Abstract

In this paper, we explore the use of an optical correlation technique to decompose different radial as well as azimuthal order modes of Laguerre Gaussian (LG) beams. We experimentally demonstrate the decomposition of single as well as composite LG beams and compare it with simulations. We report the modal decomposition with 27 dB extinction over several radial and azimuthal orders. Finally, we show that our modal decomposition is capable of sorting mode spectrum consisting of up to 10 LG modes with an accuracy of better than 97.8%.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]

2019 (1)

2018 (7)

S. Choudhary, R. Sampson, Y. Miyamoto, O. S. Magaña-Loaiza, S. M. H. Rafsanjani, M. Mirhosseini, and R. W. Boyd, “Measurement of the radial mode spectrum of photons through a phase-retrieval method,” Opt. Lett. 43(24), 6101–6104 (2018).
[Crossref] [PubMed]

F. Bouchard, N. H. Valencia, F. Brandt, R. Fickler, M. Huber, and M. Malik, “Measuring azimuthal and radial modes of photons,” Opt. Express 26(24), 31925–31941 (2018).
[Crossref] [PubMed]

D. Fu, Y. Zhou, R. Qi, S. Oliver, Y. Wang, S. M. H. Rafsanjani, J. Zhao, M. Mirhosseini, Z. Shi, P. Zhang, and R. W. Boyd, “Realization of a scalable Laguerre-Gaussian mode sorter based on a robust radial mode sorter,” Opt. Express 26(25), 33057–33065 (2018).
[Crossref] [PubMed]

G. Zhu, Z. Hu, X. Wu, C. Du, W. Luo, Y. Chen, X. Cai, J. Liu, J. Zhu, and S. Yu, “Scalable mode division multiplexed transmission over a 10-km ring-core fiber using high-order orbital angular momentum modes,” Opt. Express 26(2), 594–604 (2018).
[Crossref] [PubMed]

L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18 km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018).
[Crossref] [PubMed]

K. Pang, C. Liu, G. Xie, Y. Ren, Z. Zhao, R. Zhang, Y. Cao, J. Zhao, H. Song, H. Song, L. Li, A. N. Willner, M. Tur, R. W. Boyd, and A. E. Willner, “Demonstration of a 10 Mbit/s quantum communication link by encoding data on two Laguerre-Gaussian modes with different radial indices,” Opt. Lett. 43(22), 5639–5642 (2018).
[Crossref] [PubMed]

S. Zhu, S. Pidishety, Y. Feng, S. Hong, J. Demas, R. Sidharthan, S. Yoo, S. Ramachandran, B. Srinivasan, and J. Nilsson, “Multimode-pumped Raman amplification of a higher order mode in a large mode area fiber,” Opt. Express 26(18), 23295–23304 (2018).
[Crossref] [PubMed]

2017 (3)

2016 (3)

2014 (1)

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4(1), 7441 (2014).
[Crossref] [PubMed]

2012 (2)

D. Flamm, C. Schulze, R. Brüning, O. A. Schmidt, T. Kaiser, S. Schröter, and M. Duparré, “Fast M2 measurement for fiber beams based on modal analysis,” Appl. Opt. 51(7), 987–993 (2012).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2010 (1)

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

2009 (1)

2007 (1)

2005 (1)

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

1999 (1)

1996 (1)

Ahmed, N.

G. Xie, Y. Ren, Y. Yan, H. Huang, N. Ahmed, L. Li, Z. Zhao, C. Bao, M. Tur, S. Ashrafi, and A. E. Willner, “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre-Gaussian beams with different radial indices,” Opt. Lett. 41(15), 3447–3450 (2016).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Ai, J.

Alperin, S. N.

Andersen, J. M.

Arie, A.

Arrizón, V.

Ashrafi, S.

Bao, C.

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Berkhout, G. C. G.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Bouchard, F.

Boyd, R. W.

Brandt, F.

Brüning, R.

Cai, X.

Campos, J.

Cao, Y.

Cardano, F.

Carrada, R.

Chen, S.

Chen, Y.

Choudhary, S.

Cottrell, D. M.

Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

D’Amelio, R.

D’Errico, A.

Davis, J. A.

Demas, J.

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Dorsch, R. G.

Du, C.

Dudley, A.

