Abstract

The advantage of using a diffraction-free light beam in heterodyne detection is investigated. Optimum values of tilt and offset of the incoming signal beam for attaining the maximum heterodyne mixing efficiency are identified.

© 1992 Optical Society of America

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References

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  1. O. E. DeLange, “Optical heterodyne detection,” IEEE Spectrum 5(10), 77–86 (1968).
    [CrossRef]
  2. M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 50, 37–47 (1968).
    [CrossRef]
  3. M. C. Teich, “Laser heterodyning,” Opt. Acta 32, 1015–1021 (1985).
  4. R. A. Linke, P. S. Henry, “Coherent optical detection: a thousand calls in one circuit,” IEEE Spectrum 24(2), 52–57 (1987).
  5. S. F. Jacobs, “Optical heterodyne (coherent) detection,” Am. J. Phys. 56, 235–245 (1988).
    [CrossRef]
  6. M. A. Karim, Electro-Optical Devices & Systems (PWS-Kent, Boston, Mass., 1990).
  7. J. H. Shaprio, “Heterodyne mixing efficiency for detector arrays,” Appl. Opt. 26, 3600–3606 (1987).
    [CrossRef]
  8. J. N. Pranto, “Investigation of heterodyne mixing efficiency variations due to optical misalignments and aberations,” M.S thesis (University of New Mexico, Albuquerque, N.M., 1988).
  9. L. G. Kazovsky, N. S. Kopeika, “Heterodyne detection through rain, snow, and turbid media: effective receiver size at optical through millimeter wavelengths,” Appl. Opt. 22, 706–710 (1983).
    [CrossRef] [PubMed]
  10. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350–1356 (1966).
    [CrossRef]
  11. K. Tanaka, N. Ohta, “Effects of tilt and offset of signal field on heterodyne efficiency,” Appl. Opt. 26, 627–632 (1987).
    [CrossRef] [PubMed]
  12. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  13. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  14. K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
    [CrossRef]
  15. J. Turunen, A. Vasara, A. T. Friberg, Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
    [CrossRef] [PubMed]
  16. S. H. Lee, B. W. Stewart, W. Will, H. Fenichel, “Nondiffracting approximated Bessel beam (J1),” in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1991), paper ThI4.
  17. R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  18. P. Szwaykowski, J. O. Castaneda, “Nondiffracting beams and self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
    [CrossRef]
  19. I. N. Bronshtein, K. A. Semendyayev, Handbook of Mathematics (Van Nostrand Reinhold, New York, 1985).
  20. H. Kogelnik, A. Yariv, “Considerations of noise and schemes for its reduction in laser amplifiers,” Proc. IEEE 52, 165–173 (1964).
    [CrossRef]
  21. R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1979).

1991 (3)

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
[CrossRef]

P. Szwaykowski, J. O. Castaneda, “Nondiffracting beams and self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
[CrossRef]

1988 (2)

1987 (5)

1985 (1)

M. C. Teich, “Laser heterodyning,” Opt. Acta 32, 1015–1021 (1985).

1983 (1)

1968 (2)

O. E. DeLange, “Optical heterodyne detection,” IEEE Spectrum 5(10), 77–86 (1968).
[CrossRef]

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 50, 37–47 (1968).
[CrossRef]

1966 (1)

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350–1356 (1966).
[CrossRef]

1964 (1)

H. Kogelnik, A. Yariv, “Considerations of noise and schemes for its reduction in laser amplifiers,” Proc. IEEE 52, 165–173 (1964).
[CrossRef]

Awwal, A. A. S.

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Bronshtein, I. N.

I. N. Bronshtein, K. A. Semendyayev, Handbook of Mathematics (Van Nostrand Reinhold, New York, 1985).

Castaneda, J. O.

P. Szwaykowski, J. O. Castaneda, “Nondiffracting beams and self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
[CrossRef]

DeLange, O. E.

O. E. DeLange, “Optical heterodyne detection,” IEEE Spectrum 5(10), 77–86 (1968).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Fenichel, H.

S. H. Lee, B. W. Stewart, W. Will, H. Fenichel, “Nondiffracting approximated Bessel beam (J1),” in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1991), paper ThI4.

Friberg, A. T.

Henry, P. S.

R. A. Linke, P. S. Henry, “Coherent optical detection: a thousand calls in one circuit,” IEEE Spectrum 24(2), 52–57 (1987).

