Abstract

Blazed reflection micro-Fresnel lenses and their use in an integrated focus sensor are proposed. Theoretical analysis indicates that the optical characteristics of reflection Fresnel lenses can be improved compared with a conventional transmission micro-Fresnel lens. These reflection Fresnel lenses were fabricated using electron-beam lithography and exhibited the diffraction-limited focusing characteristics with 71% high efficiency. The focus sensor has a folded optical path and includes a beam splitter integrated with thin film components, such as a reflection elliptical Fresnel lens and a quadrant photodetector. The reflection elliptical Fresnel lens in the focus sensor exhibiting excellent astigmatic characteristics agreed with the theoretical results, and the focus error signal was detected. This sensor can be developed as the optical head of an optical disk system.

© 1989 Optical Society of America

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References

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  1. H. Nishihara, T. Suhara, “Micro Fresnel Lenses,” Prog. Opt. 24, 3–37 (1987).
  2. T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Computer-Controlled Electron-Beam Writing System for Thin Film Micro-Optics,” J. Vac. Sci. Technol. B 5, 33–36 (1987).
    [CrossRef]
  3. T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-Apertured Micro-Fresnel Lens Arrays Fabricated by Electron-Beam Lithography,” Appl. Opt. 26, 587–591 (1987).
    [CrossRef] [PubMed]
  4. T. Shiono, K. Setsune, O. Yamazaki, “Elliptical Micro-Fresnel Lenses Fabricated by Electron-Beam Writing Technique,” Trans. IEICE Jpn. J70-C, 1044–1051 (1987).
  5. K. Ozawa, N. Takagi, K. Hiranaka, S. Yanagisawa, K. Asama, “Contact-Type Linear Sensor Using Amorphous Si Diode Array,” Jpn. J. Appl. Phys. Suppl. 22, 457–460 (1982).
  6. R. Petit, Ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

1987 (4)

H. Nishihara, T. Suhara, “Micro Fresnel Lenses,” Prog. Opt. 24, 3–37 (1987).

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Computer-Controlled Electron-Beam Writing System for Thin Film Micro-Optics,” J. Vac. Sci. Technol. B 5, 33–36 (1987).
[CrossRef]

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-Apertured Micro-Fresnel Lens Arrays Fabricated by Electron-Beam Lithography,” Appl. Opt. 26, 587–591 (1987).
[CrossRef] [PubMed]

T. Shiono, K. Setsune, O. Yamazaki, “Elliptical Micro-Fresnel Lenses Fabricated by Electron-Beam Writing Technique,” Trans. IEICE Jpn. J70-C, 1044–1051 (1987).

1982 (1)

K. Ozawa, N. Takagi, K. Hiranaka, S. Yanagisawa, K. Asama, “Contact-Type Linear Sensor Using Amorphous Si Diode Array,” Jpn. J. Appl. Phys. Suppl. 22, 457–460 (1982).

Asama, K.

K. Ozawa, N. Takagi, K. Hiranaka, S. Yanagisawa, K. Asama, “Contact-Type Linear Sensor Using Amorphous Si Diode Array,” Jpn. J. Appl. Phys. Suppl. 22, 457–460 (1982).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Hiranaka, K.

K. Ozawa, N. Takagi, K. Hiranaka, S. Yanagisawa, K. Asama, “Contact-Type Linear Sensor Using Amorphous Si Diode Array,” Jpn. J. Appl. Phys. Suppl. 22, 457–460 (1982).

Nishihara, H.

H. Nishihara, T. Suhara, “Micro Fresnel Lenses,” Prog. Opt. 24, 3–37 (1987).

Ozawa, K.

K. Ozawa, N. Takagi, K. Hiranaka, S. Yanagisawa, K. Asama, “Contact-Type Linear Sensor Using Amorphous Si Diode Array,” Jpn. J. Appl. Phys. Suppl. 22, 457–460 (1982).

Setsune, K.

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-Apertured Micro-Fresnel Lens Arrays Fabricated by Electron-Beam Lithography,” Appl. Opt. 26, 587–591 (1987).
[CrossRef] [PubMed]

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Computer-Controlled Electron-Beam Writing System for Thin Film Micro-Optics,” J. Vac. Sci. Technol. B 5, 33–36 (1987).
[CrossRef]

T. Shiono, K. Setsune, O. Yamazaki, “Elliptical Micro-Fresnel Lenses Fabricated by Electron-Beam Writing Technique,” Trans. IEICE Jpn. J70-C, 1044–1051 (1987).

