Abstract

A balanced homodyne detector, with a maximum common mode rejection ratio and clearance of 75.2 dB and 37 dB, is experimentally obtained with two arbitrary photodiodes of the same model. On the basis of self-subtraction photodetector scheme, we divide the influence of photodiodes on the common mode rejection ratio into two parts, including magnitude and phase of output signal. The discrepancy of quantum efficiency and dark current affects magnitude of output signal of photodiodes, which is compensated by adjusting the splitter ratio. The difference of the equivalent capacitance and resistance affects the phase of output signal of photodiodes, which is compensated by the differential fine tuning circuit and adjustable bias voltage circuit. With these designs, the developed homodyne detector can be used for measuring accurately the squeezed state.

© 2015 Optical Society of America

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References

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  1. S. L. Braunstein and P. V. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
    [Crossref]
  2. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
    [Crossref] [PubMed]
  3. W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
    [Crossref]
  4. N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continous variables,” Phys. Rev. Lett. 94, 220502 (2005).
    [Crossref]
  5. H. Vahlbruch, M. Mehmet, S. Chelkowski, and R. Schnable, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
    [Crossref] [PubMed]
  6. Y Takeno, M Yukawa, H Yonezawa, and A Furusawa, “Observation of -9 dB quadrature squeezing with improvement of phase stability in homodyne measurement,” Opt. Express 15(7), 4321–4327 (2007).
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    [Crossref]
  8. G. Breitenbach, S. Schiller, and J. Mlynek, “Measurement of the quantum states of squeezed light,” Nature 387, 471–475 (1997).
    [Crossref]
  9. M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
    [Crossref]
  10. J. Wenger, R. T. Brouri, and P. Grangier, “Pulsed homodyne measurements of femtosecond squeezed pulses generated by single-pass parametric deamplification,” Opt. Lett. 29(11), 1267–1269 (2004).
    [Crossref] [PubMed]
  11. H. J. Zhou, W. H. Yang, Z. X. Li, X. F. Li, and Y. H. Zheng, “A bootstrapped, low-noise, and high-gain photodetector for shot noise measurement,” Rev. Sci. Instrum 85(1), 013111 (2014).
    [Crossref] [PubMed]
  12. H. J. Zhou, W. Z. Wang, C. Y. Chen, and Y. H. Zheng, “A low-noise, large-dynamic-range-enhanced amplifier based on JFET buffering input and JFET bootstrap structure,” IEEE Sensors J. 15(4), 2101–2105 (2015).
    [Crossref]
  13. O Haderka, V. Michalek, V. Urbasek, and M. Jezek, “Fast time-domain balanced homodyne detection of light,” Appl. Opt. 48(15), 2884–2889 (2009).
    [Crossref] [PubMed]
  14. H. Hansen, T. Aichele, C. Hettich, P. Lodahl, A. I. Lvovsky, J. Mlynek, and S. Schiller, “An ultra-sensitive pulsed balanced homodyne detector: application to time-domain quantum measurement,” Opt. Lett. 26(21), 1714–1716 (2001).
    [Crossref]
  15. “A primer on photodiode technology,” http://home.sandiego.edu/ekim/photodiode/pdtech.html .
  16. “Photodiode characteristics and applications,” http://www.osioptoelectronics.com/application-notes/AN-Photodiode-Parameters-Characteristics.pdf .

2015 (1)

H. J. Zhou, W. Z. Wang, C. Y. Chen, and Y. H. Zheng, “A low-noise, large-dynamic-range-enhanced amplifier based on JFET buffering input and JFET bootstrap structure,” IEEE Sensors J. 15(4), 2101–2105 (2015).
[Crossref]

2014 (1)

H. J. Zhou, W. H. Yang, Z. X. Li, X. F. Li, and Y. H. Zheng, “A bootstrapped, low-noise, and high-gain photodetector for shot noise measurement,” Rev. Sci. Instrum 85(1), 013111 (2014).
[Crossref] [PubMed]

2012 (1)

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

2011 (1)

2009 (1)

2008 (1)

H. Vahlbruch, M. Mehmet, S. Chelkowski, and R. Schnable, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (3)

S. L. Braunstein and P. V. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continous variables,” Phys. Rev. Lett. 94, 220502 (2005).
[Crossref]

2004 (1)

2001 (1)

1998 (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

1997 (1)

G. Breitenbach, S. Schiller, and J. Mlynek, “Measurement of the quantum states of squeezed light,” Nature 387, 471–475 (1997).
[Crossref]

Aichele, T.

