Abstract

We put forward a hybrid coding method of multiple orbital angular momentum (OAM) states based on the inherent orthogonality. Theoretical analysis shows this new coding method can tremendously improve the coding efficiency compared to the conventional way, and the OAM mode can be extended to all the transverse orthographic modes such as Bessel beams or Laguerre–Gauss modes. We also present a typical scheme to achieve the encoding of hybrid OAM states based on a concentric ring resonator array. We further suggest a digital device and a phase hologram pattern to decode the hybrid OAM states.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (4)

2012 (7)

2011 (3)

2010 (2)

P. Winzer, A. Gnauck, C. Doerr, M. Magarini, and L. Buhl, J. Lightwave Technol. 28, 547 (2010).
[CrossRef]

G. T. Reed, G. Mashanovich, F. Gardes, and D. Thomson, Nat. Photonics 4, 518 (2010).
[CrossRef]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

2005 (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef]

2004 (1)

1994 (1)

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1992 (1)

P. M. Hill, R. Olshansky, and W. Burns, IEEE Photon. Technol. Lett. 4, 500 (1992).
[CrossRef]

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Barnett, S.

G. Gibson, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, in Optical Science and Technology, the SPIE 49th Annual Meeting, (International Society for Optics and Photonics, 2004), pp. 367–373.

Barnett, S. M.

Beijersbergen, M.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Belmonte, A.

Bolle, C.

Boyd, R. W.

S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, Opt. Express 21, 16130 (2013).
[CrossRef]

S. Schulz, T. Machula, J. Upham, E. Karimi, and R. W. Boyd, “On chip generation and sorting of orbital angular momentum beams,” in OSA Technical Digest (online) (Optical Society of America, 2013), IT5A.2.

Bozinovic, N.

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

Brandão, P. A.

Buhl, L.

Burns, W.

P. M. Hill, R. Olshansky, and W. Burns, IEEE Photon. Technol. Lett. 4, 500 (1992).
[CrossRef]

Burrows, E. C.

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Cavalcanti, S. B.

Chu, T.

Coerwinkel, R.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Courtial, J.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, in Optical Science and Technology, the SPIE 49th Annual Meeting, (International Society for Optics and Photonics, 2004), pp. 367–373.

de Lisio, C.

Doerr, C.

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Esmaeelpour, M.

Essiambre, R.

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Feng, X.

Franke-Arnold, S.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, in Optical Science and Technology, the SPIE 49th Annual Meeting, (International Society for Optics and Photonics, 2004), pp. 367–373.

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Gardes, F.

G. T. Reed, G. Mashanovich, F. Gardes, and D. Thomson, Nat. Photonics 4, 518 (2010).
[CrossRef]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Gibson, G.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, in Optical Science and Technology, the SPIE 49th Annual Meeting, (International Society for Optics and Photonics, 2004), pp. 367–373.

Gnauck, A.

Gnauck, A. H.

Guo, G.

Hill, P. M.

P. M. Hill, R. Olshansky, and W. Burns, IEEE Photon. Technol. Lett. 4, 500 (1992).
[CrossRef]

Hu, Y.

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

Huang, Y.

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Karimi, E.

S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, Opt. Express 21, 16130 (2013).
[CrossRef]

E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, Opt. Lett. 37, 127 (2012).
[CrossRef]

S. Slussarenko, E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, J. Opt. Soc. Am. A 28, 61 (2011).
[CrossRef]

S. Schulz, T. Machula, J. Upham, E. Karimi, and R. W. Boyd, “On chip generation and sorting of orbital angular momentum beams,” in OSA Technical Digest (online) (Optical Society of America, 2013), IT5A.2.

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Kristensen, M.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Kristensen, P.

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

Li, S.

Li, X.

Li, Z.

Lipson, M.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef]

Liu, A.

Machula, T.

S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, Opt. Express 21, 16130 (2013).
[CrossRef]

S. Schulz, T. Machula, J. Upham, E. Karimi, and R. W. Boyd, “On chip generation and sorting of orbital angular momentum beams,” in OSA Technical Digest (online) (Optical Society of America, 2013), IT5A.2.

Magarini, M.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Marrucci, L.

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Gardes, and D. Thomson, Nat. Photonics 4, 518 (2010).
[CrossRef]

Mumtaz, S.

O’Brien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Olshansky, R.

P. M. Hill, R. Olshansky, and W. Burns, IEEE Photon. Technol. Lett. 4, 500 (1992).
[CrossRef]

Padgett, M.

G. Gibson, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, in Optical Science and Technology, the SPIE 49th Annual Meeting, (International Society for Optics and Photonics, 2004), pp. 367–373.

Padgett, M. J.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Pas’ko, V.

Piccirillo, B.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef]

Ramachandran, S.

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

Randel, S.

