Abstract

This paper reports integrated tracking (horizontal) and focusing (vertical) actuators using microelectromechanical (MEMS) technology for optical storage. The design, fabrication and characterization of the integrated tracking and focusing actuators are demonstrated. The integrated tracking and focusing lens actuators that consist of springs, a lens holder and comb-drive actuators are implemented to obtain the two-dimensional tuning effect of an objective lens. A two-mask process is used to define the actuators on a silicon-on-insulator (SOI) wafer. The DC displacements and the frequency responses are characterized by applying voltage to the micro lens actuators. Displacements are experimentally characterized with ± 24.6μm in tracking direction and 5.7μm in focusing direction. Moreover, the influences of the cross-axis coupling are measured and evaluated. This MEMS device which has a small form factor provides an excellent response time and size reduction. The minimization and integration of the lens actuators can offer low costs in assembly and expand the application area of the optical head.

© 2011 OSA

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References

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  1. M. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85(11), 1833–1856 (1997).
    [CrossRef]
  2. L. Y. Lin, J. L. Shen, S. S. Lee, and M. C. Wu, “Realization of novel monolithic free-space optical disk pickup heads by surface micromachining,” Opt. Lett. 21(2), 155–157 (1996).
    [CrossRef] [PubMed]
  3. K. Hane, “MEMS technologies for optical storage application,” in Proceedings of International Symposium on Optical Memory (The Japan Society of Applied Physics, Nagasaki, Japan, 2009), pp. 14–15.
  4. M. Sasaki, F. Bono, and K. Hane, “Large-displacement micro-XY-stage with paired moving plates,” Jpn. J. Appl. Phys. 47(4), 3226–3231 (2008).
    [CrossRef]
  5. T. Yamasaki, R. Hokari, and K. Hane, “Spherical silicon micro-mirrors bent by anodic bonding,” in Proceedings of IEEE Conference on Optical MEMS and Nanophotonics (Institute of Electrical and Electronics Engineers, Clearwater, FL, USA, 2009), pp. 51–52.
  6. R. Hokari and K. Hane, “A varifocal convex micromirror driven by a bending moment,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1310–1316 (2009).
    [CrossRef]
  7. H. Cheng, S. Hsiao, M. Wu, and W. Fang, “Integrated tracking and focusing systems of MEMS optical pickup head,” IEEE Trans. Magn. 43(2), 805–807 (2007).
    [CrossRef]
  8. B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
    [CrossRef]
  9. M. Wu, S. Hsiao, C. Peng, and W. Fang, “Development of tracking and focusing micro actuators for dual-stage optical pick-up head,” J. Opt. A, Pure Appl. Opt. 8(7), S323–S329 (2006).
    [CrossRef]
  10. L. Wu and H. Xie, “A millimeter-tunable-range microlens for endoscopic biomedical imaging applications,” IEEE J. Quantum Electron. 46(9), 1237–1244 (2010).
    [CrossRef]
  11. S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
    [CrossRef]
  12. Y. Chiu, J. Chiou, W. Fang, Y. Lin, and M. Wu, “Design, fabrication, and control of components in MEMS-based optical pickups,” IEEE Trans. Magn. 43(2), 780–784 (2007).
    [CrossRef]
  13. S. Timpe, D. Hook, M. Dugger, and K. Komvopoulos, “Levitation compensation method for dynamic electrostatic comb-drive actuators,” Sens. Actuators A Phys. 143(2), 383–389 (2008).
    [CrossRef]

2010 (1)

L. Wu and H. Xie, “A millimeter-tunable-range microlens for endoscopic biomedical imaging applications,” IEEE J. Quantum Electron. 46(9), 1237–1244 (2010).
[CrossRef]

2009 (1)

R. Hokari and K. Hane, “A varifocal convex micromirror driven by a bending moment,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1310–1316 (2009).
[CrossRef]

2008 (3)

B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
[CrossRef]

M. Sasaki, F. Bono, and K. Hane, “Large-displacement micro-XY-stage with paired moving plates,” Jpn. J. Appl. Phys. 47(4), 3226–3231 (2008).
[CrossRef]

S. Timpe, D. Hook, M. Dugger, and K. Komvopoulos, “Levitation compensation method for dynamic electrostatic comb-drive actuators,” Sens. Actuators A Phys. 143(2), 383–389 (2008).
[CrossRef]