Aoki, T.

N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continous variables,” Phys. Rev. Lett. 94, 220502 (2005).
[Crossref]

Ast, S.

Bachor, H. A.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Bahlbruch, H.

Bowen, W. P.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Braunstein, S. L.

S. L. Braunstein and P. V. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Breitenbach, G.

G. Breitenbach, S. Schiller, and J. Mlynek, “Measurement of the quantum states of squeezed light,” Nature 387, 471–475 (1997).
[Crossref]

Brouri, R. T.

Buchler, B. C.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Chelkowski, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, and R. Schnable, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Chen, C. Y.

H. J. Zhou, W. Z. Wang, C. Y. Chen, and Y. H. Zheng, “A low-noise, large-dynamic-range-enhanced amplifier based on JFET buffering input and JFET bootstrap structure,” IEEE Sensors J. 15(4), 2101–2105 (2015).
[Crossref]

Chua, S. S. Y.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

Eberle, T.

Fuchs, C. A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Furusawa, A

Furusawa, A.

N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continous variables,” Phys. Rev. Lett. 94, 220502 (2005).
[Crossref]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Grangier, P.

Haderka, O

Hansen, H.

Hettich, C.

Jezek, M.

Khalaidobski, A.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

Kimble, J. J.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Lam, P. K.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Li, X. F.

H. J. Zhou, W. H. Yang, Z. X. Li, X. F. Li, and Y. H. Zheng, “A bootstrapped, low-noise, and high-gain photodetector for shot noise measurement,” Rev. Sci. Instrum 85(1), 013111 (2014).
[Crossref] [PubMed]

Li, Z. X.

H. J. Zhou, W. H. Yang, Z. X. Li, X. F. Li, and Y. H. Zheng, “A bootstrapped, low-noise, and high-gain photodetector for shot noise measurement,” Rev. Sci. Instrum 85(1), 013111 (2014).
[Crossref] [PubMed]

Lodahl, P.

Loock, P. V.

S. L. Braunstein and P. V. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

Lvovsky, A. I.

McClelland, D. E.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

Mehmet, M.

M. Mehmet, S. Ast, T. Eberle, S. Steinlechner, H. Bahlbruch, and R. Schnabel, “Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB,” Opt. Express 19(25), 25763–25772 (2011).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, and R. Schnable, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Michalek, V.

Mlynek, J.

Mow-Lowry, C. M.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

Polzik, E. S.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Ralph, T. C.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Schiller, S.

Schnabel, R.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

M. Mehmet, S. Ast, T. Eberle, S. Steinlechner, H. Bahlbruch, and R. Schnabel, “Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB,” Opt. Express 19(25), 25763–25772 (2011).
[Crossref]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Schnable, R.

H. Vahlbruch, M. Mehmet, S. Chelkowski, and R. Schnable, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Shaddock, D. A.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

Sorensen, J. L.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Stefszky, M. S.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

Steinlechner, S.

Symul, T.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Takei, N.

N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continous variables,” Phys. Rev. Lett. 94, 220502 (2005).
[Crossref]

Takeno, Y

Treps, N.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Urbasek, V.

Vahlbruch, H.

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, and R. Schnable, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Wang, W. Z.

H. J. Zhou, W. Z. Wang, C. Y. Chen, and Y. H. Zheng, “A low-noise, large-dynamic-range-enhanced amplifier based on JFET buffering input and JFET bootstrap structure,” IEEE Sensors J. 15(4), 2101–2105 (2015).
[Crossref]

Wenger, J.

Yang, W. H.

H. J. Zhou, W. H. Yang, Z. X. Li, X. F. Li, and Y. H. Zheng, “A bootstrapped, low-noise, and high-gain photodetector for shot noise measurement,” Rev. Sci. Instrum 85(1), 013111 (2014).
[Crossref] [PubMed]

Yonezawa, H

Yonezawa, H.

N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continous variables,” Phys. Rev. Lett. 94, 220502 (2005).
[Crossref]

Yukawa, M

Zheng, Y. H.

H. J. Zhou, W. Z. Wang, C. Y. Chen, and Y. H. Zheng, “A low-noise, large-dynamic-range-enhanced amplifier based on JFET buffering input and JFET bootstrap structure,” IEEE Sensors J. 15(4), 2101–2105 (2015).
[Crossref]

H. J. Zhou, W. H. Yang, Z. X. Li, X. F. Li, and Y. H. Zheng, “A bootstrapped, low-noise, and high-gain photodetector for shot noise measurement,” Rev. Sci. Instrum 85(1), 013111 (2014).
[Crossref] [PubMed]

Zhou, H. J.