Reed, G. T.

G. T. Reed, G. Mashanovich, F. Gardes, and D. Thomson, Nat. Photonics 4, 518 (2010).
[CrossRef]

Ren, X.

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

Rui, G.

Ryf, R.

Santamato, E.

Schienemann, R.

R. Schienemann, “Amplitude and phase modulation,” U. S. patent2,140,769A (December20, 1938).

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef]

Schulz, S.

S. Schulz, T. Machula, J. Upham, E. Karimi, and R. W. Boyd, “On chip generation and sorting of orbital angular momentum beams,” in OSA Technical Digest (online) (Optical Society of America, 2013), IT5A.2.

Schulz, S. A.

Sierra, A.

Slussarenko, S.

Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Thompson, M. G.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Thomson, D.

G. T. Reed, G. Mashanovich, F. Gardes, and D. Thomson, Nat. Photonics 4, 518 (2010).
[CrossRef]

Torres, J. P.

Tur, M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

Upham, J.

S. Schulz, T. Machula, J. Upham, E. Karimi, and R. W. Boyd, “On chip generation and sorting of orbital angular momentum beams,” in OSA Technical Digest (online) (Optical Society of America, 2013), IT5A.2.

Vasnetsov, M.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, in Optical Science and Technology, the SPIE 49th Annual Meeting, (International Society for Optics and Photonics, 2004), pp. 367–373.

Wang, J.

Z. Zhao, J. Wang, S. Li, and A. E. Willner, Opt. Lett. 38, 932 (2013).
[CrossRef]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Wang, Z.

Willner, A. E.

Z. Zhao, J. Wang, S. Li, and A. E. Willner, Opt. Lett. 38, 932 (2013).
[CrossRef]

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

Winzer, P.

Winzer, P. J.

Woerdman, J.

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Xiao, X.

Xiong, K.

Xu, H.

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef]

Yan, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (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, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yu, J.

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Yu, S.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Yu, Y.

Yuan, X.-C.

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

Zhan, Q.

Zhang, D.

Zhang, N.

Zhao, Z.

Zhu, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. M. Hill, R. Olshansky, and W. Burns, IEEE Photon. Technol. Lett. 4, 500 (1992).
[CrossRef]

J. Lightwave Technol. (2)

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

Nat. Photonics (2)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, Nat. Photonics 6, 488 (2012).
[CrossRef]

G. T. Reed, G. Mashanovich, F. Gardes, and D. Thomson, Nat. Photonics 4, 518 (2010).
[CrossRef]

Nature (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef]

Opt. Commun. (1)

M. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Opt. Express (6)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Science (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Other (4)

S. Schulz, T. Machula, J. Upham, E. Karimi, and R. W. Boyd, “On chip generation and sorting of orbital angular momentum beams,” in OSA Technical Digest (online) (Optical Society of America, 2013), IT5A.2.

G. Gibson, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, and M. Padgett, in Optical Science and Technology, the SPIE 49th Annual Meeting, (International Society for Optics and Photonics, 2004), pp. 367–373.

R. Schienemann, “Amplitude and phase modulation,” U. S. patent2,140,769A (December20, 1938).

Y. Yue, N. Bozinovic, Y. Ren, H. Huang, M. Tur, P. Kristensen, S. Ramachandran, and A. E. Willner, in Optical Fiber Communication Conference (Optical Society of America, 2013).

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Figures (3)

Fig. 1.
Fig. 1.

Sketch of device to achieve encoding of hybrid OAM states. V1, V2, V3, and V4 are the voltages applied on the ring resonators, respectively, to generate the two-valued OAM states.

Fig. 2.
Fig. 2.

Simulated results where l0=0, l1=1, l2=2, l3=3, l4=4 when a circular array of eight elements evenly spaced is used to map the entire optical field into the digital domain. (a) The amplitude and phase of eight sampling regions measured by coherent detection when the OAM state is composed by l0, l1, l2. (b) OAM spectra of all the 16 states of output beams, which represent 4 bits.

Fig. 3.
Fig. 3.

Influence of the multimode dispersion.

Tables (2)

Tables Icon

Table 1. Coding Method of Hybrid OAM States

Tables Icon

Table 2. Comparison of Two Coding Methods

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ECV=j2(1j)exp[j(l+1)θ]j2(1j)exp[j(l1)θ],
ECVq=1/2exp(jlθ)(01),
I=mC(t)Em(r)exp(jLm(t)θ),
I=mC(t)Em(x,y)ψm(x,y,t),
ψm(x,y,t){ϕm(x,y),ϕ0(x,y)},(m=1,2),
ϕmϕn*dxdy=δmn={1m=n0mm=n.
Iϕn*dxdy={C(t)En(x,y),ψn=ϕn0,ψn=ϕ0,(n=1,2).

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