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References

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  1. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, and Winston, New York, 1972), p. 59.
  2. D. R. Tomkins, P. F. Rodney, Phys. Rev. A: 12, 599 (1975).
    [CrossRef]
  3. H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  4. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955), pp. 60–69.
  5. W. H. Carter, J. Opt. Soc. Am. 62, 1195 (1972).
    [CrossRef]
  6. R. N. Bracewell, The Fourier Transformation and Its Applications (McGraw-Hill, New York, 1978), pp. 160–163.
  7. W. H. Carter, Opt. Acta 21, 871 (1974).
    [CrossRef]

1975 (1)

D. R. Tomkins, P. F. Rodney, Phys. Rev. A: 12, 599 (1975).
[CrossRef]

1974 (1)

W. H. Carter, Opt. Acta 21, 871 (1974).
[CrossRef]

1972 (1)

1966 (1)

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transformation and Its Applications (McGraw-Hill, New York, 1978), pp. 160–163.

Carter, W. H.

Kogelnik, H.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Li, T.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Rodney, P. F.

D. R. Tomkins, P. F. Rodney, Phys. Rev. A: 12, 599 (1975).
[CrossRef]

Schiff, L. I.

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955), pp. 60–69.

Tomkins, D. R.

D. R. Tomkins, P. F. Rodney, Phys. Rev. A: 12, 599 (1975).
[CrossRef]

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, and Winston, New York, 1972), p. 59.

J. Opt. Soc. Am. (1)

Opt. Acta (1)

W. H. Carter, Opt. Acta 21, 871 (1974).
[CrossRef]

Phys. Rev. A (1)

D. R. Tomkins, P. F. Rodney, Phys. Rev. A: 12, 599 (1975).
[CrossRef]

Proc. IEEE (1)

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Other (3)

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955), pp. 60–69.

R. N. Bracewell, The Fourier Transformation and Its Applications (McGraw-Hill, New York, 1978), pp. 160–163.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, and Winston, New York, 1972), p. 59.

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Figures (3)

Fig. 1
Fig. 1

Gaussian beam propagating along the z axis.

Fig. 2
Fig. 2

Plots of H n 2 ( ξ ) exp ( ξ 2 ) for n = 0, 1, 2, 3, and 10 indicating the domain inside the rectangular spot where −(2l + 1)1/2ξ ≤ (2l + 1) 1/2 (Ref. 1, Figs. 3 and 4).

Fig. 3
Fig. 3

Fractional beam energy concentrated inside the rectangular spot as a function of m and n for a Hermite Gaussian beam.

Equations (13)

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I ( x , y , z ) = I 0 σ x ( 0 ) σ y ( 0 ) σ x ( z ) σ y ( z ) H m 2 ( x σ x ( z ) ) H n 2 ( y σ y ( z ) ) × exp ( x 2 σ x 2 y 2 σ y 2 ) ,
σ s ( z ) = σ s ( 0 ) ( 1 + z 2 z 0 s 2 ) 1 / 2 ,
z 0 s = 2 π λ σ s 2 ( 0 ) ,
σ s 2 ( z ) l = 2 s 2 I ( x , y , z ) d x d y I ( x , y , z ) d x d y .
σ s 2 ( z ) l = 2 s 2 H l 2 [ s σ s ( z ) ] exp [ s 2 σ s 2 ( z ) ] d s H l 2 [ s σ s ( z ) ] exp [ s 2 σ s 2 ( z ) ] d s ,
H l 2 [ s σ s ( z ) ] exp [ s 2 σ s 2 ( z ) ] d s = 2 l ( π ) 1 / 2 l ! σ s ( z ) ,
s 2 H l 2 [ s σ s ( z ) ] exp [ s 2 σ s 2 ( z ) ] d s = 2 l ( π ) 1 / 2 l ! σ s 3 ( z ) ( l + 1 2 ) .
σ s ( z ) l = σ s ( z ) ( 2 l + 1 ) 1 / 2 .
σ s ( z ) l = σ s ( 0 ) ( 2 l + 1 ) 1 / 2 ( 1 + z 2 / z o s 2 ) 1 / 2 .
σ s ( ) ( z ) z λ 2 π σ s ( 0 ) ( 2 l + 1 ) 1 / 2 ,
sin θ s l = λ 2 π σ s ( 0 ) ( 2 l + 1 ) 1 / 2
σ s ( 0 ) l sin θ s l = λ 2 π ( 2 l + 1 ) ,
σ s ( 0 ) l sin θ s l λ 2 π .

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