A. Trichili, A. B. Salem, A. Dudley, M. Zghal, and A. Forbes, “Encoding information using Laguerre Gaussian modes over free space turbulence media,” Opt. Lett. 41(13), 3086–3089 (2016).
[Crossref] [PubMed]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

Duparré, M.

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Feng, Y.

Ferreira, C.

Fickler, R.

Flamm, D.

Forbes, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

A. Trichili, A. B. Salem, A. Dudley, M. Zghal, and A. Forbes, “Encoding information using Laguerre Gaussian modes over free space turbulence media,” Opt. Lett. 41(13), 3086–3089 (2016).
[Crossref] [PubMed]

Fu, D.

George, J.

González, L. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005)

Gopinath, J. T.

Gvishi, R.

Holtzmann, W. G.

Hong, S.

Hu, Z.

Huang, H.

G. Xie, Y. Ren, Y. Yan, H. Huang, N. Ahmed, L. Li, Z. Zhao, C. Bao, M. Tur, S. Ashrafi, and A. E. Willner, “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre-Gaussian beams with different radial indices,” Opt. Lett. 41(15), 3447–3450 (2016).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Huber, M.

Hurvitz, G.

Kaiser, T.

Lavery, M. P. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Li, G.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Li, L.

Lightman, S.

Lin, Z.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Liu, C.

Liu, J.

Lohmann, A. W.

Luo, W.

Lyu, M.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Magaña-Loaiza, O. S.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Malik, M.

Marrucci, L.

McLaren, M.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

Mehendale, S. C.

Méndez, G.

Mendlovic, D.

Mirhosseini, M.

Miyamoto, Y.

Moreno, I.

Nilsson, J.

Oak, S. M.

Oliver, S.

Padgett, M. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Pang, K.

Piccirillo, B.

Pidishety, S.

Qi, R.

Rafsanjani, S. M. H.

Ramachandran, S.

Ren, Y.

Ruiz, U.

Salem, A. B.

Sampson, R.

Sánchez-de-La-Llave, D.

Schmidt, O. A.

Schröter, S.

Schulze, C.

Seihgal, R.

Shi, Z.

Sidharthan, R.

Siemens, M. E.

Situ, G.

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

Song, H.

Srinivasan, B.

Trichili, A.

Tur, M.

Valencia, N. H.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Voitiv, A. A.

Wang, A.

Wang, J.

L. Zhu, G. Zhu, A. Wang, L. Wang, J. Ai, S. Chen, C. Du, J. Liu, S. Yu, and J. Wang, “18 km low-crosstalk OAM + WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation,” Opt. Lett. 43(8), 1890–1893 (2018).
[Crossref] [PubMed]

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4(1), 7441 (2014).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wang, L.

Wang, Y.

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, 1922).

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Willner, A. E.

Willner, A. N.

Wu, X.

Xie, G.

Yan, Y.

G. Xie, Y. Ren, Y. Yan, H. Huang, N. Ahmed, L. Li, Z. Zhao, C. Bao, M. Tur, S. Ashrafi, and A. E. Willner, “Experimental demonstration of a 200-Gbit/s free-space optical link by multiplexing Laguerre-Gaussian beams with different radial indices,” Opt. Lett. 41(15), 3447–3450 (2016).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yoo, S.

Yu, S.

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yzuel, M. J.

Zalevsky, Z.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Zghal, M.

Zhang, P.

Zhang, R.

Zhao, J.

Zhao, Z.

Zhou, Y.

Zhu, G.

Zhu, J.

Zhu, L.

Zhu, S.

Adv. Opt. Photonics (1)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

Appl. Opt. (4)

J. Opt. Soc. Am. A (2)

Nat. Photonics (1)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (5)

Optica (2)

Phys. Rev. Lett. (1)

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

Sci. Rep. (2)

M. Lyu, Z. Lin, G. Li, and G. Situ, “Fast modal decomposition for optical fibers using digital holography,” Sci. Rep. 7(1), 6556 (2017).
[Crossref] [PubMed]

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep. 4(1), 7441 (2014).
[Crossref] [PubMed]

Other (3)

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University, 1922).

