Abstract

An error was made in calculating the complex electric field vector for the diffracted beams. We have corrected the error and repeated the optimization to achieve a phase mask design bearing the same result. The overall approach remains unchanged.

© 2008 Optical Society of America

In the article [1] we used a genetic algorithm to design a phase mask that produces a hexagonal array of helices in photoresist. The algorithm relies on the repeated calculation of the complex electric field vector, , for each diffracted beam. We recently discovered that our calculations applied a spurious rotation to , affecting the interference pattern that is formed. Consequently, the design shown in Fig.1 and Fig. 3 does not produce the intended target structure. We have corrected the error and rerun the optimization using the procedure outlined in the paper [1]. The revised design obtains an enhanced fitness, F, of 94% and is shown along with the resultant structure in Fig. 1 below. The new polarization angles ψ and χ are 0.57 and 6.21 radians respectively. The thickness, h, of the grating layer is now 640 nm. The contrast (V) of the intensity distribution has decreased somewhat to 6.56. However, we believe the effective two-photon contrast, V eff=43.0, is more than sufficient for proper transfer into SU-8 photoresist.

 

Fig. 1. The illustration in part (a) depicts the helix structure used as the target model. For clarity, we plot two turns of the helix and outline in bold a single primitive cell with dimensions a×a√3/2×c. Here, c/a describes the helices’ relative elongation and has a value of 2.2. Part (b) depicts the interference based structure that is produced by the optimized design shown in (c). The top portion of (c) represents a single unit cell of the phase mask’s relief profile. The primitive grating vectors are labeled by a 1 and a 2. Light pixels are raised and dark pixels are recessed. The polarization ellipse is given in the bottom portion of (c).

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References

1. J. W. Rinne, S. Gupta, and P. Wiltzius, “Inverse design for phase mask lithography,” Opt. Express 16, 663–670 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-2-663. [CrossRef]   [PubMed]  

References

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  1. J. W. Rinne, S. Gupta, and P. Wiltzius, "Inverse design for phase mask lithography," Opt. Express 16, 663-670 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-2-663.
    [CrossRef] [PubMed]

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Figures (1)

Fig. 1.
Fig. 1.

The illustration in part (a) depicts the helix structure used as the target model. For clarity, we plot two turns of the helix and outline in bold a single primitive cell with dimensions a×a√3/2×c. Here, c/a describes the helices’ relative elongation and has a value of 2.2. Part (b) depicts the interference based structure that is produced by the optimized design shown in (c). The top portion of (c) represents a single unit cell of the phase mask’s relief profile. The primitive grating vectors are labeled by a 1 and a 2. Light pixels are raised and dark pixels are recessed. The polarization ellipse is given in the bottom portion of (c).

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