Abstract

We consider a hybrid quantum-well structure consisting of regions whose properties alternate between active Raman gain and electromagnetically induced transparency. We present both analytical and numerical results that indicate a large light beam defection using spatially inhomogeneous pump and control lasers. We show well-isolated on-chip wavelength selection or channeling capabilities without light field attenuation or distortion, demonstrating the advantages of the system for possible important applications in integrated circuits for optical telecommunications.

© 2013 Optical Society of America

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References

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  1. C. S. R. Murthy and M. Guruswamy, WDM Optical Networks, Concepts, Design, and Algorithms (Prentice Hall PTR, 2001).
  2. H. Ishio, J. Minowa, and K. Nosu, J. Lightwave Technol. 2, 448 (1984).
    [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  4. M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
    [CrossRef]
  5. D. L. Zhou, Lan Zhou, R. Q. Wang, S. Yi, and C. P. Sun, Phys. Rev. A 76, 055801 (2007).
    [CrossRef]
  6. Q. Sun, Y. V. Rostovtsev, and M. S. Zubairy, Phys. Rev. A 74, 033819 (2006).
    [CrossRef]
  7. R. Schlesser and A. Weis, Opt. Lett. 17, 1015 (1992).
    [CrossRef]
  8. R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
    [CrossRef]
  9. G. T. Purves, G. Jundt, C. S. Adams, and I. G. Hughes, Eur. Phys. J. D 29, 433 (2004).
    [CrossRef]
  10. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
    [CrossRef]
  11. L. Karpa and M. Weitz, Nat. Phys. 2, 332 (2006).
    [CrossRef]
  12. V. A. Sautenkov, H. Li, Y. V. Rostovtsev, and M. O. Scully, Phys. Rev. A 81, 063824 (2010).
    [CrossRef]
  13. M. Olszakier, E. Ehrenfreund, E. Cohen, J. Bajaj, and G. J. Sullivan, Phys. Rev. Lett. 62, 2997 (1989).
    [CrossRef]
  14. C. J. Zhu and G. X. Huang, Phys. Rev. B 80, 235408 (2009).
    [CrossRef]
  15. C. J. Zhu and G. X. Huang, Opt. Express 1923364 (2011).
    [CrossRef]
  16. K. V. Shajesh, “Eikonal approximation,” Ph.D. dissertation (University of Oklahoma).
  17. C. J. Zhu, L. Deng, and E. W. Hagley, “Dynamic light bending in a Raman gain medium using a spatially inhomogeneous pump,” Phys. Rev. A, submitted for publication.
  18. L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
    [CrossRef]
  19. C. J. Zhu, C. Hang, and G. X. Huang, Eur. Phys. J. D 56, 231 (2010).
    [CrossRef]
  20. S. E. Harris, J. E. Field, and A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
    [CrossRef]
  21. With γj≈γj′ and |ΩL(0)|4≥|d2|2|d3|2, the condition |p12|≈|p0| minimizes the gain/loss per unit cell.
  22. J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
    [CrossRef]
  23. H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, Appl. Phys. Lett. 70, 3455 (1997).
    [CrossRef]
  24. A. Ciattoni, P. D. Porto, B. Crosignani, and A. Yariv, J. Opt. Soc. Am. B 17, 809 (2000).
    [CrossRef]

2011 (1)

2010 (2)

V. A. Sautenkov, H. Li, Y. V. Rostovtsev, and M. O. Scully, Phys. Rev. A 81, 063824 (2010).
[CrossRef]

C. J. Zhu, C. Hang, and G. X. Huang, Eur. Phys. J. D 56, 231 (2010).
[CrossRef]

2009 (1)

C. J. Zhu and G. X. Huang, Phys. Rev. B 80, 235408 (2009).
[CrossRef]

2007 (2)

D. L. Zhou, Lan Zhou, R. Q. Wang, S. Yi, and C. P. Sun, Phys. Rev. A 76, 055801 (2007).
[CrossRef]

L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

2006 (2)

Q. Sun, Y. V. Rostovtsev, and M. S. Zubairy, Phys. Rev. A 74, 033819 (2006).
[CrossRef]

L. Karpa and M. Weitz, Nat. Phys. 2, 332 (2006).
[CrossRef]

2005 (1)

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

2004 (1)

