Abstract

The low-frequency intensity noise at 25 MHz of a Fabry–Perot semiconductor laser is measured as a function of injection current. All the measurements are taken at room temperature and the laser is operated with a commercial current source (the conditions under which laser diodes are often used). At the highest injection current of twice threshold, the intensity noise is 5.5 dB above the shot-noise limit. When the longitudinal side mode suppression of the laser is 20 dB or larger, the intensity noise is modeled adequately by an expression derived from the single-mode, small-signal, linearized, semiclassical rate equations. All the parameters used in the theory are derived or referenced.

© 1996 Optical Society of America

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References

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  1. V. McOmber, “Measuring relative intensity noise of a laser,” Fiberopt. Appl. Mag. 1, 21–26 (Spring, 1992).
  2. M. Xiao, L. Wu, H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
    [CrossRef] [PubMed]
  3. E. S. Polzik, J. Carri, H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
    [CrossRef] [PubMed]
  4. J. Kitching, A. Yariv, Y. Shevy, “Amplitude noise reduction in semiconductor lasers with weak, dispersive optical feedback,” Opt. Lett. 74, 1331–1333 (1994).
    [CrossRef]
  5. H. Wang, M. J. Freeman, D. G. Steel, “Squeezed light from injection-locked quantum well lasers,” Phys. Rev. Lett. 71, 3951–3954 (1993).
    [CrossRef] [PubMed]
  6. W. H. Richardson, S. Machida, Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870 (1991).
    [CrossRef] [PubMed]
  7. G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993), pp. 285–294.
  8. Y. Yamamoto, S. Machida, O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025–4043 (1986).
    [CrossRef] [PubMed]
  9. M. J. Freeman, H. Wang, D. G. Steel, R. Craig, D. R. Scifres, “Amplitude-squeezed light from quantum-well lasers,” Opt. Lett. 18, 379–381 (1993).
    [CrossRef] [PubMed]
  10. S. Inoue, H. Ohzu, S. Machida, Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A. 46, 2757–2765 (1992).
    [CrossRef] [PubMed]
  11. H. Haken, Light (North-Holland, Amsterdam, 1981), Vol. 1, pp. 285–295.
  12. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1994), p. 676.
  13. R. J. Fronen, “Facet reflectivity and low-frequency noise in the light output of LED and superradiant diodes,” IEEE J. Quantum Electron. 25, 1653–1658 (1989).
    [CrossRef]
  14. J. Šikula, P. Vašina, I. Hüttel, “The noise of the GaAlAs super-LED radiation,” Phys. Status Solidi A 111, 367–370 (1989).
    [CrossRef]
  15. M. Ohtsu, Highly Coherent Semiconductor Lasers (Artech, Boston, Mass., 1992), p. 18.
  16. H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), Vol. 1, p. 44.
  17. Ref. 16, Vol. 2, p. 228.
  18. Ref. 16, Vol. 2, pp. 180–181.
  19. Ref. 16, Vol. 1, p. 160.
  20. Y. Yamamoto, S. Saito, T. Mukai, “AM and FM quantum noise in semiconductor lasers. Part II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
    [CrossRef]

1994 (1)

J. Kitching, A. Yariv, Y. Shevy, “Amplitude noise reduction in semiconductor lasers with weak, dispersive optical feedback,” Opt. Lett. 74, 1331–1333 (1994).
[CrossRef]

1993 (2)

H. Wang, M. J. Freeman, D. G. Steel, “Squeezed light from injection-locked quantum well lasers,” Phys. Rev. Lett. 71, 3951–3954 (1993).
[CrossRef] [PubMed]

M. J. Freeman, H. Wang, D. G. Steel, R. Craig, D. R. Scifres, “Amplitude-squeezed light from quantum-well lasers,” Opt. Lett. 18, 379–381 (1993).
[CrossRef] [PubMed]

1992 (3)

S. Inoue, H. Ohzu, S. Machida, Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A. 46, 2757–2765 (1992).
[CrossRef] [PubMed]

V. McOmber, “Measuring relative intensity noise of a laser,” Fiberopt. Appl. Mag. 1, 21–26 (Spring, 1992).

E. S. Polzik, J. Carri, H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[CrossRef] [PubMed]

1991 (1)

W. H. Richardson, S. Machida, Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870 (1991).
[CrossRef] [PubMed]

1989 (2)

