Abstract

We investigate the effects of geometrical and structural disorders on perfectly asymmetric diffraction (PAD) in Raman-Nath regime. The two types of disorders are realized by introducing random fluctuations in the position and width of one-dimensional (1D) driven atomic lattices. Raman-Nath diffraction is modified differently with respect to the geometrical and structural disorders. It is shown that the PAD is observed with a certain strength range of geometrical disorder, exceeding which it can be destroyed, while the PAD is rather robust against structural disorder. The different behaviors originate from the disorder-induced random variations of the spatial phase shifts of the standing-wave (SW) coupling field and atomic lattices with Gaussian profile. Furthermore, we find that, in the presence of geometrical disorder, the PAD is more susceptible to correlated disorder than to uncorrelated disorder. Our scheme may be useful for understanding the effects of disorder on the diffraction of light and matter waves in disordered potentials..

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

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References

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2019 (1)

2018 (5)

2017 (3)

J. H. Wu, M. Artoni, and G. C. La Rocca, “Perfect absorption and no reflection in disordered photonic crystals,” Phys. Rev. A 95, 053862 (2017).
[Crossref]

V. Bushuev, L. Dergacheva, and B. Mantsyzov, “Asymmetric pendulum effect and transparency change of PT-symmetric photonic crystals under dynamical bragg diffraction beyond the paraxial approximation,” Phys. Rev. A 95, 033843 (2017).
[Crossref]

Y. M. Liu, F. Gao, C. H. Fan, and J. H. Wu, “Asymmetric light diffraction of an atomic grating with PT symmetry,” Opt. Lett. 42, 4283–4286 (2017).
[Crossref] [PubMed]

2016 (2)

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

T.-B. Lim, K. H. Cho, Y.-H. Kim, and Y.-C. Jeong, “Enhanced light extraction efficiency of oleds with quasiperiodic diffraction grating layer,” Opt. Express 24, 17950–17959 (2016).
[Crossref] [PubMed]

2015 (2)

M. Kulishov, H. Jones, and B. Kress, “Analysis of PT -symmetric volume gratings beyond the paraxial approximation,” Opt. Express 23, 9347–9362 (2015).
[Crossref] [PubMed]

P. Vidil and B. Chalopin, “Controllable blazed grating for electrons using Kapitza-Dirac diffraction with multiple-harmonic standing waves,” Phys. Rev. A 92, 062117 (2015).
[Crossref]

2014 (2)

J. H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref] [PubMed]

L. Wang, F. Zhou, P. Hu, Y. Niu, and S. Gong, “Two-dimensional electromagnetically induced cross-grating in a four-level tripod-type atomic system,” J. Phys. B: At. Mol. Opt. Phys. 47, 225501 (2014).
[Crossref]

2012 (3)

M. Kulishov and B. Kress, “Free space diffraction on active gratings with balanced phase and gain/loss modulations,” Opt. Express 20, 29319–29328 (2012).
[Crossref]

A. Schilke, C. Zimmermann, and W. Guerin, “Photonic properties of one-dimensionally-ordered cold atomic vapors under conditions of electromagnetically induced transparency,” Phys. Rev. A 86, 023809 (2012).
[Crossref]

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

2011 (4)

L. Zhao, W. Duan, and S. Yelin, “Generation of tunable-volume transmission-holographic gratings at low light levels,” Phys. Rev. A 84, 033806 (2011).
[Crossref]

S. A. Carvalho and L. E. de Araujo, “Electromagnetically-induced phase grating: A coupled-wave theory analysis,” Opt. Express 19, 1936–1944 (2011).
[Crossref] [PubMed]

S. Q. Kuang, C. S. Jin, and C. Li, “Gain-phase grating based on spatial modulation of active raman gain in cold atoms,” Phys. Rev. A 84, 033831 (2011).
[Crossref]

R.-G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[Crossref]

2010 (5)

