Abstract

An electromagnetic beam that is not the solution to the paraxial wave equation but is the solution to Maxwell’s equation is simulated directly by the finite-difference time-domain method. Electrical and magnetic field components of the beam are presented graphically. Then the diffraction of the electromagnetic beam pulse by an aperture in a conducting screen is analyzed. The fraction of the beam power through the aperture is defined and calculated. The fields in the time domain near the aperture, which show the diffraction by the aperture, are presented graphically.

© 2001 Optical Society of America

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References

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  1. G. Goubau, “On the guided propagation of electromagnetic wave beams,” IRE Trans. Antennas Propag. AP-9, 248–256 (1961).
    [Crossref]
  2. A. G. van Nie, “Rigorous calculation of the electromagnetic field of wave beams,” Philips Res. Rep. 19, 378–394 (1964).
  3. H. Kogelnik, “On the propagation of Gaussian beam of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965).
    [Crossref]
  4. J. A. Arnaud, H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt. 8, 1687–1693 (1969).
    [Crossref] [PubMed]
  5. L. D. Dickson, “Characteristics of a propagating Gaussian beam,” Appl. Opt. 9, 1854–1861 (1970).
    [Crossref] [PubMed]
  6. G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
    [Crossref]
  7. C. S. Williams, “Gaussian beam formulas from diffraction theory,” Appl. Opt. 12, 872–876 (1973).
    [Crossref] [PubMed]
  8. D. H. Martin, J. Lesurf, “Submillimeter-wave optics,” Infrared Phys. 18, 405–412 (1978).
    [Crossref]
  9. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [Crossref]
  10. R. J. Wylde, “Millimetre-wave Gaussian beam-mode optics and corrugated feed horns,” Proc. IEEE 131-H, 258–262 (1984).
  11. J. A. Murphy, “Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors,” Int. J. Infrared Millim. Waves 8, 1165–1187 (1987).
    [Crossref]
  12. P. F. Goldsmith, Quasioptical Systems: Gaussian Beam, Quasioptical Propagation and Applications (IEEE Press, New York, 1998).
  13. J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimeter and submillimeter wave optical systems,” IEEE Trans. Microwave Theory Tech. MTT-41, 1700–1702 (1993).
    [Crossref]
  14. P. Belland, J. P. Crenn, “Changes in the characteristics of a Gaussian beam weakly diffracted by a circular aperture,” Appl. Opt. 21, 522–527 (1982).
    [Crossref] [PubMed]
  15. A. Taflove, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1998).

1993 (1)

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimeter and submillimeter wave optical systems,” IEEE Trans. Microwave Theory Tech. MTT-41, 1700–1702 (1993).
[Crossref]

1987 (1)

J. A. Murphy, “Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors,” Int. J. Infrared Millim. Waves 8, 1165–1187 (1987).
[Crossref]

1984 (1)

R. J. Wylde, “Millimetre-wave Gaussian beam-mode optics and corrugated feed horns,” Proc. IEEE 131-H, 258–262 (1984).

1982 (1)

1979 (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[Crossref]

1978 (1)

D. H. Martin, J. Lesurf, “Submillimeter-wave optics,” Infrared Phys. 18, 405–412 (1978).
[Crossref]

1973 (1)

1971 (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[Crossref]

1970 (1)

1969 (1)

1965 (1)

1964 (1)

A. G. van Nie, “Rigorous calculation of the electromagnetic field of wave beams,” Philips Res. Rep. 19, 378–394 (1964).

1961 (1)

G. Goubau, “On the guided propagation of electromagnetic wave beams,” IRE Trans. Antennas Propag. AP-9, 248–256 (1961).
[Crossref]

Arnaud, J. A.

Belland, P.

Crenn, J. P.

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[Crossref]

Deschamps, G. A.

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[Crossref]

Dickson, L. D.

Egan, A.

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimeter and submillimeter wave optical systems,” IEEE Trans. Microwave Theory Tech. MTT-41, 1700–1702 (1993).
[Crossref]

Goldsmith, P. F.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam, Quasioptical Propagation and Applications (IEEE Press, New York, 1998).

Goubau, G.

G. Goubau, “On the guided propagation of electromagnetic wave beams,” IRE Trans. Antennas Propag. AP-9, 248–256 (1961).
[Crossref]

Kogelnik, H.

Lesurf, J.

D. H. Martin, J. Lesurf, “Submillimeter-wave optics,” Infrared Phys. 18, 405–412 (1978).
[Crossref]

Martin, D. H.

D. H. Martin, J. Lesurf, “Submillimeter-wave optics,” Infrared Phys. 18, 405–412 (1978).
[Crossref]

Murphy, J. A.

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimeter and submillimeter wave optical systems,” IEEE Trans. Microwave Theory Tech. MTT-41, 1700–1702 (1993).
[Crossref]

J. A. Murphy, “Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors,” Int. J. Infrared Millim. Waves 8, 1165–1187 (1987).
[Crossref]

Taflove, A.

A. Taflove, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1998).

van Nie, A. G.

A. G. van Nie, “Rigorous calculation of the electromagnetic field of wave beams,” Philips Res. Rep. 19, 378–394 (1964).

Williams, C. S.

Withington, S.

