Abstract

Fluctuations of the stored energy and the emitted power of a semiconductor laser are derived by classical corpuscular optical theory. The fundamental noise sources are the shot noise associated with a field’s conversion to emitting or absorbing atoms and the mirror loss noise. The latter is taken into account in the form of partition noise forces linked to laser facet reflection. The theory permits the description of the nonclassical states of light, and its results agree with quantum theory. For quiet pumping conditions and for a high-reflection coated Fabry–Perot laser, 50% of internal photon noise suppression is obtained, whereas nonfluctuating optical output is possible for negligible internal loss. The influence of gain suppression on amplitude squeezing is discussed. The effect of attenuation on the propagation of laser fluctuations is studied by use of the concept of optical partition noise. This leads to the invariance of a suitably defined relative intensity noise, which becomes negative for sub-Poissonian photon statistics. The setup for the intensity noise measurement with the balanced detection technique is analyzed by use of optical partition noise.

© 1997 Optical Society of America

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  1. Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 14, 4025 (1986).
    [CrossRef]
  2. B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
    [CrossRef]
  3. D. D. Marcenac and J. E. Carroll, Proc. IEE Part J140, 157 (1993).
  4. J. L. Vey and P. Gallion, Opt. Lett. 20, 2018 (1995).
    [CrossRef] [PubMed]
  5. J. Arnaud, Opt. Quantum Electron. 27, 63 (1995).
    [CrossRef]
  6. R. Schimpe, Condensed Matter 52, 289 (1983).
  7. G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Laser (Van Nostrand Reinhold, New York, 1986).
  8. C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
    [CrossRef]
  9. R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).
  10. W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 22, 2867 (1991).
    [CrossRef]
  11. S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1989).
    [CrossRef]
  12. L. J. Freeman, H. Wang, D. G. Steel, R. Craig, and D. R. Scifres, Opt. Lett. 18, 379 (1993).
    [CrossRef] [PubMed]
  13. Yu. M. Golubev and I. V. Sokolov, Zh. Eksp. Teor. Fiz. 87, 804 (1984).
  14. J. Arnaud, Phys. Rev. A 45, 1775 (1992).
    [CrossRef] [PubMed]
  15. D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
    [CrossRef]
  16. J. Huang and L. W. Casperson, Opt. Quantum Electron. 25, 369 (1993).
    [CrossRef]
  17. M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
    [CrossRef]
  18. X. Pan, H. Olesen, B. Tromborg, and H. E. Lassen, Proc. IEEE J 139, 189 (1992).
  19. T. Takahashi and Y. Arakawa, IEEE Photon. Technol. Lett. 3, 106 (1991).
    [CrossRef]
  20. G. P. Agrawal, IEEE J. Quantum Electron. QE-23, 860 (1987).
    [CrossRef]
  21. Y. Arakawa and T. Takahashi, Electron. Lett. 25, 169 (1989).
    [CrossRef]
  22. O. Nilsson, A. Karlsson, and E. Berglind, Coherence, Amplification and Quantum Effects in Semiconductor laser (Wiley, New York, 1991), p. 88.
  23. S. Machida and Y. Yamamoto, Opt. Lett. 14, 1045 (1989).
    [CrossRef]
  24. H. P. Yuen and V. W. S. Chan, Opt. Lett. 8, 177 (1983).
    [CrossRef] [PubMed]

1995 (2)

1994 (2)

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
[CrossRef]

1993 (2)

1992 (2)

J. Arnaud, Phys. Rev. A 45, 1775 (1992).
[CrossRef] [PubMed]

X. Pan, H. Olesen, B. Tromborg, and H. E. Lassen, Proc. IEEE J 139, 189 (1992).

1991 (3)

T. Takahashi and Y. Arakawa, IEEE Photon. Technol. Lett. 3, 106 (1991).
[CrossRef]

M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
[CrossRef]

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 22, 2867 (1991).
[CrossRef]

1989 (3)

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1989).
[CrossRef]

S. Machida and Y. Yamamoto, Opt. Lett. 14, 1045 (1989).
[CrossRef]

Y. Arakawa and T. Takahashi, Electron. Lett. 25, 169 (1989).
[CrossRef]

1987 (1)

G. P. Agrawal, IEEE J. Quantum Electron. QE-23, 860 (1987).
[CrossRef]

1986 (1)

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 14, 4025 (1986).
[CrossRef]

1984 (1)

Yu. M. Golubev and I. V. Sokolov, Zh. Eksp. Teor. Fiz. 87, 804 (1984).