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

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

L. E. de Araujo, “Electromagnetically induced phase grating,” Opt. Lett. 35, 977–979 (2010).
[Crossref] [PubMed]

G. Modugno, “Anderson localization in Bose–Einstein condensates,” Reports on Prog. Phys. 73, 102401 (2010).
[Crossref]

S. F. Liew and H. Cao, “Optical properties of 1D photonic crystals with correlated and uncorrelated disorder,” J. Opt. 12, 024011 (2010).
[Crossref]

2007 (3)

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007).
[Crossref]

H. Batelaan, “Colloquium: Illuminating the Kapitza-Dirac effect with electron matter optics,” Rev. Mod. Phys. 79, 929–941 (2007).
[Crossref]

B. Wang, C. Zhou, S. Wang, and J. Feng, “Polarizing beam splitter of a deep-etched fused-silica grating,” Opt. Lett. 32, 1299–1301 (2007).
[Crossref] [PubMed]

2005 (1)

1999 (2)

M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
[Crossref]

P. Licinio, M. Lerotic, and M. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[Crossref]

1998 (3)

M. B. Sobnack, W. Tan, N. Wanstall, T. Preist, and J. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[Crossref]

H. Y. Ling, Y.-Q. Li, and M. Xiao, “Electromagnetically induced grating: Homogeneously broadened medium,” Phys. Rev. A 57, 1334–1338 (1998).
[Crossref]

M. Berry, “Lop-sided diffraction by absorbing crystals,” J. Phys. A: Math. Gen. 31, 3493–3502 (1998).
[Crossref]

1996 (1)

M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, and A. Zeilinger, “Atom waves in crystals of light,” Phys. Rev. Lett. 77, 4980–4983 (1996).
[Crossref] [PubMed]

1985 (1)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

1978 (1)

T. Kubota, “Characteristics of thick hologram grating recorded in absorptive medium,” Opt. Acta: Int. J. Opt. 25, 1035–1053 (1978).
[Crossref]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” The Bell Syst. Tech. J. 48, 2909–2947 (1969).
[Crossref]

1932 (1)

R. B. Witmer and J. M. Cork, “The measurement of x-ray emission wave-lengths by means of the ruled grating,” Phys. Rev. 42, 743–748 (1932).
[Crossref]

Abfalterer, R.

M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, and A. Zeilinger, “Atom waves in crystals of light,” Phys. Rev. Lett. 77, 4980–4983 (1996).
[Crossref] [PubMed]

Ahufinger, V.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007).
[Crossref]

Alvine, K. J.

Artoni, M.

J. H. Wu, M. Artoni, and G. C. La Rocca, “Perfect absorption and no reflection in disordered photonic crystals,” Phys. Rev. A 95, 053862 (2017).
[Crossref]

J. H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref] [PubMed]

Batelaan, H.

H. Batelaan, “Colloquium: Illuminating the Kapitza-Dirac effect with electron matter optics,” Rev. Mod. Phys. 79, 929–941 (2007).
[Crossref]

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

Bernacki, B. E.

Bernet, S.

M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, and A. Zeilinger, “Atom waves in crystals of light,” Phys. Rev. Lett. 77, 4980–4983 (1996).
[Crossref] [PubMed]

Berry, M.

M. Berry, “Lop-sided diffraction by absorbing crystals,” J. Phys. A: Math. Gen. 31, 3493–3502 (1998).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

Brown, A. W.

Bushuev, V.

V. Bushuev, L. Dergacheva, and B. Mantsyzov, “Asymmetric pendulum effect and transparency change of PT-symmetric photonic crystals under dynamical bragg diffraction beyond the paraxial approximation,” Phys. Rev. A 95, 033843 (2017).
[Crossref]

Cao, H.

S. F. Liew and H. Cao, “Optical properties of 1D photonic crystals with correlated and uncorrelated disorder,” J. Opt. 12, 024011 (2010).
[Crossref]

Carvalho, S. A.

Chalopin, B.

P. Vidil and B. Chalopin, “Controllable blazed grating for electrons using Kapitza-Dirac diffraction with multiple-harmonic standing waves,” Phys. Rev. A 92, 062117 (2015).
[Crossref]

Chen, Y. F.

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

Cho, K. H.