G. T. Purves, G. Jundt, C. S. Adams, and I. G. Hughes, Eur. Phys. J. D 29, 433 (2004).
[CrossRef]

2003 (1)

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

2000 (1)

1997 (2)

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, Appl. Phys. Lett. 70, 3455 (1997).
[CrossRef]

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

1995 (1)

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

1992 (1)

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

1989 (1)

M. Olszakier, E. Ehrenfreund, E. Cohen, J. Bajaj, and G. J. Sullivan, Phys. Rev. Lett. 62, 2997 (1989).
[CrossRef]

1984 (1)

H. Ishio, J. Minowa, and K. Nosu, J. Lightwave Technol. 2, 448 (1984).
[CrossRef]

Adams, C. S.

G. T. Purves, G. Jundt, C. S. Adams, and I. G. Hughes, Eur. Phys. J. D 29, 433 (2004).
[CrossRef]

Artoni, M.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Bajaj, J.

M. Olszakier, E. Ehrenfreund, E. Cohen, J. Bajaj, and G. J. Sullivan, Phys. Rev. Lett. 62, 2997 (1989).
[CrossRef]

Bassani, F.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Campman, K. L.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, Appl. Phys. Lett. 70, 3455 (1997).
[CrossRef]

Ciattoni, A.

Cohen, E.

M. Olszakier, E. Ehrenfreund, E. Cohen, J. Bajaj, and G. J. Sullivan, Phys. Rev. Lett. 62, 2997 (1989).
[CrossRef]

Crosignani, B.

Dangel, S.

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

Deng, L.

L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

C. J. Zhu, L. Deng, and E. W. Hagley, “Dynamic light bending in a Raman gain medium using a spatially inhomogeneous pump,” Phys. Rev. A, submitted for publication.

Dunn, M. H.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Ehrenfreund, E.

M. Olszakier, E. Ehrenfreund, E. Cohen, J. Bajaj, and G. J. Sullivan, Phys. Rev. Lett. 62, 2997 (1989).
[CrossRef]

Eschle, P.

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

Fulton, D. J.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Gao, J. Y.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Gossard, A. C.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, Appl. Phys. Lett. 70, 3455 (1997).
[CrossRef]

Guruswamy, M.

C. S. R. Murthy and M. Guruswamy, WDM Optical Networks, Concepts, Design, and Algorithms (Prentice Hall PTR, 2001).

Hagley, E. W.

C. J. Zhu, L. Deng, and E. W. Hagley, “Dynamic light bending in a Raman gain medium using a spatially inhomogeneous pump,” Phys. Rev. A, submitted for publication.

Hang, C.

C. J. Zhu, C. Hang, and G. X. Huang, Eur. Phys. J. D 56, 231 (2010).
[CrossRef]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

Holzner, R.

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

Huang, G. X.

C. J. Zhu and G. X. Huang, Opt. Express 1923364 (2011).
[CrossRef]

C. J. Zhu, C. Hang, and G. X. Huang, Eur. Phys. J. D 56, 231 (2010).
[CrossRef]

C. J. Zhu and G. X. Huang, Phys. Rev. B 80, 235408 (2009).
[CrossRef]

Hughes, I. G.

G. T. Purves, G. Jundt, C. S. Adams, and I. G. Hughes, Eur. Phys. J. D 29, 433 (2004).
[CrossRef]

Imamoglu, A.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, Appl. Phys. Lett. 70, 3455 (1997).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

Ishio, H.

H. Ishio, J. Minowa, and K. Nosu, J. Lightwave Technol. 2, 448 (1984).
[CrossRef]

Jundt, G.

G. T. Purves, G. Jundt, C. S. Adams, and I. G. Hughes, Eur. Phys. J. D 29, 433 (2004).
[CrossRef]

Karpa, L.

L. Karpa and M. Weitz, Nat. Phys. 2, 332 (2006).
[CrossRef]

La Rocca, G. C.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Li, H.

V. A. Sautenkov, H. Li, Y. V. Rostovtsev, and M. O. Scully, Phys. Rev. A 81, 063824 (2010).
[CrossRef]

Lukin, M. D.

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

Minowa, J.

H. Ishio, J. Minowa, and K. Nosu, J. Lightwave Technol. 2, 448 (1984).
[CrossRef]

Moseley, R. R.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Murthy, C. S. R.

