Abstract

This paper reports theoretical calculations of ray and wave aberrations of a focusing grating coupler (FGC) which is used as an objective in the integrated-optic disk pickup device proposed by the authors. Although a FGC is theoretically aberration free, characterizations of aberrations caused by fabrication errors are necessary to reproduce the device. Primary aberrations were discussed with ray aberrations, and astigmatism and coma were predicted to be essential and effective. The upper limits of allowable fabrication errors were estimated using the calculated results of wave aberrations. The calculation methods and results are basic and useful when designing various devices using the FGCs.

© 1987 Optical Society of America

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References

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  1. S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An Integrated-Optic Disk Pickup Device,” IEEE/OSA J. Lightwave Tech-nol. LT-4, 913 (1986).
    [CrossRef]
  2. T. Suhara, H. Nishihara, J. Koyama, “Waveguide Holograms: a New Approach to Hologram Integration,” Opt. Commun. 19, 353 (1976).
    [CrossRef]
  3. M. Miler, M. Skalsky, “Chirped and Curved Grating Coupler Focusing Both Outgoing Beam and Guided Wave,” Opt. Commun. 33, 13 (1980).
    [CrossRef]
  4. D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
    [CrossRef]
  5. T. Suhara, H. Nishihara, J. Koyama, “High-Performance Focusing Grating Coupler Fabricated by Electron-Beam Writing,” in Technical Digest of Topical Meeting on Integrated Guided-Wave Optics (Optical Society of America, Washington, DC, 1984), paper ThD4.
  6. G. Hatakoshi, H. Fujima, K. Goto, “Waveguide Grating Lenses for Optical Couplers,” Appl. Opt. 23, 1749 (1984).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), Chaps. 5 and 9.
  8. G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. V. Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Adam Hilger, Bristol, 1985), Chap. 2.

1986 (1)

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An Integrated-Optic Disk Pickup Device,” IEEE/OSA J. Lightwave Tech-nol. LT-4, 913 (1986).
[CrossRef]

1984 (1)

1981 (1)

D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

1980 (1)

M. Miler, M. Skalsky, “Chirped and Curved Grating Coupler Focusing Both Outgoing Beam and Guided Wave,” Opt. Commun. 33, 13 (1980).
[CrossRef]

1976 (1)

T. Suhara, H. Nishihara, J. Koyama, “Waveguide Holograms: a New Approach to Hologram Integration,” Opt. Commun. 19, 353 (1976).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), Chaps. 5 and 9.

Bouwhuis, G.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. V. Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Adam Hilger, Bristol, 1985), Chap. 2.

Braat, J.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. V. Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Adam Hilger, Bristol, 1985), Chap. 2.

Fujima, H.

Goto, K.

Hatakoshi, G.

Heitmann, D.

D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

Huijser, A.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. V. Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Adam Hilger, Bristol, 1985), Chap. 2.

Immink, K. S.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. V. Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Adam Hilger, Bristol, 1985), Chap. 2.

Koyama, J.

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An Integrated-Optic Disk Pickup Device,” IEEE/OSA J. Lightwave Tech-nol. LT-4, 913 (1986).
[CrossRef]

T. Suhara, H. Nishihara, J. Koyama, “Waveguide Holograms: a New Approach to Hologram Integration,” Opt. Commun. 19, 353 (1976).
[CrossRef]

T. Suhara, H. Nishihara, J. Koyama, “High-Performance Focusing Grating Coupler Fabricated by Electron-Beam Writing,” in Technical Digest of Topical Meeting on Integrated Guided-Wave Optics (Optical Society of America, Washington, DC, 1984), paper ThD4.

Miler, M.

M. Miler, M. Skalsky, “Chirped and Curved Grating Coupler Focusing Both Outgoing Beam and Guided Wave,” Opt. Commun. 33, 13 (1980).
[CrossRef]

Nishihara, H.