Herman, R. M.

Jacobs, S. F.

S. F. Jacobs, “Optical heterodyne (coherent) detection,” Am. J. Phys. 56, 235–245 (1988).
[CrossRef]

Karim, M. A.

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

M. A. Karim, Electro-Optical Devices & Systems (PWS-Kent, Boston, Mass., 1990).

Kazovsky, L. G.

Kingston, R. H.

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1979).

Kogelnik, H.

H. Kogelnik, A. Yariv, “Considerations of noise and schemes for its reduction in laser amplifiers,” Proc. IEEE 52, 165–173 (1964).
[CrossRef]

Kopeika, N. S.

Lee, S. H.

S. H. Lee, B. W. Stewart, W. Will, H. Fenichel, “Nondiffracting approximated Bessel beam (J1),” in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1991), paper ThI4.

Linke, R. A.

R. A. Linke, P. S. Henry, “Coherent optical detection: a thousand calls in one circuit,” IEEE Spectrum 24(2), 52–57 (1987).

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Ohta, N.

Pranto, J. N.

J. N. Pranto, “Investigation of heterodyne mixing efficiency variations due to optical misalignments and aberations,” M.S thesis (University of New Mexico, Albuquerque, N.M., 1988).

Semendyayev, K. A.

I. N. Bronshtein, K. A. Semendyayev, Handbook of Mathematics (Van Nostrand Reinhold, New York, 1985).

Shaprio, J. H.

Siegman, A. E.

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350–1356 (1966).
[CrossRef]

Stewart, B. W.

S. H. Lee, B. W. Stewart, W. Will, H. Fenichel, “Nondiffracting approximated Bessel beam (J1),” in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1991), paper ThI4.

Szwaykowski, P.

P. Szwaykowski, J. O. Castaneda, “Nondiffracting beams and self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
[CrossRef]

Tanaka, K.

Teich, M. C.

M. C. Teich, “Laser heterodyning,” Opt. Acta 32, 1015–1021 (1985).

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 50, 37–47 (1968).
[CrossRef]

Thewes, K.

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Turunen, J.

Vasara, A.

Wiggins, T. A.

Will, W.

S. H. Lee, B. W. Stewart, W. Will, H. Fenichel, “Nondiffracting approximated Bessel beam (J1),” in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1991), paper ThI4.

Yariv, A.

H. Kogelnik, A. Yariv, “Considerations of noise and schemes for its reduction in laser amplifiers,” Proc. IEEE 52, 165–173 (1964).
[CrossRef]

Am. J. Phys. (1)

S. F. Jacobs, “Optical heterodyne (coherent) detection,” Am. J. Phys. 56, 235–245 (1988).
[CrossRef]

Appl. Opt. (4)

IEEE Spectrum (2)

O. E. DeLange, “Optical heterodyne detection,” IEEE Spectrum 5(10), 77–86 (1968).
[CrossRef]

R. A. Linke, P. S. Henry, “Coherent optical detection: a thousand calls in one circuit,” IEEE Spectrum 24(2), 52–57 (1987).

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

M. C. Teich, “Laser heterodyning,” Opt. Acta 32, 1015–1021 (1985).

Opt. Commun. (1)

P. Szwaykowski, J. O. Castaneda, “Nondiffracting beams and self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
[CrossRef]

Opt. Laser Technol. (1)

K. Thewes, M. A. Karim, A. A. S. Awwal, “Diffraction-free beam generation using refracting system,” Opt. Laser Technol. 23, 105–108 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Proc. IEEE (3)

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350–1356 (1966).
[CrossRef]

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 50, 37–47 (1968).
[CrossRef]

H. Kogelnik, A. Yariv, “Considerations of noise and schemes for its reduction in laser amplifiers,” Proc. IEEE 52, 165–173 (1964).
[CrossRef]

Other (5)

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1979).

I. N. Bronshtein, K. A. Semendyayev, Handbook of Mathematics (Van Nostrand Reinhold, New York, 1985).

J. N. Pranto, “Investigation of heterodyne mixing efficiency variations due to optical misalignments and aberations,” M.S thesis (University of New Mexico, Albuquerque, N.M., 1988).

M. A. Karim, Electro-Optical Devices & Systems (PWS-Kent, Boston, Mass., 1990).

S. H. Lee, B. W. Stewart, W. Will, H. Fenichel, “Nondiffracting approximated Bessel beam (J1),” in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1991), paper ThI4.

