Abstract

Light beams can be characterized by their complex spatial profiles in both intensity and phase. Analogous to time signals, which can be decomposed into multiple orthogonal frequency functions, a light beam can also be decomposed into a set of spatial modes that are taken from an orthogonal basis. Such decomposition can potentially provide a tool for spatial spectrum analysis, which may enable stable, accurate, and robust extraction of physical object information that may not be readily achievable using traditional approaches. As a proof-of-concept example, we measure an object’s opening angle using orbital-angular-momentum (OAM) -based complex spectrum, achieving a >15  dB signal-to-noise ratio. Moreover, the dip (i.e., notch) positions of the OAM intensity spectrum are dependent on an object’s opening angle but independent of the opening’s angular orientation, whereas the slope of the OAM phase spectrum is dependent on the opening’s orientation but independent of the opening angle.

© 2017 Optical Society of America

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References

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2015 (3)

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2014 (4)

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2013 (3)

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N. Uribe-Patarroyo, A. Fraine, D. Simon, O. Minaeva, and A. Sergienko, Phys. Rev. Lett. 110, 043601 (2013).
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C. Schulze, A. Dudley, D. Flamm, M. Duparré, and A. Forbes, New J. Phys. 15, 073025 (2013).
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2012 (4)

J. Wang, J.-Y. Yang, I. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. Willner, Nat. Photonics 6, 488 (2012).
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2011 (1)

2010 (1)

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2008 (3)

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2004 (1)

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1992 (1)

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F. Tonolini, S. Chan, M. Agnew, A. Lindsay, and J. Leach, Sci. Rep. 4, 6542 (2014).
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M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, Nat. Commun. 3, 984 (2012).
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Ahmed, N.

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[Crossref]

Andrews, D.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
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Andrews, L.

L. Andrews and R. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Ashrafi, A.

Ashrafi, N.

Ashrafi, S.

Bai, L.

Baker, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
[Crossref]

Banzer, P.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
[Crossref]

Bao, C.

Barnett, S.

A. Jha, B. Jack, E. Yao, J. Leach, R. Boyd, G. Buller, S. Barnett, S. Franke-Arnold, and M. Padgett, Phys. Rev. A 78, 043810 (2008).
[Crossref]

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, New J. Phys. 6, 103 (2004).
[Crossref]

Bauer, T.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
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Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[Crossref]

Belmonte, A.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
[Crossref]

Bernet, S.

Berry, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
[Crossref]

Bigelow, N.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
[Crossref]

Bowman, A.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Bowman, R.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, Science 340, 844 (2013).
[Crossref]

Boyd, R.

O. Magaña-Loaiza, M. Mirhosseini, R. Cross, S. Rafsanjani, and R. Boyd, Sci. Adv. 2, e1501143 (2016).
[Crossref]

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, Nat. Commun. 3, 984 (2012).
[Crossref]

A. Jha, B. Jack, E. Yao, J. Leach, R. Boyd, G. Buller, S. Barnett, S. Franke-Arnold, and M. Padgett, Phys. Rev. A 78, 043810 (2008).
[Crossref]

Buller, G.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, Nat. Commun. 3, 984 (2012).
[Crossref]

A. Jha, B. Jack, E. Yao, J. Leach, R. Boyd, G. Buller, S. Barnett, S. Franke-Arnold, and M. Padgett, Phys. Rev. A 78, 043810 (2008).
[Crossref]

Cai, X.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, Light Sci. Appl. 6, e16251 (2017).
[Crossref]

Cao, Y.

Carrasco, S.

G. Molina-Terriza, L. Rebane, J. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc. 2, 07014 (2007).
[Crossref]

L. Torner, J. Torres, and S. Carrasco, Opt. Express 13, 873 (2005).
[Crossref]

Chan, S.

F. Tonolini, S. Chan, M. Agnew, A. Lindsay, and J. Leach, Sci. Rep. 4, 6542 (2014).
[Crossref]

Chávez-Cerda, S.

Chen, D.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, Light Sci. Appl. 6, e16251 (2017).
[Crossref]

Chen, M.

J. Lin, X.-C. Yuan, M. Chen, and C. Dainty, J. Opt. Soc. Am. A 27, 10 (2010).
[Crossref]

Chen, Y.