Cork, J. M.

R. B. Witmer and J. M. Cork, “The measurement of x-ray emission wave-lengths by means of the ruled grating,” Phys. Rev. 42, 743–748 (1932).
[Crossref]

Damski, B.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007).
[Crossref]

Dantas, M.

P. Licinio, M. Lerotic, and M. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[Crossref]

de Araujo, L. E.

Dergacheva, L.

V. Bushuev, L. Dergacheva, and B. Mantsyzov, “Asymmetric pendulum effect and transparency change of PT-symmetric photonic crystals under dynamical bragg diffraction beyond the paraxial approximation,” Phys. Rev. A 95, 033843 (2017).
[Crossref]

DeVetter, B. M.

Ding, K.

Duan, W.

L. Zhao, W. Duan, and S. Yelin, “Generation of tunable-volume transmission-holographic gratings at low light levels,” Phys. Rev. A 84, 033806 (2011).
[Crossref]

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

Fan, C. H.

Fattal, D.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

Feng, J.

Feng, J. L.

Fiorentino, M.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

Fleischer, J. W.

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Gao, F.

Gao, J. Y.

R.-G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[Crossref]

Gaylord, T. K.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

Gomard, G.

Gong, S.

L. Wang, F. Zhou, P. Hu, Y. Niu, and S. Gong, “Two-dimensional electromagnetically induced cross-grating in a four-level tripod-type atomic system,” J. Phys. B: At. Mol. Opt. Phys. 47, 225501 (2014).
[Crossref]

Guerin, W.

A. Schilke, C. Zimmermann, and W. Guerin, “Photonic properties of one-dimensionally-ordered cold atomic vapors under conditions of electromagnetically induced transparency,” Phys. Rev. A 86, 023809 (2012).
[Crossref]

He, C.

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

Hölscher, H.

Hu, P.

L. Wang, F. Zhou, P. Hu, Y. Niu, and S. Gong, “Two-dimensional electromagnetically induced cross-grating in a four-level tripod-type atomic system,” J. Phys. B: At. Mol. Opt. Phys. 47, 225501 (2014).
[Crossref]

Hünig, R.

Imoto, N.

M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
[Crossref]

Jeong, Y.-C.

Jiang, L.

R.-G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[Crossref]

Jiang, Y.

R.-G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[Crossref]

Jin, C. S.

S. Q. Kuang, C. S. Jin, and C. Li, “Gain-phase grating based on spatial modulation of active raman gain in cold atoms,” Phys. Rev. A 84, 033831 (2011).
[Crossref]

Jones, H.

Kagan, C. R.

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Kim, J. B.

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Kim, P.

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Kim, Y.-H.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” The Bell Syst. Tech. J. 48, 2909–2947 (1969).
[Crossref]

Kou, J.

R.-G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[Crossref]

Kress, B.

Kuang, S. Q.

S. Q. Kuang, C. S. Jin, and C. Li, “Gain-phase grating based on spatial modulation of active raman gain in cold atoms,” Phys. Rev. A 84, 033831 (2011).
[Crossref]

Kubota, T.

T. Kubota, “Characteristics of thick hologram grating recorded in absorptive medium,” Opt. Acta: Int. J. Opt. 25, 1035–1053 (1978).
[Crossref]

Kulishov, M.

Lemmer, U.

Lerotic, M.

P. Licinio, M. Lerotic, and M. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[Crossref]

Lewenstein, M.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007).
[Crossref]

Li, C.

S. Q. Kuang, C. S. Jin, and C. Li, “Gain-phase grating based on spatial modulation of active raman gain in cold atoms,” Phys. Rev. A 84, 033831 (2011).
[Crossref]

Li, J.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

Li, L.

T. Shui, W. X. Yang, L. Li, and X. Wang, “Lop-sided Raman-Nath diffraction in PT-antisymmetric atomic lattices,” Opt. Lett. 44, 2089–2092 (2019).
[Crossref] [PubMed]

T. Shui, W. X. Yang, S. P. Liu, L. Li, and Z. H. Zhu, “Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime,” Phys. Rev. A 97, 033819 (2018).
[Crossref]

Li, Y.-Q.

