Abstract

It shown how cosine-Gauss and Bessel–Gauss beams can be generated using the complex source point theory. Paraxial beams are treated first. An analytic expression is derived for the nonparaxial cosine-Gaussian beam, based on the complex source point approach, and numerical results are presented to illustrate its behavior. A way to generate nonparaxial Bessel–Gauss beams is also indicated.

© 2013 Optical Society of America

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References

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  2. G. Goubau and F. Schwering, IEEE Trans. Antennas Propag. 9, 248 (1961).
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  12. C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
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    [CrossRef]

2011 (1)

2009 (1)

2007 (1)

2005 (1)

2002 (1)

2001 (1)

1999 (2)

1998 (1)

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

1997 (1)

1994 (1)

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

1992 (1)

A. W. Lohmann, Optik 89, 93 (1992).

1987 (1)

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

1981 (1)

M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355(1981).
[CrossRef]

1979 (1)

A. L. Cullen and P. K. Yu, Proc. R. Soc. Lond. Ser. A 366, 155 (1979).
[CrossRef]

1978 (1)

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

1977 (1)

1973 (1)

1971 (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

1966 (1)

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

1964 (1)

A. G. van Nie, Philips Res. Rep. 19, 378 (1964).

1962 (1)

G. D. Boyd and H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).

1961 (1)

G. Goubau and F. Schwering, IEEE Trans. Antennas Propag. 9, 248 (1961).
[CrossRef]

1960 (1)

G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1960).

April, A.

Bandres, M. A.

Belanger, P.-A.

M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355(1981).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

Borghi, R.

Boyd, G. D.

G. D. Boyd and H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).

G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1960).

Casperson, L. W.

Couture, M.

M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355(1981).
[CrossRef]

Cullen, A. L.

A. L. Cullen and P. K. Yu, Proc. R. Soc. Lond. Ser. A 366, 155 (1979).
[CrossRef]

Deschamps, G. A.

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

Felsen, L.

Gordon, J. P.

G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1960).

Gori, F.

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Goubau, G.

G. Goubau and F. Schwering, IEEE Trans. Antennas Propag. 9, 248 (1961).
[CrossRef]

Guatteri, G.

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Gutiérrez-Vega, J. C.

Hall, D. G.

Kogelnik, H.

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

G. D. Boyd and H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).

Li, T.

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

Lohmann, A. W.

A. W. Lohmann, Optik 89, 93 (1992).

Padovani, C.

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Porras, M. A.

Saghafi, S.

Santarsiero, M.

Schwering, F.

G. Goubau and F. Schwering, IEEE Trans. Antennas Propag. 9, 248 (1961).
[CrossRef]

Seshadri, S. R.

Sheppard, C. J. R.

Shin, S. Y.

Siegman, A. E.

Tovar, A. A.

van Nie, A. G.

A. G. van Nie, Philips Res. Rep. 19, 378 (1964).

Wilson, T.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

Yu, P. K.

A. L. Cullen and P. K. Yu, Proc. R. Soc. Lond. Ser. A 366, 155 (1979).
[CrossRef]

Bell Syst. Tech. J. (2)

G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1960).

G. D. Boyd and H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).

Electron. Lett. (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

IEE J. Microwaves Opt. Acoust. (1)

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

G. Goubau and F. Schwering, IEEE Trans. Antennas Propag. 9, 248 (1961).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (6)

J. Phys. A (1)

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

Opt. Commun. (1)

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optik (1)

A. W. Lohmann, Optik 89, 93 (1992).

Philips Res. Rep. (1)

A. G. van Nie, Philips Res. Rep. 19, 378 (1964).

Phys. Rev. A (2)

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355(1981).
[CrossRef]

Proc. IEEE (1)

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

Proc. R. Soc. Lond. Ser. A (1)

A. L. Cullen and P. K. Yu, Proc. R. Soc. Lond. Ser. A 366, 155 (1979).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Intensity in the waist region for cosine-Gauss beams for μz=1/2. The waist is shown in (a) and (b), and the azimuthal plane y=0 in (c) and (d). (a) and (c) are for kR0=5, while (b) and (d) are for kR0=2.

Fig. 2.
Fig. 2.

Polar plots of the radiation pattern of intensity in the far field in the meridional plane η=0, for the case when μz=1/2. (a) kR0=5, (b) kR0=2, and (c) kR0=1. The intensity is normalized to unity in the forward direction.

Fig. 3.
Fig. 3.

Phase along the axis for cosine-Gauss beams, with kz suppressed.

Equations (18)

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U=exp(ikR)R,
R2=(ziz0)2+(xix0)2+(yiy0)2.
U=eikzekz0kz0(1+iZ)exp[k(x02+y02)2z0(1+iZ)]exp[k(x2+y2)2z0(1+iZ)]×exp[ik(x0x+y0y)z0(1+iZ)],
U=eikz1+iZexp[ik(x0x+y0y)z0(1+iZ)]exp[k(x2+y2)2z0(1+iZ)]×exp[ikZ(x02+y02)2z0(1+iZ)].
U=eikz1+iZcos[k(x0x+y0y)z0(1+iZ)]exp[k(x2+y2)2z0(1+iZ)]×exp[ikZ(x02+y02)2z0(1+iZ)],
U=eikz1+iZcos[kx0xz0(1+iZ)]×exp[k(x2+iZx02)2z0(1+iZ)]exp[ky22z0(1+iZ)].
U=eikz1+iZcos[kx0xz0(1+iZ)]exp[k(x2+iZx02)2z0(1+iZ)]×cos[ky0yz0(1+iZ)]exp[k(y2+iZy02)2z0(1+iZ)],
Jn(x)=in2π02πexp(ixcosθ)exp(inθ)dθ,
U=ineikz1+iZJn[kaρz0(1+iZ)]exp[kρ2+ikZa22z0(1+iZ)]e±inϕ.
U=sinkRR=ksinh(ikR)ikR,
ikR=k[(x02+y02+z02)(x2+y2+z2)+2i(x0x+y0y+z0z)]1/2.
R0=(x02+y02+z02)1/2,
ikR=kR0[1(ξ2+η2+ζ2)+2i(μxξ+μyη+μzζ)]1/2=kR0S,
S=[1(ξ2+η2+ζ2)+2i(μxξ+μyη+μzζ)]1/2,
U=sinh(kR0S)sinh(kR0)S.
S+=[1(ξ2+η2+ζ2)+2iμzζ+2iμxξ]1/2,S=[1(ξ2+η2+ζ2)+2iμzζ2iμxξ)]1/2,
U=12sinh[kR0]{sinh[kR0S+]S++sinh[kR0S]S}.
I(θ,ϕ)=exp[2kR0μz(1cosθ)]×cosh2(kR0μxsinθcosϕ).

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