Abstract

Because the function of a single crystal of potassium tantalate niobate (KTa1-xNbxO3, KTN) is largely decided by the trapped charge density inside it, it is essential to determine its value. We quantitatively estimate the charge density using two optical analysis methods, namely by investigating KTN’s deflection angle when it is used as a deflector and by investigating KTN’s focal length when it is used as a graded-index (GRIN) lens. A strobe technique is introduced with which to perform the measurement. The charge density values under different temperature conditions are shown. These results suggest that the charge density can be determined with both methods, and is constant in a specific temperature range. The charge density value is around 80 C/m3 in our setup.

© 2014 Optical Society of America

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References

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  1. J. van Raalte, “Linear electro-optic effect in Ferroelectric KTN,” J. Opt. Soc. Am. 57(5), 671–674 (1967).
    [CrossRef]
  2. K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
    [CrossRef]
  3. J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
    [CrossRef]
  4. Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
    [CrossRef]
  5. T. Imai, Y. Takayama, J. Miyazu, J. Kobayashi, “Performance of varifocal lenses using KTa1-xNbxO3 crystals with response times faster than 2 μs,” Electron. Lett. 49(23), 1470–1471 (2013).
    [CrossRef]
  6. K. Isobe, H. Kawano, A. Kumagai, A. Miyawaki, K. Midorikawa, “Implementation of spatial overlap modulation nonlinear optical microscopy using an electro-optic deflector,” Biomed. Opt. Express 4(10), 1937–1945 (2013).
    [CrossRef] [PubMed]
  7. Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. S. Toyoda, M. Ueno, S. Yagi, J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
    [CrossRef]

2013

T. Imai, Y. Takayama, J. Miyazu, J. Kobayashi, “Performance of varifocal lenses using KTa1-xNbxO3 crystals with response times faster than 2 μs,” Electron. Lett. 49(23), 1470–1471 (2013).
[CrossRef]

K. Isobe, H. Kawano, A. Kumagai, A. Miyawaki, K. Midorikawa, “Implementation of spatial overlap modulation nonlinear optical microscopy using an electro-optic deflector,” Biomed. Opt. Express 4(10), 1937–1945 (2013).
[CrossRef] [PubMed]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

S. Toyoda, M. Ueno, S. Yagi, J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[CrossRef]

2012

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

2011

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

2008

K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
[CrossRef]

1998

1967

1964

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, S. H. Wemple, “Electrooptic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[CrossRef]

Arai, J.

Fujiura, K.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
[CrossRef]

Geusic, J. E.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, S. H. Wemple, “Electrooptic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[CrossRef]

Haruna, M.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

Hoshino, H.

Imai, T.

T. Imai, Y. Takayama, J. Miyazu, J. Kobayashi, “Performance of varifocal lenses using KTa1-xNbxO3 crystals with response times faster than 2 μs,” Electron. Lett. 49(23), 1470–1471 (2013).
[CrossRef]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
[CrossRef]

Isobe, K.

Kato, K.

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

Kawano, H.

Kobayashi, J.

S. Toyoda, M. Ueno, S. Yagi, J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[CrossRef]

T. Imai, Y. Takayama, J. Miyazu, J. Kobayashi, “Performance of varifocal lenses using KTa1-xNbxO3 crystals with response times faster than 2 μs,” Electron. Lett. 49(23), 1470–1471 (2013).
[CrossRef]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

Kumagai, A.

Kurtz, S. K.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, S. H. Wemple, “Electrooptic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[CrossRef]

Midorikawa, K.

Miyawaki, A.

Miyazu, J.

T. Imai, Y. Takayama, J. Miyazu, J. Kobayashi, “Performance of varifocal lenses using KTa1-xNbxO3 crystals with response times faster than 2 μs,” Electron. Lett. 49(23), 1470–1471 (2013).
[CrossRef]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
[CrossRef]

Naganuma, K.

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

Nakamura, K.

K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
[CrossRef]

Ohmi, M.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

Okabe, Y.

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

Okano, F.

Omiya, K.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

Sakai, Y.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

Sakamoto, T.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

Sasaki, Y.

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
[CrossRef]

Sasaura, M.

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
[CrossRef]

Takayama, Y.

T. Imai, Y. Takayama, J. Miyazu, J. Kobayashi, “Performance of varifocal lenses using KTa1-xNbxO3 crystals with response times faster than 2 μs,” Electron. Lett. 49(23), 1470–1471 (2013).
[CrossRef]

Toyoda, S.

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

S. Toyoda, M. Ueno, S. Yagi, J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[CrossRef]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

Ueno, M.

S. Toyoda, M. Ueno, S. Yagi, J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[CrossRef]

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

van Raalte, J.

