Abstract

The 3-D diffraction behavior of an optical recording is investigated using the rigorous mode approach. Relationships between desirable pit shapes, write-in conditions, and read-out characteristics are discussed.

© 1988 Optical Society of America

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References

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  1. A. Korpel, “Simplified Diffraction Theory of the Video Disk,” Appl. Opt. 17, 2037 (1978).
    [CrossRef] [PubMed]
  2. H. H. Hopkins, “Diffraction Theory of Laser Read-out Systems for Optical Video Discs,” J. Opt. Soc. Am. 69, 4 (1979).
    [CrossRef]
  3. P. Sheng, “Theoretical Considerations of Optical Diffraction from RCA VideoDisc Signals,” RCA Rev. 39, 512 (1978).
  4. A. B. Marchant, “Optical Disk Readout: a Model for Coherenl Scanning,” Appl. Opt. 21, 2085 (1982).
    [CrossRef] [PubMed]
  5. M. G. Moharam, T. K. Gaylord, “Coupled-Wave Analysis of Reflection Gratings,” Appl. Opt. 20, 240 (1981).
    [CrossRef] [PubMed]
  6. Z. Zylberberg, E. Marom, “Rigorous Coupled-Wave Analysis of Pure Reflection Gratings,” J. Opt. Soc. Am. 73, 392 (1983).
    [CrossRef]

1983

1982

1981

1979

1978

P. Sheng, “Theoretical Considerations of Optical Diffraction from RCA VideoDisc Signals,” RCA Rev. 39, 512 (1978).

A. Korpel, “Simplified Diffraction Theory of the Video Disk,” Appl. Opt. 17, 2037 (1978).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Three-dimensional geometric model.

Fig. 2
Fig. 2

Block diagram of the computer program.

Fig. 3
Fig. 3

Output intensity vs numerical aperture.

Fig. 4
Fig. 4

Output intensity vs wavelength.

Fig. 5
Fig. 5

Output intensity vs pit shape.

Equations (20)

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E i + E d = E p .
E z > = 1 λ 2 { + G ( α , β , x , z ) exp [ i k ( α x + β z 1 α 2 β 2 y ) ] d α d β + + D ( μ , υ , x , z ) × exp [ i k ( μ x + υ z + 1 μ 2 υ 2 y ) ] d μ d υ } ,
G ( α , β , x z ) = { exp [ i k ( α x + β z ) ] | α | η , | β | η 0 , other
E z < = m = 1 n = 0 C m n g m n ,
g m n = sin m π α ( x + a 2 ) cos n π b ( z + b 2 ) × sin [ k 1 ( m λ 2 a ) 2 ( n λ 2 b ) 2 ( y + h ) ]
S m ( x , a ) sin m π a ( x + a 2 ) , C n ( z , b ) cos n π b ( z + b 2 ) , Q ( m , n ) 1 ( m λ 2 a ) 2 ( n λ 2 b ) 2 ,
g m n = S m ( x , a ) C n ( z , b ) × sin [ k · Q ( m , n ) · ( y + h ) ] .
E z | y = 0 > = E z | y = 0 , < E z > / y | y = 0 = E z < / y | y = 0 ,
+ [ G ( α , β , x , z ) + D ( α , β , x , z ) ] × exp [ i k ( α x + β z ) ] d α d β = { m = 1 n = 0 C m n S m ( x , a ) C n ( z , b ) × sin [ k h Q ( m , n ) ] | x | a 2 , | z | b 2 , 0 other
+ [ G ( α , β , x , z ) D ( α , β , x , z ) ] × 1 α 2 β 2 exp [ i k ( α x + β z ) ] d α d β = i m = 1 n = 0 C m n S m ( x , a ) C n ( z , b ) × cos [ k h Q ( m , n ) ] · Q ( m , n ) ,
G ( μ , υ , x , z ) + D ( μ , υ , x , z ) = m n C m n sin [ k h Q ( m , n ) ] R m ( μ ) R ˆ n ( υ ) ,
R m ( μ ) = + S m ( x , a ) exp ( i k x μ ) d x , R ˆ n ( υ ) = + C n ( z , b ) exp ( i k z υ ) d z ,
+ [ G ( α , β , x , z ) D ( α , β , x , z ) ] × 1 p α 2 β 2 R * m ( α ) R ˆ * n ( β ) d α d β = i a b 4 λ 4 C m n Q ( m , n ) × cos [ k h Q ( m , n ) ] .
m n ( Ψ m n m n + δ m n m n T m n ) C m n = Φ m n ( x , z ) ,
Ψ m n m n = sin [ k h Q ( m , n ) ] × + 1 α 2 β 2 R m ( α ) R ˆ n ( β ) R * m ( α ) R ˆ * n ( β ) d α d β
Φ m n ( x , z ) = 2 + G ( α , β , x , z ) 1 α 2 β 2 R * m ( α ) R * n ( β ) d α d β
T m n = i a b 4 λ 4 Q ( m , n ) cos [ k h Q ( m , n ) ] , δ m n m n = { 1 m = m n = n 0 other .
I D = η + η | D ( μ , υ , x , z ) | 2 d μ d υ
I i = 1 + 1 | G ( α , β , x , z ) | 2 d α d β ,
I m n m n + 1 α 2 β 2 R m ( α ) R ˆ n ( β ) R * m ( α ) R ˆ * n ( β ) d α d β , I n m m n + R m ( α ) R ˆ n ( β ) R * i n ( α ) R ˆ * n ( β ) d α d β .

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