Abstract

Diffraction gratings are used in many optical systems as beam splitters. In these applications the diffraction grating must (1) have high diffraction efficiency and (2) produce uniform intensities in the central block of diffracted beams. High diffraction efficiency is attained by making the grating a phase grating. In this paper we discuss in some detail the use of pulse width modulation (PWM) and pulse position modulation (PPM) to create grating structures that produce uniform central diffracted beams. By using these modulation techniques and proper phase relief for the grating, the diffraction grating can have a diffraction efficiency of 70% or more. Some examples of multiple beam diffraction gratings produced by using PWM and PPM are shown.

© 1979 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. O. Bryngdahl, W.-H. Lee, J. Opt. Soc. Am. 64, 1606 (1974).
    [CrossRef]
  2. H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
    [CrossRef]
  3. L. B. Boivin, Appl. Opt. 11, 1782 (1972).
    [CrossRef] [PubMed]
  4. N. Aebischer, A. B. Agbani, Nouv. Rev. Opt. 6, 37 (1975).
    [CrossRef]
  5. B. J. Thompson, Appl. Opt. 15, 312 (1976).
    [CrossRef] [PubMed]
  6. P. Matthijsse, J. Opt. Soc. Am. 68, 733 (1978).
    [CrossRef]
  7. G. Bouwhuis Burgstede, Philips Tech. Rev. 33, 1861 (1973).
  8. G. Bouwhuis, J. J. M. Braat, Appl. Opt. 17, 1993 (1978).
    [CrossRef] [PubMed]
  9. D. R. Anderson, Proc. IRE 49, 357 (1961).
  10. A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, Opt. Commun. 8, 160 (1973).
    [CrossRef]

1978 (2)

1976 (1)

1975 (1)

N. Aebischer, A. B. Agbani, Nouv. Rev. Opt. 6, 37 (1975).
[CrossRef]

1974 (1)

1973 (2)

G. Bouwhuis Burgstede, Philips Tech. Rev. 33, 1861 (1973).

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, Opt. Commun. 8, 160 (1973).
[CrossRef]

1972 (1)

1971 (1)

H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

1961 (1)

D. R. Anderson, Proc. IRE 49, 357 (1961).

Aebischer, N.

N. Aebischer, A. B. Agbani, Nouv. Rev. Opt. 6, 37 (1975).
[CrossRef]

Agbani, A. B.

N. Aebischer, A. B. Agbani, Nouv. Rev. Opt. 6, 37 (1975).
[CrossRef]

Anderson, D. R.

D. R. Anderson, Proc. IRE 49, 357 (1961).

Boivin, L. B.

Bouwhuis, G.

Bouwhuis Burgstede, G.

G. Bouwhuis Burgstede, Philips Tech. Rev. 33, 1861 (1973).

Braat, J. J. M.

Bryngdahl, O.

Dammann, H.

H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Firester, A. H.

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, Opt. Commun. 8, 160 (1973).
[CrossRef]

Gortler, K.

H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Heller, M. E.

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, Opt. Commun. 8, 160 (1973).
[CrossRef]

Hoffman, D. M.

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, Opt. Commun. 8, 160 (1973).
[CrossRef]

James, E. A.

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, Opt. Commun. 8, 160 (1973).
[CrossRef]

Lee, W.-H.

Matthijsse, P.

Thompson, B. J.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

Nouv. Rev. Opt. (1)

N. Aebischer, A. B. Agbani, Nouv. Rev. Opt. 6, 37 (1975).
[CrossRef]

Opt. Commun. (2)

H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

A. H. Firester, D. M. Hoffman, E. A. James, M. E. Heller, Opt. Commun. 8, 160 (1973).
[CrossRef]

Philips Tech. Rev. (1)

G. Bouwhuis Burgstede, Philips Tech. Rev. 33, 1861 (1973).

Proc. IRE (1)

D. R. Anderson, Proc. IRE 49, 357 (1961).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Phase profile for a regular phase grating.

Fig. 2
Fig. 2

Nonlinear limiter for generating modulated pulses.

Fig. 3
Fig. 3

Two pulse width modulated gratings. The sinusoidal signal in (a) varies in the same direction as the carrier frequency. The sinusoidal signal in (b) varies to normal to the direction of the carrier and is clearly shown by the change in the width of the grating.

Fig. 4
Fig. 4

Pulse width modulated grating profile for producing five strong central diffracted beams.

Fig. 5
Fig. 5

Pulse phase modulated grating profile for producing nine strong central diffracted beams.

Fig. 6
Fig. 6

(a) Microphotograph of a phase grating etched on glass substrate, (b) the diffraction pattern of (a). Diffraction efficiency of the grating is 87%.

Fig. 7
Fig. 7

The computer calculated spectrum of the phase grating having the phase profile in Fig. 4. The vertical scale shows the diffraction efficiencies of each harmonic. The diffraction pattern below was obtained from an amplitude grating rather than from the correct phase grating.

Fig. 8
Fig. 8

Diffraction pattern of the grating structure in Fig. 3(b).

Fig. 9
Fig. 9

The diffraction pattern and the computer calculated spectrum of the grating in Fig. 5.

Fig. 10
Fig. 10

(a) Microphotograph of the grating in Fig. 5 after photoreduction by about 70 times, (b) shows the phase grating after it has been etched into a glass substrate, (c) the diffraction pattern of the phase grating.

Equations (23)

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

g ( x ) = [ 2 f ( x ) - 1 ] sin θ + i cos θ ,
f ( x ) = m = - ( sin π m q / π m ) ] exp ( i 2 π m x / T ) .
a 0 = ( 2 q - 1 ) sin θ + i cos θ .
a 1 = a - 1 = 2 ( sin π q / π ) sin θ .
a 0 ( 2 q - 1 ) ,
a 1 2 sin π q / π ,
η = 3 a 0 2 = 0.6627 ( or 66.27 % ) .
a 0 = i cos θ ,
a 1 = ( 2 / π ) sin θ .
d ( n - 1 ) / λ = θ / 180 ° ,
f ( x ) = m = [ sin π m q ( x ) / π m ] exp [ i m ϕ ( x ) ] .
q ( x ) = ½ + ¼ [ cos 2 π α X + cos ( 4 π α X + ψ ) ] ,
q ( x ) = ½ + β / 2 cos π x / T .
a 0 = ( 2 q - 1 ) sin θ + i cos θ = β cos π x / T sin θ + i cos θ ,
a 1 = 2 sin π q ( x ) / π sin θ = 2 π cos [ π β / 2 cos ( π x / T ) ] sin θ = [ 2 / π J 0 ( π β / 2 ) = 4 / π k = 1 J 2 k ( π β / 2 ) cos 2 k π x / T ] sin θ ,
β = 2 / π J 0 ( π β / 2 ) ,
tan θ = 2 / β             or             θ = 68 ° .
q ( x ) = 1 2 + [ β / ( 2 2 N ) ] m = 0 N - 1 cos ( 2 π m α x + ψ m ) .
a 0 ( x ) = [ β sin θ / 2 N ] m = 1 N - 1 cos ( 2 π m α x + ψ m ) + i cos θ ,
η = ( β 2 / 4 ) sin 2 θ + cos 2 θ .
ϕ ( x ) = 2 π x / T + β s ( x ) ,
cos ϕ ( x ) = [ 1 / 2 N ] m = 1 N C n cos ( 2 π m α x + ψ m ) ,
f ( x ) = q / 2 + m = 1 2 ( sin π m q / π m ) cos m ϕ ( x ) .

Metrics