Abstract

On the basis of the intensity-moment formalism, certain analytical relationships are obtained for both the angular domain and the size of a transverse region of the beam that ensure a power content of at least 75% of the total power. As an illustrative application, the analytical results are compared with the exact values (numerically computed) of the amplitude of a lowest-order Gaussian beam diffracted by slits.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1995 (1)

1993 (1)

1992 (1)

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[CrossRef]

1991 (2)

1982 (1)

1980 (1)

1970 (1)

Arias, M.

Belanger, P. A.

Carter, W. H.

Collins, S. A.

Marti´nez-Herrero, R.

Meji´as, P. M.

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, Kogakusha, Ltd., Tokyo, 1965).

Serna, J.

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

Weber, H.

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, 1027–1049 (1992).
[CrossRef]

Other (2)

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, Kogakusha, Ltd., Tokyo, 1965).

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Width Δ [see Eq. (8)] of a transverse region of the beam profile that ensures a power content of at least 75% of the total power. A lowest-order Gaussian beam is assumed to be normally incident on a centered slit whose half-width D takes the values (a) 0.5ω0, (b) ω0, and (c) 2ω0. The curves plot the function Δ(z) for different values of α. A comparison is made between Δ (calculated on the basis of the generalized intensity-moment formalism) and the exact value (numerically computed) of the transverse region where 75% of the total beam power is contained.

Equations (13)

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x2=1I0 -+x2|f|2dx,
u2=1k2I0 -D+D|f(x)|2dx+α|f(D)|2λ2I0D,
u2=-+u2|F(u)|2du-+|F(u)|2du,
W2pu2,
p=161+β|f(D)|2Dπ4I0,
fz(x)=iλz1/2-D+D×exp-ik2z(x2-2xy+y2)f(y)dy,
x2f(z)=x2f(z=0)+z2u2-2zkI0 Rei-D+Dxf(x)[f(x)]*dx,
Δ2(z)=px2f(z)
G(u)-D+D[f(x)-f(D)]exp(ikxu)dx=F(u)-2 f(D)sin kDuku,
1J0 R-Ω|F(u)|2du1J0 R-Ω2|G(u)|2du+1J0 R-Ω8|f(D)|2sin2 kDuk2u2 du,
R-Ω|G(u)|2du1W2 -+u2|G(u)|2duJ016.
R-Ωsin2 kDuk2u2 du=2W+sin2 kDuk2u2 du2k2WJ08(αβ)1/2|f(D)|2.
1J0 R-Ω|F(u)|2du18+1(αβ)1/2.

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