Abstract

The propagation of Gaussian beams is analyzed for an acousto-optic deflector by varying the refractive index in two-dimensions with a row of phased array piezoelectric transducers. Inhomogeneous domains of phase grating are produced by operating the transducers at different phase shifts, resulting in two-dimensional index modulation of periodic and sinc function profiles. Also different phase shifts provide a mechanism to steer the grating lobe in various directions and, therefore, the incident angle of the laser beam on the grating plane is automatically modified without moving the beam. Additionally, the acoustic frequency can be varied to achieve the Bragg condition for the new incident angle of the laser beam so that the diffraction efficiency of the deflector is maximized. The Gaussian beam is expressed in terms of planes and the second order coupled mode theory is implemented to analyze the diffraction of the beam. The diffraction efficiency is found to be nearly unity for optimal operating parameters of the acousto-optic device.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (2)

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers,” Ultrasonics 76, 35–43 (2017).
[Crossref] [PubMed]

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional refractive index modulation by phased array transducers in acousto-optic deflectors,” Appl. Opt. 56(3), 688–694 (2017).
[Crossref] [PubMed]

2016 (1)

T.-S. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Effect of large deflection angle on the laser intensity profile produced by acousto-optic deflector scanners in high precision manufacturing,” J. Laser Appl. 28, 012012 (2016).

2015 (2)

2014 (2)

2013 (1)

S. N. Antonov, A. V. Vainer, V. V. Proklov, and Y. G. Rezvov, “Extension of the angular scanning range of the acousto-optic deflector with a two-element phased-array piezoelectric transducer,” Tech. Phys. 58(9), 1346–1351 (2013).
[Crossref]

2010 (1)

2009 (1)

A. H. Mack, M. K. Trías, and S. G. J. Mochrie, “Precision optical trapping via a programmable direct-digital-synthesis-based controller for acousto-optic deflectors,” Rev. Sci. Instrum. 80, 016101 (2009).

2008 (1)

2007 (2)

S. N. Antonov and Yu. G. Rezvov, “Efficient multi-beam Bragg acoustooptic diffraction with phase optimization of a multifrequency acoustic wave,” Tech. Phys. 52(8), 1053–1060 (2007).
[Crossref]

J. Aboujeib, A. Perennou, V. Quintard, and J. L. Bihan, “Planar phased-array transducers associated with specific electronic command for acoustooptic deflectors,” J. Opt. A, Pure Appl. Opt. 9(5), 463–469 (2007).
[Crossref]

2004 (1)

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

1999 (1)

S.-C. Wooh and Y. Shi, “Optimum beam steering of linear phased arrays,” Wave Motion 29(3), 245–265 (1999).
[Crossref]

1998 (1)

1994 (1)

1990 (1)

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter., “Transfer Function Formalism for Strong Acousto-Optic Bragg Diffraction of Light Beams with Arbitrary Profiles,” Acta Acust. United Acust. 71, 81–92 (1990).

1980 (2)

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Bragg diffraction of finite beams by thick gratings,” J. Opt. Soc. Am. 70(3), 300–304 (1980).
[Crossref]

T. D. K. Ngoc and W. G. Mayer, “Numerical integration method for reflected beam profiles near Rayleigh angle,” J. Acoust. Soc. Am. 67(4), 1149–1152 (1980).
[Crossref]

1977 (2)

1976 (2)

1973 (1)

N. Uchida and N. Niizeki, “Acoustooptic deflection materials and techniques,” Proc. IEEE 61(8), 1073–1092 (1973).
[Crossref]

1967 (1)

W. R. Klein and B. D. Cook, “Unified Approach to Ultrasonic Light Diffraction,” IEEE Trans. Sonics Ultrason. 14(3), 123–134 (1967).
[Crossref]

Aboujeib, J.

J. Aboujeib, A. Perennou, V. Quintard, and J. L. Bihan, “Planar phased-array transducers associated with specific electronic command for acoustooptic deflectors,” J. Opt. A, Pure Appl. Opt. 9(5), 463–469 (2007).
[Crossref]

Aleksov, A.

