Abstract

Properties of the self-imaging effect based on multimode interference (MMI) in large-core passive optical fibers are investigated and analyzed in detail, with the purpose of using multimode active fibers for high power single-transverse-mode emission. Although perfect self-imaging of the input field from a standard single-mode fiber (SMF-28) in a multimode fiber becomes practically impossible as its core diameter is larger than 50 µm, a quasi-reproduction of the input field occurs when the phase difference between the excited modes and the peak mode inside the multimode fiber is very small. Our simulation and experimental results indicate that, if the length of the multimode fiber segment can be controlled accurately, reproduction of the input field with a self-imaging quality factor larger than 0.9 can be obtained. In this case, a low-loss hybrid fiber cavity composed of a SMF-28 segment and a very-large-core active multimode fiber segment can be built. It is also found that for the hybrid fiber cavity, increasing the mode-field diameter of the single-mode fiber improves both the self-imaging quality and the tolerance on the required length accuracy of the multimode fiber segment. Moreover, in this paper key parameters for the design of MMI-based fiber devices are defined and their corresponding values are provided for multimode fibers with core diameters of 50 µm and 105 µm.

© 2008 Optical Society of America

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References

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  2. O. Bryngdahl, "Image formation using self-imaging techniques," J. Opt. Soc. Am. 63, 416-419 (1973).
    [CrossRef]
  3. R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
    [CrossRef]
  4. L. B. Soldano and E. C. M. Penning, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
    [CrossRef]
  5. S. W. Allison and G. T. Gillies, "Observations of and applications for self-imaging in optical fibers," Appl. Opt. 33, 1802-1805 (1994).
    [CrossRef] [PubMed]
  6. 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, 9439-9445, (2005).
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  8. W. S. Mohammed, A. Mehta, and E. G. Johnson, "Wavelength tunable fiber lens based on multimode interference," J. Lightwave Technol. 22, 469-477 (2004).
    [CrossRef]
  9. A. Mehta, W. S. Mohammed, and E. G. Johnson, "Multimode interference-based fiber-optic displacement sensor," IEEE Photon. Technol. Lett. 15, 1129-1131 (2003).
    [CrossRef]
  10. K. Hamamoto, E. Gini, C. Holtmann, and H. Melchior, "Single-transverse-mode active multi-mode-interferometer 1.45 μm high power laser diode," Appl. Phys. B 73, 571-574 (2001).
    [CrossRef]
  11. H. J. Baker, J. R. Lee, and D. R. Hall, "Self-imaging and high-beam-quality operation in multi-mode planar waveguide optical amplifiers," Opt. Express 10, 297-302 (2002).
    [PubMed]
  12. W. S. Pelouch, D. D. Smith, J. E. Koroshetz, I. T. Mckinnie, J. R. Unternahrer, S. W. Henderson, W. R. Scharpf, "Self-imaging in waveguide lasers and amplifiers", OSA Topical Meeting on Advanced Solid State Lasers, 6-9 (Optical Society of America, Washington, D. C., 2002).
  13. I. T. Mckinnie, J. E. Koroshetz, W. S. Pelouch, D. D. Smith, J. R. Unternahrer, S. W. Henderson, M. Wright, "Self-imaging waveguide Nd:YAG laser with 58% slope efficiency," OSA Topical Meeting on Advanced Solid State Lasers, 262-263 (Optical Society of America, Washington, D. C., 2002).
  14. I. T. Mckinnie, B. E. Callicoatt, C. Wood, J. E. Koroshetz, J. R. Unternahrer, M. L. Tartaglia, S. E. Christensen, O. J. Koski, M. Hinckley, M. J. Bellanca, E. Schneider, and D. D. Smith, "Self-imaging waveguide lasers," Conference on Lasers and Electro-optics, CMS1, 319-321 (2005).
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    [CrossRef]
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2008 (1)

2007 (2)

2006 (1)

2005 (2)

2004 (1)

2003 (1)

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

2002 (1)

2001 (1)

K. Hamamoto, E. Gini, C. Holtmann, and H. Melchior, "Single-transverse-mode active multi-mode-interferometer 1.45 μm high power laser diode," Appl. Phys. B 73, 571-574 (2001).
[CrossRef]

1995 (1)

L. B. Soldano and E. C. M. Penning, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

1994 (1)

1975 (1)

R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
[CrossRef]

1973 (1)

1836 (1)

H. F. Talbot, "Facts relating to optical science No. IV," Phil Mag. 9, 401-407 (1836).

Allison, S. W.

Alvarez-Chavez, J. A.

Ankele, G.

R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
[CrossRef]

Baker, H. J.

