Abstract

We have obtained packetlike solutions to the free-space homogeneous-wave equation. These solutions are Gaussian Laguerre (or Hermite) beams that propagate in a straight line at a light velocity remaining focused for all time.

© 1984 Optical Society of America

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References

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  1. J. N. Brittingham, “Focus waves modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
    [CrossRef]
  2. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  3. A. E. Siegman, “Hermite–Gaussian functions of complex argument as optical beam eigenfunctions,” J. Opt. Soc. Am. 63, 1093–1094 (1973).
    [CrossRef]

1983 (1)

J. N. Brittingham, “Focus waves modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

1973 (1)

Brittingham, J. N.

J. N. Brittingham, “Focus waves modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

Siegman, A. E.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

J. Appl. Phys. (1)

J. N. Brittingham, “Focus waves modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (1)

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

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Equations (9)

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2 G ( x , y , z , t ) - 1 c 2 2 G t 2 ( x , y , z , t ) = 0 ,
G ( x , y , z , t ) = F ( x , y , z - c t ) exp [ - j K 2 ( z + c t ) ] + c . c . ,
T 2 F - 2 j ( K 2 ) ( F z - 1 c F t ) = 0 ,
z c = z - c t .
T 2 F ( x , y , z c ) - 2 j K F z c ( x , y , z c ) = 0 ,
F 0 , 0 = z 0 z c + j z 0 exp [ - j K 2 ρ 2 z c + j z 0 ]
F 0 , m ( ρ , z c ) = z 0 m F 0 , 0 L m [ j K 2 ρ 2 ( z c + j z 0 ) ] ( z c + j z 0 ) m ,
H z = z 0 2 exp [ - j K 2 ( z + c t ) ] exp [ - j K 2 ρ 2 ( z c + j z 0 ) ] ( z c + j z 0 ) 2 × [ 1 - j K 2 ρ 2 ( z c + j z 0 ) ] .
H z = exp [ - j K 2 ( z + c t ) ] F 0 , 1 ( ρ , z c ) ,

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