2007 (2)

Y. Chiu, J. Chiou, W. Fang, Y. Lin, and M. Wu, “Design, fabrication, and control of components in MEMS-based optical pickups,” IEEE Trans. Magn. 43(2), 780–784 (2007).
[CrossRef]

H. Cheng, S. Hsiao, M. Wu, and W. Fang, “Integrated tracking and focusing systems of MEMS optical pickup head,” IEEE Trans. Magn. 43(2), 805–807 (2007).
[CrossRef]

2006 (1)

M. Wu, S. Hsiao, C. Peng, and W. Fang, “Development of tracking and focusing micro actuators for dual-stage optical pick-up head,” J. Opt. A, Pure Appl. Opt. 8(7), S323–S329 (2006).
[CrossRef]

2004 (1)

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

1997 (1)

M. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85(11), 1833–1856 (1997).
[CrossRef]

1996 (1)

Bono, F.

M. Sasaki, F. Bono, and K. Hane, “Large-displacement micro-XY-stage with paired moving plates,” Jpn. J. Appl. Phys. 47(4), 3226–3231 (2008).
[CrossRef]

Bu, J. U.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Cheng, H.

H. Cheng, S. Hsiao, M. Wu, and W. Fang, “Integrated tracking and focusing systems of MEMS optical pickup head,” IEEE Trans. Magn. 43(2), 805–807 (2007).
[CrossRef]

Cheng, X.

B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
[CrossRef]

Chiou, J.

Y. Chiu, J. Chiou, W. Fang, Y. Lin, and M. Wu, “Design, fabrication, and control of components in MEMS-based optical pickups,” IEEE Trans. Magn. 43(2), 780–784 (2007).
[CrossRef]

Chiu, Y.

Y. Chiu, J. Chiou, W. Fang, Y. Lin, and M. Wu, “Design, fabrication, and control of components in MEMS-based optical pickups,” IEEE Trans. Magn. 43(2), 780–784 (2007).
[CrossRef]

Dugger, M.

S. Timpe, D. Hook, M. Dugger, and K. Komvopoulos, “Levitation compensation method for dynamic electrostatic comb-drive actuators,” Sens. Actuators A Phys. 143(2), 383–389 (2008).
[CrossRef]

Fang, W.

Y. Chiu, J. Chiou, W. Fang, Y. Lin, and M. Wu, “Design, fabrication, and control of components in MEMS-based optical pickups,” IEEE Trans. Magn. 43(2), 780–784 (2007).
[CrossRef]

H. Cheng, S. Hsiao, M. Wu, and W. Fang, “Integrated tracking and focusing systems of MEMS optical pickup head,” IEEE Trans. Magn. 43(2), 805–807 (2007).
[CrossRef]

M. Wu, S. Hsiao, C. Peng, and W. Fang, “Development of tracking and focusing micro actuators for dual-stage optical pick-up head,” J. Opt. A, Pure Appl. Opt. 8(7), S323–S329 (2006).
[CrossRef]

Hane, K.

R. Hokari and K. Hane, “A varifocal convex micromirror driven by a bending moment,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1310–1316 (2009).
[CrossRef]

M. Sasaki, F. Bono, and K. Hane, “Large-displacement micro-XY-stage with paired moving plates,” Jpn. J. Appl. Phys. 47(4), 3226–3231 (2008).
[CrossRef]

Hokari, R.

R. Hokari and K. Hane, “A varifocal convex micromirror driven by a bending moment,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1310–1316 (2009).
[CrossRef]

Hook, D.

S. Timpe, D. Hook, M. Dugger, and K. Komvopoulos, “Levitation compensation method for dynamic electrostatic comb-drive actuators,” Sens. Actuators A Phys. 143(2), 383–389 (2008).
[CrossRef]

Hsiao, S.

H. Cheng, S. Hsiao, M. Wu, and W. Fang, “Integrated tracking and focusing systems of MEMS optical pickup head,” IEEE Trans. Magn. 43(2), 805–807 (2007).
[CrossRef]

M. Wu, S. Hsiao, C. Peng, and W. Fang, “Development of tracking and focusing micro actuators for dual-stage optical pick-up head,” J. Opt. A, Pure Appl. Opt. 8(7), S323–S329 (2006).
[CrossRef]

Hu, H.