1983 (2)

1982 (1)

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, IEEE J. Quantum Electron. QE-23, 860 (1987).
[CrossRef]

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Laser (Van Nostrand Reinhold, New York, 1986).

Arakawa, Y.

T. Takahashi and Y. Arakawa, IEEE Photon. Technol. Lett. 3, 106 (1991).
[CrossRef]

Y. Arakawa and T. Takahashi, Electron. Lett. 25, 169 (1989).
[CrossRef]

Arnaud, J.

J. Arnaud, Opt. Quantum Electron. 27, 63 (1995).
[CrossRef]

J. Arnaud, Phys. Rev. A 45, 1775 (1992).
[CrossRef] [PubMed]

Berglind, E.

O. Nilsson, A. Karlsson, and E. Berglind, Coherence, Amplification and Quantum Effects in Semiconductor laser (Wiley, New York, 1991), p. 88.

Carroll, J. E.

D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
[CrossRef]

D. D. Marcenac and J. E. Carroll, Proc. IEE Part J140, 157 (1993).

Casperson, L. W.

J. Huang and L. W. Casperson, Opt. Quantum Electron. 25, 369 (1993).
[CrossRef]

Chan, V. W. S.

Craig, R.

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Laser (Van Nostrand Reinhold, New York, 1986).

Freeman, L. J.

Gallion, P.

Golubev, Yu. M.

Yu. M. Golubev and I. V. Sokolov, Zh. Eksp. Teor. Fiz. 87, 804 (1984).

Henry, C. H.

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

Huang, J.

J. Huang and L. W. Casperson, Opt. Quantum Electron. 25, 369 (1993).
[CrossRef]

Itaya, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1989).
[CrossRef]

Jauho, A.-P.

M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
[CrossRef]

Karlsson, A.

O. Nilsson, A. Karlsson, and E. Berglind, Coherence, Amplification and Quantum Effects in Semiconductor laser (Wiley, New York, 1991), p. 88.

Lassen, H. E.

X. Pan, H. Olesen, B. Tromborg, and H. E. Lassen, Proc. IEEE J 139, 189 (1992).

Lassen, H.-E.

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).

Machida, S.

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 22, 2867 (1991).
[CrossRef]

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1989).
[CrossRef]

S. Machida and Y. Yamamoto, Opt. Lett. 14, 1045 (1989).
[CrossRef]

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 14, 4025 (1986).
[CrossRef]

Marcenac, D. D.

D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
[CrossRef]

D. D. Marcenac and J. E. Carroll, Proc. IEE Part J140, 157 (1993).

Mork, J.

M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
[CrossRef]

Nilsson, O.

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 14, 4025 (1986).
[CrossRef]

O. Nilsson, A. Karlsson, and E. Berglind, Coherence, Amplification and Quantum Effects in Semiconductor laser (Wiley, New York, 1991), p. 88.

Olesen, H.

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

X. Pan, H. Olesen, B. Tromborg, and H. E. Lassen, Proc. IEEE J 139, 189 (1992).

M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
[CrossRef]

Pan, X.

X. Pan, H. Olesen, B. Tromborg, and H. E. Lassen, Proc. IEEE J 139, 189 (1992).

Richardson, W. H.

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 22, 2867 (1991).
[CrossRef]

Schimpe, R.

R. Schimpe, Condensed Matter 52, 289 (1983).

Scifres, D. R.

Sokolov, I. V.

Yu. M. Golubev and I. V. Sokolov, Zh. Eksp. Teor. Fiz. 87, 804 (1984).

Steel, D. G.

Takahashi, T.

T. Takahashi and Y. Arakawa, IEEE Photon. Technol. Lett. 3, 106 (1991).
[CrossRef]

Y. Arakawa and T. Takahashi, Electron. Lett. 25, 169 (1989).
[CrossRef]

Tromborg, B.

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

X. Pan, H. Olesen, B. Tromborg, and H. E. Lassen, Proc. IEEE J 139, 189 (1992).

M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
[CrossRef]

Uskov, A.

