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We provide an approach to breaking the diffraction limit in coherent anti-Stokes Raman scattering (CARS) microscopy and report a theoretical analysis of detection limit (DL) forit. The additional probe beam, whose profile is doughnut shaped and wavelength is different from the size of Gaussian probe beam, interacts with the coherent phonons at the rim of the diffraction-limited spot to increase theresolution by re-engineering the point spreadfunction of the system. The signal strength reduces with the size of focal volume decreasing, besides, when CARS is used in biology, the molecules of interest are usually in low concentration, which makes the signal detection more difficult. Accordingly, a remaining crucial problem is whether the reduced signal generated in the suppressed focal volume can be detected from the noise background and the analysis of DL, so it is an important precise in implementation of CARS nanoscopy. We describe T-CARS process with full quantum theory and estimate the extreme power density levels of the pump and Stokes beams determined by saturation behavior of coherent phonons. When the pump and Stokes intensities reach such extreme values and total intensity of the excitation beams arrives at a maximum tolerable by most biological samples in acertain suppressed focal volume, the DL of T-CARS nanoscopy correspondingly varies with the exposure time. For an attainable spatial resolution of ～40 nm in three dimension and areasonable exposure time of 20 ms, the DL in the suppressed focal volume is approximately ～103. The signal can be well detected from the noise fluctuation only if the number of molecules of interest exceeds this limit.
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Keywords:
- break through the diffraction limit /
- coherent anti-Stokes Raman scattering /
- nonlinear optics /
- detection limit
[1] Evans C L, Xie X S 2008 Annu. Rev. Anal. Chem. 1 883
[2] Hajek K M, Littleton B, Turk D, Mcintyre T J, Rubinsztein-Dunlop H 2010 Opt. Express 18 19263
[3] Betzig E, Patterson G H, Sougrat R, Lindwasser O W, Olenych S, Bonifacino J S, Davidson M W, Lippincott-Schwartz J, Hess H F 2006 Science 313 1642
[4] Hell S W, Wichmann J 1994 Opt. Lett. 19 780
[5] Chen D N, Liu L, Yu B, Niu H B 2010 Acta Phys. Sin. 59 6954 (in Chinese) [陈丹妮, 刘磊, 于斌, 牛憨笨 2010 物理学报 59 6954]
[6] Beeker W P, Groß P, Lee C J, Cleff C, Offerhaus H L, Fallnich C, Herek J L, Boller K 2009 Opt. Express 17 22632
[7] Nikolaenko A, Krishnamachari V V, Potma E O 2009 Phys. Rev. A 79 13823
[8] Hajek K M, Littleton B, Turk D, McIntyre T J, Rubinsztein-Dunlop H 2010 Opt. Express 18 19263
[9] Nan X, Cheng J X, Xie X S 2003 J. Lipid Res. 44 2202
[10] Liu W, Niu H B 2011 Phys. Rev. A 83 23830
[11] Vallèe F, Bogani F 1991 Phys. Rev. B 43 12049
[12] Loudon R 1983 The Quantum Ttheory of Light (Oxford: Clarendon Press)
[13] El-Diasty F 2011 Vib. Spectrosc. 55 1
[14] Portnov A, Rosenwaks S, Bar I 2008 Appl. Phys. Lett. 93 41115
[15] Begley R F, Harvey A B, Byer R L 1974 Appl. Phys. Lett. 25 387
[16] Cui M, Bachler B R, Ogilvie J P 2009 Opt. Lett. 34 773
[17] König K 2001 J. Microsc. 200 83
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[1] Evans C L, Xie X S 2008 Annu. Rev. Anal. Chem. 1 883
[2] Hajek K M, Littleton B, Turk D, Mcintyre T J, Rubinsztein-Dunlop H 2010 Opt. Express 18 19263
[3] Betzig E, Patterson G H, Sougrat R, Lindwasser O W, Olenych S, Bonifacino J S, Davidson M W, Lippincott-Schwartz J, Hess H F 2006 Science 313 1642
[4] Hell S W, Wichmann J 1994 Opt. Lett. 19 780
[5] Chen D N, Liu L, Yu B, Niu H B 2010 Acta Phys. Sin. 59 6954 (in Chinese) [陈丹妮, 刘磊, 于斌, 牛憨笨 2010 物理学报 59 6954]
[6] Beeker W P, Groß P, Lee C J, Cleff C, Offerhaus H L, Fallnich C, Herek J L, Boller K 2009 Opt. Express 17 22632
[7] Nikolaenko A, Krishnamachari V V, Potma E O 2009 Phys. Rev. A 79 13823
[8] Hajek K M, Littleton B, Turk D, McIntyre T J, Rubinsztein-Dunlop H 2010 Opt. Express 18 19263
[9] Nan X, Cheng J X, Xie X S 2003 J. Lipid Res. 44 2202
[10] Liu W, Niu H B 2011 Phys. Rev. A 83 23830
[11] Vallèe F, Bogani F 1991 Phys. Rev. B 43 12049
[12] Loudon R 1983 The Quantum Ttheory of Light (Oxford: Clarendon Press)
[13] El-Diasty F 2011 Vib. Spectrosc. 55 1
[14] Portnov A, Rosenwaks S, Bar I 2008 Appl. Phys. Lett. 93 41115
[15] Begley R F, Harvey A B, Byer R L 1974 Appl. Phys. Lett. 25 387
[16] Cui M, Bachler B R, Ogilvie J P 2009 Opt. Lett. 34 773
[17] König K 2001 J. Microsc. 200 83
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