Abstract

High-quality coherent wavefronts are extremely useful in optical communications and lasers. Disorder is usually considered as a source of noise and deviation from ideal designs for generating high-quality beams in photonic devices. Here, we demonstrate that strong disorder can be exploited to obtain high-quality wavefronts thanks to the Anderson localization phenomenon. Our analysis on a transverse Anderson localizing optical fiber reveals that a considerable number of the guided modes have M2<2 values. These high-quality modes are distributed across the transverse profile of the disordered fiber and can be excited without requiring sophisticated spatial light modulations at the input facet. The results show the potential of such fibers for novel applications in fiber lasers and nonlinear devices, where a high beam quality is desirable.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

J. Zhao, J. E. A. Lopez, Z. Zhu, D. Zheng, S. Pang, R. A. Correa, and A. Schülzgen, Sci. Rep. 8, 3065 (2018).
[Crossref]

2017 (4)

B. Abaie, E. Mobini, S. Karbasi, T. Hawkins, J. Ballato, and A. Mafi, Light Sci. Appl. 6, e17041 (2017).
[Crossref]

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, Phys. Rev. B 96, 054209 (2017).
[Crossref]

G. Ruocco, B. Abaie, W. Schirmacher, A. Mafi, and M. Leonetti, Nat. Commun. 8, 14571 (2017).
[Crossref]

O. J. Trojak, T. Crane, and L. Sapienza, Appl. Phys. Lett. 111, 141103 (2017).
[Crossref]

2016 (2)

B. Abaie, S. R. Hosseini, S. Karbasi, and A. Mafi, Opt. Commun. 365, 208 (2016).
[Crossref]

B. Abaie and A. Mafi, Phys. Rev. B 94, 064201 (2016).
[Crossref]

2015 (1)

2014 (1)

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, Nat. Commun. 5, 3362 (2014).
[Crossref]

2013 (3)

M. Segev, Y. Silberberg, and D. N. Christodoulides, Nat. Photonics 7, 197 (2013).
[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, J. Opt. Soc. Am. B 30, 1452 (2013).
[Crossref]

C. Jauregui, J. Limpert, and A. Tünnermann, Nat. Photonics 7, 861 (2013).
[Crossref]

2012 (5)

2011 (1)

J. Wang and A. Z. Genack, Nature 471, 345 (2011).
[Crossref]

2010 (1)

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[Crossref]

2008 (1)

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

2007 (1)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[Crossref]

2006 (1)

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[Crossref]

2005 (2)

2004 (1)

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[Crossref]

2002 (1)

2000 (1)

A. Chabanov, M. Stoytchev, and A. Genack, Nature 404, 850 (2000).
[Crossref]

1989 (1)

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[Crossref]

1980 (1)

S. Abdullaev and F. K. Abdullaev, Radiofizika 23, 766 (1980).

1975 (1)

M. Dzhibladze, B. Lezhava, and T. Y. Chelidze, Soviet J. Quantum Electron. 4, 1181 (1975).
[Crossref]

Abaie, B.

G. Ruocco, B. Abaie, W. Schirmacher, A. Mafi, and M. Leonetti, Nat. Commun. 8, 14571 (2017).
[Crossref]

B. Abaie, E. Mobini, S. Karbasi, T. Hawkins, J. Ballato, and A. Mafi, Light Sci. Appl. 6, e17041 (2017).
[Crossref]

B. Abaie and A. Mafi, Phys. Rev. B 94, 064201 (2016).
[Crossref]

B. Abaie, S. R. Hosseini, S. Karbasi, and A. Mafi, Opt. Commun. 365, 208 (2016).
[Crossref]

B. Abaie, T. Hawkins, J. Ballato, and A. Mafi, in Laser Science (Optical Society of America, 2017), paper JW4A-96.

Abdullaev, F. K.

S. Abdullaev and F. K. Abdullaev, Radiofizika 23, 766 (1980).

Abdullaev, S.

S. Abdullaev and F. K. Abdullaev, Radiofizika 23, 766 (1980).

Avidan, A.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

Ballato, J.

B. Abaie, E. Mobini, S. Karbasi, T. Hawkins, J. Ballato, and A. Mafi, Light Sci. Appl. 6, e17041 (2017).
[Crossref]

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, Nat. Commun. 5, 3362 (2014).
[Crossref]

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, Opt. Mater. Express 2, 1496 (2012).
[Crossref]

B. Abaie, T. Hawkins, J. Ballato, and A. Mafi, in Laser Science (Optical Society of America, 2017), paper JW4A-96.

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[Crossref]

Bartelt, H.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[Crossref]

Cao, H.

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, Phys. Rev. B 96, 054209 (2017).
[Crossref]

Chabanov, A.

A. Chabanov, M. Stoytchev, and A. Genack, Nature 404, 850 (2000).
[Crossref]

Chelidze, T. Y.

