Geometrical Aspects of Consistent Holographic Memory Design

P. Graf; M. Lang

doi:10.1364/AO.11.001382

Applied Optics
Vol. 11,
Issue 6,
pp. 1382-1388
(1972)
•https://doi.org/10.1364/AO.11.001382

Geometrical Aspects of Consistent Holographic Memory Design

P. Graf and M. Lang

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P. Graf and M. Lang, "Geometrical Aspects of Consistent Holographic Memory Design," Appl. Opt. 11, 1382-1388 (1972)

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Abstract

Based on results of diffraction theory, it is shown that the proportions of storage plate and detector matrix, respectively, page-composer, of a fast holographic mass memory are strongly coupled. A high capacity fast data store needs a large detector array. Optimized geometry results if storage plate and detector matrix have the same size. A square detector matrix, able to read about 10¹⁰ bits in an optimum designed memory, should have a diagonal extension of about 1 m.

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		$\frac{β λ \sqrt{N}}{2 α γ z}$
z	ψ_max	N = 10⁸ bits [cm]	N = 10⁹ bits [cm]	N = 10¹⁰ bits [cm]
$\sqrt{3}$	60°	2.3	7.1	23
1.00	45°	3.9	12.4	39
0.75	37°	5.2	16.5	52
$\frac{\sqrt{3}}{3}$	30°	6.8	21.5	68
0.40	22°	9.7	30.6	97

m² = 2×10⁴ bits
N [bits]	ψ_max	L₀ [cm]	M = D [cm]	n $[\frac{bits}{{mm}^{2}}]$	n_eff $[\frac{bits}{{mm}^{2}}]$	q [mm]	a [mm]	$\frac{Δ b}{b_{0}}$ [%]
10⁸	60°	2.6	4.5	2×10⁵	1×10⁵	0.23	0.18	700
	45°	7.8	7.8	6.6×10⁴	3.3×10⁴	0.39	0.31	183
	37°	13.9	104	3.6×10⁴	1.8×10⁴	0.52	0.41	96
	30°	23.5	13.6	2.2×10⁴	1.1×10⁴	0.68	0.54	54
	22°	48.0	19.4	106×10³	5.3×10³	0.97	0.77	26
10⁹	60°	8.3	14.3	2×10⁵	1×10⁵	0.72	0.18	700
	45°	24.8	24.8	6.6×10⁴	3.3×10⁴	1.24	0.31	183
	37°	44.2	33.1	3.6×10⁴	1.8×10⁴	1.66	0.41	96
	30°	74.5	43.0	2.2×10⁴	1.1×10⁴	2.15	0.54	54
	22°	152.0	61.3	10.6×10³	5.3×10³	3.07	0.77	26
10¹⁰	60°	26	45	2×10⁵	1×10⁵	2.25	0.18	700
	45°	78	78	6.6×10⁴	3.3×10⁴	3.91	0.31	183
	37°	139	104	3.6×10⁴	1.8×10⁴	5.20	0.41	96
	30°	235	136	2.2×10⁴	1.1×10⁴	6.80	0.54	54
	22°	480	194	106×10³	5.3×10³	9.70	0.77	26

N = 2 × 10⁷ bits ; m² = 2 × 10⁴ bits ; M = 45 mm
ψ_max	L₀	D	n	n_eff	q	a	$\frac{Δ b}{b_{0}}$
60°	1.7 cm	1.3 cm	$4.8 \times 10^{5} \frac{bits}{{mm}^{2}}$	$2.4 \times 10^{5} \frac{bits}{{mm}^{2}}$	0.23 mm	0.12 mm	700 %
45°	3.7 ″	2.9 ″	9.8×10⁴ ″	4.9×10⁴ ″	0.23 ″	0.25 ″	183 %
37°	6.2 ″	4.9 ″	3.4×10⁴ ″	1.7×10⁴ ″	0.23 ″	0.43 ″	96 %
30°	12 ″	9.5 ″	9.0×10³ ″	4.5×10³ ″	0.23 ″	0.83 ″	54 %
22°	150 ″	125 ″	44 ″	22 ″	0.23 ″	12 ″	26 %

N = 10⁸ bits ; m² = 2×10⁴ bits ; M = 45 mm
ψ_max	L₀	D	n	n_eff	q	a	$\frac{Δ b}{b_{0}}$
60°	2.6 cm	4.5 cm	$2 \times 10^{5} \frac{bits}{{mm}^{2}}$	$1 \times 10^{5} \frac{bits}{{mm}^{2}}$	0.23 mm	0.18 mm	700 %
45°	16.7 ″	28.8 ″	4.8×10³ ″	2.4×10³ ″	0.23 ″	1.15 ″	183 %
37°	CONDITION (37) NOT FULFILLED
30°
22°

N = 10¹⁰ bits ; m² = 2 × 10⁴ bits ; M = 50 cm
ψ_max	L₀	D	N	n_eff	q	a	$\frac{Δ b}{b_{0}}$
60°	26.4 cm	41.6 cm	20 × 10⁵ bits/mm²	1.2 × 10⁵ bits/mm²	2.5 mm	0.16 mm	700%
45°	115 cm	180 cm	1.2 × 10⁴ ″	6.1 × 10³ ″	2.5mm	0.72 ″	183 ″
37°	CONDITION (37) NOT FULFILLED
30°
22°

Abstract

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Applied Optics