Abstract

Physical insights and characteristics of beam transformations based on multimode interference (MMI) in multimode waveguides are illuminated and analyzed. Our calculations show that, utilizing a short piece of cylindrical multimode waveguide, an input Gaussian beam can be readily transformed to frequently desired beams including top-hat, donut-shaped, taper-shaped, and Bessel-like beams in the Fresnel or the Fraunhofer diffraction range, or even in both ranges. This is a consequence of diffractive propagation of the field exiting the waveguide. The performance of the beam shaper based on MMI can be controlled via tailoring the dimensions of the multimode waveguide or changing the signal wavelength. This beam shaping technique is investigated experimentally using monolithic fiber devices consisting of a short piece of multimode fiber (~ 10 mm long) and a single-mode signal delivery fiber.

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References

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  1. F. Dickey and S. Holswade, eds., Laser Beam Shaping: Theory and Techniques (New York: Marcel Dekker, 2000).
  2. F. Dickey, D. Shealy, and S. Holswade, eds., Laser Beam Shaping Applications (New York: Marcel Dekker, 2005).
  3. Y. Matsuura, M. Miyagi, A. German, L. Nagli, and A. Katzir, “Silver-halide fiber tip as a beam homogenizer for infrared hollow waveguides,” Opt. Lett. 22(17), 1308–1310 (1997).
    [CrossRef]
  4. Y. Matsuura, D. Akiyama, and M. Miyagi, “Beam homogenizer for hollow-fiber delivery system of excimer laser light,” Appl. Opt. 42(18), 3505–3508 (2003).
    [CrossRef] [PubMed]
  5. J. R. Hayes, J. C. Flanagan, T. M. Monro, D. J. Richardson, P. Grunewald, and R. Allott, “Square core jacketed air-clad fiber,” Opt. Express 14(22), 10345–10350 (2006).
    [CrossRef] [PubMed]
  6. X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber laser beam shaping using a long-period grating,” IEEE Photon. Technol. Lett. 20(13), 1130–1132 (2008).
    [CrossRef]
  7. Z. Tian, M. Nix, and S. S.-H. Yam, “Laser beam shaping using a single-mode fiber abrupt taper,” Opt. Lett. 34(3), 229–231 (2009).
    [CrossRef] [PubMed]
  8. Y. O. Yilmaz, A. Mehta, W. S. Mohammed, and E. G. Johnson, “Fiber-optic beam shaper based on multimode interference,” Opt. Lett. 32(21), 3170–3172 (2007).
    [CrossRef] [PubMed]
  9. X. Zhu, A. Schülzgen, L. Li, and N. Peyghambarian, “Generation of controllable nondiffracting beams using multimode optical fibers,” Appl. Phys. Lett. 94(20), 201102 (2009).
    [CrossRef]
  10. X. Zhu, A. Schülzgen, H. Li, L. Li, L. Han, J. V. Moloney, and N. Peyghambarian, “Detailed investigation of self-imaging in large-core multimode optical fibers for application in fiber lasers and amplifiers,” Opt. Express 16(21), 16632–16645 (2008).
    [PubMed]
  11. W. S. Mohammed, A. Mehta, and E. G. Johnson, “Wavelength tunable fiber lens based on multimode interference,” J. Lightwave Technol. 22(2), 469–477 (2004).
    [CrossRef]
  12. A. Mehta, W. S. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15(8), 1129–1131 (2003).
    [CrossRef]
  13. R. Selvas, I. Torres-Gomez, A. Martinez-Rios, J. A. Alvarez-Chavez, D. A. May-Arrioja, P. Likamwa, A. Mehta, and E. G. Johnson, “Wavelength tuning of fiber lasers using multimode interference effects,” Opt. Express 13(23), 9439–9445 (2005).
    [CrossRef] [PubMed]
  14. X. Zhu, A. Schülzgen, H. Li, L. Li, Q. Wang, S. Suzuki, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “Single-transverse-mode output from a fiber laser based on multimode interference,” Opt. Lett. 33(9), 908–910 (2008).
    [CrossRef] [PubMed]
  15. X. Zhu, A. Schülzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15(1), 71–78 (2009).
    [CrossRef]
  16. X. Zhu, “Multimode interference in optical fibers and its applications in fiber lasers and amplifiers,” Phd’s dissertation, University of Arizona (2008).
  17. E. Sziklas and A. Siegman, “Diffraction calculations using fast Fourier transform methods,” Proc. IEEE 62(3), 410–412 (1974).
    [CrossRef]
  18. H. Li, M. Brio, L. Li, A. Schülzgen, N. Peyghambarian, and J. V. Moloney, “Multimode interference in circular step-index fibers studies with the mode expansion approach,” J. Opt. Soc. Am. B 24(10), 2707 (2007).
    [CrossRef]

2009 (3)