Shiono, T.

T. Shiono, K. Setsune, O. Yamazaki, “Elliptical Micro-Fresnel Lenses Fabricated by Electron-Beam Writing Technique,” Trans. IEICE Jpn. J70-C, 1044–1051 (1987).

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Computer-Controlled Electron-Beam Writing System for Thin Film Micro-Optics,” J. Vac. Sci. Technol. B 5, 33–36 (1987).
[CrossRef]

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-Apertured Micro-Fresnel Lens Arrays Fabricated by Electron-Beam Lithography,” Appl. Opt. 26, 587–591 (1987).
[CrossRef] [PubMed]

Suhara, T.

H. Nishihara, T. Suhara, “Micro Fresnel Lenses,” Prog. Opt. 24, 3–37 (1987).

Takagi, N.

K. Ozawa, N. Takagi, K. Hiranaka, S. Yanagisawa, K. Asama, “Contact-Type Linear Sensor Using Amorphous Si Diode Array,” Jpn. J. Appl. Phys. Suppl. 22, 457–460 (1982).

Wasa, K.

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-Apertured Micro-Fresnel Lens Arrays Fabricated by Electron-Beam Lithography,” Appl. Opt. 26, 587–591 (1987).
[CrossRef] [PubMed]

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Computer-Controlled Electron-Beam Writing System for Thin Film Micro-Optics,” J. Vac. Sci. Technol. B 5, 33–36 (1987).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Yamazaki, O.

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-Apertured Micro-Fresnel Lens Arrays Fabricated by Electron-Beam Lithography,” Appl. Opt. 26, 587–591 (1987).
[CrossRef] [PubMed]

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Computer-Controlled Electron-Beam Writing System for Thin Film Micro-Optics,” J. Vac. Sci. Technol. B 5, 33–36 (1987).
[CrossRef]

T. Shiono, K. Setsune, O. Yamazaki, “Elliptical Micro-Fresnel Lenses Fabricated by Electron-Beam Writing Technique,” Trans. IEICE Jpn. J70-C, 1044–1051 (1987).

Yanagisawa, S.

K. Ozawa, N. Takagi, K. Hiranaka, S. Yanagisawa, K. Asama, “Contact-Type Linear Sensor Using Amorphous Si Diode Array,” Jpn. J. Appl. Phys. Suppl. 22, 457–460 (1982).

Appl. Opt. (1)

J. Vac. Sci. Technol. B (1)

T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Computer-Controlled Electron-Beam Writing System for Thin Film Micro-Optics,” J. Vac. Sci. Technol. B 5, 33–36 (1987).
[CrossRef]

Jpn. J. Appl. Phys. Suppl. (1)

K. Ozawa, N. Takagi, K. Hiranaka, S. Yanagisawa, K. Asama, “Contact-Type Linear Sensor Using Amorphous Si Diode Array,” Jpn. J. Appl. Phys. Suppl. 22, 457–460 (1982).

Prog. Opt. (1)

H. Nishihara, T. Suhara, “Micro Fresnel Lenses,” Prog. Opt. 24, 3–37 (1987).

Trans. IEICE Jpn. (1)

T. Shiono, K. Setsune, O. Yamazaki, “Elliptical Micro-Fresnel Lenses Fabricated by Electron-Beam Writing Technique,” Trans. IEICE Jpn. J70-C, 1044–1051 (1987).

Other (2)

R. Petit, Ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

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Figures (19)

Fig. 1
Fig. 1

Structure of the proposed reflection micro-Fresnel lens.

Fig. 2
Fig. 2

Cross-sectional views of (a) transmission and (b) reflection gratings with uniform period for the analysis of first-order diffraction efficiency.

Fig. 3
Fig. 3

Calculated first-order diffraction efficiency curves as a function of normalized grating period when θ = 0.

Fig. 4
Fig. 4

Calculated first-order diffraction efficiency curves as a function of incident angle when Λ/λ = 5.

Fig. 5
Fig. 5

Calculated first-order diffraction efficiency curves as a function of normalized maximum grating thickness when θ = 0 and Λ/λ = 5.