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An Integrated-Optic Disk Pickup Device,” IEEE/OSA J. Lightwave Tech-nol. LT-4, 913 (1986).
[CrossRef]

T. Suhara, H. Nishihara, J. Koyama, “Waveguide Holograms: a New Approach to Hologram Integration,” Opt. Commun. 19, 353 (1976).
[CrossRef]

T. Suhara, H. Nishihara, J. Koyama, “High-Performance Focusing Grating Coupler Fabricated by Electron-Beam Writing,” in Technical Digest of Topical Meeting on Integrated Guided-Wave Optics (Optical Society of America, Washington, DC, 1984), paper ThD4.

Ortiz, C.

D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

Pasman, J.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. V. Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Adam Hilger, Bristol, 1985), Chap. 2.

Rosmalen, G. V.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. V. Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Adam Hilger, Bristol, 1985), Chap. 2.

Skalsky, M.

M. Miler, M. Skalsky, “Chirped and Curved Grating Coupler Focusing Both Outgoing Beam and Guided Wave,” Opt. Commun. 33, 13 (1980).
[CrossRef]

Suhara, T.

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An Integrated-Optic Disk Pickup Device,” IEEE/OSA J. Lightwave Tech-nol. LT-4, 913 (1986).
[CrossRef]

T. Suhara, H. Nishihara, J. Koyama, “Waveguide Holograms: a New Approach to Hologram Integration,” Opt. Commun. 19, 353 (1976).
[CrossRef]

T. Suhara, H. Nishihara, J. Koyama, “High-Performance Focusing Grating Coupler Fabricated by Electron-Beam Writing,” in Technical Digest of Topical Meeting on Integrated Guided-Wave Optics (Optical Society of America, Washington, DC, 1984), paper ThD4.

Ura, S.

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An Integrated-Optic Disk Pickup Device,” IEEE/OSA J. Lightwave Tech-nol. LT-4, 913 (1986).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), Chaps. 5 and 9.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

D. Heitmann, C. Ortiz, “Calculation and Experimental Verification of Two-Dimensional Focusing Grating Couplers,” IEEE J. Quantum Electron. QE-17, 1257 (1981).
[CrossRef]

IEEE/OSA J. Lightwave Tech-nol. (1)

S. Ura, T. Suhara, H. Nishihara, J. Koyama, “An Integrated-Optic Disk Pickup Device,” IEEE/OSA J. Lightwave Tech-nol. LT-4, 913 (1986).
[CrossRef]

Opt. Commun. (2)

T. Suhara, H. Nishihara, J. Koyama, “Waveguide Holograms: a New Approach to Hologram Integration,” Opt. Commun. 19, 353 (1976).
[CrossRef]

M. Miler, M. Skalsky, “Chirped and Curved Grating Coupler Focusing Both Outgoing Beam and Guided Wave,” Opt. Commun. 33, 13 (1980).
[CrossRef]

Other (3)

T. Suhara, H. Nishihara, J. Koyama, “High-Performance Focusing Grating Coupler Fabricated by Electron-Beam Writing,” in Technical Digest of Topical Meeting on Integrated Guided-Wave Optics (Optical Society of America, Washington, DC, 1984), paper ThD4.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), Chaps. 5 and 9.

G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. V. Rosmalen, K. S. Immink, Principles of Optical Disc Systems (Adam Hilger, Bristol, 1985), Chap. 2.

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Figures (8)

Fig. 1
Fig. 1

Schematic view of an integrated-optic disk pickup device (IODPU). The guided wave diverging from the butt-coupled laser diode is diffracted and focused by an FGC into a point on a disk. The reflected wave is coupled back by the sae FGC and detected by a photodiode array in the waveguide.

Fig. 2
Fig. 2

Schematic view of the FGC used in the IODPU. The diffracted wave is spherical in the absence of fabrication errors.

Fig. 3
Fig. 3

Configurations of the FGC and wavefronts in the presence of aberrations. The diffracted wave is no longer a spherical wave.

Fig. 4
Fig. 4

Ray pattern calculation of the FGC having a square aperture.

Fig. 5
Fig. 5

Calculated ray patterns of the FGC where λ = 0.78 μm, N = 1.52, r = 20 mm, f = 3 mm, θ = 0, and Lx = Ly = 3 mm.

