Abstract

A blazed gain grating in a four-level atomic system is theoretically demonstrated. This grating is based on the spatial modulation of Raman gain, which is created by an intensity mask in the signal field. Due to the modulo-2π phase modulation, the majority of energy in the amplified probe beam can be deflected into the first-order direction, and a diffraction efficiency higher than 100% is predicted. When an intensity mask having two symmetric domains is adopted, this proposal can give a further possibility of all-optical beam splitting.

© 2012 Optical Society of America

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References

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  1. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  2. H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
    [CrossRef]
  3. M. Mitsunaga and N. Imoto, “Observation of an electromagnetically induced grating in cold sodium atoms,” Phys. Rev. A 59, 4773–4776 (1999).
    [CrossRef]
  4. L. E. E. de Araujo, “Electromagnetically induced phase grating,” Opt. Lett. 35, 977–979 (2010).
    [CrossRef]
  5. Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
    [CrossRef]
  6. 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]
  7. 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]
  8. S. Q. Kuang, “Raman gain grating in an ultracold atomic medium,” Chin. Opt. 5, 464–469 (2012).
    [CrossRef]
  9. L. Deng and M. G. Payne, “Gain-assisted large and rapidly responding Kerr effect using a room-temperature active Raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
    [CrossRef]
  10. K. J. Jiang, L. Deng, E. W. Hagley, and M. G. Payne, “Fast-responding nonlinear phase shifter using a signal-wave gain medium,” Phys. Rev. A 77, 045804 (2008).
    [CrossRef]
  11. C. J. Zhu, C. Hang, and G. X. Huang, “Gain-assisted giant Kerr nonlinearity in a Λ-type system with two-folded lower levels,” Eur. Phys. J. D 56, 231–237 (2010).
    [CrossRef]
  12. L. Zhao, W. H. Duan, and S. F. Yelin, “All-optical beam control with high speed using image-induced blazed gratings in coherent medium,” Phys. Rev. A 82, 013809 (2010).
    [CrossRef]
  13. S. A. Carvalho and L. E. E. de Araujo, “Electromagnetically induced blazed grating at low light levels,” Phys. Rev. A 83, 053825 (2011).
    [CrossRef]
  14. A. W. Brown and M. Xiao, “All-optical switching and routing based on an electromagnetically induced absorption grating,” Opt. Lett. 30, 699–701 (2005).
    [CrossRef]
  15. 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]
  16. G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of Raman gain process,” Phys. Rev. A 70, 023802 (2004).
    [CrossRef]
  17. M. V. Pack, R. M. Camacho, and J. C. Howell, “Transient of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity,” Phys. Rev. A 76, 033835 (2007).
    [CrossRef]
  18. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

2012 (2)

S. Q. Kuang, “Raman gain grating in an ultracold atomic medium,” Chin. Opt. 5, 464–469 (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]

2011 (3)

S. A. Carvalho and L. E. E. de Araujo, “Electromagnetically induced blazed grating at low light levels,” Phys. Rev. A 83, 053825 (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]

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]

2010 (4)

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

C. J. Zhu, C. Hang, and G. X. Huang, “Gain-assisted giant Kerr nonlinearity in a Λ-type system with two-folded lower levels,” Eur. Phys. J. D 56, 231–237 (2010).
[CrossRef]

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

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

2008 (1)

K. J. Jiang, L. Deng, E. W. Hagley, and M. G. Payne, “Fast-responding nonlinear phase shifter using a signal-wave gain medium,” Phys. Rev. A 77, 045804 (2008).
[CrossRef]

2007 (2)

L. Deng and M. G. Payne, “Gain-assisted large and rapidly responding Kerr effect using a room-temperature active Raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transient of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity,” Phys. Rev. A 76, 033835 (2007).
[CrossRef]

2005 (2)

A. W. Brown and M. Xiao, “All-optical switching and routing based on an electromagnetically induced absorption grating,” Opt. Lett. 30, 699–701 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

2004 (1)

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of Raman gain process,” Phys. Rev. A 70, 023802 (2004).
[CrossRef]

1999 (1)

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

1998 (1)

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of Raman gain process,” Phys. Rev. A 70, 023802 (2004).
[CrossRef]

Brown, A. W.