Fig. 6
Fig. 6

Calculated first-order diffraction efficiency and optimum grating thickness curves for the reflection grating with Ag as a function of normalized grating period when θ = 0. The dashed line shows the efficiency curve when LR/λ = 1/2n.

Fig. 7
Fig. 7

Layout of the proposed integrated focus sensor using a reflection elliptical Fresnel lens and a thin film quadrant photodetector.

Fig. 8
Fig. 8

Model for analysis of the optical characteristics of the focus sensor, where the configuration is simplified to the transmission inline type.

Fig. 9
Fig. 9

Fabrication process of the reflection micro-Fresnel lens.

Fig. 10
Fig. 10

Microphotograph of the circular reflection micro-Fresnel lens fabricated by electron-beam lithography and the metallic thin film deposition.

Fig. 11
Fig. 11

Cross-sectional SEM photograph of the reflection micro-Fresnel lens before deposition of the reflection layer.

Fig. 12
Fig. 12

Fabrication process of the quadrant a-Si thin film photodetector.

Fig. 13
Fig. 13

Photograph of the quadrant a-Si photodetector fabricated on the glass substrate. The photodetector has four 300- × 300-μm2 elements with a 3-μm cross-shaped gap.

Fig. 14
Fig. 14

Experimental arrangement for measuring the focusing characteristics of the circular reflection micro-Fresnel lens.

Fig. 15
Fig. 15

Light spot and intensity profile observed at the focal plane in the circular reflection micro-Fresnel lens. The measured FWHM spot size (3.3 μm) corresponds with the diffraction-limited spot size.

Fig. 16
Fig. 16

Experimental arrangement for measuring the astigmatic characteristics of the reflection elliptical micro-Fresnel lens in the focus sensor.

Fig. 17
Fig. 17

Photograph of the observed light spots at the detector plane in the focus sensor for various mirror displacements.

Fig. 18
Fig. 18

Measured and theoretical relationship between the mirror displacement and the FWHM spot size in the focus sensor.

Fig. 19
Fig. 19

Measured relationship between the mirror displacement and the output voltage curve obtained by the a-Si photodetector in the focus sensor. This shows the measured focus error signal.

Equations (25)

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Φ ( x , y ) = n k ( x 2 + f x 2 f x ) + n k ( y 2 + f y 2 f y ) ,
k = 2 π / λ ,
Φ F ( x , y ) = Φ ( x , y ) 2 m π ,
Φ F ( x , y ) = n k / 2 · ( x 2 / f x + y 2 / f y ) 2 m π , ( x / x m + 1 ) 2 + ( y / y m + 1 ) 2 1 ( x / x m ) 2 + ( y / y m ) 2 ,
x m = 2 m λ f x / n ,
y m = 2 m λ f y / n .
S x = 2 x M = 2 2 M λ f x / n ,
S y = 2 y M = 2 2 M λ f y / n .
e = 1 ( S y / S x ) 2
= 1 f y / f x .
L ( x , y ) = L R [ 1 Φ F ( x , y ) / 2 π ] ,
L R = λ / 2 n .
L T = λ / ( n 1 ) .
L R / L T = ( n 1 ) / 2 n
Δ E z ( x , y ) + n j k 2 E z ( x , y ) = 0 , j = 1 , 2 .
E z ( x , y ) = m = E m ( y ) exp ( j α m x ) .
k 2 ( x , y ) = m = ( k 2 ) m exp ( j m K x ) .
d 2 / d y 2 · E m = α m 2 E m p = ( k 2 ) m p E p .
Λ min / λ = 1 / N . A .
θ B = sin 1 ( λ / 2 n Λ ) .
P ( x , y ) = exp [ j k ( x 2 + y 2 ) 2 ( s f 1 ) + f 1 2 / Δ d 1 ] ,
U 2 ( x 2 , y 2 ) = ( j / λ l ) exp ( j k l ) U ( x , y ) × exp { j k / 2 l · [ ( x 2 x ) 2 + ( y 2 y ) 2 ] } d x d y ,
U ( x , y ) = { P ( x , y ) · exp [ j Φ F ( x , y ) ] , ( 2 x / S x ) 2 + ( 2 y / S y ) 2 1 , 0 , ( 2 x / S x ) 2 + ( 2 y / S y ) 2 > 1 .
I ( x 2 , y 2 ) = | U 2 ( x 2 , y 2 ) | 2 .
S F E = S 1 + S 3 S 2 S 4 ,

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