Pattern-integrated interference [Invited]

Thomas K. Gaylord; Matthieu C. R. Leibovici; Guy M. Burrow

doi:10.1364/AO.52.000061

Applied Optics
Vol. 52,
Issue 1,
pp. 61-72
(2013)
•https://doi.org/10.1364/AO.52.000061

Pattern-integrated interference [Invited]

Thomas K. Gaylord, Matthieu C. R. Leibovici, and Guy M. Burrow

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Thomas K. Gaylord, Matthieu C. R. Leibovici, and Guy M. Burrow, "Pattern-integrated interference [Invited]," Appl. Opt. 52, 61-72 (2013)

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Abstract

Pattern-integrated interference (PII) is described as a logical progression starting from the primary precursors of interference and holography. PII produces, in a single-exposure step, a periodic interference pattern with preselected periods absent. These blocked periods, for example, can form the nonperiodic functional elements of a photonic-crystal device or the circuit elements in a periodic-layout-design semiconductor chip. Various possible system configurations for PII are presented and compared. Example PII-produced intensity patterns for a photonic-crystal microresonator filter and an optical switch are simulated and discussed.

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	Microresonator Filter	Optical Switch
Exposure wavelength, $λ$	193 nm
Objective Lens 1 parameters	$CA = 40 mm$ , $f_{o 1} = 97.98 mm$ , $NA = 0.2$
Objective Lens 2 parameters	$CA = 40 mm$ , $f_{o 2} = 26.67 mm$ , $NA = 0.6$
Compound objective lens magnification, $\| m \| = f_{o 2} / f_{o 1}$	0.27
Interference pattern period, $a$	1500 nm	420 nm
Incident angle at the sample plane, $θ_{S} = \sin^{- 1} (2 λ / 3 a)$	4.92 deg	17.84 deg
Incident angle at the photomask, $θ_{M} = \tan^{- 1} (m \tan θ_{S})$	1.34 deg	5.00 deg
Beam displacement from the optical axis, $d_{beam} = f_{1} \tan θ_{M}$	2.29 mm	8.57 mm
Estimated maximum beam radius on mask, $r_{M} = ((CA / 2) - d_{beam}) \cos θ_{M}$	17.7 mm	11.4 mm
Estimated maximum beam radius at the sample plane, $r_{S} = m ((CA / 2) - d_{beam}) \cos θ_{S}$	4.8 mm	2.9 mm
Estimated maximum size of exposed area $π {(r_{S} / \cos θ_{S})}^{2}$	$72 {mm}^{2}$	$29 {mm}^{2}$
Pattern mask size	$82.66 μm \times 5.51 μm$	$32.76 μm \times 6.17 μm$
Pattern mask blocking element dimensions	$5.51 μm \times 5.51 μm$	$1.54 μm \times 1.54 μm$

	Microresonator Filter	Optical Switch
Beam 1	$e_{1} = [1.00, 0.00, 0.1]$	$e_{1} = [0.95, - 0.21, 0.23]$
Beam 2	$e_{2} = [1.00, 0.00, 0.00]$	$e_{2} = [1.00, 0.00, 0.00]$
Beam 3	$e_{3} = [1.00, 0.00, - 0.1]$	$e_{3} = [0.96, 0.02, - 0.27]$

Metric Description
Metric	Pattern Period	Location within Unit Cell	Intensity	Normalized Value
Metric	Pattern Period	Location within Unit Cell	Intensity	Microresonator Filter	Optical Switch
${In}_{1}$	Unblocked (or “on”)	Center	Highest	1.01	1.03
${In}_{2}$			Lowest	0.99	0.98
${In}_{3}$		Any location	Highest	1.01	1.03
${In}_{4}$			Lowest	$< 1 \times 10^{- 2}$	$< 1 \times 10^{- 2}$
${In}_{5}$	Blocked (or “off”)	Center	Highest	$< 1 \times 10^{- 2}$	$< 1 \times 10^{- 2}$
${In}_{6}$			Lowest	$< 1 \times 10^{- 2}$	$< 1 \times 10^{- 2}$
${In}_{7}$		Any location	Highest	0.06	0.07
${In}_{8}$			Lowest	$< 1 \times 10^{- 2}$	$< 1 \times 10^{- 2}$

Metric Description
Metric	Pattern Period	Lattice-Vector Direction	Length	Normalized Value
Metric	Pattern Period	Lattice-Vector Direction	Length	Microresonator Filter	Optical Switch
${LV}_{1}$	Unblocked (or “on”)	a	Longest	1.01	1.01
${LV}_{2}$			Shortest	0.99	0.99
${LV}_{3}$		b	Longest	1.01	1.03
${LV}_{4}$			Shortest	0.98	0.98
			Angular Deviation	Value
${LV}_{5}$	Unblocked (or “on”)	a	Max CCW	0.81 deg	0.81 deg
${LV}_{6}$			Max CW	$- 0.81 \deg$	$- 0.82 \deg$
${LV}_{7}$		b	Max CCW	0.87 deg	0.56 deg
${LV}_{8}$			Max CW	$- 1.24 \deg$	$- 1.66 \deg$

	Microresonator Filter	Optical Switch
Exposure wavelength, $λ$	193 nm
Objective Lens 1 parameters	$CA = 40 mm$ , $f_{o 1} = 97.98 mm$ , $NA = 0.2$
Objective Lens 2 parameters	$CA = 40 mm$ , $f_{o 2} = 26.67 mm$ , $NA = 0.6$
Compound objective lens magnification, $\| m \| = f_{o 2} / f_{o 1}$	0.27
Interference pattern period, $a$	1500 nm	420 nm
Incident angle at the sample plane, $θ_{S} = \sin^{- 1} (2 λ / 3 a)$	4.92 deg	17.84 deg
Incident angle at the photomask, $θ_{M} = \tan^{- 1} (m \tan θ_{S})$	1.34 deg	5.00 deg
Beam displacement from the optical axis, $d_{beam} = f_{1} \tan θ_{M}$	2.29 mm	8.57 mm
Estimated maximum beam radius on mask, $r_{M} = ((CA / 2) - d_{beam}) \cos θ_{M}$	17.7 mm	11.4 mm
Estimated maximum beam radius at the sample plane, $r_{S} = m ((CA / 2) - d_{beam}) \cos θ_{S}$	4.8 mm	2.9 mm
Estimated maximum size of exposed area $π {(r_{S} / \cos θ_{S})}^{2}$	$72 {mm}^{2}$	$29 {mm}^{2}$
Pattern mask size	$82.66 μm \times 5.51 μm$	$32.76 μm \times 6.17 μm$
Pattern mask blocking element dimensions	$5.51 μm \times 5.51 μm$	$1.54 μm \times 1.54 μm$

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Applied Optics