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers,” Ultrasonics 76, 35–43 (2017).
[Crossref] [PubMed]

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional refractive index modulation by phased array transducers in acousto-optic deflectors,” Appl. Opt. 56(3), 688–694 (2017).
[Crossref] [PubMed]

T.-S. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Effect of large deflection angle on the laser intensity profile produced by acousto-optic deflector scanners in high precision manufacturing,” J. Laser Appl. 28, 012012 (2016).

T. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Dynamic two-dimensional refractive index modulation for high performance acousto-optic deflector,” Opt. Express 23(26), 33667–33680 (2015).
[Crossref] [PubMed]

Almehmadi, F.

Angus Silver, R.

Antonov, S. N.

S. N. Antonov, A. V. Vainer, V. V. Proklov, and Y. G. Rezvov, “Extension of the angular scanning range of the acousto-optic deflector with a two-element phased-array piezoelectric transducer,” Tech. Phys. 58(9), 1346–1351 (2013).
[Crossref]

S. N. Antonov and Yu. G. Rezvov, “Efficient multi-beam Bragg acoustooptic diffraction with phase optimization of a multifrequency acoustic wave,” Tech. Phys. 52(8), 1053–1060 (2007).
[Crossref]

Aubin, G.

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

Banerjee, P. P.

Bechtold, P.

G. R. B. E. Römer and P. Bechtold, “Electro-optic and acousto-optic laser beam scanners,” Phys. Procedia 56, 29–39 (2014).
[Crossref]

Bihan, J. L.

J. Aboujeib, A. Perennou, V. Quintard, and J. L. Bihan, “Planar phased-array transducers associated with specific electronic command for acoustooptic deflectors,” J. Opt. A, Pure Appl. Opt. 9(5), 463–469 (2007).
[Crossref]

Bourdieu, L.

Bridoux, E.

Bruneel, C.

Candela, Y.

Cao, D.

Chatterjee, M. R.

F. Almehmadi and M. R. Chatterjee, “Numerical examination of the nonlinear dynamics of a hybrid acousto-optic Bragg cell with positive feedback under profiled beam propagation,” J. Opt. Soc. Am. B 31(4), 833–841 (2014).
[Crossref]

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter., “Transfer Function Formalism for Strong Acousto-Optic Bragg Diffraction of Light Beams with Arbitrary Profiles,” Acta Acust. United Acust. 71, 81–92 (1990).

Chu, R. S.

Cook, B. D.

W. R. Klein and B. D. Cook, “Unified Approach to Ultrasonic Light Diffraction,” IEEE Trans. Sonics Ultrason. 14(3), 123–134 (1967).
[Crossref]

Dieudonné, S.

Evans, G. J.

Gabet, R.

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

Gaylord, T. K.

Gazalet, M. G.

Gosselin, S.

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

Grosso, P.

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

Haine, F.

Honnorat, N.

Jaouen, Y.

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

Kar, A.

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers,” Ultrasonics 76, 35–43 (2017).
[Crossref] [PubMed]

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional refractive index modulation by phased array transducers in acousto-optic deflectors,” Appl. Opt. 56(3), 688–694 (2017).
[Crossref] [PubMed]

T.-S. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Effect of large deflection angle on the laser intensity profile produced by acousto-optic deflector scanners in high precision manufacturing,” J. Laser Appl. 28, 012012 (2016).

T. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Dynamic two-dimensional refractive index modulation for high performance acousto-optic deflector,” Opt. Express 23(26), 33667–33680 (2015).
[Crossref] [PubMed]

Kirkby, P. A.

Klein, W. R.

W. R. Klein and B. D. Cook, “Unified Approach to Ultrasonic Light Diffraction,” IEEE Trans. Sonics Ultrason. 14(3), 123–134 (1967).
[Crossref]

Kong, J. A.

Kremer, Y.

Lapole, R.

Léger, J.-F.

Mack, A. H.

A. H. Mack, M. K. Trías, and S. G. J. Mochrie, “Precision optical trapping via a programmable direct-digital-synthesis-based controller for acousto-optic deflectors,” Rev. Sci. Instrum. 80, 016101 (2009).

