Abstract

We describe an alternative to fiber-gratings for converting higher-order LP0m(m>1) fiber modes into a nearly fundamental Gaussian shape at the output of a fiber. This schematic enables the use of light propagation in higher-order modes of a fiber, a fiber-platform that has recently shown great promise for achieving very large mode areas needed for future high-power lasers and amplifiers. The conversion will be done by using a binary phase plate in the near field of the fiber, which emits the LP0m mode. Since the binary phase plate alone cannot increase the quality factor M2 of the laser beam because of some broad sidebands, a filtering of the sidebands is done in the Fourier plane of a telescope. Of course, this will cost some of the total light power, but on the other side the M2 factor can be reduced to nearly the ideal value near 1.0, and it is shown that 76% of the total light power can be conserved for all investigated modes (2m8). A tolerance analysis for the phase plate and its adjustment is made, and different optical imaging systems to form a magnified image of the fiber mode on the phase plate are discussed in order to have more tolerance for the adjustment of the phase plate.

© 2007 Optical Society of America

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References

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2006 (1)

2005 (2)

2004 (1)

2003 (1)

2002 (1)

1999 (1)

S. Sinzinger and J. Jahns, Microoptics (Wiley-VCH, 1999), p. 107.

1993 (1)

1990 (1)

A. E. Siegman, "New developments in laser resonators," Proc. SPIE 1224, 2-14 (1990).
[CrossRef]

1987 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, "A Practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

1966 (1)

Davidson, N.

Dholakia, K.

D. McGloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

Dimarcello, F.

Friesem, A. A.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "A Practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Ghalmi, S.

Hasman, E.

Ishaaya, A. A.

Jahns, J.

S. Sinzinger and J. Jahns, Microoptics (Wiley-VCH, 1999), p. 107.

Kogelnik, H.

Leger, J. R.

Li, T.

Machavariani, G.

McGloin, D.

D. McGloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

Monberg, E.

Nicholson, J.

Ramachandran, S.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "A Practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Shimshi, L.

Siegman, A. E.

Sinzinger, S.

S. Sinzinger and J. Jahns, Microoptics (Wiley-VCH, 1999), p. 107.

Swanson, G. J.

Veldkamp, W. B.

Wang, Z.

Wisk, P.

Yan, M.

Appl. Opt. (3)

Contemp. Phys. (1)

D. McGloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Optik (1)

R. W. Gerchberg and W. O. Saxton, "A Practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Proc. SPIE (1)

A. E. Siegman, "New developments in laser resonators," Proc. SPIE 1224, 2-14 (1990).
[CrossRef]

Other (1)

S. Sinzinger and J. Jahns, Microoptics (Wiley-VCH, 1999), p. 107.

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Figures (13)

Fig. 1
Fig. 1

Intensity distributions of an LP 08 mode at a 1080   nm wavelength in the near field and at a distance of 15   mm behind the fiber, i.e., nearly in the far field: (a) Experimental result of the near field, (b) simulation data of the near field, (c) experimental data of the far field, (d) simulated data of the far field. The simulated data are displayed with a gamma corrected scale with output ∝ I γ (here: γ = 0.5 ) to imitate the nonlinear response of the Vidicon camera.

Fig. 2
Fig. 2

Scheme of the central cross section of a phase plate made of fused silica for converting an LP 08 mode at a 1080   nm wavelength into a Gaussian mode. The height of the plate at the rim (i.e., for | r | > 45   μm ), where the intensity of the fiber mode is zero, can also be at the high level. Then, the structure is really etched into a plate and is mechanically more stable.

Fig. 3
Fig. 3

Intensity distribution of an LP 02 mode at λ = 1080   nm in (a) the near field and (b) the far field.

Fig. 4
Fig. 4

Far field intensity distribution of a LP 02 mode at λ = 1080   nm plus phase plate immediately behind the fiber.

Fig. 5
Fig. 5

Sketch of the mode conversion system including the telescope for optical filtering.

Fig. 6
Fig. 6

Intensity distribution of a converted LP 02 mode at λ = 1080   nm in (a) the near field and (b) the far field after using a phase plate plus an optical filtering system.

Fig. 7
Fig. 7

Intensity distribution of an LP 08 mode at λ = 1080   nm in (a) the near field and (b) the far field.

Fig. 8
Fig. 8

Far field intensity distribution of a LP 08 mode at λ = 1080   nm plus a phase plate immediately behind the fiber.

Fig. 9
Fig. 9

Intensity distribution of a converted LP 08 mode at λ = 1080   nm in (a) the near field and (b) the far field after using a phase plate plus an optical filtering system.

Fig. 10
Fig. 10

Tolerance analysis for the LP 08 mode at λ = 1080   nm ; (a) conserved light power as function of a lateral misalignment of the phase plate; (b) conserved light power as function of an axial misalignment of the phase plate; and (c) conserved light power as function of the phase shift of the phase plate.

Fig. 11
Fig. 11

Sketch of the complete mode conversion system including a magnifying telescope between the fiber and the phase plate and a filtering telescope behind the phase plate. The first lens symbolizes a microscope objective, whereas the other lenses should be achromatic doublets or other lenses that fulfill the sine condition.

Fig. 12
Fig. 12

Nontelescopic imaging of the LP 08 mode at λ = 1080   nm with a single GRIN lens and free-space propagation in air; (a) intensity distribution in the image plane; (b) phase in the image plane; (c) intensity plot (logarithmic scale) showing the light propagation from the object plane (bottom) to the image plane (top).

Fig. 13
Fig. 13

Telescopic imaging of the LP 08 mode at λ = 1080   nm with a GRIN lens telescope consisting of two different GRIN lenses; (a) intensity distribution in the image plane; (b) phase in the image plane; (c) intensity plot (logarithmic scale) showing the light propagation from the object plane (bottom) to the image plane (top).

Tables (4)

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Table 1 Radii, at Which the Phase of the Phase Plate Has to Change between 0 and π, Respectively, for the Case of an LP08 Mode at λ = 1080 nm, if the Phase Plate Is Directly Mounted at the Fiber End

Tables Icon

Table 2 Numerically Simulated Beam Parameters for Different Modes and Different Measures to Convert Them for the Fibers Made for a Wavelength of λ = 1080 nm a

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Table 3 Numerically Simulated Beam Parameters for Different Modes and Different Measures to Convert Them for the Fibers Made for a Wavelength of λ = 1550 nm a

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Table 4 M 2 Factors and Conserved Amount of Total Light Power for Different Tolerances of the Phase Plate for the Case of the Filtered LP08 Mode at λ = 1080 nm a

Equations (11)

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M x 2 = 4 π λ σ x σ θ x ,
σ x 2 = + + x 2 I ( x , y ) d x d y + + I ( x , y ) d x d y ,
σ θ x 2 = + + θ x 2 I ˜ ( θ x , θ y ) d θ x d θ y + + I ˜ ( θ x , θ y ) d θ x d θ y .
A eff = ( I d A ) 2 I 2 d A .
Δ Φ = 2 π λ ( n 1 ) d .
( x φ ) = M ( x φ ) ,
M = ( A B C D ) = ( cos α f sin α sin α f cos α ) ,
α = 2 n 1 n 0 z ; f = 1 2 n 0 n 1 .
n ( r ) = n 0   sech ( g r ) = n 0 cosh ( g r ) = 2 n 0 exp ( g r ) + exp ( g r ) ,
g = 2 n 1 n 0 ,
M = ( A B C D ) = ( cos α d 2 f sin α d 1 cos α + f sin α + d 2 cos α d 1 d 2 f sin α 1 f sin α cos α d 1 f sin α ) .

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