Fig. 6
Fig. 6

Ray pattern caused by astigmatism, (a) The focal length along the x axis does not coincide with that along the y axis, (b) The ray pattern diameter is proportional to that of the exit pupil aperture.

Fig. 7
Fig. 7

Ray patterns caused by coma, (a) Coma tails to the ΔY axis when C30 = C12 = 0. (b) Coma tails to a line inclined to both the ΔX axis and the ΔY axis in the general case.

Fig. 8
Fig. 8

Calculated root mean square deformations vs each kind of error for a FGC where (a) λ = 0.78 μm, N = 1.52, r = 20 mm, f = 3 mm, θ = 0, and Lx = Ly = 3 mm; (b) λ = 0.78 μm, N = 1.52, r = 10 mm, f = 2 mm, θ = 0, and Lx = Ly = 1 mm.

Equations (55)

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Φ FG = k x 2 + ( y f sin θ ) 2 + ( f cos θ ) 2 kN x 2 + ( y + r ) 2 = 2 m π + const .
Φ DF = Φ IN + Φ FG ,
Φ DF = k x 2 + ( y f sin θ ) 2 + ( f cos θ ) 2 ,
Φ A = Φ DF Φ G = Φ IN + Φ FG Φ G ,
Φ G = k ( x f x ) 2 + ( y f y ) 2 + f z 2 ,
Φ IN = k N ( x + r sin δ ) 2 + ( y + r cos δ ) 2 ,
Φ FG = k ( x / M x ) 2 + ( y / M y f sin θ ) 2 + ( f cos θ ) 2 kN ( x / M x ) 2 + ( y / M y + r ) 2 ,
Φ A = k N ( x + r sin δ ) 2 + ( y + r cos δ ) 2 k ( x / M x ) 2 + ( y / M y f sin θ ) 2 + ( f cos θ ) 2 kN ( x / M x ) 2 + ( y / M y + r ) 2 + k ( x f x ) 2 + ( y f y ) 2 + f z 2 .
Δ X = ( x f x ) 2 + ( y f y ) 2 + f z 2 k Φ A x ,
Δ Y = ( x f x ) 2 + ( y f y ) 2 + f z 2 k Φ A y .
Φ A = D 10 x + D 01 y + A 20 2 x 2 + A 11 xy + A 02 2 y 2 + C 30 3 x 3 + C 21 x 2 y + C 12 x y 2 + C 03 3 y 3 + S 40 4 x 4 + S 31 x 3 y + S 22 2 x 2 y 2 + S 13 x y 3 + S 04 4 y 4 +
D 10 = 0 ,
D 01 = 0 ,
A 20 = A 02 A 2 .
f x / f = N sin δ ,
f y / f = N cos δ ( k / k ) ( N sin θ ) / M y ,
f = f x 2 + f y 2 + f z 2 ,
f = k [ 1 + ( f z / f ) 2 ] k f ( 1 M x 2 + cos 2 θ M y 2 ) + kN M x 2 r k N r .
Φ A = A 2 2 ( x 2 y 2 ) + A 11 xy + C 30 3 x 3 + C 21 x 2 y + C 12 x y 2 + C 03 3 y 3 + S 40 4 x 4 + S 31 x 3 y + S 22 2 x 2 y 2 + S 13 x y 3 + S 04 4 y 4 .
Δ X = ( Φ G / k 2 ) ρ ( A 2 sin ψ + A 11 cos ψ ) ,
Δ Y = ( Φ G / k 2 ) ρ ( A 11 sin ψ A 2 cos ψ ) ,
x = ρ sin ψ , y = ρ cos ψ .