H. Y. Ling, Y.-Q. Li, and M. Xiao, “Electromagnetically induced grating: Homogeneously broadened medium,” Phys. Rev. A 57, 1334–1338 (1998).
[Crossref]

Licinio, P.

P. Licinio, M. Lerotic, and M. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[Crossref]

Liew, S. F.

S. F. Liew and H. Cao, “Optical properties of 1D photonic crystals with correlated and uncorrelated disorder,” J. Opt. 12, 024011 (2010).
[Crossref]

Lim, T.-B.

Limonov, M. F.

A. D. Sinelnik, M. V. Rybin, S. Y. Lukashenko, M. F. Limonov, and K. B. Samusev, “Evolution of optical diffraction patterns on disordered woodpile photonic structures,” Phys. Solid State 60, 1387–1393 (2018).
[Crossref]

Ling, H. Y.

H. Y. Ling, Y.-Q. Li, and M. Xiao, “Electromagnetically induced grating: Homogeneously broadened medium,” Phys. Rev. A 57, 1334–1338 (1998).
[Crossref]

Liu, S. P.

T. Shui, W. X. Yang, S. P. Liu, L. Li, and Z. H. Zhu, “Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime,” Phys. Rev. A 97, 033819 (2018).
[Crossref]

Liu, X. P.

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

Liu, Y. M.

Loewen, E. G.

C. A. Palmer and E. G. Loewen, Diffraction Grating Handbook (Newport Corporation, 2005).

Loo, Y.-L.

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Lu, H. Y.

Lu, M. H.

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

Lukashenko, S. Y.

A. D. Sinelnik, M. V. Rybin, S. Y. Lukashenko, M. F. Limonov, and K. B. Samusev, “Evolution of optical diffraction patterns on disordered woodpile photonic structures,” Phys. Solid State 60, 1387–1393 (2018).
[Crossref]

Mantsyzov, B.

V. Bushuev, L. Dergacheva, and B. Mantsyzov, “Asymmetric pendulum effect and transparency change of PT-symmetric photonic crystals under dynamical bragg diffraction beyond the paraxial approximation,” Phys. Rev. A 95, 033843 (2017).
[Crossref]

Mitsunaga, M.

M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
[Crossref]

Modugno, G.

G. Modugno, “Anderson localization in Bose–Einstein condensates,” Reports on Prog. Phys. 73, 102401 (2010).
[Crossref]

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

Niu, Y.

L. Wang, F. Zhou, P. Hu, Y. Niu, and S. Gong, “Two-dimensional electromagnetically induced cross-grating in a four-level tripod-type atomic system,” J. Phys. B: At. Mol. Opt. Phys. 47, 225501 (2014).
[Crossref]

Oberthaler, M. K.

M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, and A. Zeilinger, “Atom waves in crystals of light,” Phys. Rev. Lett. 77, 4980–4983 (1996).
[Crossref] [PubMed]

Oh, S. J.

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Paetzold, U. W.

Palmer, C. A.

C. A. Palmer and E. G. Loewen, Diffraction Grating Handbook (Newport Corporation, 2005).

Pégard, N. C.

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Peng, Z.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

Preist, T.

M. B. Sobnack, W. Tan, N. Wanstall, T. Preist, and J. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[Crossref]

Rocca, G. C. La

J. H. Wu, M. Artoni, and G. C. La Rocca, “Perfect absorption and no reflection in disordered photonic crystals,” Phys. Rev. A 95, 053862 (2017).
[Crossref]

J. H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref] [PubMed]

Rybin, M. V.

A. D. Sinelnik, M. V. Rybin, S. Y. Lukashenko, M. F. Limonov, and K. B. Samusev, “Evolution of optical diffraction patterns on disordered woodpile photonic structures,” Phys. Solid State 60, 1387–1393 (2018).
[Crossref]

Sambles, J.

M. B. Sobnack, W. Tan, N. Wanstall, T. Preist, and J. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[Crossref]

Samusev, K. B.