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimeter and submillimeter wave optical systems,” IEEE Trans. Microwave Theory Tech. MTT-41, 1700–1702 (1993).
[Crossref]

Wylde, R. J.

R. J. Wylde, “Millimetre-wave Gaussian beam-mode optics and corrugated feed horns,” Proc. IEEE 131-H, 258–262 (1984).

Appl. Opt. (5)

Electron. Lett. (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. A. Murphy, S. Withington, A. Egan, “Mode conversion at diffracting apertures in millimeter and submillimeter wave optical systems,” IEEE Trans. Microwave Theory Tech. MTT-41, 1700–1702 (1993).
[Crossref]

Infrared Phys. (1)

D. H. Martin, J. Lesurf, “Submillimeter-wave optics,” Infrared Phys. 18, 405–412 (1978).
[Crossref]

Int. J. Infrared Millim. Waves (1)

J. A. Murphy, “Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors,” Int. J. Infrared Millim. Waves 8, 1165–1187 (1987).
[Crossref]

IRE Trans. Antennas Propag. (1)

G. Goubau, “On the guided propagation of electromagnetic wave beams,” IRE Trans. Antennas Propag. AP-9, 248–256 (1961).
[Crossref]

Philips Res. Rep. (1)

A. G. van Nie, “Rigorous calculation of the electromagnetic field of wave beams,” Philips Res. Rep. 19, 378–394 (1964).

Phys. Rev. A (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[Crossref]

Proc. IEEE (1)

R. J. Wylde, “Millimetre-wave Gaussian beam-mode optics and corrugated feed horns,” Proc. IEEE 131-H, 258–262 (1984).

Other (2)

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam, Quasioptical Propagation and Applications (IEEE Press, New York, 1998).

A. Taflove, Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1998).

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Figures (8)

Fig. 1
Fig. 1

Configuration of a FDTD lattice terminated by UPML slabs and beam truncation.

Fig. 2
Fig. 2

Field distributions of the electromagnetic beam. F=35 GHz, waist w0=λ. (a) Ez, (b) Hy, (c) Hx.

Fig. 3
Fig. 3

Contour diagram of the envelope of the Ez field of the beam.

Fig. 4
Fig. 4

Contour diagram of the envelope of the Ez field of the Gaussian beam.

Fig. 5
Fig. 5

Spectrum of the excitation given by Eq. (9).

Fig. 6
Fig. 6

Loss rate of power due to truncation by the aperture.

Fig. 7
Fig. 7

Contour diagram of the Ez field of the beam near the stop. (a) a/w=1.0, (b) a/w=1.5, (c) a/w=2.0, (d) a/w=2.5, (e) without stop.

Fig. 8
Fig. 8

Calculated BFE’s for different a/w. (a) a/w=1.0 and a/w=1.5, (b) a/w=2.0 and a/w=2.5, (c) a/w=3.0.

Tables (1)

Tables Icon

Table 1 Comparison of the Loss Rates of Power

Equations (21)

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×E=-jωμs¯¯·H,×H=jωs¯¯·E,
s¯¯=sx-1sy000sxsy-10sxsy
sx=κx+σxjω0,sy=κy+σyjω0.
Dzn+1(i, j)=Tx-Tx+Dzn(i, j)+1Tx+ ΔtΔs[Hyn+1/2(i+1, j)-Hyn+1/2(i, j)-Hxn+1/2(i, j+1)+Hxn+1/2(i, j)],
Bxn+1/2(i, j)=Ty-Ty+Bxn-1/2(i, j)-1Ty+ ΔtΔs[Ezn(i, j)-Ezn(i, j-1)],
Byn+1/2(i, j)=Tx-Tx+Byn-1/2(i, j)+1Tx+ ΔtΔs[Ezn(i, j)-Ezn(i-1, j)],
Ezn+1(i, j)=Ty-Ty+Ezn(i, j)+1Ty+ 10r(i, j)×[Dzn+1(i, j)-Dzn(i, j)],
Hxn+1/2(i, j)=Hxn-1/2(i, j)+1μ0[Tx+Bxn+1/2(i, j)-Tx-Bxn-1/2(i, j)],
Hyn+1/2(i, j)=Hyn-1/2(i, j)+1μ0[Ty+Byn+1/2(i, j)-Ty-Byn-1/2(i, j)],
Tx+=κx+σxΔt20,Tx-=κx-σxΔt20;
Ty+=κy+σyΔt20,Ty-=κy-σyΔt20.
Ei=cos(2πfct)exp-(t-t0)2T2.
Ei=cos(2πfct)exp(-y2/w02).
Ez(i, j)|maxHy(i, j)|max=0.96475·Z0;
Ez(i, j)|maxHx(i, j)|max=0.1432·Z0,
Ez=exp-jP+kr22q=w0w(z) exp-jπr2λR(z)-tan-1 λzπw02exp-r2w2(z).
Ei=cos(2πfct)exp-(t-t0)2T2exp-y2w02,
Pi=s|Ezi(ω)|2ds,
Pt=s|Ezt(ω)|2ds,
Ploss=Pi-PtPi.
BFE=xy|Ezi(x, y)-Ezt(x, y)|2dxdyxy|Ezi(x, y)|2dxdy n,

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