Magnusson, R.

Marin, B.

Mayer, W. G.

T. D. K. Ngoc and W. G. Mayer, “Numerical integration method for reflected beam profiles near Rayleigh angle,” J. Acoust. Soc. Am. 67(4), 1149–1152 (1980).
[Crossref]

Mochrie, S. G. J.

A. H. Mack, M. K. Trías, and S. G. J. Mochrie, “Precision optical trapping via a programmable direct-digital-synthesis-based controller for acousto-optic deflectors,” Rev. Sci. Instrum. 80, 016101 (2009).

Moharam, M. G.

Molchanov, V. Ya.

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

Naga Srinivas Nadella, K. M.

Ngoc, T. D. K.

T. D. K. Ngoc and W. G. Mayer, “Numerical integration method for reflected beam profiles near Rayleigh angle,” J. Acoust. Soc. Am. 67(4), 1149–1152 (1980).
[Crossref]

Niizeki, N.

N. Uchida and N. Niizeki, “Acoustooptic deflection materials and techniques,” Proc. IEEE 61(8), 1073–1092 (1973).
[Crossref]

Perennou, A.

J. Aboujeib, A. Perennou, V. Quintard, and J. L. Bihan, “Planar phased-array transducers associated with specific electronic command for acoustooptic deflectors,” J. Opt. A, Pure Appl. Opt. 9(5), 463–469 (2007).
[Crossref]

Poon, T.-C.

D. Cao, P. P. Banerjee, and T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contrapropagating sound,” Appl. Opt. 37(14), 3007–3014 (1998).
[Crossref] [PubMed]

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter., “Transfer Function Formalism for Strong Acousto-Optic Bragg Diffraction of Light Beams with Arbitrary Profiles,” Acta Acust. United Acust. 71, 81–92 (1990).

Proklov, V. V.

S. N. Antonov, A. V. Vainer, V. V. Proklov, and Y. G. Rezvov, “Extension of the angular scanning range of the acousto-optic deflector with a two-element phased-array piezoelectric transducer,” Tech. Phys. 58(9), 1346–1351 (2013).
[Crossref]

Quintard, V.

J. Aboujeib, A. Perennou, V. Quintard, and J. L. Bihan, “Planar phased-array transducers associated with specific electronic command for acoustooptic deflectors,” J. Opt. A, Pure Appl. Opt. 9(5), 463–469 (2007).
[Crossref]

Ravez, M.

Rezvov, Y. G.

S. N. Antonov, A. V. Vainer, V. V. Proklov, and Y. G. Rezvov, “Extension of the angular scanning range of the acousto-optic deflector with a two-element phased-array piezoelectric transducer,” Tech. Phys. 58(9), 1346–1351 (2013).
[Crossref]

Rezvov, Yu. G.

S. N. Antonov and Yu. G. Rezvov, “Efficient multi-beam Bragg acoustooptic diffraction with phase optimization of a multifrequency acoustic wave,” Tech. Phys. 52(8), 1053–1060 (2007).
[Crossref]

Römer, G. R. B. E.

G. R. B. E. Römer and P. Bechtold, “Electro-optic and acousto-optic laser beam scanners,” Phys. Procedia 56, 29–39 (2014).
[Crossref]

Salama, I.

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers,” Ultrasonics 76, 35–43 (2017).
[Crossref] [PubMed]

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional refractive index modulation by phased array transducers in acousto-optic deflectors,” Appl. Opt. 56(3), 688–694 (2017).
[Crossref] [PubMed]

Salama, I. A.

T.-S. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Effect of large deflection angle on the laser intensity profile produced by acousto-optic deflector scanners in high precision manufacturing,” J. Laser Appl. 28, 012012 (2016).

T. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Dynamic two-dimensional refractive index modulation for high performance acousto-optic deflector,” Opt. Express 23(26), 33667–33680 (2015).
[Crossref] [PubMed]

Sapriel, J.

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

Shi, Y.

S.-C. Wooh and Y. Shi, “Optimum beam steering of linear phased arrays,” Wave Motion 29(3), 245–265 (1999).
[Crossref]

Silver, R. A.