R. J. Fronen, “Facet reflectivity and low-frequency noise in the light output of LED and superradiant diodes,” IEEE J. Quantum Electron. 25, 1653–1658 (1989).
[CrossRef]

J. Šikula, P. Vašina, I. Hüttel, “The noise of the GaAlAs super-LED radiation,” Phys. Status Solidi A 111, 367–370 (1989).
[CrossRef]

1987 (1)

M. Xiao, L. Wu, H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[CrossRef] [PubMed]

1986 (1)

Y. Yamamoto, S. Machida, O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025–4043 (1986).
[CrossRef] [PubMed]

1983 (1)

Y. Yamamoto, S. Saito, T. Mukai, “AM and FM quantum noise in semiconductor lasers. Part II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993), pp. 285–294.

Carri, J.

E. S. Polzik, J. Carri, H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[CrossRef] [PubMed]

Casey, H. C.

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), Vol. 1, p. 44.

Craig, R.

Dutta, N. K.

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993), pp. 285–294.

Freeman, M. J.

M. J. Freeman, H. Wang, D. G. Steel, R. Craig, D. R. Scifres, “Amplitude-squeezed light from quantum-well lasers,” Opt. Lett. 18, 379–381 (1993).
[CrossRef] [PubMed]

H. Wang, M. J. Freeman, D. G. Steel, “Squeezed light from injection-locked quantum well lasers,” Phys. Rev. Lett. 71, 3951–3954 (1993).
[CrossRef] [PubMed]

Fronen, R. J.

R. J. Fronen, “Facet reflectivity and low-frequency noise in the light output of LED and superradiant diodes,” IEEE J. Quantum Electron. 25, 1653–1658 (1989).
[CrossRef]

Haken, H.

H. Haken, Light (North-Holland, Amsterdam, 1981), Vol. 1, pp. 285–295.

Hüttel, I.

J. Šikula, P. Vašina, I. Hüttel, “The noise of the GaAlAs super-LED radiation,” Phys. Status Solidi A 111, 367–370 (1989).
[CrossRef]

Inoue, S.

S. Inoue, H. Ohzu, S. Machida, Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A. 46, 2757–2765 (1992).
[CrossRef] [PubMed]

Kimble, H. J.

E. S. Polzik, J. Carri, H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[CrossRef] [PubMed]

M. Xiao, L. Wu, H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[CrossRef] [PubMed]

Kitching, J.

J. Kitching, A. Yariv, Y. Shevy, “Amplitude noise reduction in semiconductor lasers with weak, dispersive optical feedback,” Opt. Lett. 74, 1331–1333 (1994).
[CrossRef]

Machida, S.

S. Inoue, H. Ohzu, S. Machida, Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A. 46, 2757–2765 (1992).
[CrossRef] [PubMed]

W. H. Richardson, S. Machida, Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870 (1991).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025–4043 (1986).
[CrossRef] [PubMed]

McOmber, V.

V. McOmber, “Measuring relative intensity noise of a laser,” Fiberopt. Appl. Mag. 1, 21–26 (Spring, 1992).

Mukai, T.

Y. Yamamoto, S. Saito, T. Mukai, “AM and FM quantum noise in semiconductor lasers. Part II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

Nilsson, O.

Y. Yamamoto, S. Machida, O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025–4043 (1986).
[CrossRef] [PubMed]

Ohtsu, M.

M. Ohtsu, Highly Coherent Semiconductor Lasers (Artech, Boston, Mass., 1992), p. 18.

Ohzu, H.

S. Inoue, H. Ohzu, S. Machida, Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A. 46, 2757–2765 (1992).
[CrossRef] [PubMed]

Panish, M. B.

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), Vol. 1, p. 44.

Polzik, E. S.

E. S. Polzik, J. Carri, H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[CrossRef] [PubMed]

Richardson, W. H.

W. H. Richardson, S. Machida, Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870 (1991).
[CrossRef] [PubMed]

Saito, S.

Y. Yamamoto, S. Saito, T. Mukai, “AM and FM quantum noise in semiconductor lasers. Part II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1994), p. 676.

Scifres, D. R.

Shevy, Y.

J. Kitching, A. Yariv, Y. Shevy, “Amplitude noise reduction in semiconductor lasers with weak, dispersive optical feedback,” Opt. Lett. 74, 1331–1333 (1994).
[CrossRef]

Šikula, J.

J. Šikula, P. Vašina, I. Hüttel, “The noise of the GaAlAs super-LED radiation,” Phys. Status Solidi A 111, 367–370 (1989).
[CrossRef]

Steel, D. G.

