Abstract

The use of an optical local oscillator for coherent detection with a photodiode can significantly reduce the responsivity of the detector because of saturation effects. Consequently, local-oscillator shot-noise-limited operation of the detector may not be possible. This effect is analyzed and formulations are developed for the optimum optical local-oscillator power level and the resultant maximum possible signal-to-noise ratio in terms of parameters derived from the photodiode current versus the optical power response curve. An effective heterodyne responsivity that can be used as a part of the specifications when one is procuring photodiodes for use in coherent detection systems is defined.

© 1995 Optical Society of America

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References

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  1. M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, “NOAA’s pulsed, coherent, IR Doppler lidar-characteristics and data,” in Physics and Technology of Coherent Infrared Radar 1, R. C. Harney, ed., Proc. Soc. Photo-Opt. Instrum. Eng.300, 60–65 (1982).
  2. D. A. Bowdle, J. Rothermel, J. M. Vaughan, D. W. Brown, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains. 1. Lidar intercomparison,” J. Geophys. Res. 96, 5327–5335 (1991).
    [CrossRef]
  3. D. Long, “Photovoltaic and photoconductive infrared detectors,” in Optical and Infrared Detectors, R. J. Keys, ed., Vol. 5 of Springer Series on Applied Optics (Springer-Verlag, New York, 1977), p. 101.
  4. R. G. Frehlich, “Conditions for optimal performance of mono-static coherent laser radar,” Opt. Lett. 15, 643–645 (1990).
    [CrossRef] [PubMed]
  5. R. H. Hamstra, P. Wendland, “Noise and frequency response of silicon photodiode operational amplifier combination,” Appl. Opt. 11, 1539–1547 (1972).
    [CrossRef] [PubMed]
  6. J. M. Hunt, J. F. Holmes, F. Amzajerdian, “Optimum local oscillator levels for coherent detection using photoconductors,” Appl. Opt. 27, 3135–3141 (1988).
    [CrossRef] [PubMed]
  7. M. C. Teich, R. J. Keyes, R. H. Kingston, “Optimum heterodyne detection at 10.6 μm in photoconductive Ge:Cu,” Appl. Phys. Lett. 9, 357–360 (1966).
    [CrossRef]
  8. R. H. Kingston, “The ideal photondetector,” in Detection of Optical and Infrared Radiation, D. L. MacAdam, ed., Vol. 10 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1977), Chap. 2.
  9. P. W. Kruse, “The photon detection process,” in Optical and Infrared Detectors, R. J. Keys, ed., Vol. 5 of Springer Series on Applied Optics (Springer-Verlag, New York, 1977), p. 5.
  10. F. R. Arams, E. W. Sard, B. J. Peyton, F. P. Pace, “Infared 10.6-micron heterodyne detection with gigahertz IF capability,” IEEE J. Quantum Electron. QE-3, 484–492 (1967).
    [CrossRef]
  11. N. A. Penin, N. Sh. Khaykin, B. V. Yurist, “Investigation of the noise factor of an optical heterodyne receiver with an extrinsic photoresistor,” Radiotekh. Elektron.792–796 (1972).
  12. R. G. Frehlich, “Estimation of the nonlinearity of a photodetector,” Appl. Opt. 31, 5926–5929 (1992).
    [CrossRef] [PubMed]

1992 (1)

1991 (1)

D. A. Bowdle, J. Rothermel, J. M. Vaughan, D. W. Brown, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains. 1. Lidar intercomparison,” J. Geophys. Res. 96, 5327–5335 (1991).
[CrossRef]

1990 (1)

1988 (1)

1972 (2)

R. H. Hamstra, P. Wendland, “Noise and frequency response of silicon photodiode operational amplifier combination,” Appl. Opt. 11, 1539–1547 (1972).
[CrossRef] [PubMed]

N. A. Penin, N. Sh. Khaykin, B. V. Yurist, “Investigation of the noise factor of an optical heterodyne receiver with an extrinsic photoresistor,” Radiotekh. Elektron.792–796 (1972).

