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In this study, we proposed a method to determine the optimal focal position for microholographic storage systems, using vector diffraction theory; the theory provides exact solutions when the numerical aperture (NA) exceeds 0.6. The best diffraction focus was determined by the position and wavelength corresponding to minimal spherical aberration. The calculated refractive index modulation, polarization illumination, and boundary conditions at the interface of different media were analyzed. From the results of our analysis, we could confirm the size of micrograting as a function of NA and wavelength, based on vector diffraction theory, compared with scalar diffraction theory which defines the micrograting by
A micro holographic storage system (MHSS) is one of the best candidates for nextgeneration high density optical memories [
In this paper, we propose a method to determine the optimal focal position using vector diffraction theory for MHSS;the method provides exact solutions when the NA exceeds 0.6. In
Recording and reading principles of micro holographic storage system (MHSS): (
Notation scheme for the field vectors and coordinates of the optical system.
The electric field structure of the optical system is given by Equation 1, the wellknown diffraction integral. Note that the notations used for the field vectors and coordinates of the system are illustrated in
The MHDS should be considered exact focal point shift due to dual wavelengths (green: recording and reading beams; red: focusing beam) and the refractive index of the photopolymer.
Scheme of focal shift associated with (
In this paper, the micrograting was modulated by 532 nm wavelength, objective lens (OL) of 0.65 NA, and photopolymer. The micrograting pattern of the two beams was created by the corresponding spatial modulation of the complex refractive index in the photopolymer. The modulation range of the micrograting, created by focused Gaussian beams, was approximately confined to the double Rayleigh range, 2
Calculated refractive index modulation of a grating induced by two counterpropagating beams. The intensity pattern created using vector diffraction theory: (
Optical parameters for numerical simulation model.
Effective NA  0.6/0.7/0.8  

Polarization  Circular  
Media  Recording  Photopolymer 
Substrate  Glass 

Wavelength  405/532/633 nm 
For comparison, we calculated the FWHM by the
Comparison of micrograting size using scalar diffraction theory and vector diffraction theory analyses.
λ (nm)  NA  λ/(2NA) (nm)  Scalar (nm)  Vector (nm)  

Transverse  Total  
532  0.6  443  457  444  458 
0.7  380  390  405  422  
0.8  332  342  325  349  
405  0.6  337  348  338  349 
0.7  289  297  308  321  
0.8  253  260  248  266 
In the case of scalar diffraction theory, the recorded micrograting size was equal to 0.514
Comparison of the full width at half maximum (FWHM) in the photopolymer for scalar and vector diffraction theory: (
Experimental setup for MHSS. BE: beam expander, M, mirror; L, lens; BS, beam splitter; PBS, polarization beam splitter; HWP, half wave plate; QWP, quarter wave plate. Green, recording and reading beam; Red, guide beam for optical alignment.
The TGI shown in
Proposed experimental setup: TwymanGreen interferometer (TGI) for exact focusing and optical alignment.
To verify the recording and reading of the micrograting, OL of 0.65 NA is used. The OL was an aspherical, aberration free lens, commonly used for high diffraction efficiency and quality. The Aprilis photopolymer (HMC050G06) was used for the recording and reading of MHDS. The thickness of the photopolymer was 400 μm, and the two glass substrates had thickness of 600 μm. The shutter had an exposure time of 100 ms. The recording energy (for are cording power signal of 240 μW and reference beam of 240 μW) was 24 μJ. During the reading process, a reflected power of 2 μW was detected. The calculated diffraction efficiency was 0.83%; note that this value is calculated by confined volume of the micrograting and limitations of the optical system (NA
Interferogram results obtained from (
In conclusion, we proposed a method to obtain the optimal focal position for MHSS using vector diffraction theory. The optimal focal position corresponded to minimal SA. We analyzed the micrograting size in the photopolymer for different wavelengths and NAs, based on vector diffraction theory, and compared the results defined by
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2013016979).
The authors declare no conflict of interest.