Abstract

Employing the van Cittert–Zernike theorem of classical coherence theory, we derive a general expression for the efficiency with which quasi-monochromatic random light can be coupled to an optical fiber by means of a lens. For the important case of a source with Gaussian intensity distribution, we obtain and discuss the dependence of the coupling efficiency to single-mode fibers on the lens-to-fiber coupling geometry as well as on the ratio of lens size to speckle size. A specialization to the emerging fields of both incoherent and coherent fiber-based lidar applications shows that a maximum coupling efficiency of 42% can be obtained for a monostatic system.

© 1998 Optical Society of America

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References

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1998

1995

D. K. Jacob, M. B. Mark, and B. D. Duncan, Opt. Eng. 34, 3122 (1995).
[CrossRef]

1992

1991

1990

E. A. Swanson and R. S. Bondurant, Proc. SPIE 1218, 70 (1990).
[CrossRef]

1979

1975

1974

1966

Bondurant, R. S.

E. A. Swanson and R. S. Bondurant, Proc. SPIE 1218, 70 (1990).
[CrossRef]

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers (Wiley, New York, 1995).

Chan, K. P.

Cohen, S. C.

Degnan, J. J.

Duncan, B. D.

D. K. Jacob, M. B. Mark, and B. D. Duncan, Opt. Eng. 34, 3122 (1995).
[CrossRef]

Frehlich, R. G.

Goodman, J. W.

J. W. Goodman, in Laser Speckle and Related Phenomena, J. C. Dainty ed., (Springer-Verlag, Berlin, 1975), p. 9.

Jacob, D. K.

D. K. Jacob, M. B. Mark, and B. D. Duncan, Opt. Eng. 34, 3122 (1995).
[CrossRef]

Kavaya, M. J.

Killinger, D. K.

Klein, B. J.

Kudielka, K. H.

Leeb, W. R.

Mark, M. B.

D. K. Jacob, M. B. Mark, and B. D. Duncan, Opt. Eng. 34, 3122 (1995).
[CrossRef]

Rye, B. J.

Siegman, A. E.

Sugimoto, N.

Swanson, E. A.

E. A. Swanson and R. S. Bondurant, Proc. SPIE 1218, 70 (1990).
[CrossRef]

Winzer, P. J.

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Figures (2)

Fig. 1
Fig. 1

A thin lens of clear aperture AR (diameter dR) couples the incident (random) radiation Ei into a (single-mode) optical fiber (mode field E0), whose end face lies in plane B; the aperture plane is denoted A, and f is the focal length of the lens.

Fig. 2
Fig. 2

(a) Optimum lens-to-fiber coupling geometry, aopt, as a function of AR/Ac. (b) Coupling efficiency ηc as a function of AR/Ac for a=aopt,det=1.585 (solid curve) and for a=1.954, i.e., optimized for AR/Ac=2 (dashed curve). Squares: best obtainable value for ηc. The two additional abscissa axes facilitate the transition to lidar applications, with dR/dT denoting the ratio of transmit-to-receive aperture diameter; α is valid for high truncation ratios dT/2WT0, and β applies to a typical truncation ratio of dT/2WT=1.45.

Equations (9)

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Pc=BEi,BrE0,B*rdr2.
ηc=PcPa=AEi,ArE0,A*rdr2AEi,Ar2dr,
ηc=1ARAμAr1,r2E0,A*r1E0,Ar2dr1dr2,
μAr1,r2=Ei,Ar1Ei,A*r2Ei,Ar12Ei,Ar221/2.
μAr1,r2=exp-r1-r22/ρ2,
E0,Ar=2πwλfexp-rπwλf2,
a=πwdRλf2,
ηc=4a201x1x2 exp-a22+ARAcx12+x22×I02ARAcx1x2dx1dx2,
ηhet=BEi,BrELO,B*rdr2BELO,Br2drAEi,Ar2dr,

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