H. Wang, M. J. Freeman, D. G. Steel, “Squeezed light from injection-locked quantum well lasers,” Phys. Rev. Lett. 71, 3951–3954 (1993).
[CrossRef] [PubMed]

M. J. Freeman, H. Wang, D. G. Steel, R. Craig, D. R. Scifres, “Amplitude-squeezed light from quantum-well lasers,” Opt. Lett. 18, 379–381 (1993).
[CrossRef] [PubMed]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1994), p. 676.

Vašina, P.

J. Šikula, P. Vašina, I. Hüttel, “The noise of the GaAlAs super-LED radiation,” Phys. Status Solidi A 111, 367–370 (1989).
[CrossRef]

Wang, H.

M. J. Freeman, H. Wang, D. G. Steel, R. Craig, D. R. Scifres, “Amplitude-squeezed light from quantum-well lasers,” Opt. Lett. 18, 379–381 (1993).
[CrossRef] [PubMed]

H. Wang, M. J. Freeman, D. G. Steel, “Squeezed light from injection-locked quantum well lasers,” Phys. Rev. Lett. 71, 3951–3954 (1993).
[CrossRef] [PubMed]

Wu, L.

M. Xiao, L. Wu, H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[CrossRef] [PubMed]

Xiao, M.

M. Xiao, L. Wu, H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[CrossRef] [PubMed]

Yamamoto, Y.

S. Inoue, H. Ohzu, S. Machida, Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A. 46, 2757–2765 (1992).
[CrossRef] [PubMed]

W. H. Richardson, S. Machida, Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870 (1991).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025–4043 (1986).
[CrossRef] [PubMed]

Y. Yamamoto, S. Saito, T. Mukai, “AM and FM quantum noise in semiconductor lasers. Part II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

Yariv, A.

J. Kitching, A. Yariv, Y. Shevy, “Amplitude noise reduction in semiconductor lasers with weak, dispersive optical feedback,” Opt. Lett. 74, 1331–1333 (1994).
[CrossRef]

Fiberopt. Appl. Mag. (1)

V. McOmber, “Measuring relative intensity noise of a laser,” Fiberopt. Appl. Mag. 1, 21–26 (Spring, 1992).

IEEE J. Quantum Electron. (2)

Y. Yamamoto, S. Saito, T. Mukai, “AM and FM quantum noise in semiconductor lasers. Part II. Comparison of theoretical and experimental results for AlGaAs lasers,” IEEE J. Quantum Electron. QE-19, 47–58 (1983).
[CrossRef]

R. J. Fronen, “Facet reflectivity and low-frequency noise in the light output of LED and superradiant diodes,” IEEE J. Quantum Electron. 25, 1653–1658 (1989).
[CrossRef]

Opt. Lett. (2)

J. Kitching, A. Yariv, Y. Shevy, “Amplitude noise reduction in semiconductor lasers with weak, dispersive optical feedback,” Opt. Lett. 74, 1331–1333 (1994).
[CrossRef]

M. J. Freeman, H. Wang, D. G. Steel, R. Craig, D. R. Scifres, “Amplitude-squeezed light from quantum-well lasers,” Opt. Lett. 18, 379–381 (1993).
[CrossRef] [PubMed]

Phys. Rev. A (1)

Y. Yamamoto, S. Machida, O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025–4043 (1986).
[CrossRef] [PubMed]

Phys. Rev. A. (1)

S. Inoue, H. Ohzu, S. Machida, Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A. 46, 2757–2765 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

H. Wang, M. J. Freeman, D. G. Steel, “Squeezed light from injection-locked quantum well lasers,” Phys. Rev. Lett. 71, 3951–3954 (1993).
[CrossRef] [PubMed]

W. H. Richardson, S. Machida, Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867–2870 (1991).
[CrossRef] [PubMed]

M. Xiao, L. Wu, H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. 59, 278–281 (1987).
[CrossRef] [PubMed]

E. S. Polzik, J. Carri, H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. 68, 3020–3023 (1992).
[CrossRef] [PubMed]

Phys. Status Solidi A (1)

J. Šikula, P. Vašina, I. Hüttel, “The noise of the GaAlAs super-LED radiation,” Phys. Status Solidi A 111, 367–370 (1989).
[CrossRef]

Other (8)

M. Ohtsu, Highly Coherent Semiconductor Lasers (Artech, Boston, Mass., 1992), p. 18.

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), Vol. 1, p. 44.

