Abstract

The propagation characteristics of the fundamental Gaussian laser beam in absorptive and active media are investigated. There is a general reduction in the spreading of the beam on propagation in both absorptive and active media. In addition, in an active medium there is a shift of the focal plane and a reduction in the waist size of the beam.

© 2004 Optical Society of America

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References

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  1. H. Kogelnik, Appl. Opt. 4, 1562 (1965).
    [CrossRef]
  2. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1978), Chap. 6, p. 230.
  3. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chaps. 1 and 6.
  4. S. R. Seshadri, J. Opt. Soc. Am. A 15, 2712 (1998).
    [CrossRef]

1998 (1)

1965 (1)

Kogelnik, H.

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1978), Chap. 6, p. 230.

Seshadri, S. R.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chaps. 1 and 6.

Appl. Opt. (1)

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

Other (2)

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1978), Chap. 6, p. 230.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chaps. 1 and 6.

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Equations (25)

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×E=ik0H,
×H=-ik0E,
=n2=r1+iσ/ω0r,
Ex=Fz, Ey=0, Ez=-Fx,
Hx=-1ik02Fxy, Hy=ik0-1ik02y2F, Hz=-1ik02Fyz,
2ρ2+1ρρ+2z2+k02Fρ,z=0.
Fρ,z=expik0nzfρ,z.
2ρ2+1ρρ+2ik0nzfρ,z=0.
fρ,0=Nik0nexp-ρ2w02,
fρ,z=Nik0n11+iz/bexp-ρ2w021+iz/b,
b=1/2k0nw02.
Fρ,z=expik0nzNik0n1+iz/bexp-ρ2w021+iz/b.
Exρ,z=Hyρ,zn=expik0nzN1+iz/bexp-ρ2w021+iz/b.
S=zˆSz=zˆc2ReExHy*,
Szρ,z=c2nrN2exp-2k0nizpzexp-2qzρ2w02pz,
n=nr+ini.
b=b0nr+ini,
pz=1+2nizn2b0+z2n2b02,
qz=1+nizn2b0.
N=4/cnrπw021/2.
Pz=0dρ2πρSzρ,z=exp-2k0nizqz.
-Pzz=Pz2k0ni1+1k02w02n2+niz/b0.
ρ2av=1Pz2π0dρρρ2Szρ,z=w022pzqz.
ρ2av=w0221+z2nr2b02, ni=0.
ρ2avmin=w0221-ni24nr2,

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