M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
[CrossRef]

Vey, J. L.

Wang, H.

Willatzen, M.

M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
[CrossRef]

Yamamoto, Y.

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 22, 2867 (1991).
[CrossRef]

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1989).
[CrossRef]

S. Machida and Y. Yamamoto, Opt. Lett. 14, 1045 (1989).
[CrossRef]

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 14, 4025 (1986).
[CrossRef]

Yuen, H. P.

Condensed Matter (1)

R. Schimpe, Condensed Matter 52, 289 (1983).

Electron. Lett. (1)

Y. Arakawa and T. Takahashi, Electron. Lett. 25, 169 (1989).
[CrossRef]

IEEE J. Quantum Electron. (4)

G. P. Agrawal, IEEE J. Quantum Electron. QE-23, 860 (1987).
[CrossRef]

C. H. Henry, IEEE J. Quantum Electron. QE-18, 259 (1982).
[CrossRef]

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

T. Takahashi and Y. Arakawa, IEEE Photon. Technol. Lett. 3, 106 (1991).
[CrossRef]

M. Willatzen, A. Uskov, J. Mork, H. Olesen, B. Tromborg, and A.-P. Jauho, IEEE Photon. Technol. Lett. 3, 606 (1991).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (2)

J. Arnaud, Opt. Quantum Electron. 27, 63 (1995).
[CrossRef]

J. Huang and L. W. Casperson, Opt. Quantum Electron. 25, 369 (1993).
[CrossRef]

Phys. Rev. A (2)

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 14, 4025 (1986).
[CrossRef]

J. Arnaud, Phys. Rev. A 45, 1775 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 22, 2867 (1991).
[CrossRef]

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1989).
[CrossRef]

Proc. IEEE J (1)

X. Pan, H. Olesen, B. Tromborg, and H. E. Lassen, Proc. IEEE J 139, 189 (1992).

Zh. Eksp. Teor. Fiz. (1)

Yu. M. Golubev and I. V. Sokolov, Zh. Eksp. Teor. Fiz. 87, 804 (1984).

Other (4)

D. D. Marcenac and J. E. Carroll, Proc. IEE Part J140, 157 (1993).

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Laser (Van Nostrand Reinhold, New York, 1986).

O. Nilsson, A. Karlsson, and E. Berglind, Coherence, Amplification and Quantum Effects in Semiconductor laser (Wiley, New York, 1991), p. 88.

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Figures (9)

Fig. 1
Fig. 1

Vacuum fluctuations and partition noise.

Fig. 2
Fig. 2

Noise propagation in an absorbing medium.

Fig. 3
Fig. 3

Shot-noise-normalized internal amplitude noise of a quietly pumped high-reflection-coated Fabry–Perot laser for different pump levels. r=I/Ith-1, R=0.7.

Fig. 4
Fig. 4

Normalized external intensity noise of a normally pumped high-reflection-coated Fabry-Perot laser for various values of the pumping rate.

Fig. 5
Fig. 5

Normalized external intensity noise for high-power-level, quiet pumping conditions and various values of internal loss. R=0.7.

Fig. 6
Fig. 6

Normalized external intensity noise at low frequency, for quiet pumping conditions, as a function of the mirror reflectivity and for various values of the internal loss.

Fig. 7
Fig. 7

Shot-noise-normalized external noise at low frequency as a function of εP̅ for high emitted power. R=0.7, αD =4cm-1.

Fig. 8
Fig. 8

Balanced detection scheme.

Fig. 9
Fig. 9

Difference spectrum Sp1-p2(ω) as a function of the transmission coeffecient T for different Sp(ω).