A. D. Sinelnik, M. V. Rybin, S. Y. Lukashenko, M. F. Limonov, and K. B. Samusev, “Evolution of optical diffraction patterns on disordered woodpile photonic structures,” Phys. Solid State 60, 1387–1393 (2018).
[Crossref]

Sanpera, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007).
[Crossref]

Schauer, S.

Schilke, A.

A. Schilke, C. Zimmermann, and W. Guerin, “Photonic properties of one-dimensionally-ordered cold atomic vapors under conditions of electromagnetically induced transparency,” Phys. Rev. A 86, 023809 (2012).
[Crossref]

Schmager, R.

Schmiedmayer, J.

M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, and A. Zeilinger, “Atom waves in crystals of light,” Phys. Rev. Lett. 77, 4980–4983 (1996).
[Crossref] [PubMed]

Sen, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007).
[Crossref]

Sen, U.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007).
[Crossref]

Shu, S. L.

Shui, T.

T. Shui, W. X. Yang, L. Li, and X. Wang, “Lop-sided Raman-Nath diffraction in PT-antisymmetric atomic lattices,” Opt. Lett. 44, 2089–2092 (2019).
[Crossref] [PubMed]

T. Shui, W. X. Yang, S. P. Liu, L. Li, and Z. H. Zhu, “Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime,” Phys. Rev. A 97, 033819 (2018).
[Crossref]

Sinelnik, A. D.

A. D. Sinelnik, M. V. Rybin, S. Y. Lukashenko, M. F. Limonov, and K. B. Samusev, “Evolution of optical diffraction patterns on disordered woodpile photonic structures,” Phys. Solid State 60, 1387–1393 (2018).
[Crossref]

Sobnack, M. B.

M. B. Sobnack, W. Tan, N. Wanstall, T. Preist, and J. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[Crossref]

Stone, H. A.

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Sun, X. C.

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

Tan, W.

M. B. Sobnack, W. Tan, N. Wanstall, T. Preist, and J. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[Crossref]

Tian, S. C.

Tong, C. Z.

Vidil, P.

P. Vidil and B. Chalopin, “Controllable blazed grating for electrons using Kapitza-Dirac diffraction with multiple-harmonic standing waves,” Phys. Rev. A 92, 062117 (2015).
[Crossref]

Wan, R. G.

Wan, R.-G.

R.-G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[Crossref]

Wang, B.

Wang, L.

L. Wang, F. Zhou, P. Hu, Y. Niu, and S. Gong, “Two-dimensional electromagnetically induced cross-grating in a four-level tripod-type atomic system,” J. Phys. B: At. Mol. Opt. Phys. 47, 225501 (2014).
[Crossref]

Wang, L. J.

Wang, S.

Wang, X.

Wanstall, N.

M. B. Sobnack, W. Tan, N. Wanstall, T. Preist, and J. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[Crossref]

Witmer, R. B.

R. B. Witmer and J. M. Cork, “The measurement of x-ray emission wave-lengths by means of the ruled grating,” Phys. Rev. 42, 743–748 (1932).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

Worgull, M.

Wu, J. H.

J. H. Wu, M. Artoni, and G. C. La Rocca, “Perfect absorption and no reflection in disordered photonic crystals,” Phys. Rev. A 95, 053862 (2017).
[Crossref]

Y. M. Liu, F. Gao, C. H. Fan, and J. H. Wu, “Asymmetric light diffraction of an atomic grating with PT symmetry,” Opt. Lett. 42, 4283–4286 (2017).
[Crossref] [PubMed]

J. H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref] [PubMed]

Xiao, M.

Xu, Y. L.

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

Yang, W. X.

T. Shui, W. X. Yang, L. Li, and X. Wang, “Lop-sided Raman-Nath diffraction in PT-antisymmetric atomic lattices,” Opt. Lett. 44, 2089–2092 (2019).
[Crossref] [PubMed]

T. Shui, W. X. Yang, S. P. Liu, L. Li, and Z. H. Zhu, “Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime,” Phys. Rev. A 97, 033819 (2018).
[Crossref]

Yelin, S.

