Abstract

We analyze the evolution of beam quality when propagating through a parabolic index (PI) fiber. The deterioration in beam quality is expressed in terms of the fiber parameters, and a methodology for minimizing the deterioration is presented. The fiber optimization procedure is evaluated numerically for an application where the PI fiber is used to deliver the signal produced by a tapered fiber-bundle beam combiner. It was demonstrated that delivery with no beam quality deterioration can be achieved with proper fiber design.

© 2012 Optical Society of America

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Corrections

Roey Zuitlin, Yariv Shamir, Yoav Sintov, and Mark Shtaif, "Modeling the evolution of spatial beam parameters in parabolic index fibers: erratum," Opt. Lett. 38, 1067-1067 (2013)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-38-7-1067

References

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  1. Y. Koike, T. Ishigure, and E. Nihei, J. Lightwave Technol. 13, 1475 (1994).
    [CrossRef]
  2. T. Ishigure, E. Nihei, and Y. Koike, Appl. Opt. 35, 2048 (1996).
    [CrossRef]
  3. J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
    [CrossRef]
  4. D. Gloge and E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).
  5. Y. Shamir, R. Zuitlin, Y. Sintov, and M. Shtaif, Opt. Lett. 37, 1412 (2012).
    [CrossRef]
  6. Y. Shamir, Y. Sintov, and M. Shtaif, Proc. SPIE 7580, 78501R (2010).
    [CrossRef]
  7. Y. Shamir, Y. Sintov, and M. Shtaif, J. Opt. Soc. Am. B 27, 2669 (2010).
    [CrossRef]
  8. Y. Shamir, Y. Sintov, and M. Shtaif, Opt. Lett. 36, 2874 (2011).
    [CrossRef]
  9. A. E. Siegman, Proc. SPIE 1224, 2 (1990).
    [CrossRef]
  10. D. Marcuse, Light Transmission Optics (Van-Nostrand, 1982).

2012 (1)

2011 (1)

2010 (2)

Y. Shamir, Y. Sintov, and M. Shtaif, Proc. SPIE 7580, 78501R (2010).
[CrossRef]

Y. Shamir, Y. Sintov, and M. Shtaif, J. Opt. Soc. Am. B 27, 2669 (2010).
[CrossRef]

2001 (1)

J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
[CrossRef]

1996 (1)

1994 (1)

Y. Koike, T. Ishigure, and E. Nihei, J. Lightwave Technol. 13, 1475 (1994).
[CrossRef]

1990 (1)

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

1973 (1)

D. Gloge and E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Arrue, J.

J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
[CrossRef]

Gloge, D.

D. Gloge and E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Ishigure, T.

T. Ishigure, E. Nihei, and Y. Koike, Appl. Opt. 35, 2048 (1996).
[CrossRef]

Y. Koike, T. Ishigure, and E. Nihei, J. Lightwave Technol. 13, 1475 (1994).
[CrossRef]

Koike, Y.

T. Ishigure, E. Nihei, and Y. Koike, Appl. Opt. 35, 2048 (1996).
[CrossRef]

Y. Koike, T. Ishigure, and E. Nihei, J. Lightwave Technol. 13, 1475 (1994).
[CrossRef]

Marcatili, E. A. J.

D. Gloge and E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van-Nostrand, 1982).

Nihei, E.

T. Ishigure, E. Nihei, and Y. Koike, Appl. Opt. 35, 2048 (1996).
[CrossRef]

Y. Koike, T. Ishigure, and E. Nihei, J. Lightwave Technol. 13, 1475 (1994).
[CrossRef]

Shamir, Y.

Shtaif, M.

Siegman, A. E.

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

Sintov, Y.

Zubia, J.

J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
[CrossRef]

Zuitlin, R.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Gloge and E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973).

J. Lightwave Technol. (1)

Y. Koike, T. Ishigure, and E. Nihei, J. Lightwave Technol. 13, 1475 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Fiber Technol. (1)

J. Zubia and J. Arrue, Opt. Fiber Technol. 7, 101 (2001).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

Y. Shamir, Y. Sintov, and M. Shtaif, Proc. SPIE 7580, 78501R (2010).
[CrossRef]

Other (1)

D. Marcuse, Light Transmission Optics (Van-Nostrand, 1982).

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Figures (3)

Fig. 1.
Fig. 1.

M2 results throughout a 100μm/0.11NA PI fiber for (a) centered injection of 15μm/0.08NA fundamental mode and (b) offset (x=20μm, y=10μm) injection of the same mode. Thick dotted curve, BPM simulation; thin solid line, analytical model.

Fig. 2.
Fig. 2.

(a) XY section of the simulation intensity at the TFB combiner’s tip, with a nearly equal power split ratio and (b) M2 results throughout a 100μm/0.29NA PI fiber when injected by a three-port TFB combiner output field. Thick dotted curve, BPM simulation; thin solid line, analytical model.

Fig. 3.
Fig. 3.

Relative deterioration in BPP for different PI fiber core NAs. Solid black, 75 μm diameter; solid gray, 100 μm diameter; dashed black, 150 μm diameter; dashed gray, 200 μm diameter. Launching field was the output of a simulated three-port adiabatic TFB combiner.

Equations (18)

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Bx2(z)=(4λπMx2)2=162λ24π2σx2(z)σkx2(z),
σx2(z)=x2|E(x,y,z)|2dxdy(x|E(x,y,z)|2dxdy)2,
σkx2(z)=kx2|E˜(kx,ky,z)|2dkxdky(kx|E˜(kx,ky,z)|2dkxdky)2,
E(x,y,z)=n,m=0Nmax,MmaxeiϕmnAmnψmn(x,y,z),
n(x,y)=n012n1(x2+y2),
ψmn(x,y,z)=2/π2m+nm!n!wHm(2xw)×Hn(2yw)ex2+y2w2eiβmnz,
xHn(x)=0.5Hn+1(x)+nHn1(x)
σx2(z)=w22[A+Bcos(2Δβz)Csin(2Δβz)][x0cos(Δβz)+kx0w22sin(Δβz)]2,
Δβ=βm+1,nβm,n=n1/n0,
A=n,m=0N,MApn2(m+12),
B=n,m=0N,Mcos(ϕmnϕm+2,n)AmnAm+2,n×(m+1)(m+2),
C=n,m=0N,Msin(ϕmnϕm+2,n)AmnAm+2,n×(m+1)(m+2).
F{e12x2Hn(x)}=(i)3ne12k2Hn(k),
σkx2(z)=2w2[ABcos(2Δβz)+Csin(2Δβz)][2w2x0sin(Δβz)kx0cos(Δβz)]2.
Bx2(z)=162λ24π2{σx02σkx02+[(σx02w2w2σkx024)2C2]sin2(2Δβz)+C(σx02w2w2σkx024)sin(4Δβz)},
(σx02w2w2σkx024)=0,
Bx2(z)=162λ24π2{σx02σkx02C2sin2(2Δβz)}.
ΔB=BmaxB(z=0)B(z=0).

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