Y. Chen, S. Zheng, X. Jin, H. Chi, and X. Zhang, J. Appl. Phys. 121, 184506 (2017).
[Crossref]

Cheng, Y.

K. Liu, Y. Cheng, Y. Gao, X. Li, Y. Qin, and H. Wang, Appl. Phys. Lett. 110, 164102 (2017).
[Crossref]

Y. Yuan, H. Wang, Y. Qin, and Y. Cheng, IEEE Antennas Wireless Propag. Lett. 15, 1024 (2016).
[Crossref]

K. Liu, Y. Cheng, Z. Yang, H. Wang, Y. Qin, and X. Li, IEEE Antennas Wireless Propag. Lett. 14, 711 (2015).
[Crossref]

Chi, H.

Y. Chen, S. Zheng, X. Jin, H. Chi, and X. Zhang, J. Appl. Phys. 121, 184506 (2017).
[Crossref]

Courtial, J.

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, New J. Phys. 6, 103 (2004).
[Crossref]

Cross, R.

O. Magaña-Loaiza, M. Mirhosseini, R. Cross, S. Rafsanjani, and R. Boyd, Sci. Adv. 2, e1501143 (2016).
[Crossref]

Cui, K.

Cvijetic, N.

N. Cvijetic, G. Milione, E. Ip, and T. Wang, Sci. Rep. 5, 15422 (2015).
[Crossref]

Dainty, C.

J. Lin, X.-C. Yuan, M. Chen, and C. Dainty, J. Opt. Soc. Am. A 27, 10 (2010).
[Crossref]

Dennis, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
[Crossref]

Denz, C.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, J. Opt. 19, 013001 (2016).
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Dolinar, S.

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

Don, M.

Dong, J.

H. Zhou, D. Fu, J. Dong, P. Zhang, D. Chen, X. Cai, F. Li, and X. Zhang, Light Sci. Appl. 6, e16251 (2017).
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Figures (4)

Fig. 1.
Fig. 1. Concept of using the OAM spectrum to measure an object’s parameters. The beam’s intensity profile and OAM spectrum (a) before object truncation, (b) right after object truncation, and (c) some distance after object truncation.
Fig. 2.
Fig. 2. (a) Experimental setup. The SLM-3, L-1, L-2, collimator, and power monitor form the complex OAM spectrum analyzer. Col, collimator; HWP, half-wave plate; M, mirror; SLM, spatial light modulator; L, lens. (b) The shape and position of the object. θ, opening angle of the object; δ, orientation of the object relative to the y axis.
Fig. 3.
Fig. 3. a1–a8: various orientations (states) of an object having an opening angle of 2π/3. b1–b8: the image of the light beam truncated by objects a1–a8, respectively. (c) The OAM intensity spectrum measured for the light truncated by objects a1–a8. (d) The OAM intensity spectrum measured for the light truncated by objects having various opening angles. (e) The relationship between the opening angles and the first-dip position in the OAM intensity spectrum. (f) The OAM intensity spectrum measured for the light truncated by an object having an opening angle of 2π/3 when the distance from the object to the OAM spectrum analyzer is 0, 35, 52, and 104 cm. The distance from the object to the OAM spectrum analyzer is zero in (c)–(e).
Fig. 4.
Fig. 4. (a), (b) OAM phase spectrum measured for the light truncated by an object having an opening angle of 2π/3 but various negative/positive orientation angles. (c) The relationship between the orientation angle of the object and the slope of the OAM phase spectrum. (d) The OAM phase spectrum measured for the light truncated by an object having various opening angles and an orientation angle of π/8. In this figure, the distance from the object to the OAM spectrum analyzer is zero. In the measurement, the data is calculated by an arctan function, which is between π/2 and π/2, and we may also add a π or π phase shift to the measurement for the convenience of slope calculation.

Equations (2)

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{exp(jT0)=exp(j1ϕ)+exp(j2ϕ)exp(jT45)=exp(j1ϕ)+jexp(j2ϕ)exp(jT90)=exp(j1ϕ)exp(j2ϕ)exp(jT135)=exp(j1ϕ)jexp(j2ϕ).
Δϕ=atan((I0I90)/(I45I135)).

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