Abstract

We describe optical disks that store data holographically in three dimensions by using either angle multiplexing or wavelength multiplexing. Data are stored and retrieved in parallel blocks or pages, and each page consists of approximately 106 bits. The storage capacity of such disks is derived as a function of disk thickness, pixel size, page size, and scanning parameters. The optimum storage density is approximately 120 bits/μm2.

© 1994 Optical Society of America

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References

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  1. P. J. Van Heerden, “Theory of optical information storage in solids,” Appl. Opt. 2, 393–400 (1963).
    [CrossRef]
  2. K. Bløtekjaer, “Limitations on holographic storage capacity of photochromic and photorefractive media,” Appl. Opt. 18, 57–67 (1979).
    [CrossRef] [PubMed]
  3. D. von der Linde, A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
    [CrossRef]
  4. J.-P. Huignard, J.-P. Herriau, F. Micheron, “Coherent selective erasure of superimposed volume holograms in LiNbO3,” Appl. Phys. Lett. 26, 256–258 (1975).
    [CrossRef]
  5. L. d’Auria, J.-P. Huignard, C. Slezak, E. Spitz, “Experimental holographic read-write memory using 3-D storage,” Appl. Opt. 13, 808–818 (1974).
    [CrossRef] [PubMed]
  6. Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
    [CrossRef]
  7. D. Psaltis, “Parallel optical memories,” Byte 17, 179–182 (1992).
  8. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  9. C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1–6 (1992).
    [CrossRef]
  10. F. H. Mok, “Applications of holographic storage in lithium niobate,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WE1.
  11. F. T. S. Yu, S. D. Wu, A. W. Mayers, S. M. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
    [CrossRef]
  12. G. A. Rakuljic, V. Leyva, A. Yariv, “Optical-data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
    [CrossRef] [PubMed]
  13. H.-Y. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1994).
  14. K. Curtis, G. W. Burr, D. Psaltis, “Comparison of angle-multiplexed, wavelength-multiplexed, and phase-coded holographic memories,” in Annual Meeting, Vol. 16 of 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper TuH3.
  15. F. Mok, D. Psaltis, G. Burr, “Spatial and angle multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 334–345 (1992).

1992 (3)

D. Psaltis, “Parallel optical memories,” Byte 17, 179–182 (1992).

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1–6 (1992).
[CrossRef]

G. A. Rakuljic, V. Leyva, A. Yariv, “Optical-data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
[CrossRef] [PubMed]

1991 (2)

F. T. S. Yu, S. D. Wu, A. W. Mayers, S. M. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

1979 (1)

1975 (2)

D. von der Linde, A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
[CrossRef]

J.-P. Huignard, J.-P. Herriau, F. Micheron, “Coherent selective erasure of superimposed volume holograms in LiNbO3,” Appl. Phys. Lett. 26, 256–258 (1975).
[CrossRef]

1974 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1963 (1)

Bløtekjaer, K.

Burr, G.

F. Mok, D. Psaltis, G. Burr, “Spatial and angle multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 334–345 (1992).

Burr, G. W.

K. Curtis, G. W. Burr, D. Psaltis, “Comparison of angle-multiplexed, wavelength-multiplexed, and phase-coded holographic memories,” in Annual Meeting, Vol. 16 of 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper TuH3.

Curtis, K.

K. Curtis, G. W. Burr, D. Psaltis, “Comparison of angle-multiplexed, wavelength-multiplexed, and phase-coded holographic memories,” in Annual Meeting, Vol. 16 of 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper TuH3.

d’Auria, L.

Glass, A. M.

D. von der Linde, A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
[CrossRef]

Gu, C.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1–6 (1992).
[CrossRef]

Herriau, J.-P.

J.-P. Huignard, J.-P. Herriau, F. Micheron, “Coherent selective erasure of superimposed volume holograms in LiNbO3,” Appl. Phys. Lett. 26, 256–258 (1975).
[CrossRef]

Hisamoto, D.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Hong, J.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1–6 (1992).
[CrossRef]

Huignard, J.-P.

J.-P. Huignard, J.-P. Herriau, F. Micheron, “Coherent selective erasure of superimposed volume holograms in LiNbO3,” Appl. Phys. Lett. 26, 256–258 (1975).
[CrossRef]

L. d’Auria, J.-P. Huignard, C. Slezak, E. Spitz, “Experimental holographic read-write memory using 3-D storage,” Appl. Opt. 13, 808–818 (1974).
[CrossRef] [PubMed]

Itoh, K.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Izawa, R.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Kaga, T.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Kawamoto, Y.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Kisu, T.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kume, E.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Leyva, V.

Li, H.-Y.

H.-Y. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1994).

Mayers, A. W.

F. T. S. Yu, S. D. Wu, A. W. Mayers, S. M. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

McMichael, I.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1–6 (1992).
[CrossRef]

Micheron, F.