X. Zhu, A. Schülzgen, L. Li, and N. Peyghambarian, “Generation of controllable nondiffracting beams using multimode optical fibers,” Appl. Phys. Lett. 94(20), 201102 (2009).
[CrossRef]

Z. Tian, M. Nix, and S. S.-H. Yam, “Laser beam shaping using a single-mode fiber abrupt taper,” Opt. Lett. 34(3), 229–231 (2009).
[CrossRef] [PubMed]

X. Zhu, A. Schülzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15(1), 71–78 (2009).
[CrossRef]

2008 (3)

2007 (2)

2006 (1)

2005 (1)

2004 (1)

2003 (2)

A. Mehta, W. S. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15(8), 1129–1131 (2003).
[CrossRef]

Y. Matsuura, D. Akiyama, and M. Miyagi, “Beam homogenizer for hollow-fiber delivery system of excimer laser light,” Appl. Opt. 42(18), 3505–3508 (2003).
[CrossRef] [PubMed]

1997 (1)

1974 (1)

E. Sziklas and A. Siegman, “Diffraction calculations using fast Fourier transform methods,” Proc. IEEE 62(3), 410–412 (1974).
[CrossRef]

Akiyama, D.

Allott, R.

Alvarez-Chavez, J. A.

Brio, M.

Flanagan, J. C.

German, A.

Grunewald, P.

Gu, X.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber laser beam shaping using a long-period grating,” IEEE Photon. Technol. Lett. 20(13), 1130–1132 (2008).
[CrossRef]

Han, L.

Hayes, J. R.

Johnson, E. G.

Katzir, A.

Li, H.

Li, L.

Likamwa, P.

Martinez-Rios, A.

Matsuura, Y.

May-Arrioja, D. A.

Mehta, A.

Miyagi, M.

Mohammed, W.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber laser beam shaping using a long-period grating,” IEEE Photon. Technol. Lett. 20(13), 1130–1132 (2008).
[CrossRef]

Mohammed, W. S.

Moloney, J. V.

Monro, T. M.

Nagli, L.

Nix, M.

Peyghambarian, N.

Qian, L.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber laser beam shaping using a long-period grating,” IEEE Photon. Technol. Lett. 20(13), 1130–1132 (2008).
[CrossRef]

Richardson, D. J.

Schülzgen, A.

Selvas, R.

Siegman, A.

E. Sziklas and A. Siegman, “Diffraction calculations using fast Fourier transform methods,” Proc. IEEE 62(3), 410–412 (1974).
[CrossRef]

Smith, P. W. E.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber laser beam shaping using a long-period grating,” IEEE Photon. Technol. Lett. 20(13), 1130–1132 (2008).
[CrossRef]

Suzuki, S.

Sziklas, E.

E. Sziklas and A. Siegman, “Diffraction calculations using fast Fourier transform methods,” Proc. IEEE 62(3), 410–412 (1974).
[CrossRef]

Temyanko, V. L.

X. Zhu, A. Schülzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15(1), 71–78 (2009).
[CrossRef]

X. Zhu, A. Schülzgen, H. Li, L. Li, Q. Wang, S. Suzuki, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “Single-transverse-mode output from a fiber laser based on multimode interference,” Opt. Lett. 33(9), 908–910 (2008).
[CrossRef] [PubMed]

Tian, Z.

Torres-Gomez, I.

Wang, Q.

Yam, S. S.-H.

Yilmaz, Y. O.

Zhu, X.

X. Zhu, A. Schülzgen, L. Li, and N. Peyghambarian, “Generation of controllable nondiffracting beams using multimode optical fibers,” Appl. Phys. Lett. 94(20), 201102 (2009).
[CrossRef]

X. Zhu, A. Schülzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15(1), 71–78 (2009).
[CrossRef]

X. Zhu, A. Schülzgen, H. Li, L. Li, Q. Wang, S. Suzuki, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “Single-transverse-mode output from a fiber laser based on multimode interference,” Opt. Lett. 33(9), 908–910 (2008).
[CrossRef] [PubMed]

X. Zhu, A. Schülzgen, H. Li, L. Li, L. Han, J. V. Moloney, and N. Peyghambarian, “Detailed investigation of self-imaging in large-core multimode optical fibers for application in fiber lasers and amplifiers,” Opt. Express 16(21), 16632–16645 (2008).
[PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

X. Zhu, A. Schülzgen, L. Li, and N. Peyghambarian, “Generation of controllable nondiffracting beams using multimode optical fibers,” Appl. Phys. Lett. 94(20), 201102 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Zhu, A. Schülzgen, H. Li, L. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “High power fiber lasers and amplifiers based on multimode interference,” IEEE J. Sel. Top. Quantum Electron. 15(1), 71–78 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. Mehta, W. S. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photon. Technol. Lett. 15(8), 1129–1131 (2003).
[CrossRef]

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber laser beam shaping using a long-period grating,” IEEE Photon. Technol. Lett. 20(13), 1130–1132 (2008).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Express (3)

Opt. Lett. (4)

Proc. IEEE (1)

E. Sziklas and A. Siegman, “Diffraction calculations using fast Fourier transform methods,” Proc. IEEE 62(3), 410–412 (1974).
[CrossRef]

Other (3)

X. Zhu, “Multimode interference in optical fibers and its applications in fiber lasers and amplifiers,” Phd’s dissertation, University of Arizona (2008).

