Abstract

In this work, we propose a method for designing an adjustable amplitude-phase hybrid grating in which by relative lateral shearing of its amplitude and phase parts, the intensity share between different diffraction orders can be controlled. The method is based on superimposing two pure-amplitude and pure-phase gratings with sinusoidal or binary profiles having the same periods and lines’ orientations. It is shown that, in the diffraction of a Gaussian beam from such hybrid gratings, the intensity share of each of the diffraction orders is related to the shear value and the amplitude of the transmission functions of the superimposed pure-amplitude and pure-phase gratings. For instance, when both of the amplitude and phase profiles are sinusoidal and the shear value between them is a quarter of the period, for given values of the transmissions amplitudes of the profiles, all positive (or negative) diffraction orders are removed. We also show that, by changing the values of the transmission's amplitudes, the intensity share for the higher orders can be increased. This kind of grating might find application in optical switching and in devices requiring power sharing between different channels such as in beam-steering devices, in optical interconnects, and in optical fiber communication.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (5)

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonics Nanostructures-Fundamentals Appl. 37, 100736 (2019).
[Crossref]

A. Trichili, K. H. Park, M. Zghal, B. S. Ooi, and M. S. Alouini, “Communicating using spatial mode multiplexing: Potentials, challenges, and perspectives,” IEEE Commun. Surv. & Tutorials 21(4), 3175–3203 (2019).
[Crossref]

D. Hebri, S. Rasouli, and A. M. Dezfouli, “Theory of diffraction of vortex beams from structured apertures and generation of elegant elliptical vortex Hermite–Gaussian beams,” J. Opt. Soc. Am. A 36(5), 839–852 (2019).
[Crossref]

S. Rasouli and A. M. Khazaei, “An azimuthally-modified linear phase grating: Generation of varied radial carpet beams over different diffraction orders with controlled intensity sharing among the generated beams,” Sci. Rep. 9(1), 12472 (2019).
[Crossref]

S. N. Khonina and A. V. Ustinov, “Binary multi-order diffraction optical elements with variable fill factor for the formation and detection of optical vortices of arbitrary order,” Appl. Opt. 58(30), 8227–8236 (2019).
[Crossref]

2018 (3)

2017 (3)

2016 (2)

2015 (2)

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

D. Xu, G. Tan, and S. Wu, “Large-angle and high-efficiency tunable phase grating using fringe field switching liquid crystal,” Opt. Express 23(9), 12274–12285 (2015).
[Crossref]

2014 (2)

2012 (2)

S. Rasouli and M. Ghorbani, “Nonlinear refractive index measuring using a double-grating interferometer in pump-probe configuration and Fourier transform analysis,” J. Opt. 14(3), 035203 (2012).
[Crossref]

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wave-front distortions induced by atmospheric turbulence using two-channel moiré deflectometry,” J. Opt. 14(9), 095704 (2012).
[Crossref]

2010 (2)

L. Zhao, W. Duan, and S. F. Yelin, “All-optical beam control with high speed using image-induced blazed gratings in coherent media,” Phys. Rev. A 82(1), 013809 (2010).
[Crossref]

H. Jau, T. Lin, R. Fung, S. Huang, J. H. Liu, and A. Y. G. Fuh, “Optically-tunable beam steering grating based on azobenzene doped cholesteric liquid crystal,” Opt. Express 18(16), 17498–17503 (2010).
[Crossref]

2007 (2)

M. Aschwanden, M. Beck, and A. Stemmer, “Diffractive transmission grating tuned by dielectric elastomer actuator,” IEEE Photonics Technol. Lett. 19(14), 1090–1092 (2007).
[Crossref]

L. L. Doskolovich, N. L. Kazanskiy, S. N. Khonina, R. V. Skidanov, N. Heikkila, S. Siitonen, and J. Turunen, “Design and investigation of color separation diffraction gratings,” Appl. Opt. 46(15), 2825–2830 (2007).
[Crossref]

2004 (1)

M. A. Golub, “Laser Beam Splitting by Diffractive Optics,” Opt. Photonics News 15(2), 36–41 (2004).
[Crossref]

2003 (2)

H. Ren, Y. H. Fan, and S. T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82(19), 3168–3170 (2003).
[Crossref]

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “Techniques for encoding composite diffractive optical elements,” Proc. SPIE 5036, 493–498 (2003).
[Crossref]

2001 (1)

2000 (2)

1998 (1)

I. Amidror, “The Fourier-spectrum of circular sine and cosine gratings with arbitrary radial phases,” Opt. Commun. 149(1-3), 127–134 (1998).
[Crossref]

1990 (1)

O. Bryngdahl and F. Wyrowski, “Digital Holography–Computer-Generated Holograms,” Prog. Opt. 61, 1–86 (1990).
[Crossref]

1978 (1)

1971 (2)

Akhmanov, S. A.

