Abstract

We present an experimental observation of phase locking effects in the intensity noise spectrum of a semiconductor laser. These noise correlations are created in the medium by coherent carrier-population oscillations induced by the beatnote between the lasing and non-lasing modes of the laser. This phase locking leads to a modification of the intensity noise profile at around the cavity free-spectral-range value. The noise correlations are evidenced by varying the relative phase shift between the laser mode and the non-lasing adjacent side modes.

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).
  2. G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge, 2010), pp. 255–260.
  3. G. Baili, F. Bretenaker, M. Alouini, L. Morvan, D. Dolfi, and I. Sagnes, “Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers,” J. Lightwave Technol. 26, 952–961 (2008).
    [CrossRef]
  4. M. Harris, R. Loudon, T. J. Shepherd, and J. M. Vaughan, “Noise cancellation in laser emission,” Phys. Rev. Lett. 69, 2360–2363 (1992).
    [CrossRef] [PubMed]
  5. R. Loudon, C. J. Shackleton, M. Harris, T. J. Shepherd, and J. M. Vaughan, “Gain and noise in subthreshold longitudinal laser modes,” Phys. Rev. A. 50, 658–674 (1994).
    [CrossRef] [PubMed]
  6. A. El Amili, B.-X. Miranda, F. Goldfarb, G. Baili, G. Beaudoin, I. Sagnes, F. Bretenaker, and M. Alouini, “Observation of slow light in the noise spectrum of a vertical external cavity surface-emitting laser,” Phys. Rev. Lett. 105, 223902 (2010).
    [CrossRef]
  7. A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, “High power single-frequency continuously-tunable compact extended-cavity semiconductor laser,” Opt. Express 17, 9503–9508 (2009).
    [CrossRef] [PubMed]
  8. A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in a semiconductor laser,” IEEE J. Quantum Electron.QE-11, 510–515 (1975).
    [CrossRef]
  9. G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147–159 (1988).
    [CrossRef]
  10. M. P. van Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Opt. Commun. 110, 137–140 (1994).
    [CrossRef]
  11. V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express 18, 5008–5014 (2010).
    [CrossRef] [PubMed]

2010

A. El Amili, B.-X. Miranda, F. Goldfarb, G. Baili, G. Beaudoin, I. Sagnes, F. Bretenaker, and M. Alouini, “Observation of slow light in the noise spectrum of a vertical external cavity surface-emitting laser,” Phys. Rev. Lett. 105, 223902 (2010).
[CrossRef]

V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express 18, 5008–5014 (2010).
[CrossRef] [PubMed]

2009

2008

1994

M. P. van Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Opt. Commun. 110, 137–140 (1994).
[CrossRef]

R. Loudon, C. J. Shackleton, M. Harris, T. J. Shepherd, and J. M. Vaughan, “Gain and noise in subthreshold longitudinal laser modes,” Phys. Rev. A. 50, 658–674 (1994).
[CrossRef] [PubMed]

1992

M. Harris, R. Loudon, T. J. Shepherd, and J. M. Vaughan, “Noise cancellation in laser emission,” Phys. Rev. Lett. 69, 2360–2363 (1992).
[CrossRef] [PubMed]

1988

Agrawal, G. P.

Alouini, M.

Aspect, A.

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge, 2010), pp. 255–260.

Baili, G.

Beaudoin, G.

A. El Amili, B.-X. Miranda, F. Goldfarb, G. Baili, G. Beaudoin, I. Sagnes, F. Bretenaker, and M. Alouini, “Observation of slow light in the noise spectrum of a vertical external cavity surface-emitting laser,” Phys. Rev. Lett. 105, 223902 (2010).
[CrossRef]

A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, “High power single-frequency continuously-tunable compact extended-cavity semiconductor laser,” Opt. Express 17, 9503–9508 (2009).
[CrossRef] [PubMed]

Bogatov, A. P.

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in a semiconductor laser,” IEEE J. Quantum Electron.QE-11, 510–515 (1975).
[CrossRef]

Bretenaker, F.

Dolfi, D.

El Amili, A.

A. El Amili, B.-X. Miranda, F. Goldfarb, G. Baili, G. Beaudoin, I. Sagnes, F. Bretenaker, and M. Alouini, “Observation of slow light in the noise spectrum of a vertical external cavity surface-emitting laser,” Phys. Rev. Lett. 105, 223902 (2010).
[CrossRef]

Eliseev, P. G.

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in a semiconductor laser,” IEEE J. Quantum Electron.QE-11, 510–515 (1975).
[CrossRef]

Fabre, C.

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge, 2010), pp. 255–260.

Garnache, A.

Ghosh, R.

Goldfarb, F.