L. Zhao, W. Duan, and S. Yelin, “Generation of tunable-volume transmission-holographic gratings at low light levels,” Phys. Rev. A 84, 033806 (2011).
[Crossref]

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

Zeilinger, A.

M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, and A. Zeilinger, “Atom waves in crystals of light,” Phys. Rev. Lett. 77, 4980–4983 (1996).
[Crossref] [PubMed]

Zhang, X.

Zhao, L.

L. Zhao, W. Duan, and S. Yelin, “Generation of tunable-volume transmission-holographic gratings at low light levels,” Phys. Rev. A 84, 033806 (2011).
[Crossref]

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

Zhou, C.

Zhou, F.

L. Wang, F. Zhou, P. Hu, Y. Niu, and S. Gong, “Two-dimensional electromagnetically induced cross-grating in a four-level tripod-type atomic system,” J. Phys. B: At. Mol. Opt. Phys. 47, 225501 (2014).
[Crossref]

Zhu, X. Y.

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

Zhu, Z. H.

T. Shui, W. X. Yang, S. P. Liu, L. Li, and Z. H. Zhu, “Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime,” Phys. Rev. A 97, 033819 (2018).
[Crossref]

Zimmermann, C.

A. Schilke, C. Zimmermann, and W. Guerin, “Photonic properties of one-dimensionally-ordered cold atomic vapors under conditions of electromagnetically induced transparency,” Phys. Rev. A 86, 023809 (2012).
[Crossref]

Zou, Y.

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

Adv. Phys. (1)

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007).
[Crossref]

Am. J. Phys. (1)

P. Licinio, M. Lerotic, and M. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[Crossref]

Appl. Phys. Lett. (1)

X. Y. Zhu, Y. L. Xu, Y. Zou, X. C. Sun, C. He, M. H. Lu, X. P. Liu, and Y. F. Chen, “Asymmetric diffraction based on a passive parity-time grating,” Appl. Phys. Lett. 109, 111101 (2016).
[Crossref]

J. Opt. (1)

S. F. Liew and H. Cao, “Optical properties of 1D photonic crystals with correlated and uncorrelated disorder,” J. Opt. 12, 024011 (2010).
[Crossref]

J. Phys. A: Math. Gen. (1)

M. Berry, “Lop-sided diffraction by absorbing crystals,” J. Phys. A: Math. Gen. 31, 3493–3502 (1998).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (1)

L. Wang, F. Zhou, P. Hu, Y. Niu, and S. Gong, “Two-dimensional electromagnetically induced cross-grating in a four-level tripod-type atomic system,” J. Phys. B: At. Mol. Opt. Phys. 47, 225501 (2014).
[Crossref]

Nat. Photonics (2)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

J. B. Kim, P. Kim, N. C. Pégard, S. J. Oh, C. R. Kagan, J. W. Fleischer, H. A. Stone, and Y.-L. Loo, “Wrinkles and deep folds as photonic structures in photovoltaics,” Nat. Photonics 6, 327–332 (2012).
[Crossref]

Opt. Acta: Int. J. Opt. (1)

T. Kubota, “Characteristics of thick hologram grating recorded in absorptive medium,” Opt. Acta: Int. J. Opt. 25, 1035–1053 (1978).
[Crossref]

Opt. Express (5)

Opt. Lett. (6)

Opt. Mater. Express (1)

Phys. Rev. (1)

R. B. Witmer and J. M. Cork, “The measurement of x-ray emission wave-lengths by means of the ruled grating,” Phys. Rev. 42, 743–748 (1932).
[Crossref]

Phys. Rev. A (11)

S. Q. Kuang, C. S. Jin, and C. Li, “Gain-phase grating based on spatial modulation of active raman gain in cold atoms,” Phys. Rev. A 84, 033831 (2011).
[Crossref]

R.-G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[Crossref]

L. Zhao, W. Duan, and S. Yelin, “Generation of tunable-volume transmission-holographic gratings at low light levels,” Phys. Rev. A 84, 033806 (2011).
[Crossref]