S. A. Akhmanov and S. Y. Nikitin, Physical Optics (Clarendon, 1997).

Alouini, M. S.

A. Trichili, K. H. Park, M. Zghal, B. S. Ooi, and M. S. Alouini, “Communicating using spatial mode multiplexing: Potentials, challenges, and perspectives,” IEEE Commun. Surv. & Tutorials 21(4), 3175–3203 (2019).
[Crossref]

Amidror, I.

I. Amidror, “The Fourier-spectrum of circular sine and cosine gratings with arbitrary radial phases,” Opt. Commun. 149(1-3), 127–134 (1998).
[Crossref]

Amiri, P.

P. Amiri, A. M. Dezfouli, and S. Rasouli, “Efficient characterization of optical vortices via diffraction from parabolic-line linear gratings,” J. Opt. Soc. Am. B, under review (2020).
[Crossref]

Aschwanden, M.

M. Aschwanden, M. Beck, and A. Stemmer, “Diffractive transmission grating tuned by dielectric elastomer actuator,” IEEE Photonics Technol. Lett. 19(14), 1090–1092 (2007).
[Crossref]

Azizian-Kalandaragh, Y.

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonics Nanostructures-Fundamentals Appl. 37, 100736 (2019).
[Crossref]

Beck, M.

M. Aschwanden, M. Beck, and A. Stemmer, “Diffractive transmission grating tuned by dielectric elastomer actuator,” IEEE Photonics Technol. Lett. 19(14), 1090–1092 (2007).
[Crossref]

Brunner, R.

Bryngdahl, O.

O. Bryngdahl and F. Wyrowski, “Digital Holography–Computer-Generated Holograms,” Prog. Opt. 61, 1–86 (1990).
[Crossref]

Dammann, H.

Daniel, W.

Danilov, P. A.

Dashti, M.

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wave-front distortions induced by atmospheric turbulence using two-channel moiré deflectometry,” J. Opt. 14(9), 095704 (2012).
[Crossref]

Demetri, P.

Dezfouli, A. M.

D. Hebri, S. Rasouli, and A. M. Dezfouli, “Theory of diffraction of vortex beams from structured apertures and generation of elegant elliptical vortex Hermite–Gaussian beams,” J. Opt. Soc. Am. A 36(5), 839–852 (2019).
[Crossref]

P. Amiri, A. M. Dezfouli, and S. Rasouli, “Efficient characterization of optical vortices via diffraction from parabolic-line linear gratings,” J. Opt. Soc. Am. B, under review (2020).
[Crossref]

Doskolovich, L. L.

Duan, W.

L. Zhao, W. Duan, and S. F. Yelin, “All-optical beam control with high speed using image-induced blazed gratings in coherent media,” Phys. Rev. A 82(1), 013809 (2010).
[Crossref]

Fan, Y. H.

H. Ren, Y. H. Fan, and S. T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82(19), 3168–3170 (2003).
[Crossref]

Fuh, A. Y. G.

Fung, R.

Gabriella, C.

Ghorbani, M.

S. Rasouli and M. Ghorbani, “Nonlinear refractive index measuring using a double-grating interferometer in pump-probe configuration and Fourier transform analysis,” J. Opt. 14(3), 035203 (2012).
[Crossref]

Golub, M. A.

M. A. Golub, “Laser Beam Splitting by Diffractive Optics,” Opt. Photonics News 15(2), 36–41 (2004).
[Crossref]

Hasegawa, S.

Hayasaki, Y.

Hebri, D.

Heikkila, N.

Huang, S.

Ichioka, Y.

Ionin, A. A.

Ito, H.