M. Dzhibladze, B. Lezhava, and T. Y. Chelidze, Soviet J. Quantum Electron. 4, 1181 (1975).
[Crossref]

Christodoulides, D. N.

M. Segev, Y. Silberberg, and D. N. Christodoulides, Nat. Photonics 7, 197 (2013).
[Crossref]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

Correa, R. A.

J. Zhao, J. E. A. Lopez, Z. Zhu, D. Zheng, S. Pang, R. A. Correa, and A. Schülzgen, Sci. Rep. 8, 3065 (2018).
[Crossref]

Crane, T.

O. J. Trojak, T. Crane, and L. Sapienza, Appl. Phys. Lett. 111, 141103 (2017).
[Crossref]

De Raedt, H.

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[Crossref]

de Vries, P.

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[Crossref]

Dzhibladze, M.

M. Dzhibladze, B. Lezhava, and T. Y. Chelidze, Soviet J. Quantum Electron. 4, 1181 (1975).
[Crossref]

El-Dardiry, R. G. S.

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, Phys. Rev. B 86, 125132 (2012).
[Crossref]

Faez, S.

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, Phys. Rev. B 86, 125132 (2012).
[Crossref]

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[Crossref]

Frazier, R. J.

Garcia, P. D.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[Crossref]

Genack, A.

A. Chabanov, M. Stoytchev, and A. Genack, Nature 404, 850 (2000).
[Crossref]

Genack, A. Z.

J. Wang and A. Z. Genack, Nature 471, 345 (2011).
[Crossref]

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[Crossref]

Hawkins, T.

B. Abaie, E. Mobini, S. Karbasi, T. Hawkins, J. Ballato, and A. Mafi, Light Sci. Appl. 6, e17041 (2017).
[Crossref]

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, Nat. Commun. 5, 3362 (2014).
[Crossref]

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, Opt. Mater. Express 2, 1496 (2012).
[Crossref]

B. Abaie, T. Hawkins, J. Ballato, and A. Mafi, in Laser Science (Optical Society of America, 2017), paper JW4A-96.

Hosseini, S. R.

B. Abaie, S. R. Hosseini, S. Karbasi, and A. Mafi, Opt. Commun. 365, 208 (2016).
[Crossref]

Hu, B.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[Crossref]

Jauregui, C.

C. Jauregui, J. Limpert, and A. Tünnermann, Nat. Photonics 7, 861 (2013).
[Crossref]

Karbasi, S.

Klosner, J. M.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[Crossref]

Kobelke, J.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[Crossref]

Koch, K. W.

Koirala, M.

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, Phys. Rev. B 96, 054209 (2017).
[Crossref]

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, Phys. Rev. B 86, 125132 (2012).
[Crossref]

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[Crossref]

Lahini, Y.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

Lederer, F.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[Crossref]

Leeb, W. R.

Leonetti, M.

G. Ruocco, B. Abaie, W. Schirmacher, A. Mafi, and M. Leonetti, Nat. Commun. 8, 14571 (2017).
[Crossref]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

Lezhava, B.

M. Dzhibladze, B. Lezhava, and T. Y. Chelidze, Soviet J. Quantum Electron. 4, 1181 (1975).
[Crossref]

Li, L.

Limpert, J.

C. Jauregui, J. Limpert, and A. Tünnermann, Nat. Photonics 7, 861 (2013).
[Crossref]

Lodahl, P.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[Crossref]

Lopez, J. E. A.

J. Zhao, J. E. A. Lopez, Z. Zhu, D. Zheng, S. Pang, R. A. Correa, and A. Schülzgen, Sci. Rep. 8, 3065 (2018).
[Crossref]

Mafi, A.

B. Abaie, E. Mobini, S. Karbasi, T. Hawkins, J. Ballato, and A. Mafi, Light Sci. Appl. 6, e17041 (2017).
[Crossref]

G. Ruocco, B. Abaie, W. Schirmacher, A. Mafi, and M. Leonetti, Nat. Commun. 8, 14571 (2017).
[Crossref]

B. Abaie, S. R. Hosseini, S. Karbasi, and A. Mafi, Opt. Commun. 365, 208 (2016).
[Crossref]

B. Abaie and A. Mafi, Phys. Rev. B 94, 064201 (2016).
[Crossref]

A. Mafi, Adv. Opt. Photon. 7, 459 (2015).
[Crossref]

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, Nat. Commun. 5, 3362 (2014).
[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, J. Opt. Soc. Am. B 30, 1452 (2013).
[Crossref]

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, Opt. Mater. Express 2, 1496 (2012).
[Crossref]

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, Opt. Express 20, 18692 (2012).
[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, Opt. Lett. 37, 2304 (2012).
[Crossref]

A. Mafi and J. V. Moloney, J. Lightwave Technol. 23, 2267 (2005).
[Crossref]

L. Li, A. Schülzgen, V. Temyanko, T. Qiu, M. Morrell, Q. Wang, A. Mafi, J. Moloney, and N. Peyghambarian, Opt. Lett. 30, 1141 (2005).
[Crossref]

B. Abaie, T. Hawkins, J. Ballato, and A. Mafi, in Laser Science (Optical Society of America, 2017), paper JW4A-96.

Miller, S.

