Abstract

We describe an optical detection scheme that reduces laser excess noise in measurements of small optical phase shifts. The scheme improves the sensitivity of the balanced differential detection. Analysis of the scheme and comparison with the conventional detection are presented. The scheme is applied in electro-optic probing of electrical signals in integrated circuits, where the excess laser noise is reduced by ∼20 dB.

© 2003 Optical Society of America

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References

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  1. J. A. Valdmanis, G. Mourou, “Subpicosecond electrooptic sampling: principles and applications,” IEEE J. Quantum Electron. 22, 69–78 (1986).
    [CrossRef]
  2. K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Sel. Top. Quantum. Electron. 24, 198–220 (1988).
    [CrossRef]
  3. Special issue on Optical probing of ultrafast devices and integrated circuits, Opt. Quantum. Electron. 28, 1996.
  4. H. H. Haus, Electromagnetic Noise and Quantum Optical Measurements, (Springer, New York, 2000) Chap. 8.
    [CrossRef]
  5. P. C. D. Hobbs, “Ultrasensitive laser measurements without tears,” Appl. Opt. 36, 903–920 (1997).
    [CrossRef] [PubMed]
  6. H. Hansen, T. Aichele, C. Hettich, P. Lodahl, A. I. Lvovsky, J. Mlynek, S. Schiller, “Ultrasensitive pulsed, balanced homodyne detector: application to time-domain quantum measurements,” Opt. Lett. 26, 1714–1716 (2001).
    [CrossRef]
  7. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  8. M. Aillerie, N. Theofanous, M. D. Fontana, “Measurement of the electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
    [CrossRef]
  9. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  10. Reflection-mode probing without the beam splitter is realized in Ref. 2. It has the same depth of modulation as scheme A, and it avoids the reflection loss of 4%.

2001

2000

M. Aillerie, N. Theofanous, M. D. Fontana, “Measurement of the electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

1997

1996

Special issue on Optical probing of ultrafast devices and integrated circuits, Opt. Quantum. Electron. 28, 1996.

1988

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Sel. Top. Quantum. Electron. 24, 198–220 (1988).
[CrossRef]

1986

J. A. Valdmanis, G. Mourou, “Subpicosecond electrooptic sampling: principles and applications,” IEEE J. Quantum Electron. 22, 69–78 (1986).
[CrossRef]

1941

Aichele, T.

Aillerie, M.

M. Aillerie, N. Theofanous, M. D. Fontana, “Measurement of the electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

Bloom, D. M.

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Sel. Top. Quantum. Electron. 24, 198–220 (1988).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

Fontana, M. D.

M. Aillerie, N. Theofanous, M. D. Fontana, “Measurement of the electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

Hansen, H.

Haus, H. H.

H. H. Haus, Electromagnetic Noise and Quantum Optical Measurements, (Springer, New York, 2000) Chap. 8.
[CrossRef]

Hettich, C.

Hobbs, P. C. D.

Jones, R. C.

Lodahl, P.

Lvovsky, A. I.

Mlynek, J.

Mourou, G.

J. A. Valdmanis, G. Mourou, “Subpicosecond electrooptic sampling: principles and applications,” IEEE J. Quantum Electron. 22, 69–78 (1986).
[CrossRef]

Rodwell, M. J. W.

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Sel. Top. Quantum. Electron. 24, 198–220 (1988).
[CrossRef]

Schiller, S.

Theofanous, N.

M. Aillerie, N. Theofanous, M. D. Fontana, “Measurement of the electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

Valdmanis, J. A.

J. A. Valdmanis, G. Mourou, “Subpicosecond electrooptic sampling: principles and applications,” IEEE J. Quantum Electron. 22, 69–78 (1986).
[CrossRef]

Weingarten, K. J.

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Sel. Top. Quantum. Electron. 24, 198–220 (1988).
[CrossRef]

Appl. Opt.

Appl. Phys. B

M. Aillerie, N. Theofanous, M. D. Fontana, “Measurement of the electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

IEEE J. Quantum Electron.

J. A. Valdmanis, G. Mourou, “Subpicosecond electrooptic sampling: principles and applications,” IEEE J. Quantum Electron. 22, 69–78 (1986).
[CrossRef]

IEEE J. Sel. Top. Quantum. Electron.

K. J. Weingarten, M. J. W. Rodwell, D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Sel. Top. Quantum. Electron. 24, 198–220 (1988).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Opt. Quantum. Electron.

Special issue on Optical probing of ultrafast devices and integrated circuits, Opt. Quantum. Electron. 28, 1996.

Other

H. H. Haus, Electromagnetic Noise and Quantum Optical Measurements, (Springer, New York, 2000) Chap. 8.
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

Reflection-mode probing without the beam splitter is realized in Ref. 2. It has the same depth of modulation as scheme A, and it avoids the reflection loss of 4%.

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Figures (2)

Fig. 1
Fig. 1

Two detection schemes for electro-optic phase shift measurements (a) and their complex amplitude diagrams (b). In the conventional setup (scheme A) E 1 and E 2 indicate two orthogonal polarizations incident on the Wollaston prism (WP). The phase difference (π/2 + δ) is acquired due to the waveplate (λ/4) and the sample (S). E + and E - are the results of addition and subtraction in the WP. In the laser noise suppression setup (scheme B) E 1 and E 2 are the components emerging from the sample. The components add in projection on the s-plane of the polarizing beam splitter (PBS) and subtract in projection on the p-plane. The s-polarization is reduced by α-1 in the PBS. The λ/4 waveplate removes π/2 phase shift between E p and αE s (figure shows E p * out of phase for clarity). Two components are added and subtracted in the WP.

Fig. 2
Fig. 2

Laser spectral intensity measured by one of the photodetectors for schemes A and B. The electro-optic signal at 400 kHz is shown magnified in the inset. The dashed line indicates the detector noise.

Equations (10)

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

n1,2n0±n03r41Ex2,
I+=I0 sin2π4+δ2I021+δ
I-=I0 cos2π4+δ2I021-δ.
ε0=E00; ε1=E+E-.
ε1=Sπ2NwpNpS-π2NsSπ2ε0,
Nwp=eiπ/400e-iπ/4
Np=α001
Ns=eiδ/200e-iδ/2
Sθ=cosθ-sinθsinθcosθ
I±=α2 I0α±δ.

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