Jau, H.

Jia, P.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Jones, A. L.

Kazanskiy, N. L.

Khazaei, A. M.

S. Rasouli and A. M. Khazaei, “An azimuthally-modified linear phase grating: Generation of varied radial carpet beams over different diffraction orders with controlled intensity sharing among the generated beams,” Sci. Rep. 9(1), 12472 (2019).
[Crossref]

Khonina, S.

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonics Nanostructures-Fundamentals Appl. 37, 100736 (2019).
[Crossref]

Khonina, S. N.

Kirilenko, M.

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonics Nanostructures-Fundamentals Appl. 37, 100736 (2019).
[Crossref]

Kirk, J. P.

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “Techniques for encoding composite diffractive optical elements,” Proc. SPIE 5036, 493–498 (2003).
[Crossref]

Kuchmizhak, A. A.

Kudryashov, S. I.

Kujawinska, M.

K. Patorski and M. Kujawinska, Handbook of the Moiré Fringe Technique (Elsevier, 1993).

Kulchin, Y. N.

Lancis, J.

Lei, T.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Li, Y.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Li, Z.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Lin, J.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Lin, T.

Liu, G. N.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Liu, J. H.

Mãnguez-Vega, G.

Massimo, S.

Mendoza-Yero, O.

Min, C.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Naqavi, A.

Nikitin, S. Y.

S. A. Akhmanov and S. Y. Nikitin, Physical Optics (Clarendon, 1997).

Niu, H.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Ogura, Y.

Ooi, B. S.

A. Trichili, K. H. Park, M. Zghal, B. S. Ooi, and M. S. Alouini, “Communicating using spatial mode multiplexing: Potentials, challenges, and perspectives,” IEEE Commun. Surv. & Tutorials 21(4), 3175–3203 (2019).
[Crossref]

Park, K. H.

A. Trichili, K. H. Park, M. Zghal, B. S. Ooi, and M. S. Alouini, “Communicating using spatial mode multiplexing: Potentials, challenges, and perspectives,” IEEE Commun. Surv. & Tutorials 21(4), 3175–3203 (2019).
[Crossref]

Patorski, K.

K. Patorski and M. Kujawinska, Handbook of the Moiré Fringe Technique (Elsevier, 1993).

Paul, M.

Peter Herzig, H.

Porfirev, A.

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonics Nanostructures-Fundamentals Appl. 37, 100736 (2019).
[Crossref]

Porfirev, A. P.

Rasouli, S.

S. Rasouli and A. M. Khazaei, “An azimuthally-modified linear phase grating: Generation of varied radial carpet beams over different diffraction orders with controlled intensity sharing among the generated beams,” Sci. Rep. 9(1), 12472 (2019).
[Crossref]

D. Hebri, S. Rasouli, and A. M. Dezfouli, “Theory of diffraction of vortex beams from structured apertures and generation of elegant elliptical vortex Hermite–Gaussian beams,” J. Opt. Soc. Am. A 36(5), 839–852 (2019).
[Crossref]

D. Hebri, S. Rasouli, and M. Yeganeh, “Intensity-based measuring of the topological charge alteration by the diffraction of vortex beams from amplitude sinusoidal radial gratings,” J. Opt. Soc. Am. B 35(4), 724–730 (2018).
[Crossref]

S. Rasouli, F. Sakha, and M. Yeganeh, “Infinite-mode double-grating interferometer for investigating thermal-lens–acting fluid dynamics,” Meas. Sci. Technol. 29(8), 085201 (2018).
[Crossref]

S. Rasouli and M. Shahmohammadi, “A portable and long-range displacement and vibration sensor that chases moving moiré fringes using the three-point intensity detection method,” OSA Continuum 1(3), 1012–1025 (2018).
[Crossref]

S. Rasouli and D. Hebri, “Contrast enhanced quarter-Talbot images,” J. Opt. Soc. Am. A 34(12), 2145–2156 (2017).
[Crossref]

S. Rasouli and M. Ghorbani, “Nonlinear refractive index measuring using a double-grating interferometer in pump-probe configuration and Fourier transform analysis,” J. Opt. 14(3), 035203 (2012).
[Crossref]

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wave-front distortions induced by atmospheric turbulence using two-channel moiré deflectometry,” J. Opt. 14(9), 095704 (2012).
[Crossref]

P. Amiri, A. M. Dezfouli, and S. Rasouli, “Efficient characterization of optical vortices via diffraction from parabolic-line linear gratings,” J. Opt. Soc. Am. B, under review (2020).
[Crossref]

Ren, H.