1967 (1)

F. R. Arams, E. W. Sard, B. J. Peyton, F. P. Pace, “Infared 10.6-micron heterodyne detection with gigahertz IF capability,” IEEE J. Quantum Electron. QE-3, 484–492 (1967).
[CrossRef]

1966 (1)

M. C. Teich, R. J. Keyes, R. H. Kingston, “Optimum heterodyne detection at 10.6 μm in photoconductive Ge:Cu,” Appl. Phys. Lett. 9, 357–360 (1966).
[CrossRef]

Amzajerdian, F.

Arams, F. R.

F. R. Arams, E. W. Sard, B. J. Peyton, F. P. Pace, “Infared 10.6-micron heterodyne detection with gigahertz IF capability,” IEEE J. Quantum Electron. QE-3, 484–492 (1967).
[CrossRef]

Bowdle, D. A.

D. A. Bowdle, J. Rothermel, J. M. Vaughan, D. W. Brown, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains. 1. Lidar intercomparison,” J. Geophys. Res. 96, 5327–5335 (1991).
[CrossRef]

Brown, D. W.

D. A. Bowdle, J. Rothermel, J. M. Vaughan, D. W. Brown, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains. 1. Lidar intercomparison,” J. Geophys. Res. 96, 5327–5335 (1991).
[CrossRef]

Frehlich, R. G.

Hall, F. F.

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, “NOAA’s pulsed, coherent, IR Doppler lidar-characteristics and data,” in Physics and Technology of Coherent Infrared Radar 1, R. C. Harney, ed., Proc. Soc. Photo-Opt. Instrum. Eng.300, 60–65 (1982).

Hamstra, R. H.

Hardesty, R. M.

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, “NOAA’s pulsed, coherent, IR Doppler lidar-characteristics and data,” in Physics and Technology of Coherent Infrared Radar 1, R. C. Harney, ed., Proc. Soc. Photo-Opt. Instrum. Eng.300, 60–65 (1982).

Holmes, J. F.

Hunt, J. M.

Keyes, R. J.

M. C. Teich, R. J. Keyes, R. H. Kingston, “Optimum heterodyne detection at 10.6 μm in photoconductive Ge:Cu,” Appl. Phys. Lett. 9, 357–360 (1966).
[CrossRef]

Khaykin, N. Sh.

N. A. Penin, N. Sh. Khaykin, B. V. Yurist, “Investigation of the noise factor of an optical heterodyne receiver with an extrinsic photoresistor,” Radiotekh. Elektron.792–796 (1972).

Kingston, R. H.

M. C. Teich, R. J. Keyes, R. H. Kingston, “Optimum heterodyne detection at 10.6 μm in photoconductive Ge:Cu,” Appl. Phys. Lett. 9, 357–360 (1966).
[CrossRef]

R. H. Kingston, “The ideal photondetector,” in Detection of Optical and Infrared Radiation, D. L. MacAdam, ed., Vol. 10 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1977), Chap. 2.

Kruse, P. W.

P. W. Kruse, “The photon detection process,” in Optical and Infrared Detectors, R. J. Keys, ed., Vol. 5 of Springer Series on Applied Optics (Springer-Verlag, New York, 1977), p. 5.

Lawrence, T. R.

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, “NOAA’s pulsed, coherent, IR Doppler lidar-characteristics and data,” in Physics and Technology of Coherent Infrared Radar 1, R. C. Harney, ed., Proc. Soc. Photo-Opt. Instrum. Eng.300, 60–65 (1982).

Long, D.

D. Long, “Photovoltaic and photoconductive infrared detectors,” in Optical and Infrared Detectors, R. J. Keys, ed., Vol. 5 of Springer Series on Applied Optics (Springer-Verlag, New York, 1977), p. 101.

Pace, F. P.

F. R. Arams, E. W. Sard, B. J. Peyton, F. P. Pace, “Infared 10.6-micron heterodyne detection with gigahertz IF capability,” IEEE J. Quantum Electron. QE-3, 484–492 (1967).
[CrossRef]

Penin, N. A.

N. A. Penin, N. Sh. Khaykin, B. V. Yurist, “Investigation of the noise factor of an optical heterodyne receiver with an extrinsic photoresistor,” Radiotekh. Elektron.792–796 (1972).

Peyton, B. J.

F. R. Arams, E. W. Sard, B. J. Peyton, F. P. Pace, “Infared 10.6-micron heterodyne detection with gigahertz IF capability,” IEEE J. Quantum Electron. QE-3, 484–492 (1967).
[CrossRef]

Post, M. J.