V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express 18, 5008–5014 (2010).
[CrossRef] [PubMed]

A. El Amili, B.-X. Miranda, F. Goldfarb, G. Baili, G. Beaudoin, I. Sagnes, F. Bretenaker, and M. Alouini, “Observation of slow light in the noise spectrum of a vertical external cavity surface-emitting laser,” Phys. Rev. Lett. 105, 223902 (2010).
[CrossRef]

Grynberg, G.

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge, 2010), pp. 255–260.

Harris, M.

R. Loudon, C. J. Shackleton, M. Harris, T. J. Shepherd, and J. M. Vaughan, “Gain and noise in subthreshold longitudinal laser modes,” Phys. Rev. A. 50, 658–674 (1994).
[CrossRef] [PubMed]

M. Harris, R. Loudon, T. J. Shepherd, and J. M. Vaughan, “Noise cancellation in laser emission,” Phys. Rev. Lett. 69, 2360–2363 (1992).
[CrossRef] [PubMed]

Hendriks, R. F. M.

M. P. van Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Opt. Commun. 110, 137–140 (1994).
[CrossRef]

Laurain, A.

Loudon, R.

R. Loudon, C. J. Shackleton, M. Harris, T. J. Shepherd, and J. M. Vaughan, “Gain and noise in subthreshold longitudinal laser modes,” Phys. Rev. A. 50, 658–674 (1994).
[CrossRef] [PubMed]

M. Harris, R. Loudon, T. J. Shepherd, and J. M. Vaughan, “Noise cancellation in laser emission,” Phys. Rev. Lett. 69, 2360–2363 (1992).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).

Miranda, B.-X.

A. El Amili, B.-X. Miranda, F. Goldfarb, G. Baili, G. Beaudoin, I. Sagnes, F. Bretenaker, and M. Alouini, “Observation of slow light in the noise spectrum of a vertical external cavity surface-emitting laser,” Phys. Rev. Lett. 105, 223902 (2010).
[CrossRef]

V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express 18, 5008–5014 (2010).
[CrossRef] [PubMed]

Morvan, L.

Myara, M.

Pal, V.

Sagnes, I.

Shackleton, C. J.

R. Loudon, C. J. Shackleton, M. Harris, T. J. Shepherd, and J. M. Vaughan, “Gain and noise in subthreshold longitudinal laser modes,” Phys. Rev. A. 50, 658–674 (1994).
[CrossRef] [PubMed]

Shepherd, T. J.

R. Loudon, C. J. Shackleton, M. Harris, T. J. Shepherd, and J. M. Vaughan, “Gain and noise in subthreshold longitudinal laser modes,” Phys. Rev. A. 50, 658–674 (1994).
[CrossRef] [PubMed]

M. Harris, R. Loudon, T. J. Shepherd, and J. M. Vaughan, “Noise cancellation in laser emission,” Phys. Rev. Lett. 69, 2360–2363 (1992).
[CrossRef] [PubMed]

Sverdlov, B. N.

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in a semiconductor laser,” IEEE J. Quantum Electron.QE-11, 510–515 (1975).
[CrossRef]

Trofimoff, P.

van der Poel, C. J.

M. P. van Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Opt. Commun. 110, 137–140 (1994).
[CrossRef]

van Exter, M. P.

M. P. van Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Opt. Commun. 110, 137–140 (1994).
[CrossRef]

Vaughan, J. M.

R. Loudon, C. J. Shackleton, M. Harris, T. J. Shepherd, and J. M. Vaughan, “Gain and noise in subthreshold longitudinal laser modes,” Phys. Rev. A. 50, 658–674 (1994).
[CrossRef] [PubMed]

M. Harris, R. Loudon, T. J. Shepherd, and J. M. Vaughan, “Noise cancellation in laser emission,” Phys. Rev. Lett. 69, 2360–2363 (1992).
[CrossRef] [PubMed]

Woerdman, J. P.

M. P. van Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Opt. Commun. 110, 137–140 (1994).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Commun.

M. P. van Exter, R. F. M. Hendriks, J. P. Woerdman, and C. J. van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Opt. Commun. 110, 137–140 (1994).
[CrossRef]

Opt. Express

Phys. Rev. A.

R. Loudon, C. J. Shackleton, M. Harris, T. J. Shepherd, and J. M. Vaughan, “Gain and noise in subthreshold longitudinal laser modes,” Phys. Rev. A. 50, 658–674 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. El Amili, B.-X. Miranda, F. Goldfarb, G. Baili, G. Beaudoin, I. Sagnes, F. Bretenaker, and M. Alouini, “Observation of slow light in the noise spectrum of a vertical external cavity surface-emitting laser,” Phys. Rev. Lett. 105, 223902 (2010).
[CrossRef]

M. Harris, R. Loudon, T. J. Shepherd, and J. M. Vaughan, “Noise cancellation in laser emission,” Phys. Rev. Lett. 69, 2360–2363 (1992).
[CrossRef] [PubMed]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge, 2010), pp. 255–260.