H. Ren, Y. H. Fan, and S. T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82(19), 3168–3170 (2003).
[Crossref]

Riccardo, B.

Richard, M.

Rossi, M.

Sakha, F.

S. Rasouli, F. Sakha, and M. Yeganeh, “Infinite-mode double-grating interferometer for investigating thermal-lens–acting fluid dynamics,” Meas. Sci. Technol. 29(8), 085201 (2018).
[Crossref]

Sandfuchs, O.

Shahmohammadi, M.

Shirai, N.

Siitonen, S.

Skidanov, R. V.

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, and V. A. Soifer, “Techniques for encoding composite diffractive optical elements,” Proc. SPIE 5036, 493–498 (2003).
[Crossref]

Stemmer, A.

M. Aschwanden, M. Beck, and A. Stemmer, “Diffractive transmission grating tuned by dielectric elastomer actuator,” IEEE Photonics Technol. Lett. 19(14), 1090–1092 (2007).
[Crossref]

Suzuki, T.

Syubaev, S. A.

Tan, G.

Tanida, J.

Thomae, D.

Toyoda, H.

Trichili, A.

A. Trichili, K. H. Park, M. Zghal, B. S. Ooi, and M. S. Alouini, “Communicating using spatial mode multiplexing: Potentials, challenges, and perspectives,” IEEE Commun. Surv. & Tutorials 21(4), 3175–3203 (2019).
[Crossref]

Turunen, J.

Ustinov, A. V.

Vitrik, O. B.

Wu, S.

Wu, S. T.

H. Ren, Y. H. Fan, and S. T. Wu, “Prism grating using polymer stabilized nematic liquid crystal,” Appl. Phys. Lett. 82(19), 3168–3170 (2003).
[Crossref]

Wyrowski, F.

O. Bryngdahl and F. Wyrowski, “Digital Holography–Computer-Generated Holograms,” Prog. Opt. 61, 1–86 (1990).
[Crossref]

Xu, D.

Xu, W.

Xu, X.

T. Lei, M. Zhang, Y. Li, P. Jia, G. N. Liu, X. Xu, Z. Li, C. Min, J. Lin, C. Yu, H. Niu, and X. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light: Sci. Appl. 4(3), e257 (2015).
[Crossref]

Yeganeh, M.

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Supplementary Material (20)

NameDescription
» Visualization 1       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=1, and Vp=p at propagation distance Z=1 m fo
» Visualization 2       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=1, and Vp=p at propagation distance Z=1 m for di
» Visualization 3       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a binary phase grating with d=0.16 mm, Va=1, and Vp=p at propagation distance Z=1 m for di
» Visualization 4       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a binary phase grating with d=0.16 mm, Va=1, and Vp=p at propagation distance Z=1 m for differ
» Visualization 5       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=1, and Vp=1 at propagation distance Z=1 m fo
» Visualization 6       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=1, and Vp=1 at propagation distance Z=1 m for di
» Visualization 7       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a binary phase grating with d=0.16 mm, Va=1, and Vp=1 at propagation distance Z=1 m for di
» Visualization 8       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a binary phase grating with d=0.16 mm, Va=1, and Vp=1 at propagation distance Z=1 m for differ
» Visualization 9       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=0.5, and Vp=0.5p at propagation distance Z=1
» Visualization 10       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=0.5, and Vp=0.5p at propagation distance Z=1 m f
» Visualization 11       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a binary phase grating with d=0.16 mm, Va=0.5, and Vp=0.5p at propagation distance Z=1 m f
» Visualization 12       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a binary phase grating with d=0.16 mm, Va=0.5, and Vp=0.5p at propagation distance Z=1 m for d
» Visualization 13       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=1, and Vp=0.25p at propagation distance Z=1
» Visualization 14       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=1, and Vp=0.25p at propagation distance Z=1 m fo
» Visualization 15       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a binary phase grating with d=0.16 mm, Va=1, and Vp=0.25p at propagation distance Z=1 m fo
» Visualization 16       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a binary phase grating with d=0.16 mm, Va=1, and Vp=0.25p at propagation distance Z=1 m for di
» Visualization 17       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=0.25, and Vp=p at propagation distance Z=1 m
» Visualization 18       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a sinusoidal phase grating with d=0.16 mm, Va=0.25, and Vp=p at propagation distance Z=1 m for
» Visualization 19       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear sinusoidal amplitude grating and a binary phase grating with d=0.16 mm, Va=0.25, and Vp=p at propagation distance Z=1 m for
» Visualization 20       Simulated diffraction pattern of a Gaussian beam with w=0.5 mm from a hybrid grating formed in the superimposition of a linear binary amplitude grating and a binary phase grating with d=0.16 mm, Va=0.25, and Vp=p at propagation distance Z=1 m for dif