Ref. 16, Vol. 2, p. 228.

Ref. 16, Vol. 2, pp. 180–181.

Ref. 16, Vol. 1, p. 160.

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers (Van Nostrand Reinhold, New York, 1993), pp. 285–294.

H. Haken, Light (North-Holland, Amsterdam, 1981), Vol. 1, pp. 285–295.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1994), p. 676.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup used to measure the low-frequency intensity noise of the Sharp LTO25MDO 30-mW laser diode.

Fig. 2
Fig. 2

Shot-noise density of a LED at 25 MHz is proportional to the dc voltage level. Experimental data points are shown as +’s and a least-squares fit by the solid line. The triangles represent data obtained with the beam focused too tightly onto the detector. At approximately 800 mV, the high intensity causes the detector to saturate.

Fig. 3
Fig. 3

The dc output of the photodiode is linear with optical power to greater than 1 V. The data, taken with several beam diameters, are shown by +’s.

Fig. 4
Fig. 4

Experimental results for the intensity noise normalized to the shot-noise level S o (ω)/SSNL at 25 MHz are shown as +’s, and the MSR is shown as a solid curve. These two quantities are anticorrelated: S o (ω)/SSNL decreases with injection current whereas the MSR increases with injection current. This is especially evident at R = 0.29 where mode hopping occurred.

Fig. 5
Fig. 5

Single-mode theory, shown by the solid curve, adequately fits experimental data points that have MSR’s of at least 20 dB (+’s). The circles are data points that have a mode suppression ratio of less than 20 dB. A least-squares fit gives β = 5.3 × 10−4 with a standard deviation σ = 1.1 × 10−5.

Fig. 6
Fig. 6

Power versus injection current plot (+’s) to determine N o (or n o N), the number of carriers needed to achieve transparency in the lasing medium. At I o = 20.5 mA, transparency has been attained; the laser begins to gain exponentially as shown where the dashed line intersects the solid line. Then, because the number of carriers increases linearly with I for I < I th and I th = 62.4 mA, we solve the relationship I o /I th = n o to obtain n o = 0.33.

Tables (1)

Tables Icon

Table 1 Parameters for a 788-nm Buried Heterostructure Lasera

Equations (28)

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P ˙ = ( G - γ ) P + R s p + F P ( t ) ,
N ˙ = I a / q - γ e N - G P + F N ( t ) ,
G = A ( N - N 0 ) - b P .
F i ( t ) = 0 ,
F i ( t ) F j ( t ) = 2 D i j δ ( t - t ) .
S P ( ω ) = l i m T δ P ( ω , T ) 2 .
l i m T 1 T [ F i * ( ω , T ) F j ( ω , T ) ] = 2 D i j ,
D P P = 2 R s p P ,
D P N = - 2 R s p P ,
D N N = 2 ( R s p P + γ e N ) .
S P ( ω ) = 2 R s p P [ P Γ N 2 + ( γ e N / R s p + P ) A 2 P 2 - 2 Γ N A P 2 ] ( Γ P Γ N + G A P ) 2 ,
Γ P = R s p P ,
Γ N = γ e + γ e N N + A P .
S o ( ω ) = ( ω L ν g α m ) 2 S P ( ω ) ,
S SNL = 2 ν g α m P ( ω L ) 2 .
S o ( ω ) S SNL = R s p ν g α m [ P Γ N 2 + ( γ e N / R s p + P ) A 2 P 2 - 2 Γ N A P 2 ] ( Γ P Γ N + G A P ) 2 .
R s p = β B N 2 V ,
R = I I t h - 1 ,
N = ( 1 - i l ) I t h q γ e ,
P = ( 1 - i l ) I t h R q G ,
γ e N = B V .
S o ( ω ) S SNL = ν g α m [ β B ( 1 - n o ) 2 ( 1 - i l ) 2 I t h 2 V G 2 q 2 γ e 2 R 2 + 1 G R ] .
n g = n - ν n ν .
G = ν g ( α m t + α i ) .
α m t = 1 2 L ln ( 1 R 1 R 2 ) .
R 1 = ( n 0 n s - n 1 2 ) 2 ( n 0 n s + n 1 2 ) 2 ,
α m = 1 2 L ln ( 1 R 1 ) .
P o = [ ω L ν g α m ] P ,

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