C. S. R. Murthy and M. Guruswamy, WDM Optical Networks, Concepts, Design, and Algorithms (Prentice Hall PTR, 2001).

Nosu, K.

H. Ishio, J. Minowa, and K. Nosu, J. Lightwave Technol. 2, 448 (1984).
[CrossRef]

Olszakier, M.

M. Olszakier, E. Ehrenfreund, E. Cohen, J. Bajaj, and G. J. Sullivan, Phys. Rev. Lett. 62, 2997 (1989).
[CrossRef]

Payne, M. G.

L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

Porto, P. D.

Purves, G. T.

G. T. Purves, G. Jundt, C. S. Adams, and I. G. Hughes, Eur. Phys. J. D 29, 433 (2004).
[CrossRef]

Richard, R.

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

Röhricht, B.

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

Rostovtsev, Y. V.

V. A. Sautenkov, H. Li, Y. V. Rostovtsev, and M. O. Scully, Phys. Rev. A 81, 063824 (2010).
[CrossRef]

Q. Sun, Y. V. Rostovtsev, and M. S. Zubairy, Phys. Rev. A 74, 033819 (2006).
[CrossRef]

Rusch, U.

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

Sautenkov, V. A.

V. A. Sautenkov, H. Li, Y. V. Rostovtsev, and M. O. Scully, Phys. Rev. A 81, 063824 (2010).
[CrossRef]

Schlesser, R.

Schmid, H.

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

Schmidt, H.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, Appl. Phys. Lett. 70, 3455 (1997).
[CrossRef]

Scully, M. O.

V. A. Sautenkov, H. Li, Y. V. Rostovtsev, and M. O. Scully, Phys. Rev. A 81, 063824 (2010).
[CrossRef]

Shajesh, K. V.

K. V. Shajesh, “Eikonal approximation,” Ph.D. dissertation (University of Oklahoma).

Shepherd, S.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Silvestri, L.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Sinclair, B. D.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Sullivan, G. J.

M. Olszakier, E. Ehrenfreund, E. Cohen, J. Bajaj, and G. J. Sullivan, Phys. Rev. Lett. 62, 2997 (1989).
[CrossRef]

Sun, C. P.

D. L. Zhou, Lan Zhou, R. Q. Wang, S. Yi, and C. P. Sun, Phys. Rev. A 76, 055801 (2007).
[CrossRef]

Sun, Q.

Q. Sun, Y. V. Rostovtsev, and M. S. Zubairy, Phys. Rev. A 74, 033819 (2006).
[CrossRef]

Wang, R. Q.

D. L. Zhou, Lan Zhou, R. Q. Wang, S. Yi, and C. P. Sun, Phys. Rev. A 76, 055801 (2007).
[CrossRef]

Weis, A.

Weitz, M.

L. Karpa and M. Weitz, Nat. Phys. 2, 332 (2006).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Wu, J. H.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Xu, J. H.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Yariv, A.

Yi, S.

D. L. Zhou, Lan Zhou, R. Q. Wang, S. Yi, and C. P. Sun, Phys. Rev. A 76, 055801 (2007).
[CrossRef]

Zhou, D. L.

D. L. Zhou, Lan Zhou, R. Q. Wang, S. Yi, and C. P. Sun, Phys. Rev. A 76, 055801 (2007).
[CrossRef]

Zhou, Lan

D. L. Zhou, Lan Zhou, R. Q. Wang, S. Yi, and C. P. Sun, Phys. Rev. A 76, 055801 (2007).
[CrossRef]

Zhu, C. J.

C. J. Zhu and G. X. Huang, Opt. Express 1923364 (2011).
[CrossRef]

C. J. Zhu, C. Hang, and G. X. Huang, Eur. Phys. J. D 56, 231 (2010).
[CrossRef]

C. J. Zhu and G. X. Huang, Phys. Rev. B 80, 235408 (2009).
[CrossRef]

C. J. Zhu, L. Deng, and E. W. Hagley, “Dynamic light bending in a Raman gain medium using a spatially inhomogeneous pump,” Phys. Rev. A, submitted for publication.

Zubairy, M. S.