Van Uitert, L. G.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, S. H. Wemple, “Electrooptic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[CrossRef]

Wemple, S. H.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, S. H. Wemple, “Electrooptic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[CrossRef]

Yagi, S.

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

S. Toyoda, M. Ueno, S. Yagi, J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[CrossRef]

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

Yuyama, I.

Appl. Opt.

Appl. Phys. Express

Y. Sasaki, Y. Okabe, M. Ueno, S. Toyoda, J. Kobayashi, S. Yagi, K. Naganuma, “Resolution enhancement of KTa1-xNbxO3 electro-optic deflector by optical beam shaping,” Appl. Phys. Express 6(10), 102201 (2013).
[CrossRef]

J. Miyazu, T. Imai, S. Toyoda, M. Sasaura, S. Yagi, K. Kato, Y. Sasaki, K. Fujiura, “New beam scanning model for high-speed operation using KTa1-xNbxO3 crystals,” Appl. Phys. Express 4(11), 111501 (2011).
[CrossRef]

S. Toyoda, M. Ueno, S. Yagi, J. Kobayashi, “First estimation of power consumption of KTaxNb1-xO3 crystal upon application of high voltage under high frequency,” Appl. Phys. Express 6(12), 122601 (2013).
[CrossRef]

Appl. Phys. Lett.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, S. H. Wemple, “Electrooptic properties of some ABO3 perovskites in the paraelectric phase,” Appl. Phys. Lett. 4(8), 141–143 (1964).
[CrossRef]

Biomed. Opt. Express

Electron. Lett.

Y. Okabe, Y. Sasaki, M. Ueno, T. Sakamoto, S. Toyoda, S. Yagi, K. Naganuma, K. Fujiura, Y. Sakai, J. Kobayashi, K. Omiya, M. Ohmi, M. Haruna, “200 kHz swept light source equipped with KTN deflector for optical coherence tomography,” Electron. Lett. 48(4), 201 (2012).
[CrossRef]

T. Imai, Y. Takayama, J. Miyazu, J. Kobayashi, “Performance of varifocal lenses using KTa1-xNbxO3 crystals with response times faster than 2 μs,” Electron. Lett. 49(23), 1470–1471 (2013).
[CrossRef]

J. Appl. Phys.

K. Nakamura, J. Miyazu, Y. Sasaki, T. Imai, M. Sasaura, K. Fujiura, “Space-charge-controlled electro-optic effect: Optical beam deflection by electro-optic effect and space-charge-controlled electrical conduction,” J. Appl. Phys. 104(1), 013105 (2008).
[CrossRef]

J. Opt. Soc. Am.

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Figures (6)

Fig. 1
Fig. 1

Lens effect of KTN crystal after charge injection.

Fig. 2
Fig. 2

(a) Illustration of deflection angle measurement system, DFB, pigtail DFB laser, FG, function generator, OS, oscilloscope, CM, cylinder lens, PH, pinhole, PD, Peltier device, PS, power supplier, CP, current probe, CM, InGaAs camera. (b) Profiles of voltage supplied to KTN crystal (black), and pulse for DFB laser output (red) in this system.

Fig. 3
Fig. 3

Single result of full scanning angle measurement.

Fig. 4
Fig. 4

Results for deflection angle distribution at different temperatures. (a) Nonlinear relation between deflection angle and AC voltage. (b) Linear distribution by relating displacement current and deflection angle.

Fig. 5
Fig. 5

Principle of focal length measurement method. (a) Wave front curve analysis by analytic geometry. (b) Experimental method for focal length measurement.

Fig. 6
Fig. 6

Approach for focal length of crystal. (a) Output beams from different incident heights (TAC = 27.4°C). (b) Cubic polynomial fitting of tilt of beams from different heights.

Tables (2)

Tables Icon

Table 1 Results of Charge Density eN from Deflection Angle Measurement

Tables Icon

Table 2 Results of Charge Density eN from Focal Length Measurement

Equations (10)

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

nΔn(x)=n 1 2 n 3 g 11 ε 2 E 2 (x)=n 1 2 n 3 g 11 e 2 N 2 ( x d 2 + εV eNd ) 2 .
θ(x)=L d dx Δn(x)= n 3 g 11 e 2 N 2 L( x d 2 + εV eNd ),
f= 1 n 2 eN g 11 sin( LneN g 11 ) .
θ max = n 3 g 11 eNL( ε V pp d ),
I c =C dV dt = 2πνS d ε V pp ,
θ max = n 3 g 11 eNL 2πνS I c =B I c ,
eN= 2πνBS n 3 g 11 L ,
f= ( 1+ dF( h ) dh ) 3 2 d 2 F( h ) d h 2 | h=0 .
α( h )= a 1 h+ a 0 ,
f= 1 a 1 .

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