D. A. Bowdle, J. Rothermel, J. M. Vaughan, D. W. Brown, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains. 1. Lidar intercomparison,” J. Geophys. Res. 96, 5327–5335 (1991).
[CrossRef]

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, “NOAA’s pulsed, coherent, IR Doppler lidar-characteristics and data,” in Physics and Technology of Coherent Infrared Radar 1, R. C. Harney, ed., Proc. Soc. Photo-Opt. Instrum. Eng.300, 60–65 (1982).

Richter, R. A.

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, “NOAA’s pulsed, coherent, IR Doppler lidar-characteristics and data,” in Physics and Technology of Coherent Infrared Radar 1, R. C. Harney, ed., Proc. Soc. Photo-Opt. Instrum. Eng.300, 60–65 (1982).

Rothermel, J.

D. A. Bowdle, J. Rothermel, J. M. Vaughan, D. W. Brown, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains. 1. Lidar intercomparison,” J. Geophys. Res. 96, 5327–5335 (1991).
[CrossRef]

Sard, E. W.

F. R. Arams, E. W. Sard, B. J. Peyton, F. P. Pace, “Infared 10.6-micron heterodyne detection with gigahertz IF capability,” IEEE J. Quantum Electron. QE-3, 484–492 (1967).
[CrossRef]

Teich, M. C.

M. C. Teich, R. J. Keyes, R. H. Kingston, “Optimum heterodyne detection at 10.6 μm in photoconductive Ge:Cu,” Appl. Phys. Lett. 9, 357–360 (1966).
[CrossRef]

Vaughan, J. M.

D. A. Bowdle, J. Rothermel, J. M. Vaughan, D. W. Brown, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains. 1. Lidar intercomparison,” J. Geophys. Res. 96, 5327–5335 (1991).
[CrossRef]

Wendland, P.

Yurist, B. V.

N. A. Penin, N. Sh. Khaykin, B. V. Yurist, “Investigation of the noise factor of an optical heterodyne receiver with an extrinsic photoresistor,” Radiotekh. Elektron.792–796 (1972).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

M. C. Teich, R. J. Keyes, R. H. Kingston, “Optimum heterodyne detection at 10.6 μm in photoconductive Ge:Cu,” Appl. Phys. Lett. 9, 357–360 (1966).
[CrossRef]

IEEE J. Quantum Electron. (1)

F. R. Arams, E. W. Sard, B. J. Peyton, F. P. Pace, “Infared 10.6-micron heterodyne detection with gigahertz IF capability,” IEEE J. Quantum Electron. QE-3, 484–492 (1967).
[CrossRef]

J. Geophys. Res. (1)

D. A. Bowdle, J. Rothermel, J. M. Vaughan, D. W. Brown, M. J. Post, “Aerosol backscatter measurements at 10.6 micrometers with airborne and ground-based CO2 Doppler lidars over the Colorado high plains. 1. Lidar intercomparison,” J. Geophys. Res. 96, 5327–5335 (1991).
[CrossRef]

Opt. Lett. (1)

Radiotekh. Elektron. (1)

N. A. Penin, N. Sh. Khaykin, B. V. Yurist, “Investigation of the noise factor of an optical heterodyne receiver with an extrinsic photoresistor,” Radiotekh. Elektron.792–796 (1972).

Other (4)

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, “NOAA’s pulsed, coherent, IR Doppler lidar-characteristics and data,” in Physics and Technology of Coherent Infrared Radar 1, R. C. Harney, ed., Proc. Soc. Photo-Opt. Instrum. Eng.300, 60–65 (1982).

D. Long, “Photovoltaic and photoconductive infrared detectors,” in Optical and Infrared Detectors, R. J. Keys, ed., Vol. 5 of Springer Series on Applied Optics (Springer-Verlag, New York, 1977), p. 101.

R. H. Kingston, “The ideal photondetector,” in Detection of Optical and Infrared Radiation, D. L. MacAdam, ed., Vol. 10 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1977), Chap. 2.

P. W. Kruse, “The photon detection process,” in Optical and Infrared Detectors, R. J. Keys, ed., Vol. 5 of Springer Series on Applied Optics (Springer-Verlag, New York, 1977), p. 5.

