Fabrication of optical mosaic gratings: a self-referencing alignment method

Lei Shi; Lijiang Zeng

doi:10.1364/OE.19.008985

Optics Express
Vol. 19,
Issue 10,
pp. 8985-8993
(2011)
•https://doi.org/10.1364/OE.19.008985

Fabrication of optical mosaic gratings: a self-referencing alignment method

Lei Shi and Lijiang Zeng

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Lei Shi and Lijiang Zeng, "Fabrication of optical mosaic gratings: a self-referencing alignment method," Opt. Express 19, 8985-8993 (2011)

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Abstract

We propose and demonstrate a self-referencing alignment technique to conveniently enlarge fabricated grating area. The latent image gratings are used as the reference objects to align (adjust and lock) the attitude and position of the substrate relative to the exposure beams between and during consecutive exposures. The adjustment system and the fringe-locking system are combined into the exposure system, eliminating the drift errors between them and making the whole system low-cost and compact. For the fabricated 1 × 4 mosaics of 50 × (30 + 30 + 30 + 30) mm² area and 1 × 2 mosaics of 90 × (80 + 80) mm² area, the typical peak-valley −1st-order wavefront errors measured by a 100-mm-diameter interferometer are not more than 0.06 λ and 0.09 λ, respectively.

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Fig. 1 Mosaic system: holographic exposure, and alignment of attitude and phase. (a) Oblique view. (b) Side view of the capture of L fringes.

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Fig. 2 Mosaic steps, including projections of relevant elements in the directions of beams B₁ and B₂ onto the grating substrate G and the L fringes. (a) Step I, the first exposure. (b) Step II, the recording of the reference L₁ ^II fringes. (c) The recorded reference L₁ ^II fringes. (d) Step III, the second exposure with the real-time L₁ ^III fringes locked to the reference L₁ ^II fringes. (e) Step IV, after moving G for monitoring the L₁ ^IV and L₂ ^IV fringes simultaneously, the recording of the reference L₂ ^IV fringes with the real-time L₁ ^IV fringes locked to the reference L₁ ^II fringes. (f) The recorded reference L₂ ^IV fringes. (g) Step V, after moving G, the third exposure with the real-time L₂ ^V fringes locked to the reference L₂ ^IV fringes. (h) Completed exposure areas and their groove position. In half image pairs of L fringes the arrows indicate the borders between the reference and real-time fringes. On the surface of G both the exposure fringes and the latent grating are partly plotted, to clearly show the phase difference between them.

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Fig. 3 The −1st-order interferograms and wavefronts of (a) a 1 × 2 mosaic grating and (b) a 1 × 4 mosaic grating. The peak-valley and root-mean-square errors in (a) are 0.087 λ and 0.018 λ, respectively; the ones in (b) are 0.060 λ and 0.012 λ, respectively.

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Fig. 4 The SEM images of one grating’s (a) ordinary area and (b) area for generating L fringes, and another grating’s (c) one ordinary area and (d) another ordinary area.

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Tables (2)

Table 1 The Phase Changes According to the Mosaic Steps

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Table 2 The Groove Data from the SEM Images of Ordinary Areas and Areas for Generating L Fringes

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Equations (6)

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P_{Ei}^{j} \equiv 0,

P_{Li}^{k} = P_{Ei}^{k} + C,

| \mod (\frac{Δ x'}{d} + \frac{1}{2}, 1) - \frac{1}{2} | = \frac{1}{e} \sqrt{3 {(Δ p_{1})}^{2} + 2 {(Δ p_{3})}^{2}},

| Δ θ_{z} | = \frac{d}{h' e} \sqrt{3 {(Δ p_{1})}^{2} + 3 {(Δ p_{2})}^{2}},

δ_{P} = \frac{0
.5}{e} \sqrt{3 {(Δ p_{1})}^{2} + 2 {(Δ p_{3})}^{2}} λ,

δ_{V} = \frac{0
.5}{e} \sqrt{3 {(Δ p_{1})}^{2} + 3 {(Δ p_{2})}^{2}} λ,

Step	Function	Locked P _Li ^k	Recorded P _Li ^k	Achieved P _Ei ^k
I	Expose Area 1	—	—	P _E1 ^I ≡ 0
II	Record L₁ ^II fringes	—	P _L1 ^II = Δβ + C	P _E1 ^II = Δβ
III	Expose Area 2	P _L1 ^III = P _L1 ^II	—	P _E1 ^III = Δβ, P _E2 ^III ≡ 0
IV	Transfer the locking (Record L₂ ^IV fringes)	P _L1 ^IV = P _L1 ^II	P _L2 ^IV = C	P _E1 ^IV = Δβ, P _E2 ^IV = 0
V	Expose Area 3	P _L2 ^V = P _L2 ^IV	—	P _E2 ^V = 0, P _E3 ^V ≡ 0

Substrate number	Area for generating L fringes		One ordinary area		Another ordinary area		Transmittivity of A₁
Substrate number	Duty Cycle	Height / nm	Duty Cycle	Height / nm	Duty Cycle	Height / nm	Transmittivity of A₁
1#	0.38^a	222^a	0.35^b	221^b	—	—	1.4%
2#	0.34	214	0.35	208	—	—	5%
3#	—	—	0.32^c	218^c	0.35^d	243^d	—
4#	—	—	0.32	223	0.32	219	—

Step	Function	Locked P _Li ^k	Recorded P _Li ^k	Achieved P _Ei ^k
I	Expose Area 1	—	—	P _E1 ^I ≡ 0
II	Record L₁ ^II fringes	—	P _L1 ^II = Δβ + C	P _E1 ^II = Δβ
III	Expose Area 2	P _L1 ^III = P _L1 ^II	—	P _E1 ^III = Δβ, P _E2 ^III ≡ 0
IV	Transfer the locking (Record L₂ ^IV fringes)	P _L1 ^IV = P _L1 ^II	P _L2 ^IV = C	P _E1 ^IV = Δβ, P _E2 ^IV = 0
V	Expose Area 3	P _L2 ^V = P _L2 ^IV	—	P _E2 ^V = 0, P _E3 ^V ≡ 0

Substrate number	Area for generating L fringes		One ordinary area		Another ordinary area		Transmittivity of A₁
Substrate number	Duty Cycle	Height / nm	Duty Cycle	Height / nm	Duty Cycle	Height / nm	Transmittivity of A₁
1#	0.38^a	222^a	0.35^b	221^b	—	—	1.4%
2#	0.34	214	0.35	208	—	—	5%
3#	—	—	0.32^c	218^c	0.35^d	243^d	—
4#	—	—	0.32	223	0.32	219	—

Abstract

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Figures (4)

Tables (2)

Equations (6)

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