Brio, M.

Broeng, J.

Bryngdahl, O.

Gillies, G. T.

Gini, E.

K. Hamamoto, E. Gini, C. Holtmann, and H. Melchior, "Single-transverse-mode active multi-mode-interferometer 1.45 μm high power laser diode," Appl. Phys. B 73, 571-574 (2001).
[CrossRef]

Gu, X.

Hall, D. R.

Hamamoto, K.

K. Hamamoto, E. Gini, C. Holtmann, and H. Melchior, "Single-transverse-mode active multi-mode-interferometer 1.45 μm high power laser diode," Appl. Phys. B 73, 571-574 (2001).
[CrossRef]

Holtmann, C.

K. Hamamoto, E. Gini, C. Holtmann, and H. Melchior, "Single-transverse-mode active multi-mode-interferometer 1.45 μm high power laser diode," Appl. Phys. B 73, 571-574 (2001).
[CrossRef]

Honninger, I. M.

Jakobsen, C.

Jalali, B.

Johnson, E. G.

Lee, J. R.

Li, H.

Li, L.

Liem, A.

Likamwa, P.

Limpert, J.

Martinez-Rios, A.

May-Arrioja, D. A.

Mehta, A.

Melchior, H.

K. Hamamoto, E. Gini, C. Holtmann, and H. Melchior, "Single-transverse-mode active multi-mode-interferometer 1.45 μm high power laser diode," Appl. Phys. B 73, 571-574 (2001).
[CrossRef]

Mohammed, W. S.

Moloney, J. V.

Nolte, S.

Penning, E. C. M.

L. B. Soldano and E. C. M. Penning, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Petersson, A.

Peyghambarian, N.

Raghunathan, V.

Renner, H.

Rice, R. R.

Robin, N. D.

Roser, F.

Salin, F.

Schreiber, T.

Schülzgen, A.

Selvas, R.

Smith, P. W. E.

Soldano, L. B.

L. B. Soldano and E. C. M. Penning, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Suzuki, S.

Talbot, H. F.

H. F. Talbot, "Facts relating to optical science No. IV," Phil Mag. 9, 401-407 (1836).

Temyanko, V. L.

Torres-Gomez, I.

Tunnermann, A.

Ulrich, R.

R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
[CrossRef]

Wang, Q.

Zellmer, H.

Zhu, X.

Appl. Opt. (1)

Appl. Phys. B (1)

K. Hamamoto, E. Gini, C. Holtmann, and H. Melchior, "Single-transverse-mode active multi-mode-interferometer 1.45 μm high power laser diode," Appl. Phys. B 73, 571-574 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

J. Lightwave Technol. (2)

W. S. Mohammed, A. Mehta, and E. G. Johnson, "Wavelength tunable fiber lens based on multimode interference," J. Lightwave Technol. 22, 469-477 (2004).
[CrossRef]

L. B. Soldano and E. C. M. Penning, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Express (4)

Opt. Lett. (2)

Phil Mag. (1)

H. F. Talbot, "Facts relating to optical science No. IV," Phil Mag. 9, 401-407 (1836).

Other (3)

W. S. Pelouch, D. D. Smith, J. E. Koroshetz, I. T. Mckinnie, J. R. Unternahrer, S. W. Henderson, W. R. Scharpf, "Self-imaging in waveguide lasers and amplifiers", OSA Topical Meeting on Advanced Solid State Lasers, 6-9 (Optical Society of America, Washington, D. C., 2002).

I. T. Mckinnie, J. E. Koroshetz, W. S. Pelouch, D. D. Smith, J. R. Unternahrer, S. W. Henderson, M. Wright, "Self-imaging waveguide Nd:YAG laser with 58% slope efficiency," OSA Topical Meeting on Advanced Solid State Lasers, 262-263 (Optical Society of America, Washington, D. C., 2002).

I. T. Mckinnie, B. E. Callicoatt, C. Wood, J. E. Koroshetz, J. R. Unternahrer, M. L. Tartaglia, S. E. Christensen, O. J. Koski, M. Hinckley, M. J. Bellanca, E. Schneider, and D. D. Smith, "Self-imaging waveguide lasers," Conference on Lasers and Electro-optics, CMS1, 319-321 (2005).

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Figures (17)

Fig. 1.
Fig. 1.

A simple fiber structure for studying the self-imaging properties of MM optical fibers.

Fig. 2.
Fig. 2.

Field distributions of the excited modes and their in-phase superposition in the MM fiber segment of the MMI structure. (a) Core diameter of the MM fiber is 50 µm; (b) Core diameter of the MM fiber is 105 µm.

