Abstract

An xyz beam splitter is described that uses a diffraction grating upon which light is incident in a plane parallel to the grating grooves to produce symmetric conical diffraction into the ±1 orders, with all higher orders being suppressed or evanescent. The ±1 orders are mutually orthogonal when the wavelength/grating period ratio λ/Λ=1/2, independent of the angle of incidence ϕ. Orthogonality of, the ±1 orders with the direction of incidence occurs at ϕ=arctan(1/2)=35.264°. By choice of a symmetric triangular-groove profile (isoceles with a 120° apex angle), bidirectional blazing occurs into the desired ±1 orders, with little or no light appearing in the vestigial 0 order.

© 1993 Optical Society of America

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References

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  1. J. T. Luxon, D. E. Parker, Industrial Lasers and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1985), Chap. 9.
  2. C. Barns, Exp. Tech. 14 (4), 49 (1990).
    [CrossRef]
  3. G. H. Spencer, M. V. R. K. Murty, J. Opt. Soc. Am. 52, 672 (1962).
    [CrossRef]
  4. M. Nevière, D. Maystre, W. R. Hunter, J. Opt. Soc. Am. 68, 1106 (1978).
    [CrossRef]
  5. R. A. Depine, Opt. Lett. 16, 1457 (1991).
    [CrossRef] [PubMed]
  6. E. N. Hogert, M. A. Rebollo, N. G. Gaggioli, Opt. Laser Technol. 23, 341 (1991).
    [CrossRef]
  7. For q=12, the orthogonal ±1 orders graze parallel to the grating surface when ϕ = 45° and become evanescent at higher angles.
  8. G. W. Stroke, in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1967), Vol. 29, pp. 426–754.
    [CrossRef]
  9. A. A. Spikhal'skii, Opt. Laser Technol. 21, 395 (1989).
    [CrossRef]
  10. R. M. A. Azzam, N. M. Bashara, Phys. Rev. B 12, 4721 (1972).
    [CrossRef]
  11. T. K. Gaylord, M. G. Moharam, Proc. IEEE. 73, 894 (1985).
    [CrossRef]

1991 (2)

E. N. Hogert, M. A. Rebollo, N. G. Gaggioli, Opt. Laser Technol. 23, 341 (1991).
[CrossRef]

R. A. Depine, Opt. Lett. 16, 1457 (1991).
[CrossRef] [PubMed]

1990 (1)

C. Barns, Exp. Tech. 14 (4), 49 (1990).
[CrossRef]

1989 (1)

A. A. Spikhal'skii, Opt. Laser Technol. 21, 395 (1989).
[CrossRef]

1985 (1)

T. K. Gaylord, M. G. Moharam, Proc. IEEE. 73, 894 (1985).
[CrossRef]

1978 (1)

1972 (1)

R. M. A. Azzam, N. M. Bashara, Phys. Rev. B 12, 4721 (1972).
[CrossRef]

1962 (1)

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Phys. Rev. B 12, 4721 (1972).
[CrossRef]

Barns, C.

C. Barns, Exp. Tech. 14 (4), 49 (1990).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Phys. Rev. B 12, 4721 (1972).
[CrossRef]

Depine, R. A.

Gaggioli, N. G.

E. N. Hogert, M. A. Rebollo, N. G. Gaggioli, Opt. Laser Technol. 23, 341 (1991).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord, M. G. Moharam, Proc. IEEE. 73, 894 (1985).
[CrossRef]

Hogert, E. N.

E. N. Hogert, M. A. Rebollo, N. G. Gaggioli, Opt. Laser Technol. 23, 341 (1991).
[CrossRef]

Hunter, W. R.

Luxon, J. T.

J. T. Luxon, D. E. Parker, Industrial Lasers and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1985), Chap. 9.

Maystre, D.

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, Proc. IEEE. 73, 894 (1985).
[CrossRef]

Murty, M. V. R. K.

Nevière, M.

Parker, D. E.

J. T. Luxon, D. E. Parker, Industrial Lasers and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1985), Chap. 9.

Rebollo, M. A.

E. N. Hogert, M. A. Rebollo, N. G. Gaggioli, Opt. Laser Technol. 23, 341 (1991).
[CrossRef]

Spencer, G. H.

Spikhal'skii, A. A.

A. A. Spikhal'skii, Opt. Laser Technol. 21, 395 (1989).
[CrossRef]

Stroke, G. W.

G. W. Stroke, in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1967), Vol. 29, pp. 426–754.
[CrossRef]

Exp. Tech. (1)

C. Barns, Exp. Tech. 14 (4), 49 (1990).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Laser Technol. (2)

E. N. Hogert, M. A. Rebollo, N. G. Gaggioli, Opt. Laser Technol. 23, 341 (1991).
[CrossRef]

A. A. Spikhal'skii, Opt. Laser Technol. 21, 395 (1989).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

R. M. A. Azzam, N. M. Bashara, Phys. Rev. B 12, 4721 (1972).
[CrossRef]

Proc. IEEE. (1)

T. K. Gaylord, M. G. Moharam, Proc. IEEE. 73, 894 (1985).
[CrossRef]

Other (3)

J. T. Luxon, D. E. Parker, Industrial Lasers and Their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1985), Chap. 9.

For q=12, the orthogonal ±1 orders graze parallel to the grating surface when ϕ = 45° and become evanescent at higher angles.

G. W. Stroke, in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1967), Vol. 29, pp. 426–754.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Symmetrical conical diffraction geometry for the xyz beam splitter in which x coincides with the direction of the incident beam i and y and z correspond to the +1 and −1 diffracted orders, respectively.

Fig. 2
Fig. 2

Diagram of wave vector components parallel to the grating surface.

Fig. 3
Fig. 3

Angle β between the plane of the ± 1 orders and the grating plane as a function of the angle of incidence ϕ for different values of q.

Fig. 4
Fig. 4

Bidirectional blazing by use of a symmetric triangular-groove-profile grating, (b) Cross-sectional view showing the unit vectors normal to the groove facets.

Equations (18)

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k + 1 s = k is + k , k 1 s = k is k ,
k is = ( k sin ϕ ) a x k = 2 π / λ , K = ( 2 π / Λ ) a y .
a i = ( sin ϕ , 0 , cos ϕ ) ,
a ± 1 = [ sin ϕ , ± q , ( cos 2 ϕ q 2 ) 1 / 2 ] ,
q = K / k = λ / Λ .
cos θ ± 1 = a + 1 a 1 = 1 2 q 2 .
cos β = a z ( a 1 × a + 1 ) / ( a 1 × a + 1 ) | ,
cos β = sin ϕ / ( 1 q 2 ) 1 / 2 .
tan ϕ = ( 1 q 2 ) 1 / 2 .
ϕ = arctan1 ( 1 2 ) = 35.264 °
k 2 s 2 = k 2 sin 2 ϕ + 4 K 2 = k 2 sin 2 ϕ + 2 k 2 > k s 2 .
a n 1 = ( 0 , sin α , cos α ) , a n 2 = ( 0 , sin α , cos α ) .
a n 1 ( a i ) = a n 2 ( a i ) = cos 45 ° .
cos α cos ϕ = 1 2 .
( a i × a n 1 ) ( a i × a n 2 ) = 0 .
cos 2 α ( 2 cos 2 ϕ ) = 1 .
cos ϕ = 2 / 3 , cos α = 3 / 2 .
γ = 180 ° 2 α = 120 ° .

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