Abstract

We develop a method for encoding information in the longitudinal component of a focused field. Focused beams display a non-zero contribution of the electric field in the direction of propagation. However, the associated irradiance is very weak and difficult to isolate from the transverse part of the beam. For these reasons, the longitudinal component of a focused field could be a good choice for encoding and securing information. Using the Richards and Wolf formalism we show how to encrypt information in the longitudinal domain of the focal area. In addition, we use quantum imaging techniques to enhance the security and to prevent unauthorized access to the information. To the best of our knowledge, this is the first report on using the longitudinal component of the focused fields in optical security.

© 2016 Optical Society of America

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References

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  32. M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38(17), 3198–3201 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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2015 (1)

2014 (3)

2013 (4)

2012 (1)

A. Carnicer, I. Juvells, D. Maluenda, R. Martínez-Herrero, and P. M. Mejías, “On the longitudinal component of paraxial fields,” Eur. J. Phys. 33(5), 1235–1247 (2012).
[Crossref]

2011 (1)

2010 (4)

2009 (3)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34(3), 331–333 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (2)

2006 (3)

2005 (2)

2004 (2)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

2001 (1)

2000 (1)

1999 (1)

1995 (1)

1994 (1)

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33(6), 1752–1756 (1994).
[Crossref]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” P. Royal Soc. London A Mater. 253(1274), 358–379 (1959).
[Crossref]

Arcos, S.

Arrizón, V.

Barrera, J. F.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260(1), 109–112 (2006).
[Crossref]

Bokor, N.

Bolognini, N.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260(1), 109–112 (2006).
[Crossref]

Carnicer, A.

Castro, A.

Chen, W.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[Crossref] [PubMed]

Chen, X.

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[Crossref] [PubMed]

Cho, M.

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Davidson, N.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Dowling, T.

Frauel, Y.

González, L. A.

Hao, X.

Henao, R.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260(1), 109–112 (2006).
[Crossref]

Hennelly, B. M.

Horner, J. L.

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33(6), 1752–1756 (1994).
[Crossref]

Ide, M.

Javidi, B.

D. Maluenda, A. Carnicer, R. Martínez-Herrero, I. Juvells, and B. Javidi, “Optical encryption using photon-counting polarimetric imaging,” Opt. Express 23(2), 655–666 (2015).
[Crossref] [PubMed]

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38(17), 3198–3201 (2013).
[Crossref] [PubMed]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36(1), 22–24 (2011).
[Crossref] [PubMed]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15(16), 10253–10265 (2007).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Secure holographic memory by double-random polarization encryption,” Appl. Opt. 43(14), 2915–2919 (2004).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]

P. Réfrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
[Crossref] [PubMed]

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33(6), 1752–1756 (1994).
[Crossref]

B. Javidi and A. Carnicer, “Roadmap in optical encryption and security,” J. Opt. (accepted for publication).

Joseph, J.

Juvells, I.

Khonina, S. N.

Kozawa, Y.

Kuang, C.

Kumar, A.

Kumar, P.

Kuroda, K.

Lasser, T.

Leitgeb, R. A.

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Leutenegger, M.

Levy, U.

Liu, X.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Maluenda, D.

Martínez-Herrero, R.

Matoba, O.

Mejías, P. M.

A. Carnicer, I. Juvells, D. Maluenda, R. Martínez-Herrero, and P. M. Mejías, “On the longitudinal component of paraxial fields,” Eur. J. Phys. 33(5), 1235–1247 (2012).
[Crossref]

Millan, M. S.

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Montes-Usategui, M.

Nakano, K.

Naughton, T. J.

Nomura, T.

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Obi, T.

Ohyama, N.

Okada-Shudo, Y.

Peng, X.

Pérez-Cabré, E.

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36(1), 22–24 (2011).
[Crossref] [PubMed]

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Ponce, R.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Rao, R.

Réfrégier, P.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” P. Royal Soc. London A Mater. 253(1274), 358–379 (1959).
[Crossref]

Sato, S.

Serrano-Heredia, A.

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Sheppard, C. J. R.

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shimura, T.

Singh, K.

Suzuki, H.

Takeda, M.

Tan, X.

Tashima, H.

Tebaldi, M.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260(1), 109–112 (2006).
[Crossref]

Torroba, R.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260(1), 109–112 (2006).
[Crossref]

Unnikrishnan, G.

Volotovsky, S. G.

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Wang, T.

Wei, H.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” P. Royal Soc. London A Mater. 253(1274), 358–379 (1959).
[Crossref]

Yamaguchi, M.

Yu, B.

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Zhang, P.

Adv. Opt. Photonics (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

Appl. Opt. (5)

Eur. J. Phys. (1)

A. Carnicer, I. Juvells, D. Maluenda, R. Martínez-Herrero, and P. M. Mejías, “On the longitudinal component of paraxial fields,” Eur. J. Phys. 33(5), 1235–1247 (2012).
[Crossref]

J. Opt. Soc. Am. A (3)

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Opt. Commun. (1)

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260(1), 109–112 (2006).
[Crossref]

Opt. Eng. (1)

B. Javidi and J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33(6), 1752–1756 (1994).
[Crossref]

Opt. Express (7)

Opt. Lett. (12)

P. Réfrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
[Crossref] [PubMed]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36(1), 22–24 (2011).
[Crossref] [PubMed]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38(17), 3198–3201 (2013).
[Crossref] [PubMed]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions,” Opt. Lett. 34(3), 331–333 (2009).
[Crossref] [PubMed]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[Crossref] [PubMed]

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30(13), 1644–1646 (2005).
[Crossref] [PubMed]

