Abstract

We measure the polarization state of each guided transversal mode propagating in step-index large-mode-area fibers (V4) using a correlation-filter based measurement technique in combination with a Stokes parameter measurement. The entire emerging beam, expressed in terms of a phase-dependent superposition of linearly polarized modes, demonstrates spatially varying polarization properties. By knowing the information about modal amplitudes and phase differences, full information about the optical field is available.

© 2010 Optical Society of America

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References

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2010

D. Flamm, S. Schröter, and M. Duparré, Proc. SPIE 7579, 75790R (2010).
[CrossRef]

O. A. Schmidt, D. Flamm, and M. Duparré, Proc. SPIE 7714, 77140W (2010).
[CrossRef]

2009

2007

2006

1997

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

1994

V. A. Soifer and M. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).

1991

M. Born and E. Wolf, Principles of Optics (Pergamon, 1991).

1980

1977

1971

Ahmed, M. A.

Berry, H. G.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1991).

Duparré, M.

O. A. Schmidt, D. Flamm, and M. Duparré, Proc. SPIE 7714, 77140W (2010).
[CrossRef]

D. Flamm, S. Schröter, and M. Duparré, Proc. SPIE 7579, 75790R (2010).
[CrossRef]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, Opt. Express 17, 9347 (2009).
[CrossRef] [PubMed]

Eickhoff, W.

Flamm, D.

O. A. Schmidt, D. Flamm, and M. Duparré, Proc. SPIE 7714, 77140W (2010).
[CrossRef]

D. Flamm, S. Schröter, and M. Duparré, Proc. SPIE 7579, 75790R (2010).
[CrossRef]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, Opt. Express 17, 9347 (2009).
[CrossRef] [PubMed]

Gabrielse, G.

Gloge, D.

Golub, M.

V. A. Soifer and M. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).

Graf, T.

Kaiser, T.

Livingston, A. E.

Mansuripur, M.

Polynkin, P.

Rashleigh, S. C.

Schermer, R. T.

Schmidt, O. A.

O. A. Schmidt, D. Flamm, and M. Duparré, Proc. SPIE 7714, 77140W (2010).
[CrossRef]

Schröter, S.

D. Flamm, S. Schröter, and M. Duparré, Proc. SPIE 7579, 75790R (2010).
[CrossRef]

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, Opt. Express 17, 9347 (2009).
[CrossRef] [PubMed]

Soifer, V. A.

V. A. Soifer and M. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).

Ulrich, R.

Vogel, M. M.

Voss, A.

Wielandy, S.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1991).

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

Yoda, H.

Zhan, Q.

Adv. Opt. Photon.

Appl. Opt.

J. Lightwave Technol.

Opt. Express

Opt. Lett.

Proc. SPIE

D. Flamm, S. Schröter, and M. Duparré, Proc. SPIE 7579, 75790R (2010).
[CrossRef]

O. A. Schmidt, D. Flamm, and M. Duparré, Proc. SPIE 7714, 77140W (2010).
[CrossRef]

Other

V. A. Soifer and M. Golub, Laser Beam Mode Selection by Computer Generated Holograms (CRC Press, 1994).

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1991).

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Figures (6)

Fig. 1
Fig. 1

A superposition of two polarization degenerated LP 11 e eigenstates with an intramodal phase difference of π / 4 generates elliptical polarization. In this example, in the x direction twice as much power is guided than in the y direction. Although elliptically polarized, such modes are consequently designated as LP modes, because their intensity profiles are identical.

Fig. 2
Fig. 2

Experimental setup: MO, microscope objective; NP, nanopositioning unit; λ / 4 , quarter-wave plate; P, polarizer; L, imaging lens; and FL, Fourier lens.

Fig. 3
Fig. 3

(a) Measured near field. (b) Relative modal spectrum.

Fig. 4
Fig. 4

Measurement with sin 2 fit of the modal weights of the fundamental mode depending on the polarizer orientation in the undisturbed (blue curve, rectangles) and the bent case (red curve, circles).

Fig. 5
Fig. 5

Poincaré sphere representation of normalized Stokes parameters of the polarized modes occurring elliptically from the vector beam shown in Fig. 6.

Fig. 6
Fig. 6

(a) Measured near field. (b) Reconstructed near-field intensity with local polarization properties. The modal power spectrum reads as 13% LP 01 , 24% LP 11 e , 50% LP 11 o , 6% LP 21 e , and 7% LP 21 o .

Equations (6)

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U ( r ) = l = 1 l max g = 1 2 c l g ψ l ( r ) e g .
U ( r ) = l = 1 l max ψ l ( r ) [ c l 1 c l 2 ] ,
= l = 1 l max ψ l ( r ) exp ( i ϕ l ) [ ϱ l 1 ϱ l 2 exp ( i δ l ) ] .
T l ( r ) = ψ l * ( r ) .
T l 1 = ( ψ 0 * + ψ l * ) / 2 , T l 2 = ( ψ 0 * + i ψ l * ) / 2 .
S l = [ S 0 S 1 S 2 S 3 ] l = [ ϱ l 1 2 + ϱ l 2 2 ϱ l 1 2 ϱ l 2 2 2 ϱ l 1 ϱ l 2 cos δ l 2 ϱ l 1 ϱ l 2 sin δ l ] .

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