J.-P. Huignard, J.-P. Herriau, F. Micheron, “Coherent selective erasure of superimposed volume holograms in LiNbO3,” Appl. Phys. Lett. 26, 256–258 (1975).
[CrossRef]

Mok, F.

F. Mok, D. Psaltis, G. Burr, “Spatial and angle multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 334–345 (1992).

Mok, F. H.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1–6 (1992).
[CrossRef]

F. H. Mok, “Applications of holographic storage in lithium niobate,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WE1.

Murai, F.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Nakagome, Y.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Nishida, T.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Psaltis, D.

D. Psaltis, “Parallel optical memories,” Byte 17, 179–182 (1992).

K. Curtis, G. W. Burr, D. Psaltis, “Comparison of angle-multiplexed, wavelength-multiplexed, and phase-coded holographic memories,” in Annual Meeting, Vol. 16 of 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper TuH3.

F. Mok, D. Psaltis, G. Burr, “Spatial and angle multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 334–345 (1992).

Rajan, S. M.

F. T. S. Yu, S. D. Wu, A. W. Mayers, S. M. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Rakuljic, G. A.

Saxena, R.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1–6 (1992).
[CrossRef]

Slezak, C.

Spitz, E.

Takeda, E.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Takeuchi, K.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Tanaka, H.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Van Heerden, P. J.

von der Linde, D.

D. von der Linde, A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
[CrossRef]

Watanabe, Y.

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

Wu, S. D.

F. T. S. Yu, S. D. Wu, A. W. Mayers, S. M. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Yariv, A.

Yu, F. T. S.

F. T. S. Yu, S. D. Wu, A. W. Mayers, S. M. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. (1)

D. von der Linde, A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
[CrossRef]

Appl. Phys. Lett. (1)

J.-P. Huignard, J.-P. Herriau, F. Micheron, “Coherent selective erasure of superimposed volume holograms in LiNbO3,” Appl. Phys. Lett. 26, 256–258 (1975).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Byte (1)

D. Psaltis, “Parallel optical memories,” Byte 17, 179–182 (1992).

IEEE J. Solid-State Circuits (1)

Y. Nakagome, H. Tanaka, K. Takeuchi, E. Kume, Y. Watanabe, T. Kaga, Y. Kawamoto, F. Murai, R. Izawa, D. Hisamoto, T. Kisu, T. Nishida, E. Takeda, K. Itoh, “An experimental 1.5-V 64-Mb DRAM,” IEEE J. Solid-State Circuits 26, 465–472 (1991).
[CrossRef]

J. Opt. Soc. Am. A (1)

C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1–6 (1992).
[CrossRef]

Opt. Commun. (1)

F. T. S. Yu, S. D. Wu, A. W. Mayers, S. M. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Opt. Lett. (1)

Other (4)

H.-Y. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1994).

K. Curtis, G. W. Burr, D. Psaltis, “Comparison of angle-multiplexed, wavelength-multiplexed, and phase-coded holographic memories,” in Annual Meeting, Vol. 16 of 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper TuH3.

F. Mok, D. Psaltis, G. Burr, “Spatial and angle multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 334–345 (1992).

F. H. Mok, “Applications of holographic storage in lithium niobate,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper WE1.

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Figures (10)

Fig. 1
Fig. 1

Three-dimensional holographic disk.

Fig. 2
Fig. 2

Recording geometry.

Fig. 3
Fig. 3

Angular multiplexing by reflection and transmission holograms from both sides of the signal beam.

Fig. 4
Fig. 4

Angle multiplexing: extra area taken up by defocusing and reference-beam angle change.

Fig. 5
Fig. 5

Angle multiplexing: N/A versus L for various values of θ2.

Fig. 6
Fig. 6

Angle multiplexing: optimum N/A (optimized with respect to δ) and N p as functions of thickness L.

Fig. 7
Fig. 7

Wavelength multiplexing: defocusing and wavelength change.

Fig. 8
Fig. 8

Wavelength multiplexing: optimum N/A (optimized with respect to δ) as a function of L for various values of λ21.

Fig. 9
Fig. 9

Wavelength multiplexing: optimum N/A and Nλ as functions of thickness L for λ21 = 1.08 and λ21 = 1.5.

Fig. 10
Fig. 10

Comparison of angle multiplexing and wavelength multiplexing. Here λ21 = 1.08, θ1 = 10°, and θ2 = 20°. The density when angle multiplexing is used is denoted by (N/A)θ, and the density when wavelength multiplexing is used is denoted by (N/A)λ.

Tables (1)

Tables Icon

Table 1 Value of Parameters used in Fig. 10a

Equations (52)

Equations on this page are rendered with MathJax. Learn more.