F. Dickey and S. Holswade, eds., Laser Beam Shaping: Theory and Techniques (New York: Marcel Dekker, 2000).

F. Dickey, D. Shealy, and S. Holswade, eds., Laser Beam Shaping Applications (New York: Marcel Dekker, 2005).

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Figures (13)

Fig. 1
Fig. 1

Schematic depiction of beam transformation using MM waveguides.

Fig. 2
Fig. 2

(a) Distributions of three considered facet fields of a 50 μm cylindrical waveguide and (b) their corresponding far-field intensity profiles. Top-hat (red); taper-shaped (green); donut-shaped (blue).

Fig. 3
Fig. 3

Design of an all-fiber device for laser beam shaping (the figure is not to scale).

Fig. 4
Fig. 4

Intensity distribution of the laser beam propagating in free space when the signal wavelength is 1572 nm. (a) The plot ranges from 1 mm to 20 mm; (b) the plot ranges from 0 mm to 1 mm.

Fig. 5
Fig. 5

Intensity distribution of the laser beam propagating in free space when the signal wavelength is 1580 nm. (a) The plot ranges from 1 mm to 20 mm; (b) the plot ranges from 0 mm to 1 mm.

Fig. 6
Fig. 6

(a) Four often desired intensity profiles generated at a distance of 20 mm from the fiber facet and (b) the corresponding field distribution at the MM fiber facet. Red curve (top-hat); green curve (taper-shaped); red curve (donut-shaped); black curve (Bessel-like).

Fig. 7
Fig. 7

Wavelength dependence of the fiber-optic beam transformer for the four cases shown in Fig. 5. (a) Top-hat, (b) taper-shaped, (c) donut-shaped, and (d) Bessel-like.

Fig. 8
Fig. 8

Far-field intensity profiles at a 20 mm distance from the MM fiber facet for all-fiber beam transformers with different MM fiber lengths. (a) Top-hat; (b) taper-shaped; (c) donut-shaped; (d) Bessel-like.

Fig. 9
Fig. 9

Energy percentages of the excited modes in the MM fibers with diameters of 25 μm (red circles), 50 μm (green squares), and 105 μm (blue diamonds), respectively, when the signal delivery SM fiber is SMF-28.

Fig. 10
Fig. 10

Comparisons of the far-field intensity profiles of the desired beams generated from beam transformers using 25 μm, 50 μm, and 105 μm MM fibers, respectively. (a) top-hat; (b) Bessel-like; (c) taper-shaped; (d) donut-shaped.

Fig. 11
Fig. 11

(a) top-hat, (b) donut-shaped, (c) taper-shaped, and (d) Bessel-like intensity profiles created experimentally and recorded by a CCD camera at a distance of 20 mm from the MM fiber facet. (For comparison, the intensity profile of the beam exiting directly from the SM fiber is also plotted.).

Fig. 12
Fig. 12

(a) Bessel-like and (b) Donut-shaped intensity profiles created experimentally and recorded by a CCD camera at a distance of 20 mm from the 105 μm MM fiber facet.

Fig. 13
Fig. 13

(a) top-hat, (b) donut-shaped, (c) taper-shaped, and (d) Bessel-like intensity profiles created experimentally and recorded by a CCD camera at a distance of 20 mm from a beam transformer consisting of a 105 μm MM fiber and an SM fiber with a mode-field diameter of 23 μm. (For comparison, the intensity profile of the beam exiting directly from the LMA SM fiber is also plotted.).

Equations (6)

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E i n ( x , y , z = 0 ) = 1 M 1 N C m n e m n ( x , y , z = 0 ) ,
C m n = S E i n ( x , y , 0 ) × e m n * ( x , y , 0 ) d s S | e m n ( x , y , 0 ) | 2 d s .
E o u t ( x , y , L ) = 1 M 1 N C m n e m n ( x , y , 0 ) e i β m n L ,
E O u t ( r , φ , L ) = n = 1 N C n e n ( r , φ ) e i β n L ,
E f s ( r , φ ) = 1 i λ D e i π r 2 λ D S ' E o u t ( r ' , φ ' ) e i π r ' 2 λ D J 0 ( 2 π r ' r λ D ) d s ' ,
E f s ( r , φ ) = F T 1 { F T [ E o u t ( r ' , φ ' ) ] exp [ i 2 π D λ 1 ( λ ξ ) 2 ( λ η ) 2 ] } ,

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