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

M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
[Crossref]

J. H. Wu, M. Artoni, and G. C. La Rocca, “Perfect absorption and no reflection in disordered photonic crystals,” Phys. Rev. A 95, 053862 (2017).
[Crossref]

A. Schilke, C. Zimmermann, and W. Guerin, “Photonic properties of one-dimensionally-ordered cold atomic vapors under conditions of electromagnetically induced transparency,” Phys. Rev. A 86, 023809 (2012).
[Crossref]

H. Y. Ling, Y.-Q. Li, and M. Xiao, “Electromagnetically induced grating: Homogeneously broadened medium,” Phys. Rev. A 57, 1334–1338 (1998).
[Crossref]

T. Shui, W. X. Yang, S. P. Liu, L. Li, and Z. H. Zhu, “Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime,” Phys. Rev. A 97, 033819 (2018).
[Crossref]

V. Bushuev, L. Dergacheva, and B. Mantsyzov, “Asymmetric pendulum effect and transparency change of PT-symmetric photonic crystals under dynamical bragg diffraction beyond the paraxial approximation,” Phys. Rev. A 95, 033843 (2017).
[Crossref]

P. Vidil and B. Chalopin, “Controllable blazed grating for electrons using Kapitza-Dirac diffraction with multiple-harmonic standing waves,” Phys. Rev. A 92, 062117 (2015).
[Crossref]

Phys. Rev. Lett. (3)

M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, and A. Zeilinger, “Atom waves in crystals of light,” Phys. Rev. Lett. 77, 4980–4983 (1996).
[Crossref] [PubMed]

J. H. Wu, M. Artoni, and G. C. La Rocca, “Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices,” Phys. Rev. Lett. 113, 123004 (2014).
[Crossref] [PubMed]

M. B. Sobnack, W. Tan, N. Wanstall, T. Preist, and J. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[Crossref]

Phys. Solid State (1)

A. D. Sinelnik, M. V. Rybin, S. Y. Lukashenko, M. F. Limonov, and K. B. Samusev, “Evolution of optical diffraction patterns on disordered woodpile photonic structures,” Phys. Solid State 60, 1387–1393 (2018).
[Crossref]

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[Crossref]

Reports on Prog. Phys. (1)

G. Modugno, “Anderson localization in Bose–Einstein condensates,” Reports on Prog. Phys. 73, 102401 (2010).
[Crossref]

Rev. Mod. Phys. (1)

H. Batelaan, “Colloquium: Illuminating the Kapitza-Dirac effect with electron matter optics,” Rev. Mod. Phys. 79, 929–941 (2007).
[Crossref]

The Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” The Bell Syst. Tech. J. 48, 2909–2947 (1969).
[Crossref]

Other (2)