Sitter, D. N.

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter., “Transfer Function Formalism for Strong Acousto-Optic Bragg Diffraction of Light Beams with Arbitrary Profiles,” Acta Acust. United Acust. 71, 81–92 (1990).

Srinivas Nadella, K. M.

Tamir, T.

Trías, M. K.

A. H. Mack, M. K. Trías, and S. G. J. Mochrie, “Precision optical trapping via a programmable direct-digital-synthesis-based controller for acousto-optic deflectors,” Rev. Sci. Instrum. 80, 016101 (2009).

Uchida, N.

N. Uchida and N. Niizeki, “Acoustooptic deflection materials and techniques,” Proc. IEEE 61(8), 1073–1092 (1973).
[Crossref]

Vainer, A. V.

S. N. Antonov, A. V. Vainer, V. V. Proklov, and Y. G. Rezvov, “Extension of the angular scanning range of the acousto-optic deflector with a two-element phased-array piezoelectric transducer,” Tech. Phys. 58(9), 1346–1351 (2013).
[Crossref]

Wang, T.

Wang, T.-S.

T.-S. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Effect of large deflection angle on the laser intensity profile produced by acousto-optic deflector scanners in high precision manufacturing,” J. Laser Appl. 28, 012012 (2016).

Wooh, S.-C.

S.-C. Wooh and Y. Shi, “Optimum beam steering of linear phased arrays,” Wave Motion 29(3), 245–265 (1999).
[Crossref]

Zhang, C.

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers,” Ultrasonics 76, 35–43 (2017).
[Crossref] [PubMed]

T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, “Two-dimensional refractive index modulation by phased array transducers in acousto-optic deflectors,” Appl. Opt. 56(3), 688–694 (2017).
[Crossref] [PubMed]

T.-S. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Effect of large deflection angle on the laser intensity profile produced by acousto-optic deflector scanners in high precision manufacturing,” J. Laser Appl. 28, 012012 (2016).

T. Wang, C. Zhang, A. Aleksov, I. A. Salama, and A. Kar, “Dynamic two-dimensional refractive index modulation for high performance acousto-optic deflector,” Opt. Express 23(26), 33667–33680 (2015).
[Crossref] [PubMed]

Acta Acust. United Acust. (1)

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter., “Transfer Function Formalism for Strong Acousto-Optic Bragg Diffraction of Light Beams with Arbitrary Profiles,” Acta Acust. United Acust. 71, 81–92 (1990).

Appl. Opt. (3)

Electron. Lett. (1)

G. Aubin, J. Sapriel, V. Ya. Molchanov, R. Gabet, P. Grosso, S. Gosselin, and Y. Jaouen, “Multichannel acousto-optic cells for fast optical crossconnect,” Electron. Lett. 40(7), 448–449 (2004).
[Crossref]

IEEE Trans. Sonics Ultrason. (1)

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Figures (10)

Fig. 1
Fig. 1 Dynamic phased array transducers for acoustic beam steering to produce tilted phase fronts with a sinc-function diffraction pattern of the acoustic waves.
Fig. 2
Fig. 2 Geometry for laser beam propagation in an AOD medium of two-dimensional refractive index variation caused by phased array transducers, O ' D = d.
Fig. 3
Fig. 3 Comparison between the plane wave superposition of a Gaussian beam and the exact Gaussian beam profile given by Eq. (7).
Fig. 4
Fig. 4 Comparison of the Gaussian beam profiles at the exit surface of a TeO2 AOD for one-dimensional refractive index modulation based on CKT 1-D model and the reduction of the current 2-D model to 1-D problem.
Fig. 5
Fig. 5 Magnitude of the electric field (|E|) at the exit boundary for an AOD of thickness L, calculated using the Gaussian beam diffraction model of this study and the CKT model for F = 75 MHz, L = 2.24 cm and θin = 0.324o.
Fig. 6
Fig. 6 Magnitude of the electric field (|E|) at the exit boundary for an AOD of thickness 2L, calculated using the Gaussian beam diffraction model of this study and the CKT model for F = 75 MHz, L = 2.24 cm and θin = 0.324o.
Fig. 7
Fig. 7 Diffraction efficiency of TeO2 ideal AODs as a function of the incident angle θin for different operating parameters including the phase shift (δ) of acoustic waves between two consecutive transducers.
Fig. 8
Fig. 8 Diffraction efficiency of Ge ideal AODs as a function of the incident angle θin for different operating parameters including the phase shift (δ) of acoustic waves between two consecutive transducers.
Fig. 9
Fig. 9 Comparison between the ideal and real values of the diffraction efficiency and deflection angle for He-Ne lasers and a phased array TeO2 AOD with pitch S = 10.5 µm for the real AOD.
Fig. 10
Fig. 10 Comparison between the ideal and real values of the diffraction efficiency and deflection angle for CO2 lasers and a phased array Ge AOD with pitch S = 13.75 µm for the real AOD.