Camacho, R. M.

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transient of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity,” Phys. Rev. A 76, 033835 (2007).
[CrossRef]

Carvalho, S. A.

S. A. Carvalho and L. E. E. de Araujo, “Electromagnetically induced blazed grating at low light levels,” Phys. Rev. A 83, 053825 (2011).
[CrossRef]

Dasgupta, S.

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of Raman gain process,” Phys. Rev. A 70, 023802 (2004).
[CrossRef]

de Araujo, L. E. E.

S. A. Carvalho and L. E. E. de Araujo, “Electromagnetically induced blazed grating at low light levels,” Phys. Rev. A 83, 053825 (2011).
[CrossRef]

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

Deng, L.

K. J. Jiang, L. Deng, E. W. Hagley, and M. G. Payne, “Fast-responding nonlinear phase shifter using a signal-wave gain medium,” Phys. Rev. A 77, 045804 (2008).
[CrossRef]

L. Deng and M. G. Payne, “Gain-assisted large and rapidly responding Kerr effect using a room-temperature active Raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

Duan, W. H.

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

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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]

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]

Hagley, E. W.

K. J. Jiang, L. Deng, E. W. Hagley, and M. G. Payne, “Fast-responding nonlinear phase shifter using a signal-wave gain medium,” Phys. Rev. A 77, 045804 (2008).
[CrossRef]

Hang, C.

C. J. Zhu, C. Hang, and G. X. Huang, “Gain-assisted giant Kerr nonlinearity in a Λ-type system with two-folded lower levels,” Eur. Phys. J. D 56, 231–237 (2010).
[CrossRef]

Howell, J. C.

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transient of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity,” Phys. Rev. A 76, 033835 (2007).
[CrossRef]

Huang, G. X.

C. J. Zhu, C. Hang, and G. X. Huang, “Gain-assisted giant Kerr nonlinearity in a Λ-type system with two-folded lower levels,” Eur. Phys. J. D 56, 231–237 (2010).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

Jiang, K. J.

K. J. Jiang, L. Deng, E. W. Hagley, and M. G. Payne, “Fast-responding nonlinear phase shifter using a signal-wave gain medium,” Phys. Rev. A 77, 045804 (2008).
[CrossRef]

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]

Kim, K.

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[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]

Kuang, S. Q.

S. Q. Kuang, “Raman gain grating in an ultracold atomic medium,” Chin. Opt. 5, 464–469 (2012).
[CrossRef]

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, 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, Y. Q.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

Ling, H. Y.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[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]

Pack, M. V.

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transient of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity,” Phys. Rev. A 76, 033835 (2007).
[CrossRef]

Payne, M. G.

K. J. Jiang, L. Deng, E. W. Hagley, and M. G. Payne, “Fast-responding nonlinear phase shifter using a signal-wave gain medium,” Phys. Rev. A 77, 045804 (2008).
[CrossRef]

L. Deng and M. G. Payne, “Gain-assisted large and rapidly responding Kerr effect using a room-temperature active Raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

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]

Shin, S. G.

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

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]

Xiao, M.

A. W. Brown and M. Xiao, “All-optical switching and routing based on an electromagnetically induced absorption grating,” Opt. Lett. 30, 699–701 (2005).
[CrossRef]

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

Xiao, Z. H.

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

Yelin, S. F.

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

Zhao, L.

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

Zhu, C. J.

C. J. Zhu, C. Hang, and G. X. Huang, “Gain-assisted giant Kerr nonlinearity in a Λ-type system with two-folded lower levels,” Eur. Phys. J. D 56, 231–237 (2010).
[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]

Chin. Opt. (1)

S. Q. Kuang, “Raman gain grating in an ultracold atomic medium,” Chin. Opt. 5, 464–469 (2012).
[CrossRef]

Eur. Phys. J. D (1)

C. J. Zhu, C. Hang, and G. X. Huang, “Gain-assisted giant Kerr nonlinearity in a Λ-type system with two-folded lower levels,” Eur. Phys. J. D 56, 231–237 (2010).
[CrossRef]

J. Phys. B (1)

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (10)