C. A. Palmer and E. G. Loewen, Diffraction Grating Handbook (Newport Corporation, 2005).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) Sketch of 1D atomic grating, which consists of 1D optical lattices of driven cold 87Rb atoms. The area shown in purple is the spatial distribution of the atomic density. (b) Schematic of diagram of a four-level N-type atomic system interacting with three applied laser fields.
Fig. 2
Fig. 2 The Raman-Nath diffraction intensities as a function of sin θ for (a) φc = 0, Δ d = 0MHz and (b) φc = 0.15π, Δ d = 2MHz. Other parameters are N0 = 5 ×1012cm−3, µ31 = 2.5377 ×10−29C m, Ω c 0 = 6MHz, Ω c 1 = 1.53MHz, Ω d = 2MHz, Δ p = 7MHz, Δ c = 0MHz, λp = 795.5nm, Λ/λp = 4, d = 0.2Λ, M = 11 and L = 30µm.
Fig. 3
Fig. 3 Two examples of 20 random configurations of (a) uncorrelated geometric disorder [Eq. (2)] and (b) correlated geometric disorder [Eq. (3)]. The dependence of Raman-Nath diffraction spectra on the (c) uncorrelated and (d) correlated geometric disorders. Each curve represents a diffraction profile induced by a random configuration of geometric disorder. The spatial correlation functions CRx) and CIx) for the real part χ(x) and imaginary part χ(x) of the spatial susceptibility with the (e) uncorrelated and (f) correlated geometric disorders. The strength of geometric disorder Δ g = 0.07 and other parameters are the same as in Fig. 2(a).
Fig. 4
Fig. 4 The average Raman-Nath diffraction spectra 〈Ip(θ)〉 of the atomic grating for different strengths of (a) uncorrelated and (b) correlated geometric disorders. The corresponding evolutions of the average Raman-Nath diffraction 〈Ip(θ)〉 with the strengths of (c)uncorrelated and (d) correlated disorders. The average diffraction spectra are attained through averaging over 50 different random configurations of disorder (NR = 50). Other parameters are the same as in Fig. 2(a).
Fig. 5
Fig. 5 The evolutions of the average Raman-Nath diffraction 〈Ip(θ)〉 with the strengths Δ g of (a) uncorrelated (b) correlated geometric disorders. Other parameters are the same as in Fig. 2(b).
Fig. 6
Fig. 6 The average Raman-Nath diffraction spectra 〈Ip(θ)〉 of the atomic grating for different strengths of (a) uncorrelated and (b) correlated structural disorders. The corresponding evolutions of the average Raman-Nath diffraction 〈Ip(θ)〉 with the strengths of (c)uncorrelated and (d) correlated disorders. Other parameters are the same as in Fig. 2(a).
Fig. 7
Fig. 7 The evolutions of the average Raman-Nath diffraction 〈Ip(θ)〉 with the strengths Δ s of (a) uncorrelated (b) correlated structural disorders. Other parameters are the same as in Fig. 2(b).
Fig. 8
Fig. 8 The evolutions of the average Raman-Nath diffraction 〈Ip(θ)〉 with the strengths Δ N and ΔΩ of uncorrelated disorders in (a) the average atomic density N0 and (b) the standing-wave Rabi frequency Ω c 1. Other parameters are the same as in Fig. 2(a).

Equations (14)

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N j ( x ) = N 0 2 π d exp [ ( x x j ) 2 d j 2 ] ,
x j = j Λ + δ x j = j Λ + Λ ζ j ,
x j ( c ) = j Λ + i = 1 j δ x i = j Λ + Λ i = 1 j ζ i ,
d j = d + δ d j = d + d η j ,
d j ( c ) = d + i = 1 j δ d i = d + d i = 1 j η i .
Ω c ( x ) = Ω c 0 + Ω c 1 sin ( 2 π x Λ φ c ) ,
H I = ( Δ c 0 0 Ω c ( x ) 0 Δ p Ω d Ω p 0 Ω d * ( Δ p Δ d ) 0 Ω c * ( x ) Ω p * 0 0 ) ,
d ρ d t = i [ H I , ρ ] + L [ ρ ( t ) ] .
L [ ρ ( t ) ] = ( σ 44 γ 43 ρ 43 γ 42 ρ 42 γ 41 ρ 41 γ 43 ρ 34 σ 33 γ 32 ρ 32 γ 31 ρ 31 γ 42 ρ 24 γ 32 ρ 23 σ 22 γ 21 ρ 21 γ 41 ρ 14 γ 31 ρ 13 γ 21 ρ 12 σ 11 ) ,
χ j ( x ) = N j ( x ) | μ 31 | 2 ε 0 Ω p ρ 31 = N j ( x ) | μ 31 | 2 ε 0 [ i κ 3 ( κ 4 + κ 5 ) Ω c 2 ( x ) ] Ω d 2 κ 1 κ 2 ,
T ( x ) = { e β I ( x ) L e i β R ( x ) L , if x [ Λ / 2 , ( 2 M + 1 ) Λ / 2 ] 0 , otherwise ,
E p ( θ ) = C + E 0 T ( x ) e i 2 π x sin θ / λ p d x ,
I p ( θ ) = 1 ( M Λ ) 2 | + T ( x ) e i 2 π x sin θ / λ p d x | 2 .
I p ( θ ) = 1 N R m = 1 N R I p ( θ , m ) ,

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