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UEC Int’l Mini-Conference No.53 11

Generation of Distortionless 2-Dimensional Optical Vortex Array by

Dammann Grating using Electron-Beam Fabrication
a,b
a,b
*Tonmoy Hasan CHOWDHURY and Yoko MIYAMOTO
a Department of Engineering Science, the University of Electro-Communications
b Institute for Advanced Science, the University of Electro-Communications
1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan
*Email: c2333125@edu.cc.uec.ac.jp
Keywords: Dammann grating, optical vortex array, orbital angular momentum, electron beam fabrication
Abstract:
The generation of a distortionless 7 × 7 optical vortex array by Dammann grating using electron beam fabrication is
reported. The vortex array is generated by combining two Dammann gratings placed orthogonally to each other and
incorporating phase singularity at the center of the grating. Raster scan systems such as an electron beam writer can
introduce additional phase modulation to the generated vortex beam, which can be compensated by adding
compensating cubic and quadratic phase terms to the phase pattern.
Description:
A Dammann grating is a binary phase grating that produces a one- or two-dimensional array of diffracted light of
equal brightness. Moreno et al. [1] have shown that a 2D array can be generated by combining two Dammann gratings
placed orthogonally to each other and incorporated a phase singularity at the center of each grating to create a vortex
beam array.
Previously, Kohara from Miyamoto laboratory [2] generated such a vortex array by electron beam fabricated hologram.
An improvement was achieved in the vortex array by controlling the overlap between the adjacent beams. Raster scan
systems like an e-beam writer can introduce additional phase modulation to the generated vortex beam. Kohara’s
vortex array contains distortions that may have been due to this additional phase modulation. I aim to remove this
distortion.
Miyamoto et al. [3] have shown that the additional
phase modulation caused by the electron beam writer
can be compensated by adding compensating cubic
and quadratic phase terms to the phase pattern. I have
used rotational symmetry to find out the contribution
of astigmatism and cubic phase in the generated
vortex beam (Figure 1). The generated vortex beam
was compared with the simulated result by the
angular spectrum method to determine the value for
compensation. From the experimental data, it is
observed that a positive cubic phase and negative
astigmatism are impacting the generated vortex
beam, which can be compensated in phase pattern by negative cubic phase and positive astigmatism.
Discussion:
After fabrication considering cubic and quadratic phase terms, it was observed that the generated vortex beam was not
compensated for distortions (Figure 2). The contribution of 2-fold rotational symmetry components increased from
0.59% to 1.49%. This indicates that the value used in the compensated pattern was not appropriate for the e-beam
writer condition. I am currently investigating this discrepancy.
References:
[1] I. Moreno et al. “Encoding generalized phase functions on Dammann gratings”, Optics letters 35, 1536, (2010).
[2] S. Kohara, 電子線レジストを用いたダマン回折格子による±24 次までの光渦配列の生成と応用, master thesis,
the University of Electro-Communications (2024).
[3] Y. Miyamoto et al., “Characterization and Compensation of Phase Distortions in Holograms for Generating and
Detecting Doughnut Beams” Opt. Rev. 20 (2013) 127.

*The author is supported by AiQuSci MEXT scholarship