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Figures (5)

Fig. 1
Fig. 1

Plot of J02 (αρ) versus ρ.

Fig. 2
Fig. 2

Coordinate system with tilt θ.

Fig. 3
Fig. 3

Heterodyne efficiency versus tilt angle when a2/b2 = 1.0, x1/a1 = 0.0, xs = 0.8, and zl/zd = zs/zd = 0.5

Fig. 4
Fig. 4

Heterodyne efficiency versus x1/a1 when a1 = 1.0, a2/b2 = 1.0, xs = 0.8, and zl/zd = zs/zd = 0.5. □ □, 10−4 deg; |, 0.5 deg; ×, 1.0 deg; ◇, 1.4 deg; △, 2 deg.

Fig. 5
Fig. 5

Heterodyne efficiency versus detector size a2/b2 when x1/a1 = 0.0, xs = 0.8, and zl/zd = zs/zd = 0.5. □, 10−4 deg; |, 0.1 deg; ◇, 0.5 deg; ▽, 1.0 deg; △, 2.0 deg; ×, 1.4 deg.

Equations (8)

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E ( x , y , z ; k ) = exp ( i β z ) J 0 ( α ρ ) ,
E ( x , y , z ; k ) = exp [ i β ( z - z p ) ] r = 0 × ( - 1 ) r [ ( α / 2 ) ( x 2 + y 2 ) ] 2 r ( r ! ) 2 ,
U s d ( x d , y d , z d ) = ( 1 / cos θ ) exp { i [ α 0 ( x d - x s ) + γ 0 ( z d - z s ) ] } × r = 0 ( - 1 ) r ( r ! ) 2 { ( α / 2 ) × [ ( x d - z d tan θ + x 1 ) 2 + y d 2 ] 1 / 2 } 2 r ,
U l d ( x d , y d , z d ) = exp [ i β ( z d - z l ) ] × r = 0 ( - 1 ) r ( r ! ) 2 ( α / 2 ) 2 r ( x d 2 + y d 2 ) r .
γ = U l d U s d * d A 2 U l d U l d * d A U s d U s d * d A ,
U l d ( x d , y d , z d ) U s d * ( x d , y d , z d ) = exp [ i β ( z d - z l ) ] r = 0 ( - 1 ) r ( r ! ) 2 ( α / 2 ) 2 r ( x d 2 + y d 2 ) r × ( sec θ ) exp { - i [ α 0 ( x d - x s ) + γ 0 ( z d - z s ) ] } × r = 0 ( - 1 ) r ( r ! ) 2 { ( α / 2 ) [ ( x d - z d tan θ - x 1 ) 2 + y d 2 ] 1 / 2 } 2 r .
s U l d ( x d , y d , z d ) U s d * ( x d , y d , z d ) d s 2 = ( sec θ ) exp [ i ( β z d - β z l + α 0 x s + γ 0 z s - γ 0 z d ) ] × - a 2 a 2 - b 2 b 2 exp ( - i α 0 x d ) r = 0 ( - 1 ) r ( r ! ) 2 ( α / 2 ) 2 r × [ ( x d - z d tan θ + x 1 ) 2 + y d 2 ] r × r = 0 ( - 1 ) r ( r ! ) 2 ( α / 2 ) 2 r ( x d 2 + y d 2 ) r d x d d y d 2 ,
γ t | ( sec θ ) exp [ i ( β z d - β z l + α 0 x s + γ 0 z s - γ 0 z d ) ] { - a 2 a 2 - b 2 b 2 exp ( - i α 0 x d ) r = 0 ( - 1 ) r ( r ! ) 2 ( α / 2 ) 2 r [ ( x d - z d tan θ - x 1 ) 2 + y d 2 ] r } × r = 0 ( - 1 ) r ( r ! ) 2 ( α / 2 ) 2 r ( x d 2 + y d 2 ) r d x d d y d | 2 ( - a 2 a 2 - b 2 b 2 { r = 0 ( - 1 ) r ( r ! ) 2 ( α / 2 ) 2 r [ ( x d - z d tan θ - x 1 ) 2 + y d 2 ] r } 2 d x d d y d ) × - a 2 a 2 - b 2 b 2 [ r = 0 ( - 1 ) r ( r ! ) 2 ( α / 2 ) 2 r ( x d 2 + y d 2 ) r ] 2 d x d d y d

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