B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
[CrossRef]

Jung, H.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Kim, J. H.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Kim, J.-Y.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Kim, S.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Kim, S.-

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Komvopoulos, K.

S. Timpe, D. Hook, M. Dugger, and K. Komvopoulos, “Levitation compensation method for dynamic electrostatic comb-drive actuators,” Sens. Actuators A Phys. 143(2), 383–389 (2008).
[CrossRef]

Lee, J.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Lee, S. S.

Lin, L. Y.

Lin, Y.

Y. Chiu, J. Chiou, W. Fang, Y. Lin, and M. Wu, “Design, fabrication, and control of components in MEMS-based optical pickups,” IEEE Trans. Magn. 43(2), 780–784 (2007).
[CrossRef]

Ma, J.

B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
[CrossRef]

Pan, L.

B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
[CrossRef]

Park, G.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Park, J.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Peng, C.

M. Wu, S. Hsiao, C. Peng, and W. Fang, “Development of tracking and focusing micro actuators for dual-stage optical pick-up head,” J. Opt. A, Pure Appl. Opt. 8(7), S323–S329 (2006).
[CrossRef]

Sasaki, M.

M. Sasaki, F. Bono, and K. Hane, “Large-displacement micro-XY-stage with paired moving plates,” Jpn. J. Appl. Phys. 47(4), 3226–3231 (2008).
[CrossRef]

Shen, J. L.

Tang, Y.

B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
[CrossRef]

Timpe, S.

S. Timpe, D. Hook, M. Dugger, and K. Komvopoulos, “Levitation compensation method for dynamic electrostatic comb-drive actuators,” Sens. Actuators A Phys. 143(2), 383–389 (2008).
[CrossRef]

Wu, L.

L. Wu and H. Xie, “A millimeter-tunable-range microlens for endoscopic biomedical imaging applications,” IEEE J. Quantum Electron. 46(9), 1237–1244 (2010).
[CrossRef]

Wu, M.

Y. Chiu, J. Chiou, W. Fang, Y. Lin, and M. Wu, “Design, fabrication, and control of components in MEMS-based optical pickups,” IEEE Trans. Magn. 43(2), 780–784 (2007).
[CrossRef]

H. Cheng, S. Hsiao, M. Wu, and W. Fang, “Integrated tracking and focusing systems of MEMS optical pickup head,” IEEE Trans. Magn. 43(2), 805–807 (2007).
[CrossRef]

M. Wu, S. Hsiao, C. Peng, and W. Fang, “Development of tracking and focusing micro actuators for dual-stage optical pick-up head,” J. Opt. A, Pure Appl. Opt. 8(7), S323–S329 (2006).
[CrossRef]

M. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85(11), 1833–1856 (1997).
[CrossRef]

Wu, M. C.

Xie, H.

L. Wu and H. Xie, “A millimeter-tunable-range microlens for endoscopic biomedical imaging applications,” IEEE J. Quantum Electron. 46(9), 1237–1244 (2010).
[CrossRef]

Yee, Y.

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

Zhang, B.

B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. Wu and H. Xie, “A millimeter-tunable-range microlens for endoscopic biomedical imaging applications,” IEEE J. Quantum Electron. 46(9), 1237–1244 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Hokari and K. Hane, “A varifocal convex micromirror driven by a bending moment,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1310–1316 (2009).
[CrossRef]

IEEE Trans. Magn. (2)

H. Cheng, S. Hsiao, M. Wu, and W. Fang, “Integrated tracking and focusing systems of MEMS optical pickup head,” IEEE Trans. Magn. 43(2), 805–807 (2007).
[CrossRef]

Y. Chiu, J. Chiou, W. Fang, Y. Lin, and M. Wu, “Design, fabrication, and control of components in MEMS-based optical pickups,” IEEE Trans. Magn. 43(2), 780–784 (2007).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. Wu, S. Hsiao, C. Peng, and W. Fang, “Development of tracking and focusing micro actuators for dual-stage optical pick-up head,” J. Opt. A, Pure Appl. Opt. 8(7), S323–S329 (2006).
[CrossRef]

Jpn. J. Appl. Phys. (3)