H. J. Zhou, W. Z. Wang, C. Y. Chen, and Y. H. Zheng, “A low-noise, large-dynamic-range-enhanced amplifier based on JFET buffering input and JFET bootstrap structure,” IEEE Sensors J. 15(4), 2101–2105 (2015).
[Crossref]

H. J. Zhou, W. H. Yang, Z. X. Li, X. F. Li, and Y. H. Zheng, “A bootstrapped, low-noise, and high-gain photodetector for shot noise measurement,” Rev. Sci. Instrum 85(1), 013111 (2014).
[Crossref] [PubMed]

Appl. Opt. (1)

Classical and Quantum Gravity (1)

M. S. Stefszky, C. M. Mow-Lowry, S. S. Y. Chua, D. A. Shaddock, B. C. Buchler, H. Vahlbruch, A. Khalaidobski, R. Schnabel, P. K. Lam, and D. E. McClelland, “Balanced homodyne detection of optical quantum states at audio-band frequencies and below,” Classical and Quantum Gravity 29, 145015 (2012).
[Crossref]

IEEE Sensors J. (1)

H. J. Zhou, W. Z. Wang, C. Y. Chen, and Y. H. Zheng, “A low-noise, large-dynamic-range-enhanced amplifier based on JFET buffering input and JFET bootstrap structure,” IEEE Sensors J. 15(4), 2101–2105 (2015).
[Crossref]

Nature (1)

G. Breitenbach, S. Schiller, and J. Mlynek, “Measurement of the quantum states of squeezed light,” Nature 387, 471–475 (1997).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (1)

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnabel, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, “Experimental investigation of continuous-variable quantum teleportation,” Phys. Rev. A 67, 032302 (2005).
[Crossref]

Phys. Rev. Lett. (2)

N. Takei, H. Yonezawa, T. Aoki, and A. Furusawa, “High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continous variables,” Phys. Rev. Lett. 94, 220502 (2005).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, and R. Schnable, “Observation of squeezed light with 10-dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

S. L. Braunstein and P. V. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

Rev. Sci. Instrum (1)

H. J. Zhou, W. H. Yang, Z. X. Li, X. F. Li, and Y. H. Zheng, “A bootstrapped, low-noise, and high-gain photodetector for shot noise measurement,” Rev. Sci. Instrum 85(1), 013111 (2014).
[Crossref] [PubMed]

Science (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, J. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Other (2)

“A primer on photodiode technology,” http://home.sandiego.edu/ekim/photodiode/pdtech.html .

“Photodiode characteristics and applications,” http://www.osioptoelectronics.com/application-notes/AN-Photodiode-Parameters-Characteristics.pdf .

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Figures (6)

Fig. 1
Fig. 1 The self-subtraction photodetector scheme.
Fig. 2
Fig. 2 The equivalent circuit of a photodiode. Id: dark current that is current when no light is present; Is: signal current; Cd: junction capacitance; Rd: shunt resistance; Rs: series resistance; Rf: load resistance.
Fig. 3
Fig. 3 The schematic of photodetector with the DFTC and ABV.
Fig. 4
Fig. 4 Experimental setup for regulation procedure. HPW: half-wave plate; PBS: polarization beam splitter; EOAM: electro-optic amplitude modulator; D: ETX500 InGaAs photo-diode; SA: spectrum analyzer; OSC: digitizing oscilloscope; SG: signal generator.
Fig. 5
Fig. 5 The typical result of the balancing process. Curve a, the spectrum of the unbalanced detector (one photodiode blocked, one photodiode illuminated); curve b, the spectrum of the balanced detector (two photodiodes illuminated); curve c, the electronic noise spectrum (two photodiodes blocked); curve d, the spectrum analyzer internal noise.
Fig. 6
Fig. 6 Linearity and clearance of the balanced homodyne detection system.

Equations (4)

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

I f = ( I s + I d ) R d ( R d + R s + R f ) j R d 2 ( R s + R f ) ω C d ( R d + R s + R f ) 2 + R d 2 ( R s + R f ) 2 ω 2 C d 2
φ f = arctan R d ( R s + R f ) ω C d R d + R s + R f
φ f = arctan [ ( R s + R f ) ω C d ) ]
C d = ε 0 ε A d = ε 0 ε A 2 ε 0 ε μ ρ ( V + V i n ) 2

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