized broadband CARS spectroscopy for non-resonant background removal[J]. Optical Instruments, 2022, 44(4): 49
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