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Figures (7)

Fig. 1
Fig. 1

Coherent optical receiver.

Fig. 2
Fig. 2

Detector equivalent circuit.

Fig. 3
Fig. 3

Detector current versus optical local-oscillator power, along with a least-squares fit.

Fig. 4
Fig. 4

Circuit for measuring i d .

Fig. 5
Fig. 5

Proper root of Eq. (22) versus the parameter γ.

Fig. 6
Fig. 6

SNR reduction factor due to diode saturation.

Fig. 7
Fig. 7

SNR reduction factor due to the local-oscillator shot-noise-limited assumption.

Tables (1)

Tables Icon

Table 1 Properties of the Diodes Presented in Fig. 3

Equations (33)

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u = A LO cos ( ω 0 t ) + A S cos ( ω 0 t + ω h t ) ,
I = u u * Z 0 = 1 Z 0 [ A LO cos ( ω 0 t ) + A S cos ( ω 0 t + ω h t ) ] 2 ,
i d = ρ 0 I A = A ρ 0 A LO 2 2 Z 0 + A ρ 0 A S 2 2 Z 0 + A ρ 0 A LO A S Z 0 cos ( ω h t ) ,
i d = ρ 0 P LO + ρ 0 P S + 2 ρ 0 ( P LO P S ) 1 / 2 cos ( ω h t ) ,
i DC = ρ 0 ( P LO + P S ) ρ 0 P LO ,
i s = 2 ρ 0 ( P LO P S ) 1 / 2 cos ( ω h t ) .
S = 2 ρ 0 2 P LO P S R e 2 .
N = 2 e B ρ 0 P LO R e 2 + 4 B K T e R e ,
S N = ρ 0 2 P LO P S B ( e ρ 0 P LO + 2 K T e R e ) .
e ρ 0 P LO 2 K T e R e .
S N = ρ 0 P S B e .
i d ( P in ) = ρ 0 P in - ρ 0 α P in 2
i d = i d ( P LO ) + P LO [ i d ( P LO ) ] P het = i DC + i S cos ( ω h t ) ,
i DC = ρ 0 P LO ( 1 - α P LO ) ,
i S = 2 ρ 0 ( 1 - 2 α P LO ) ( P LO P S ) 1 / 2 .
S = 2 ρ 0 2 ( 1 - 2 α P LO ) 2 P LO P S R e 2 ,
N = [ 2 e ρ 0 P LO ( 1 - α P LO ) B R e 2 + 4 K T e B R e ] .
S N = ρ 0 P S B e [ ( 1 - 2 α P LO ) 2 P LO P LO ( 1 - α P LO ) + 2 K T e ρ 0 e R e ] .
P LO ( S N ) = 0
[ ( 1 - 2 α P LO ) 2 - 4 P LO α ( 1 - 2 α P LO ) ] [ P LO ( 1 - α P LO ) + Q ] - ( 1 - 2 α P LO ) 3 P LO = 0 ,
Q = 2000 T e α ρ 0 e R e .
P LO 3 - 3 2 α P LO 2 - 3 Q α P LO + Q 2 α 2 = 0.
X 3 - / 2 3 X 2 - 3 γ X + ½ γ = 0 ,
γ = 2000 K T e α ρ 0 e R e = Q α ,
X = α P LOM .
SNR - RF 1 = [ ( 1 - 2 α P LO ) 2 ( P LO + 2 K T e ρ 0 e R e ) P LO ( 1 - α P LO ) + 2 K T e ρ 0 e R e ] .
SNR - RF 2 = [ ( 1 - 2 α P LO ) 2 P LO P LO ( 1 - α P LO ) + 2 K T e ρ 0 e R e ] .
S = 2 ρ het 2 P LO P S R e 2 ,
ρ het = ρ 0 ( 1 - 2 α P LO ) .
SNR = P S B e [ 2 ρ het 2 P LO ρ 0 P LO ( 1 + ρ het ρ 0 ) + 4 K T e e R e ] .
ρ 0 = η e λ h c ,
X = α P LOM = 1 2 ( 1 - ρ het ρ 0 ) .
P LOM = X Q γ ,

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