S. Miller, Optical Fiber Telecommunications (Elsevier, 2012).

Mirr, C. R.

Mobini, E.

B. Abaie, E. Mobini, S. Karbasi, T. Hawkins, J. Ballato, and A. Mafi, Light Sci. Appl. 6, e17041 (2017).
[Crossref]

Moloney, J.

Moloney, J. V.

Morandotti, R.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

Morrell, M.

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

Nolte, S.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[Crossref]

Pang, S.

J. Zhao, J. E. A. Lopez, Z. Zhu, D. Zheng, S. Pang, R. A. Correa, and A. Schülzgen, Sci. Rep. 8, 3065 (2018).
[Crossref]

Pertsch, T.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[Crossref]

Peschel, U.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[Crossref]

Peyghambarian, N.

Pozzi, F.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

Qiu, T.

Ruocco, G.

G. Ruocco, B. Abaie, W. Schirmacher, A. Mafi, and M. Leonetti, Nat. Commun. 8, 14571 (2017).
[Crossref]

Sapienza, L.

O. J. Trojak, T. Crane, and L. Sapienza, Appl. Phys. Lett. 111, 141103 (2017).
[Crossref]

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[Crossref]

Sarma, R.

M. Koirala, R. Sarma, H. Cao, and A. Yamilov, Phys. Rev. B 96, 054209 (2017).
[Crossref]

Schirmacher, W.

G. Ruocco, B. Abaie, W. Schirmacher, A. Mafi, and M. Leonetti, Nat. Commun. 8, 14571 (2017).
[Crossref]

Schülzgen, A.

J. Zhao, J. E. A. Lopez, Z. Zhu, D. Zheng, S. Pang, R. A. Correa, and A. Schülzgen, Sci. Rep. 8, 3065 (2018).
[Crossref]

L. Li, A. Schülzgen, V. Temyanko, T. Qiu, M. Morrell, Q. Wang, A. Mafi, J. Moloney, and N. Peyghambarian, Opt. Lett. 30, 1141 (2005).
[Crossref]

Schuster, K.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[Crossref]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[Crossref]

Sebbah, P.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[Crossref]

Segev, M.

M. Segev, Y. Silberberg, and D. N. Christodoulides, Nat. Photonics 7, 197 (2013).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[Crossref]

Siegman, A. E.

A. E. Siegman, in Diode Pumped Solid State Lasers: Applications and Issues (Optical Society of America, 1998), paper MQ1.

A. E. Siegman, Lasers (Technology & Engineering, 1986).

Silberberg, Y.

M. Segev, Y. Silberberg, and D. N. Christodoulides, Nat. Photonics 7, 197 (2013).
[Crossref]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

Smolka, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[Crossref]

Sorel, M.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. (a) SEM image of the tip of glass-TALOF. The darker sites are the air-holes. (b) Magnified SEM image shows the details of the air-holes in a portion of the fiber cross section.
Fig. 2.
Fig. 2. (a) Numerically calculated mode and (b) its M2 values in x and y coordinates. (c) Histogram of the calculated Mx2 for 1000 localized modes. (d) Density histogram representative of the location of the modes. (e) The same as part c in the presence of an additional 500 calculated modes. (f) Density histogram representative of the location of the modes in part e.
Fig. 3.
Fig. 3. (a) Histogram of Mx2 values for a TALOF with optimal parameters. (b) Density histogram of the mode locations. Modes are distributed uniformly across the transverse profile of the disordered fiber.
Fig. 4.
Fig. 4. (a) and (b) Two experimentally exited modes and their M2 values in the x and y coordinates. Mx2, My21 are indicative of nearly diffraction-limited beam quality of the localized modes.
Fig. 5.
Fig. 5. Histogram of M2 evaluated for 30 localized modes in the (a) x coordinate and (b) y coordinate. Several modes have M2<2.
Fig. 6.
Fig. 6. (a) Experimental setup for spatial coherence measurement: a localized mode is excited, and the beam at the output of the glass-TALOF is used in a Young double-slit setting. (b) The localized beam profile used for spatial coherence evaluation. (c) Interference pattern generated by the localized mode. (d) Intensity distribution averaged over all vertical lines in the interference pattern of part c.

Equations (3)

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σx2=dA(xx¯)2I(x,y),σy2=dA(yy¯)2I(x,y)
x¯=dAxI(x,y),y¯=dAyI(x,y),
NV22,where  V=2πaλn22n12.