Spectrum analysis of liquid immersion to transparent microsphere based optical nanoscopy
Introduction
Due to the presence of diffraction, the resolution of conventional optical microscopy is limited to about half of the illuminating wavelength, which greatly hinders the real-time observation of sub-diffraction-limited objects. The essence of this limit lies in the loss of evanescent wave in the far field. Till now, there have been a lot of methods to beat this diffraction limit, such as fluorescence optical microscopy [1], structured illumination microscopy [2], [3], synthetic aperture microscopy [4], Far-field superlens [5], and hyperlens [6], [7]. However, their complicated structure or engineering design or technical limitations impede the application to some extent.
In this context, Wang presented a relative simple method [8]. By setting a transparent microsphere with a proper size on the surface of object and then look it through a microscopy, resolution between λ/8 and λ/14 can be achieved. Though it can acquire 50 nm resolution, the image is blurred and the contrast is poor. Further studies by Hao et al. [9], [10] showed that the quality of image, especially the contrast, can be significantly enhanced if the microsphere was semi-immersed in the liquid. But semi-immersed microsphere is technically complicated due to the dynamical droplet's evaporation process which leads to gradually varying resolution and magnification. Then Arash et al. [11] experimentally demonstrated that BaTiO3 microsphere with refractive index about 1.9 totally immersed in the liquid can image sub-diffraction-limit objects. And the influences of the refractive index of liquid to the magnification of imaging were also experimentally studied [12], [13], [14], [15], [16], [17]. In these studies, they all attribute this high resolution to the photonic nanojet focusing phenomenon [18], [19]. But the imaging and focusing are two distinctive physical phenomena that do not always have necessary connection in resolution, especially the evanescent wave are included.
In this paper, the influence of liquid immersion to microsphere based optical super-resolution imaging is theoretically investigated. Through tracking part of the evanescent wave of the object's spectrum, the refractive index range of the immersed liquid which can achieve super-resolution can be derived. The direct imaging calculation with FDTD and angular spectrum propagation method are also taken.
Section snippets
Spectrum analysis of microsphere imaging
To investigate the super-resolution imaging properties of microsphere immersed in the different liquid, we choose the two slits with width of 100 nm and spacing 300 nm (center to center) as the object to be imaged. This object cannot be resolved by the conventional microscope. First, the spectrum of the object is calculated. According to the theory of Fourier optics, the transmission of the two slits can be written as
Then its spectrum equals the Fourier transformation of u
Direct imaging calculation
To verify the spectrum analysis presented above, a direct imaging calculation of the structure in Fig. 3 with different refractive index of liquid immersed is taken. First the FDTD method is used to simulate the structure and then the light field distribution on the collecting line is propagated backward in the negative y direction with angular spectrum diffraction to form a virtual image on the image plane. Fig. 6(a) and (c) shows the intensity distribution in the x–y plane for nL = 1.0 and nL =
Discussion
In Section 2, we conclude that to resolve the two slits with spacing of 300 nm, at least the spectrum component kx = 1.5k0 should be captured in the far-field. Now, let us investigate the propagation of this spectrum component in the microsphere immersed in the liquid with nL = 1.33. For the microsphere/liquid interface, the critical angle of total reflection is asind(nL/n) = 44.43̊. The spectrum component kx = 1.5k0, will propagate in the microsphere with angleβ of a cosd(kx/nk0) = 37.86̊. And the
Conclusion
In conclusion, spectrum analysis method is taken to investigate the influences of liquid immersion to microsphere imaging. Through track part of the evanescent wave of the object's spectrum, the imaging resolution and magnification of different liquid immersion can be achieved. The simulation of the imaging process is also taken to verify this spectrum analysis method. The results show that the super-resolution imaging of BaTiO3 microsphere can be achieved only when the microsphere is immersed
Acknowledgments
This research was supported by the National Nature Science Foundation of China (No.11174281, 61275061, 11074251). The authors thank their colleagues for their discussions and suggestions to this research.
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