S. Pachava, A. Dixit, and B. Srinivasan, “Modal decomposition of optical fiber output in OAM basis using optical correlation technique,” in Laser Congress 2018 (ASSL), OSA Technical Digest (Optical Society of America, 2018), paper AM6A.29.
[Crossref]

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005)

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Figures (10)

Fig. 1
Fig. 1 Experimental realization of dot product operation.
Fig. 2
Fig. 2 (a) Experimental setup for implementing the optical correlation technique. DFB: Distributed feedback laser; L1 (f = 10 cm), L2 (f = 20 cm): Convex lens; PH: Pin-hole; P: Polarizer; SLM: Spatial light modulator; M: mirror; LLF: Laser line filter at 1064 nm; CCD: Charge-coupled device camera. (b) Phase response of the SLM at 1064 nm wavelength.
Fig. 3
Fig. 3 (a), (b) Intensity patterns of LG00, LG01 modes respectively. (c), (d) Decomposition CGHs of LG00 and LG01 modes respectively, R: decomposition CGH radius. (e) Normalized power measured for different combination of generation (Tx) and decomposition (Rx) CGH settings as a function of decomposition CGH radius.
Fig. 4
Fig. 4 First and second rows - Fourier plane images obtained by optically correlating LG00 beam with LG00 (matched) and LG01 (orthogonal) modes; Third and fourth rows - LG01 beam with LG00 (orthogonal) and LG01 (matched) modes.
Fig. 5
Fig. 5 (a), (b) Intensity patterns of LG10, LG11 modes respectively. (c), (d) Decomposition CGHs of LG10 and LG11 modes respectively, R: decomposition CGH radius. (e) Normalized power measured for different combination of generation (Tx) and decomposition (Rx) CGH settings as a function of decomposition CGH radius.
Fig. 6
Fig. 6 First and second rows - Fourier plane images obtained by optically correlating LG10 beam with LG10 (matched) and LG11 (orthogonal) modes; Third and fourth rows – LG11 beam with LG10 (orthogonal) and LG11 (matched) modes.
Fig. 7
Fig. 7 Normalized power measured from optical correlation technique for different combinations of generated and decomposition LG modes with radial mode order p = 0, 1 and azimuthal mode order l = −4 to + 4. Diagonal elements represent parity and the off-diagonal elements represent the magnitude of coupling to neighboring modes. Q1-Q4 corresponds to the different quadrants in the above plot.
Fig. 8
Fig. 8 (a) Decomposition power extinction Vs. generated power extinction of composite beams LG00 and LG01, LG10 and LG11 for R = 1 mm. (b) Decomposition power extinction Vs. generated power extinction of LG00 and LG01 composite beam for R = 1 mm and R = 0.9 mm.
Fig. 9
Fig. 9 (a) Intensity structure of the generated composite beam consisting of LG-21 and LG21 modes. (b) Weights of the generated (markers) and decomposition (bars) LG mode spectrum for radial orders p = 0, 1 plotted as a function of different azimuthal mode indices l = −4 to + 4. (c) Intensity structure simulated using the experimentally obtained modal weights.
Fig. 10
Fig. 10 (a) Intensity structure of the generated composite beam consisting of 10 LG modes. (b) Weights of the generated (markers) and decomposition (bars) LG mode spectrum for radial orders p = 0, 1 plotted as a function of different azimuthal mode indices l = −4 to + 4. (c) Intensity structure simulated using the experimentally obtained modal weights.

Equations (10)

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L G l,p = C l,p exp( ρ 2 w 2 ) ( 2 ρ w ) | l | L G p | l | ( 2 ρ 2 w 2 )exp( ilϕ ),
U= l,p W l,p L G l,p
W l,p = U L G l,p * rdrdϕ
U f ( u,v )= exp( ikf )exp( ik r 2 2f ) iλf UL G l,p * exp( i2πρr λf cos( Θϕ ) ) ρdρdϕ,
s( x,y )=a( x,y )exp( iθ( x,y ) )
Ψ( a,θ )=f(a)sin(θ),
Uexp( if(a)sin( θ ) )=U J m [ f(a) ]exp( imθ ) ,
f(a)= J 1 1 [ Aa ],
Uexp( if(a)sin( θ+2π( u 0 x+ v 0 y ) ) )=U J m [ f(a) ]exp( im( θ+2π( u 0 x+ v 0 y ) ) )
U.a( x,y )exp( iθ( x,y )+2π( u 0 x+ v 0 y ) )

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