Abstract

The recently calculated high diffraction efficiencies for TE- and TM-polarized light (perfect blaze) for echelette gratings are explained by four-wave interference, which is formed as a double periodical pattern in the cross section of the grating plane. The blazed grating profile should match this interference pattern for a single reference light wavelength. The recently published data are the special case of a general design. The prognoses of the model are connected with large grating constants in comparison with the light wavelength, where short grating constants need comparison with numerical methods.

© 2012 Optical Society of America

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References

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  1. B. H. Kleemann, Opt. Lett. 37, 1002 (2012).
    [CrossRef]
  2. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  3. R. Güther and B. H. Kleemann, “Optical grating for Littrow mounting,” pending patent (submitted May2012).
  4. E. Popov, L. Tsonev, and D. Maystre, J. Mod. Opt. 37, 367 (1990).
    [CrossRef]
  5. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, 1980), pp. 176–201.
  6. H. P. Herzig, ed., Micro-optics, Elements, Systems and Applications (Taylor & Francis, 1997).

2012 (1)

1990 (1)

E. Popov, L. Tsonev, and D. Maystre, J. Mod. Opt. 37, 367 (1990).
[CrossRef]

Güther, R.

R. Güther and B. H. Kleemann, “Optical grating for Littrow mounting,” pending patent (submitted May2012).

Herzig, H. P.

H. P. Herzig, ed., Micro-optics, Elements, Systems and Applications (Taylor & Francis, 1997).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Kleemann, B. H.

B. H. Kleemann, Opt. Lett. 37, 1002 (2012).
[CrossRef]

R. Güther and B. H. Kleemann, “Optical grating for Littrow mounting,” pending patent (submitted May2012).

Maystre, D.

E. Popov, L. Tsonev, and D. Maystre, J. Mod. Opt. 37, 367 (1990).
[CrossRef]

Petit, R.

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, 1980), pp. 176–201.

Popov, E.

E. Popov, L. Tsonev, and D. Maystre, J. Mod. Opt. 37, 367 (1990).
[CrossRef]

Tsonev, L.

E. Popov, L. Tsonev, and D. Maystre, J. Mod. Opt. 37, 367 (1990).
[CrossRef]

J. Mod. Opt. (1)

E. Popov, L. Tsonev, and D. Maystre, J. Mod. Opt. 37, 367 (1990).
[CrossRef]

Opt. Lett. (1)

Other (4)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

R. Güther and B. H. Kleemann, “Optical grating for Littrow mounting,” pending patent (submitted May2012).

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, 1980), pp. 176–201.

H. P. Herzig, ed., Micro-optics, Elements, Systems and Applications (Taylor & Francis, 1997).

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Figures (2)

Fig. 1.
Fig. 1.

Profile of an echelle blaze grating with 90° apex angle in a rotated reference system with four waves connected with Littrow mounting.

Fig. 2.
Fig. 2.

Symbolical draft of a two-dimensional pattern of interference fringes with different matching blaze profiles. The ellipses symbolize a rotated rectangular cos2(x) cos2(y) pattern after Eq. (4).

Tables (1)

Tables Icon

Table 1. Perfect Blazing, Found by Numerical Calculation [1], in Comparison with the Interference Fringes Based Design and a Further Two-Wavelength Usable Example

Equations (15)

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φ=(π/4)(α/2).
rTE(Θi)=cos(Θi)n^2sin2(Θi)cos(Θi)+n^2sin2(Θi)
rTM(Θi)=n^2cos(Θi)n^2sin2(Θi)n^2cos(Θi)+n^2sin2(Θi)
ITE,TM(x,y)=16cos2[kcos(φ)x+arg(rTE,TM(φ))/2]cos2[ksin(φ)y+arg(rTE,TM((π/2)φ))/2]
xp=λ0/(2cos(φ))
yp=λ0/(2sin(φ)).
x0=λ0[1arg(rTE,TM(φ))/π]/[4cos(φ)]
y0=λ0[1arg(rTE,TM(π/2φ))/π]/[4sin(φ)]
M=a/yp,
N=b/xp.
L=2gsin(α)/λ0.
M=sin2(φ)L/cos(2φ),
N=cos2(φ)L/cos(2φ),
φ=arccos[L/(M+N)]/2.
L=NM.

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