K. J. Jiang, L. Deng, E. W. Hagley, and M. G. Payne, “Fast-responding nonlinear phase shifter using a signal-wave gain medium,” Phys. Rev. A 77, 045804 (2008).
[CrossRef]

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

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

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of Raman gain process,” Phys. Rev. A 70, 023802 (2004).
[CrossRef]

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transient of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity,” Phys. Rev. A 76, 033835 (2007).
[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]

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]

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

S. A. Carvalho and L. E. E. de Araujo, “Electromagnetically induced blazed grating at low light levels,” Phys. Rev. A 83, 053825 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

L. Deng and M. G. Payne, “Gain-assisted large and rapidly responding Kerr effect using a room-temperature active Raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Other (1)

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the four-level atomic system in ARG configuration. The pumping field Ep, probe field E, and signal field Es interact with the atomic transitions |3|1, |3|2, and |4|2, respectively. Δp, Δ and Δs are detunings of the pumping, probe, and signal fields, respectively. Here, two-photon detuning of Raman resonance is δ=ΔpΔ.

Fig. 2.
Fig. 2.

Schematic diagram of the beam setup for creating a blazed gain grating in an ultracold atomic medium. An intensity mask at the object plane of the lens creates an intensity image of the signal field in cold atoms at the image plane. The probe beam is diffracted at an angle θ by this grating. BS and PBS are the beam splitter and polarizing beam splitter, respectively.

Fig. 3.
Fig. 3.

(a) Periodic intensity image in the signal field, and D is the spatial spacing. This image has finite width 6D. (b) Numerical amplitude distribution of signal field according to the intensity image of Fig. 3(a). (c) Induced x-dependent amplitude (black dashed curve) and phase (red solid curve) of the transmission function T(x). (d) Fraunhofer diffraction patterns for blazed gain grating of Fig. 3(c) (red solid curve), and the grating without phase modulation (black dashed curve).

Fig. 4.
Fig. 4.

(a) Periodic intensity image that has two domains in the signal field to split the probe beam. The number of spatial periods in each domain is six. (b) Numerical amplitude distribution of signal field according to the intensity image of Fig. 4(a). For simplicity, only three periods in each domain are presented. (c) Amplitude (black dashed curve) and phase (red solid curve) of the transmission function T(x) as a function of x, which is induced by the signal field in Fig. 4(b). (d) Fraunhofer diffraction pattern of the diffraction grating of Fig. 4(c).

Equations (10)

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

HI=[δ|22|+Δp|33|+(δ+Δs)|44|(g|32|+Ωp|31|+Ωs|42|+H.c.)].
ρ˙11=iΩp(ρ31ρ13)+Γ31ρ33+Γ41ρ44,ρ˙22=ig(ρ32ρ23)+iΩs(ρ42ρ24)+Γ32ρ33+Γ42ρ44,ρ˙33=iΩp(ρ13ρ31)+ig(ρ23ρ32)Γ31ρ33Γ32ρ33,ρ˙31=(iΔp+γ31)ρ31+iΩp(ρ11ρ33)+igρ21,ρ˙32=(iΔ+γ32)ρ32iΩsρ34+iΩpρ12+ig(ρ22ρ33),ρ˙42=(iΔs+γ42)ρ42igρ43+iΩs(ρ22ρ44),ρ˙41=[i(Δs+δ)+γ41]ρ41+iΩsρ21iΩpρ43,ρ˙43=[i(ΔΔs)γ43]ρ43+iΩsρ23iΩpρ41igρ42,ρ˙21=(iδ+γ21)ρ21+igρ31+iΩsρ41iΩpρ23,1=ρ11+ρ22+ρ33+ρ44,
Ωs2=γ2a{x/D}+b,
i2k2E2x+Ez=ikχE,
iNF2E2x+Ez=(α+iβ)E,
T(x)=eα(x)Leiβ(x)L.
I(θ)=|E(θ)|2sin2(NπDsinθ/λ)N2sin2(πDsinθ/λ),
E(θ)=01T(x)exp(ikDxsinθ)dx.
Ωs2=γ2a{|x|/D}+b.
I(θ)=1N2|6+6T(x)exp(ikDxsinθ)dx|2.

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