Tables (1)

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Table 1 Simulation parameters for TeO2 and Ge crystals to deflect He-Ne and CO2-lasers respectively [31].

Equations (18)

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n II ( x s , z s ) =n 2 ( λ 0 )+Δncos( 2π Λ z s )( sin( b x s ) b x s )
sin( b L m /2 ) b L m /2 = 1 2
E i ' ( x',z' )= A 0 w 00 w( x' ) e ( z' w( x' ) ) 2 e i k 0 x' e iϕ( x' ) e i k 0 z ' 2 2R( x' )
w a = x R ' ( d 2 + x R ' 2 ) cos 2 θ 0 w 00 2 sin 2 θ 0 +dsin θ 0 ( x R ' cos θ 0 w 00 ) 2 sin 2 θ 0
w b = x R ' ( d 2 + x R ' 2 ) cos 2 θ 0 w 00 2 sin 2 θ 0 dsin θ 0 ( x R ' cos θ 0 w 00 ) 2 sin 2 θ 0
( x' z' )=( ( x+L/2 )cos θ 0 +zsin θ 0 +d ( x+L/2 )sin θ 0 +zcos θ 0 )
E i ( x,z )=A( d ) e [ ( x+L/2 )sin θ 0 +zcos θ 0 w( d ) ] 2 e i k 0 [ ( x+L/2 )sin θ 0 +zcos θ 0 ] 2 2R( d ) e i k 0 [ ( x+L/2 )cos θ 0 +z.sin θ 0 ]
E i ( x,z )= G( k 0z )exp[ i( k 1x x+ k 0z z ) ] d k 0z
G( k 0z )= 1 2π E i ( L/2,z ) e i k 1x L/2 e i k 0z z dz
E i ( L/2,z )=A( d ) e ( zcos θ 0 w a ) 2 e i k 0 ( zcos θ 0 ) 2 2R( d ) e i k 0 sin θ 0 z
G( k 0z )= A( d ) 2π π 1 w a 2 +i k 0 cos θ 0 2R( d ) e ( k 0z k 0 sin θ 0 ) 2 4( 1 w a 2 +i k 0 cos θ 0 2R( d ) ) e i k 1x L/2
E 0 ( x,z )= G( k 0z ) t 0 ( k 0z )exp( i k 3,0x x+i k 0z z )d k 0z
E 1 ( x,z )= G( k 0z ) t 1 ( k 0z )exp( i k 3,1x x+i k 1z z )d k 0z
k 1 sin θ 0 p 2π w a + w b k 0z k 1 sin θ 0 +p 2π w a + w b
E 0,m = [ G( k 0z ) t 0 ( k 0z )exp( i k 3,0x x+i k 0z z ) ] k 0z = k 0z,m
E 1,m = [ G( k 0z ) t 1 ( k 0z )exp( i k 3,1x x+i k 1z z ) ] k 0z = k 0z,m
E 0 ( x,z )Δ k 0z m=1 M E 0,m Δ k 0z 2 ( E 0,1 + E 0,M )
E 1 ( x,z )Δ k 0z m=1 M E 1,m Δ k 0z 2 ( E 1,1 + E 1,M )

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