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in a semiconductor laser,” IEEE J. Quantum Electron.QE-11, 510–515 (1975).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Experimental set-up used to measure and analyze the intensity noise spectrum of our VECSEL. OFR: optical isolator based on a Faraday rotator. PBS: polarization beam splitter; BS: beam splitter; SC: Servo-control; D: photodiode; FP1, FP2: Fabry-Perot interferometers; OSC: oscilloscope; S1, S2: shutters used to cut the beam; RFA: radio frequency amplifier; ESA: electronic spectrum analyzer. Inset: Sketch of the laser optical spectrum. p = 0 labels the lasing mode while p ≠ 0 holds for the non-lasing side modes.

Fig. 2
Fig. 2

(a) Round-trip gain versus side mode frequency detuning νν 0. The thin line is the unsaturated gain. The dashed line is the saturated gain for the light at ν 0. The full and dotted-dashed lines are the gains seen by the side modes for α = 0 and α = 7, respectively. (b) Round-trip phase modification experienced by the side modes for α = 0 (full line) and α = 7 (dotted-dashed line).

Fig. 3
Fig. 3

Intensity noise spectra at frequencies close to the successive harmonics of the resonator FSR |p|Δ. The beat note at Δ (upper left spectrum) shows an intensity noise profile completely different from the spectra taken at higher beat frequencies. The spectrum at Δ ≈ 1.5 GHz (p = ±1) is fitted by a coherent sum of Lorentzian profile by using the expression of Eq. (5). By contrast, at higher beat frequencies, the spectra for p = ±2, ±3, ±4 are fitted by a simple incoherent sum of two Lorentzian profiles as in Eq. (4). For these spectra, the laser output power is 20 mW.

Fig. 4
Fig. 4

Theoretical and experimental evolutions of the frequency shift δfp as a function of the frequency shift |p|Δ of the side modes. The theoretical evolution is calculated with the same parameters as in Fig. 2. The experimental results vary by about 20 % from acquisition to acquisition, due to changes in the operation point of the laser.

Fig. 5
Fig. 5

(a) Principle of the filtering of the side modes using the transmission of a low-finesse Fabry-Perot cavity. (b) Noise spectrum after transmission of the laser beam by the Fabryt-Perot cavity FP1. The spectra labeled (1), (2), and (3) are obtained with the cavity resonance frequency tuned on the frequencies of modes p = 0, −1, and +1, respectively. The spectra labeled (2) and (3) are fitted by Lorentzians. The fit of the spectrum labeled (1) leads to Φ = 2.75 rad.

Fig. 6
Fig. 6

Noise spectra recorded around the FSR Δ ≈ 1.5 GHz and obtained by varying the phase shift ϕ FP r upon reflection on FP2. Each spectrum is fitted using Φ′ instead of Φ in Eq. (5) and using Eq. (7) with Φ = 3.5 rad, leading to the determination of ϕ FP r .

Fig. 7
Fig. 7

Evolution of the phase shift ϕ FP r created by reflection on cavity FP2 versus reflection coefficient R. The full line is theoretical and the dots are extracted from fits of the experimental data like the ones of Fig. 6.

Fig. 8
Fig. 8

(a) 3D representation of the fits extracted from Fig. 6, plus an extra one which is not shown in Fig. 6. (b) Theoretical evolution of the noise spectrum based on Eq. (5). The values of the parameters used here are those extracted from the first spectrum of Fig. 6.

Equations (7)

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δ f p ν 0 L m L + n 0 L m ( δ n p + δ n p ) ,
g ( ν ) = g 0 1 + 𝒮 { 1 𝒮 [ ( 1 + 𝒮 ) + α 2 π ( ν 0 ν ) τ c ] ( 1 + 𝒮 ) 2 + [ 2 π ( ν 0 ν ) τ c ] 2 } ,
δ n ( ν ) = c 4 π ν 0 g 0 𝒮 1 + 𝒮 2 π ( ν 0 ν ) τ c + α ( 1 + 𝒮 ) ( 1 + 𝒮 ) 2 + [ 2 π ( ν 0 ν ) τ c ] 2 ,
y = | A 1 γ 1 2 i × 2 π ( f f 1 ) + γ 1 | 2 + | A 1 γ 1 2 i × 2 π ( f f 1 ) + γ 1 | 2 ,
y = | A 1 γ 1 2 i × 2 π ( f f 1 ) + γ 1 + A 1 γ 1 e i Φ 2 i × 2 π ( f f 1 ) + γ 1 | 2 .
Φ = 2 ϕ 0 ( ϕ 1 + ϕ 1 ) ,
Φ = 2 ( ϕ 0 ϕ FP r ) ( ϕ 1 + ϕ 1 ) = Φ 2 ϕ FP r .

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