Q. Sun, Y. V. Rostovtsev, and M. S. Zubairy, Phys. Rev. A 74, 033819 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, Appl. Phys. Lett. 70, 3455 (1997).
[CrossRef]

Eur. Phys. J. D (2)

C. J. Zhu, C. Hang, and G. X. Huang, Eur. Phys. J. D 56, 231 (2010).
[CrossRef]

G. T. Purves, G. Jundt, C. S. Adams, and I. G. Hughes, Eur. Phys. J. D 29, 433 (2004).
[CrossRef]

J. Lightwave Technol. (1)

H. Ishio, J. Minowa, and K. Nosu, J. Lightwave Technol. 2, 448 (1984).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Phys. (1)

L. Karpa and M. Weitz, Nat. Phys. 2, 332 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (3)

D. L. Zhou, Lan Zhou, R. Q. Wang, S. Yi, and C. P. Sun, Phys. Rev. A 76, 055801 (2007).
[CrossRef]

Q. Sun, Y. V. Rostovtsev, and M. S. Zubairy, Phys. Rev. A 74, 033819 (2006).
[CrossRef]

V. A. Sautenkov, H. Li, Y. V. Rostovtsev, and M. O. Scully, Phys. Rev. A 81, 063824 (2010).
[CrossRef]

Phys. Rev. B (1)

C. J. Zhu and G. X. Huang, Phys. Rev. B 80, 235408 (2009).
[CrossRef]

Phys. Rev. Lett. (6)

R. Holzner, P. Eschle, S. Dangel, R. Richard, H. Schmid, U. Rusch, and B. Röhricht, Phys. Rev. Lett. 78, 3451 (1997).
[CrossRef]

L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

M. Olszakier, E. Ehrenfreund, E. Cohen, J. Bajaj, and G. J. Sullivan, Phys. Rev. Lett. 62, 2997 (1989).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoğlu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

Rev. Mod. Phys. (1)

M. D. Lukin, Rev. Mod. Phys. 75, 457 (2003).
[CrossRef]

Other (5)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

With γj≈γj′ and |ΩL(0)|4≥|d2|2|d3|2, the condition |p12|≈|p0| minimizes the gain/loss per unit cell.

C. S. R. Murthy and M. Guruswamy, WDM Optical Networks, Concepts, Design, and Algorithms (Prentice Hall PTR, 2001).

K. V. Shajesh, “Eikonal approximation,” Ph.D. dissertation (University of Oklahoma).

C. J. Zhu, L. Deng, and E. W. Hagley, “Dynamic light bending in a Raman gain medium using a spatially inhomogeneous pump,” Phys. Rev. A, submitted for publication.

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Figures (4)

Fig. 1.
Fig. 1.

Light deflection in an HMQWS. (a) The geometry of the HMQWS and the configuration of the light fields. (b) A unit cell of the HMQWS consists of an ARG segment (left side) and an EIT segment (right side). Energy levels and wave functions in each well are calculated numerically.

Fig. 2.
Fig. 2.

Deflection angle (a) and Im(Kp)=kpIm(χp) per unit propagation distance (b) as functions of the injection position x0 and the frequency deviation of the probe field δω, respectively. For L=100μm there is a small overall probe field gain. With our notations and choice of energy levels, δω<0 implies a smaller two-photon detuning δ2.

Fig. 3.
Fig. 3.

Index of refraction as a function of the probe injection position x0 and the frequency deviation of the probe field δω. Parameters are the same as in Fig. 2.

Fig. 4.
Fig. 4.

DEMUX operation. The numerical simulation of beam propagation in MQWs with different probe-field frequencies given by δω=240GHz (channel 2), δω=0Hz (channel 1), and δω=240GHz (channel 0), respectively. The probe injection point is x0=9μm. The dashed line represents the initial probe injection direction.

Equations (6)

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

dds(ndRds)=n,
χpNε0[|p12|2|ΩL|2d2|d2|2|d3|2+|p10|2d2|ΩL|2],
θL(nx)x=x0,
θ2x0LNε0σ02(|p12|2|ΩL(0)|2δ2|d2d3|2+|p10|2δ2|ΩL(0)|2).
2E+2[E·(lnn)]+n2kp2E=0,
iEpz=12n0kp(2δnx2Ep+2δnxEpx+δn2Epx2)12kp2Epx2kpδnn0Ep.

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