Fig. 3.
Fig. 3.

Self-imaging quality factor γ along the MM fiber segment with a core diameter of (a) 50 µm or (b) 105 µm, respectively.

Fig. 4.
Fig. 4.

Energy percentage of the excited modes and the phase differences at a self-imaging point between the excited modes and the mode of highest intensity inside MM fiber with core diameters of (a) 50 µm and (b) 105 µm fiber, respectively.

Fig. 5.
Fig. 5.

(a). The maximum self-imaging quality factor γ max and (b) the self-imaging length interval within one meter MM fiber segment of different core diameters.

Fig. 6.
Fig. 6.

Two peaks of z=10.3 and 43.28 mm in Fig. 3(a) and (b) are magnified in (a) and (b), respectively.

Fig. 7.
Fig. 7.

Self-imaging quality factor γ along a MM fiber segment with a core diameter of 105 µm when the input SM fiber has a MFD of 23 µm and 40 µm, respectively. (a) MFD=23 µm; (b) MFD=40 µm.

Fig. 8.
Fig. 8.

Individual parameters, Δλim, nL and dλn/(dL/L), of the 50 µm and 105 µm fiber are plotted in a wavelength range of 1.5-1.6 µm, respectively. (a) Δλim, nL of the 50 µm fiber; (b) dλn/(dL/L) of the 50 µm fiber; (c) Δλim, nL of the 105 µm fiber; (d) dλn/(dL/L) of the 105 µm fiber.

Fig. 9.
Fig. 9.

Experimental setup for the transmission spectrum measurement of an MMI structure.

Fig. 10.
Fig. 10.

Transmission spectra of MMI structures with fiber lengths of 20 cm and 100 cm and with fiber core diameters of 50 µm and 105 µm, respectively. (a) Spectra of the 50 µm fiber; (b) Spectra of the 105 µm fiber.

Fig. 11.
Fig. 11.

The self-imaging wavelength interval and the self-imaging wavelength shift for 1 cm change of the fiber length of the MMI structure with different MM fiber lengths. (a) The wavelength interval of the self-imaging; (b) The self-imaging wavelength shift for 1 cm change of the fiber length.

Fig. 12.
Fig. 12.

Transmission at the self-imaging wavelength for MMI structures with different MMI fiber lengths. (a) Transmission at the self-imaging wavelength for MMI structures consist of a 50 µm MM fiber and a SMF-28; (b) Transmission at the self-imaging wavelength for MMI structures consist of a 105 µm MM fiber and a SMF-28 (square) or a LMFD-10 (circle), respectively.

Fig. 13.
Fig. 13.

Experimental setup for direct observation of self-imaging in a MM fiber.

Fig. 14.
Fig. 14.

The intensity distribution of the facet of the 50 µm MM fiber segment of a MMI structure when a tunable single-frequency signal is launched and the transmission spectrum of the corresponding MMI structure.

Fig. 15.
Fig. 15.

The facet image, its three-dimensional plot, and the far-field image of the 50µm MM fiber segment of a MMI structure when a signal of 1557 nm is input. (a) MM fiber facet image; (b) Threedimensional plot of (a); (c) Far-field image.

Fig. 16.
Fig. 16.

The facet image, its three-dimensional plot, and the far-field image of a 105 µm MM fiber segment of a MMI structure when a signal of 1575 nm is input. (a) MM fiber facet image; (b) Three-dimensional plot of (a); (c) Far-field image.

Fig. 17.
Fig. 17.

The facet image, its three-dimensional plot, and the far-field image of a 105 µm MM fiber segment when a signal at the self-imaging wavelength is input and a LMFD-10 fiber is used. (a) MM fiber facet image; (b) Three-dimensional plot of (a); (c) Far-field image.

Equations (7)

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E SM ( r , ϕ , z = 0 ) = 1 N C n e n ( r , ϕ , z = 0 ) ,
C n = S E SM ( r , ϕ ) × e n * ( r , ϕ ) d s S e n ( r , ϕ ) 2 d s .
E MM ( r , ϕ , z ) = 1 N C n e n ( r , ϕ , 0 ) e i β n z = e i β 1 z 1 N C n e n ( r , ϕ , 0 ) e i ( β n β 1 ) z ,
( β n β 1 ) z self− imaging = Δ β n z self− imaging = m n 2 π . ( m n integer )
Δ n eff , n L = m n λ , ( m n integer , n = 2 , 3 , , N )
Δ λ im , n = 1 L λ d Δ n eff , n d λ Δ n eff , n λ
d λ n d L = 1 L ( 1 λ 1 Δ n eff , n d Δ n eff , n d λ )

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