Δ X = ( Φ G / k 2 ) A 2 2 + A 11 2 ρ sin ψ ,
Δ Y = ± ( Φ G / k 2 ) A 2 2 + A 11 2 ρ cos ψ .
Δ X = ( Φ G / k 2 ) C 21 ρ 2 sin 2 ψ ,
Δ Y = Φ G k 2 ( C 03 + C 21 2 ρ 2 + C 03 C 21 2 ρ 2 cos 2 ψ ) .
Δ X = Φ G k 2 ( C 12 + C 30 2 ρ 2 + C 12 C 30 2 ρ 2 cos 2 ψ ) ,
Δ Y = ( Φ G / k 2 ) C 12 ρ 2 sin 2 ψ .
Δ X = ( Φ G / k 2 ) ( S 40 x 3 + 3 S 31 x 2 y + S 22 x y 2 + S 13 y 3 ) ,
Δ Y = ( Φ G / k 2 ) ( S 31 x 3 + S 22 x 2 y + 3 S 13 x y 2 + S 04 y 3 ) .
Δ Φ P = λ 2 π [ Φ A ( P ) ] 2 dS dS [ Φ A ( P ) dS dS ] 2 ,
RMSD < 0.07 λ
| Δ λ | < 9.8 × 10 4 ,
| Δ N | < 9.8 × 10 4 ,
| Δ r | < 3.0 × 10 3 ,
| δ | < 6.9 × 10 4 ,
| Δ L x | < 3.0 × 10 4 ,
| Δ L y | < 3.6 × 10 4 .
| Δ λ | < 8.6 × 10 3 ,
| Δ N | < 8.2 × 10 3 ,
| Δ r | < 1.4 × 10 2 ,
| δ | < 3.9 × 10 3 ,
| Δ L x | < 1.6 × 10 3 ,
| Δ L y | < 2.1 × 10 3 .
A 2 = k 1 + cos 2 θ ( N cos 2 θ r + 2 N sin θ 2 sin 2 θ f ) Δ λ + kN 1 + cos 2 θ ( 2 sin θ f + cos 2 θ r ) Δ N kN cos 2 θ ( 1 + cos 2 θ ) r Δ r + 2 k cos 2 θ 1 + cos 2 θ ( 1 f + N r ) Δ L x + 2 k ( N sin θ 1 ) ( 1 + cos 2 θ ) f Δ L y ,
A 11 = kN ( 1 r + sin θ f ) sin δ ,
C 30 = 3 kN 2 ( 1 f 2 1 r 2 ) sin δ ,
C 21 = k 2 ( 2 sin θ N f 2 + N sin θ f r + N r 2 ) Δ λ + kN 2 ( 1 f 2 1 r 2 sin θ f r ) Δ N + kN 2 r ( 2 r + sin θ f ) Δ r + kN r ( sin θ f 1 r ) Δ L x + k 2 ( N 2 sin θ f 2 N r 2 ) Δ L y ,
C 12 = kN 2 ( 1 f 2 + 2 r 2 ) sin δ ,
C 03 = 3 k 2 f ( 2 sin θ N f + N sin θ f ) Δ λ + 3 kN 2 f ( 1 f sin θ r ) Δ N + 3 kN sin θ 2 f r Δ r 3 k sin θ f ( 1 f + N r ) Δ L x + 3 kN 2 f 2 Δ L y ,
S 40 = k 2 ( N r 3 3 N 2 f 2 r 2 f 3 ) Δ λ + kN r 2 ( 3 2 f 2 1 r 2 ) Δ N + 3 kN 2 r ( 1 r 2 1 2 f 2 ) Δ r + k 2 ( 3 N f 2 r 1 f 3 4 N r 3 ) Δ L x + 3 k 2 f 3 Δ L y ,
S 31 = 3 kN 2 r 3 sin δ
S 22 = k ( 1 f 3 N r 3 + 3 N 4 f 2 r ) Δ λ + kN r ( 3 4 f 2 + 1 r 2 ) Δ N 3 kN r ( 1 4 f 2 + 1 r 2 ) Δ r + k 2 ( 1 f 3 + 4 N r 3 + 3 N f 2 r ) Δ L x + k 2 ( 1 f 3 + 4 N r 3 ) Δ L y ,
S 13 = kN r 3 sin δ ,
S 04 = k 2 f 2 ( 2 f + 3 N 2 r ) Δ λ + 3 kN 4 f 2 r Δ N 3 kN 4 f 2 r Δ r + 3 k 2 f 2 ( 1 f + N r ) Δ L x k 2 f 3 Δ L x .

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