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31(8), 1044–1046 (2006).
[Crossref] [PubMed]

N. Davidson and N. Bokor, “High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens,” Opt. Lett. 29(12), 1318–1320 (2004).
[Crossref] [PubMed]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
[Crossref] [PubMed]

R. Martínez-Herrero, I. Juvells, and A. Carnicer, “On the physical realizability of highly focused electromagnetic field distributions,” Opt. Lett. 38(12), 2065–2067 (2013).
[Crossref] [PubMed]

P. Royal Soc. London A Mater. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” P. Royal Soc. London A Mater. 253(1274), 358–379 (1959).
[Crossref]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Proc. IEEE (1)

O. Matoba, T. Nomura, E. Pérez-Cabré, M. S. Millan, and B. Javidi, “Optical Techniques for Information Security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Other (3)

B. Javidi and A. Carnicer, “Roadmap in optical encryption and security,” J. Opt. (accepted for publication).

L. Novotni and B. Hecht, Principles of Nano-Optics (Cambridge University, 2012)

J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985)

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Figures (5)

Fig. 1
Fig. 1

Notation and coordinate systems at the Gaussian reference sphere and at the focal plane.

Fig. 2
Fig. 2

(a) Optical setup to implement for the proposed encryption procedure: L1: Fourier lens; LA and LB: relay optics lenses; f1, fA, fB and f2 are the focal lengths of lenses L1, LA, LB and the microscope objective respectively; SLM: spatial light modulator; HWP and QWP: half and quarter wave plates; LP: linear polarizer; CCD: camera.

Fig. 3
Fig. 3

Encrypted components: (a) |E’x|2 and (b) |E’z|2.

Fig. 4
Fig. 4

Photon counting encrypted components: (a) |E’x|ph, (b) |E’y|ph.

Fig. 5
Fig. 5

Recovered signals using the correct key M2: (a) decrypted plaintext t (b) photon-counting decrypted plaintext tph, (c) correlation signal ρ using the correct key M2 and NP = 0.1 photons/pixel, (d) ρ using an incorrect key M2 and NP = 0.1 photons/pixel, (e) correlation signal ρ using the correct key M2 and NP = 0.15 photons/pixel, (f) ρ using an incorrect key M2 and NP = 0.15 photons/pixel.

Equations (23)

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E(r,φ,z)=A 0 θ 0 0 2π E ( θ,ϕ )exp( ikrsinθcos( φϕ ) )exp( ikzcosθ )sinθdθdϕ
E ( θ,ϕ )=P( θ )( a e 1 ( ϕ )+b e 2 ( ϕ,θ ) ).
e 1 ( ϕ )=(sinϕ,cosϕ,0) e 2 i ( ϕ )=(cosϕ,sinϕ,0) e 2 ( ϕ,θ )=(cosθcosϕ,cosθsinϕ,sinθ).
s=(α,β,γ)=( sinθcosϕ,sinθsinϕ,cosθ ).
a= E 0 e 1 = E 0x sinϕ+ E 0y cosϕ b= E 0 e 2 i = E 0x cosϕ+ E 0y sinϕ.
exp( ikrsinθcos( φϕ ) )=exp( i 2π λ ( αx+βy ) )
E(x,y,0)= FT λf [ E cosθ ]= FT λf [ ( ( E 0 e 1 ) e 1 +( E 0 e 2 ι ) e 2 ) cosθ ],
I z = | E z | 2 dxdy.
I T = I x + I y + I z = ( | E x | 2 + | E y | 2 + | E z | 2 ) dxdy.
E z = cosθ bsinθ= cosθ ( E 0 e 2 i )sinθ= cosθ ( E 0x cosϕ+ E 0y sinϕ )sinθ..
E z (x,y,0)= FT λf [ E z cosθ ]= FT λf [ ( E 0x cosϕ+ E 0y sinϕ ) sinθ cosθ ].
E 0x cosϕ+ E 0y sinϕ= cosθ sinθ FT λf 1 [ E z (x,y,0) ].
E 0 =exp( iϕ ) cosθ sinθ FT λf 1 [ E z ], E z = FT λf [ exp( iϕ ) E 0 sinθ cosθ ].
E 0 = cosθ sinθ FT λf 1 [ E z ], E z = FT λf [ E 0 sinθ cosθ ].
E z = FT λf [ α FT λf 1 [ E x ]+β FT λf 1 [ E y ] 1 α 2 β 2 ].
E ' 0x =exp( iϕ ) cosθ sinθ M 2 FT λf [ M 1 t ], E ' 0y =iE ' 0x .
E z ' = FT λf [ exp( iϕ )E ' 0x sinθ cosθ ]= FT λf [ M 2 FT λf [ M 1 t ] ].
t=| FT λf 1 [ M 2 1 α FT λf 1 [ E ' x ]+β FT λf 1 [ E ' y ] 1 α 2 β 2 ] |.
| E x ' | ph ( x, y )={ 0, if rand( x, y )exp( n p ( x,y ) ) 1, otherwise
n p ( x,y )= N p | E x ' ( x,y ) | 2 n,m=1 N,M | E x ' ( n,m ) | 2
E x 'ph = | E x ' | ph E x ' | E x ' | and E y 'ph = | E y ' | ph E y ' | E y | .
ρ( x,y ) = n,m=1 N,M [ t ph ( m+x,n+y ) t ph ][ t( m,n ) t ] n,m=1 N,M [ t ph ( m,n ) t ph ] 2 n,m=1 N,M [ t( m,n ) t ] 2 ,
H=exp( iϕ ) cosθ sinθ M 2 .

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