S. Kim, J. Park, G. Park, J. Lee, J. Lee, H. Jung, J.-Y. Kim, S.- Kim, Y. Yee, J. H. Kim, J. H. Kim, and J. U. Bu, “An optical flying head assembly for a small-form-factor plastic disk in PCMCIA-like drive,” Jpn. J. Appl. Phys. 43(7B), 4752–4758 (2004).
[CrossRef]

B. Zhang, J. Ma, L. Pan, X. Cheng, H. Hu, and Y. Tang, “High-sensitivity actuator with new magnetic circuit in optical pickup,” Jpn. J. Appl. Phys. 47(7), 5809–5811 (2008).
[CrossRef]

M. Sasaki, F. Bono, and K. Hane, “Large-displacement micro-XY-stage with paired moving plates,” Jpn. J. Appl. Phys. 47(4), 3226–3231 (2008).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

M. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85(11), 1833–1856 (1997).
[CrossRef]

Sens. Actuators A Phys. (1)

S. Timpe, D. Hook, M. Dugger, and K. Komvopoulos, “Levitation compensation method for dynamic electrostatic comb-drive actuators,” Sens. Actuators A Phys. 143(2), 383–389 (2008).
[CrossRef]

Other (2)

T. Yamasaki, R. Hokari, and K. Hane, “Spherical silicon micro-mirrors bent by anodic bonding,” in Proceedings of IEEE Conference on Optical MEMS and Nanophotonics (Institute of Electrical and Electronics Engineers, Clearwater, FL, USA, 2009), pp. 51–52.

K. Hane, “MEMS technologies for optical storage application,” in Proceedings of International Symposium on Optical Memory (The Japan Society of Applied Physics, Nagasaki, Japan, 2009), pp. 14–15.

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic structure of the micro lens actuator. (b) Structure of the micro lens actuator. (c) Magnified view of the integrated comb-drive area.

Fig. 2
Fig. 2

Schematic diagrams of the integrated tracking and focusing comb structures: (a) and (b) initial position; (c) and (d) actuated situation.

Fig. 3
Fig. 3

(a) Simulated displacement of the tracking actuator; (b) simulated displacement of the focusing actuator.

Fig. 4
Fig. 4

Fabrication process flow of the integrated tracking and focusing micro lens actuators.

Fig. 5
Fig. 5

(a) SEM images of the fabricated actuators unloaded lens; (b) optical image of the actuators assembled with micro ball lens; (c) and (d) SEM images of the comb-drive structures: (c) front side; (d) back side.

Fig. 6
Fig. 6

Displacements versus the square of the applied voltage at different coupling voltages: (a) displacements in tracking direction; (b) displacements in focusing direction.

Fig. 7
Fig. 7

Frequency responses of the actuators before/after the micro ball lens is loaded: (a) frequency response of the tracking actuator; (b) frequency response of the focusing actuator.

Tables (1)

Tables Icon

Table 1 Main design parameters of the integrated comb-drive tracking and focusing actuators

Equations (12)

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

W x = 1 2 C x U 1 2 = ε 2g x( h 1 z) U 1 2 (0<x< h 1 , h 3 <z< h 1 ),
W z = 1 2 C z U 1 2 = ε 2g 2l(z h 3 ) U 2 2 (0<x< h 1 , h 3 <z< h 1 ),
W =n W x +2n W z = ε 2g [ nx( h 1 z) U 1 2 +4nl(z h 3 ) U 2 2 ] = ε 2g ( n h 1 U 1 2 xn U 1 2 xz+4nl U 2 2 z4nl h 3 U 2 2 ),
F x = W x = nε 2g ( h 1 U 1 2 z U 1 2 )= k x x,
F z = W z = nε 2g ( 4l U 2 2 x U 1 2 )= k z z.
x= 2nε U 1 2 (g h 1 k z 2nεl U 2 2 ) 4 g 2 k x k z n 2 ε 2 U 1 4 ,
z= nε(8gl k x U 2 2 nε h 1 U 1 4 ) 4 g 2 k x k z n 2 ε 2 U 1 4 .
x=± 2nε U 1 2 (g h 1 k z 2nεl U 2 2 ) 4 g 2 k x k z n 2 ε 2 U 1 4 .
x=± nε h 1 2g k x U 1 2 ,
z= 2nεl g k z U 2 2 .
k x = E h 1 w f 3 l f 3 ,
k z = E w f h 1 3 l f 3 ,

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