N = N s N θ N p 2 .
Δ θ R = 8 λ n π L cos θ S sin ( θ R + θ S ) ,
sin ( θ R + θ S ) Δ θ R = 8 λ n π L cos θ S ,
θ 1 θ 2 sin ( θ R + θ S ) d θ R = 8 λ ( N θ - 1 ) n π L cos θ S .
N θ = 1 + ( n π L 8 λ ) cos ( θ S + θ 1 ) - cos ( θ S + θ 2 ) cos θ S ,
N θ = 1 + ( n π L 8 λ ) cos θ 1 - cos θ 2 ,
N s = A a = A w w ,
w = N p δ + L tan θ = N p δ + L [ ( n δ / λ ) 2 - 1 ] 1 / 2 .
w = w + L tan θ 2 .
a = w w = w ( w + L tan θ 2 ) ,
N = A N p 2 N θ w w = A N p 2 1 + n π L 8 λ ( cos θ 1 - cos θ 2 ) { N p δ + L [ ( n δ / λ ) 2 - 1 ] 1 / 2 } { N p δ + L [ ( n δ / λ ) 2 - 1 ] 1 / 2 + L tan θ 2 }
w = λ N p n [ y 3 / 2 + c 3 / 2 ( y 3 - 1 ) 1 / 2 ] ,
y = ( n δ λ ) 2 / 3 ,
c = ( n L λ N p ) 2 / 3 .
y 3 = c y + 1.
y = 1 2 + ( 1 4 - c 3 27 ) 1 / 2 3 + 1 2 - ( 1 4 - c 3 27 ) 1 / 2 3 ,
δ o = λ n y 3 / 2 .
δ min = λ ( 4 z 2 + 1 ) ,
θ i = sin - 1 ( λ δ ) .
θ r = sin - 1 ( 1 n sin θ i ) , = sin - 1 ( λ n δ min ) .
L min = λ N p n ( y min 3 - 1 y min ) 3 / 2 ,
y min = ( n δ min λ ) 3 / 2 .
N / A = 1 δ min 2 1 + α x ( 1 + β x ) ( 1 + γ x ) ,
x = n L λ N p ,
α = π N p 8 ( cos θ 1 - cos θ 2 ) ,
β = 1 y min 3 / 2 ( y min 3 - 1 ) 1 / 2 ,
γ = β + tan θ 2 y min 3 .
N / A - 1 δ min 2 α / β γ [ ( 1 β - 1 α ) 1 / 2 + ( 1 γ - 1 α ) 1 / 2 ] 2 ,
L = L o = λ N p n { - 1 α + [ ( 1 β - 1 α ) 1 / 2 ( 1 γ - 1 α ) ] 1 / 2 } ,
N / A = ( n λ ) 2 1 + α c 3 / 2 [ y 3 / 2 + c 3 / 2 ( y 3 - 1 ) 1 / 2 ] [ y 3 / 2 + c 3 / 2 ( y 3 - 1 ) 1 / 2 + c 3 / 2 tan θ 2 ] .
N / A ( n λ ) 2 π N p ( cos θ 1 - cos θ 2 ) 16 tan θ 2 ( λ N p n L ) 1 / 2 .
N = N s N λ N p 2 ,
N s = A w 2 ,
w = N p δ + L [ ( n δ / λ 2 ) 2 - 1 ] 1 / 2
Δ ν = v c n L ,
N λ = 1 + ν 1 - ν 2 2 Δ ν = 1 + n L 2 ( 1 λ 1 - 1 λ 2 ) ,
N = A N p 2 1 + n L 2 ( 1 λ 1 - 1 λ 2 ) { N p δ + L [ ( n δ / λ 2 ) 2 - 1 ] 1 / 2 } 2 .
N / A = 1 1 δ min 2 1 + α x ( 1 + β x ) 2 ,
x = n L λ 2 N p ,
α = N p 2 ( λ 2 λ 1 - 1 ) ,
β = 1 y min 3 / 2 ( y min 3 - 1 ) 1 / 2 .
N / A = 1 δ min 2 α 2 4 β ( α - β ) ,
L = L o = λ 2 N p n ( - 2 α + 1 β ) .
N / A = ( n λ 2 ) 2 1 + α c 3 / 2 [ y 3 / 2 + c 3 / 2 ( y 3 - 1 ) 1 / 2 ] 2 ,
N / A n 2 N p 8 1 λ 2 ( 1 λ 1 - 1 λ 2 ) .
1 λ 2 ( 1 λ 1 - 1 λ 2 ) 1 4 λ 1 2 ,
λ 2 λ 1 = 2.
N / A n 2 N p 8 Δ λ λ 1 3 ,
N / A n 2 δ min 2 ( 1 λ 1 - 1 λ 2 ) L 1 λ 2 2 ( 1 λ 1 - 1 λ 2 ) ,
α x 1 β x .
L = L K = n N p δ min 2 4 λ 2 = 4 z 2 + 1 4 n λ 2 N p ,
N p = a δ = b δ .

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