Equations (64)

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SI=4(kT/R),
ρ1(t)+ρ2(t)=ρ(t),ρ1¯+ρ2¯=ρ¯,
Δρ12¯=Δρ22¯=ρ¯R(1-R).
fρi(t)=0,fρi(t)fρi*(t-τ)=Δρi2¯δ(τ),i{1, 2},
Δn2(z+dz)¯=(1-αdz)2Δn2(z)¯+αdz(1-αdz)n(z)¯.
Sρ(ω, z+dz)=(1-αdz)2Sρ(ω, z)+αdz(1-αdz)ρ(z)¯.
Δn2(z)¯=F(z)n(z)¯,
F(z)=F(0)exp(-αz)+1-exp(-αz).
RIN(ω)=2 Sρ(ω, z)-ρ(z)¯ρ(z)¯2=2 Sρ(ω, z+dz)-ρ(z+dz)¯ρ(z+dz)¯2.
Pt=G-1τPP+FP(t),
Nt=Ie-GP-NτE+FN(t),
G=A(N-N0).
1τP=1τM+1τD,
1τM=-ln RτRT1-RτRT
1τD=cngαD
τRT=2 Lngc
G¯=1/τP,
G=S-AS.
nSP=S¯(S¯-AS¯)=S¯G¯=S¯τP.
A¯=(nSP-1)G¯.
ρ(t)=(1-R)P(t)τRT+fM(t)=P(t)τM+fM(t),
FP(t)=fS(t)-fD(t)-fM(t)-fA(t),
FN(t)=fI(t)+fA(t)-fS(t)-fE(t),
fi(t)fj*(t-τ)=2Dijδ(τ),
(ij)(M, S, P, A, I, N),
Dij=0,ij.
2DMM=P¯/tM,
2DDD=P¯/tD,
2DSS=P¯S¯=nspP¯/tP,
2DAA=P¯AS¯=(nsp-1)P¯/tP,
2DII=I¯/e,
2DEE=N¯/tE,
2DPP=2nSPP¯/τP,
2DNN=2nSPP¯/τP+2N¯/τE,
2DPN=-(2nSP-1)P¯/τP,
2DPP=2nSPP¯/τP,
2DNN=(2nSP-1)P¯/τP+N¯/τE,
2DPN=-(2nSP-1)P¯/τP.
δPˆ(ω)δNˆ(ω)=Δ-1(ω)jω+2/τR-(1/τP)ωR02τPjωFˆP(ω)FˆN(ω),
ωR02=AP¯/τP,
2/τR=AP¯+1/τE,
Δ(ω)=ωR02-ω2+2jω/τR,
SPP(ω)=2[(ω2+4/τR2)DPP(ω)+ωR04τP2DNN(ω)+4(ωR02τP/τR)DPN(ω)]|Δ(ω)|-2.
SPP(ω)=2 P¯τP(AP¯)2+ω2nSP|Δ(ω)|2.
SPP(0)τP2=G¯P¯+P¯τP=2DPP+2DNN+4DPN.
[SPP(0)]quietpump=1/2[SPP(0)]normalpump.
δρˆ(ω)=δPˆ(ω)τM+fˆM(ω).
Sρρ(ω)=SPP(ω)τM2+[1-4ωR02/τMτR|Δ|2]2DMM.
Sρρ(0)=P¯/τM=ρ¯.
Sρρ(0)=ρ¯(1-τP/τM)=ρ¯τP/τD.
G=A(N-N0)(1-εP¯),
δPˆ(ω)=[(jω+2/τRε)FˆP(ω)+{τP/[1+K(P¯)]}ωR02FˆN(ω)]Δε-1(ω),
K(P¯)=εP¯/(1-εP¯),
2τRε=2τR-AεP¯2,
Δε(ω)=ωR02+2K(P¯)/(τRετP)-ω2-jω[2/τRε+K(P¯)/τP].
[SPPε(0)]quietpump=1/2[SPPε(0)]normalpump=P¯τP (1-εP¯)2(1+εP¯)2.
Sρρε(0)ρ¯1-4εP¯τPτMforsmallεP¯.
Sρρε(0)ρ¯Sρρ(0)ρ¯+2 τPτM(εP¯)2forsmallεP¯.
ρ¯1=(1-T)ρ¯,ρ¯2=Tρ¯.
Sρ1(ω)=(1T)2Sρ(ω)reflection of initial fluctuation+T(1T)ρ¯added partition noise
Sρ2(ω)=T2Sρ(ω)transmission of initial fluctuation+T(1T)ρ¯added partition noise
Sρ1+ρ2(ω)=Sρ(ω),
Sρ1-ρ2(ω)=(2T-1)2Sρ(ω)+4T(1-T)ρ¯.
RIN(ω)=2 Sρ1+ρ2(ω)-Sρ1-ρ2(ω)(ρ1¯+ρ2¯)2.

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