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Figures (8)

Fig. 1.
Fig. 1. From the left to right columns, the intensity and phase profiles of a Gaussian beam with $w=0.5$ mm, the amplitude and phase profiles of amplitude-phase hybrid gratings having sinusoidal/binary profile with $d=0.16$ mm, $V_a=1$, and $V_p=\pi$, and the corresponding intensity and phase profiles of the transmitted beam immediately after the gratings. For all cases $\Delta x=0$
Fig. 2.
Fig. 2. Diffracted patterns of a Gaussian beam with $w=0.5$ mm and $\lambda =532$ nm from different amplitude-phase hybrid gratings formed in the superimposition of two pure-amplitude and pure-phase gratings having sinusoidal/binary profile with $d=0.16$ mm, $V_a=1$, and $V_p=\pi$, for different lateral shear values of the pure-amplitude and pure-phase parts, $\Delta x$, at a propagation distance $Z=1.2$ m (See Visualization 1, Visualization 2, Visualization 3, and Visualization 4).
Fig. 3.
Fig. 3. The same diffraction pattern of Fig. 2 with the same parameters except here $V_a=1$ and $V_p=1$ (See also Visualization 5, Visualization 6, Visualization 7, and Visualization 8).
Fig. 4.
Fig. 4. The same diffraction pattern of Fig. 2 with the same parameters except $V_a=0.5$ and $V_p=0.5\pi$. See also Visualization 9, Visualization 10, Visualization 11, and Visualization 12.
Fig. 5.
Fig. 5. The same diffraction pattern of Fig. 2 with the same parameters except here $V_a=1$ and $V_p=0.25\pi$. See also Visualization 13, Visualization 14, Visualization 15, and Visualization 16.
Fig. 6.
Fig. 6. The same diffraction pattern of Fig. 2 with the same parameters except here $V_a=0.25$ and $V_p=\pi$. See also Visualization 17, Visualization 18, Visualization 19, andVisualization 20.
Fig. 7.
Fig. 7. The ratios of the mean values of the intensities over the first order diffracted pattern ($I_{+1}$) to the mean value of the (a) incident beam intensity ($I_{0}^{-}$) and (b) transmitted beam intensity ($I_{0}^{+}$) for the cases were presented in Figs. 2 and 3.
Fig. 8.
Fig. 8. Plots of the ratios of the mean values of the intensities over the different diffracted order ($I_{+i}$) to the mean value of the incident beam intensity ($I_{0}^{-}$) as a function of shear value $\Delta x$, for the cases were presented in Figs. 26.

Equations (5)

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t ( x , y ) = 1 2 ( 1 + V a c o s [ 2 π d x ] ) exp ( i V p c o s [ 2 π d ( x Δ x ) ] ) .
u ( x , y ; 0 ) = exp ( x 2 + y 2 w 2 ) ,
u ( x , y ; + 0 ) = t ( x , y ) u ( x , y ; 0 ) ,
u ( x , y ; z ) = e i k z i z λ + + u ( x , y ; + 0 ) exp ( i α [ ( x x ) 2 + ( y y ) 2 ] ) d x d y ,
u ( x , y ; + 0 ) = 1 2 exp ( x 2 + y 2 w 2 ) ( 1 + V a | c o s [ 2 π d x ] | ) exp ( i V p | c o s [ 2 π d ( x Δ x ) ] | ) .