Abstract

We present the theory and measurements of the amplitude noise spectrum from a semiconductor laser with weak optical feedback (Pfb/Pout ≈ 10−6) from an external cavity containing an element of dispersive loss. The laser noise is found to be reduced over most of the low-frequency spectrum, although an increase in the noise is observed at frequencies corresponding to multiples of the external-cavity free spectral range. The low-frequency noise reduction closely follows theoretical predictions, and a reduction of as much as 7 dB is measured at an injection current of 1.5 times the threshold current. The potential of this method for contributing to the production of amplitude-squeezed light is discussed.

© 1994 Optical Society of America

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References

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1993

1992

1990

1987

1986

Y. Yamamoto, S. Machida, O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

1980

R. Lang, K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

1969

H. Haug, Phys. Rev. 184, 338 (1969).
[CrossRef]

Craig, R.

Dahmani, B.

Drullinger, R.

Freeman, M. J.

Haug, H.

H. Haug, Phys. Rev. 184, 338 (1969).
[CrossRef]

Hollberg, L.

Iannelli, J.

Kitching, J.

Kobayashi, K.

R. Lang, K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Lang, R.

R. Lang, K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Machida, S.

Y. Yamamoto, S. Machida, O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

Nabiev, R.

Nilsson, O.

Y. Yamamoto, S. Machida, O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

Richardson, W. H.

W. H. Richardson, R. M. Shelby, Phys. Rev. Lett. 64, 400 (1990).
[CrossRef] [PubMed]

Scifres, D. R.

Shelby, R. M.

W. H. Richardson, R. M. Shelby, Phys. Rev. Lett. 64, 400 (1990).
[CrossRef] [PubMed]

Shevy, Y.

Steel, D. G.

Vahala, K.

Wang, H.

Yamamoto, Y.

Y. Yamamoto, S. Machida, O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

Yariv, A.

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Figures (4)

Fig. 1
Fig. 1

Theoretical prediction of the noise reduction at 116 MHz for different feedback coupling rates (in units of 109 s−1) in a pump-suppressed semiconductor laser. The inset shows the squeezing enhancement at a pump rate of R = il/ith − 1 = 4. The parameter values used are τp = τpe = 9.1 × 10−12 s, τsp = 4.3 × 10−9 s, nsp = 1.25, β = 10−5, α = −3.4, τ = 1.4 × 10−8 s, ηint = 0.85, and ηext = 0.9.

Fig. 2
Fig. 2

Experimental setup: LD, laser diode; L’s, lenses; BS’s, beam splitters; M’s, mirrors; P’s, polarizers; D’s, detectors; ND, neutral-density filter; PZT, piezoelectric transducer; Isol., isolator; A, amplifier; B, magnetic field. The amplitude noise power is measured at D3, and the feedback power is monitored at D1.

Fig. 3
Fig. 3

Frequency dependence of the amplitude noise power at an injection current of 76 mA for free-running (trace A), Pfb/Pout = 4 × 10−7 (trace B), and SQL (trace C) conditions.

Fig. 4
Fig. 4

Amplitude noise power at 116 MHz, normalized to the SQL, as a function of feedback power at injection currents of 76 mA (filled circles) and 97 mA (open squares). The solid curves are the theoretical predictions based on Eq. (4).

Equations (5)

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d A ^ ( t ) d t = - 1 2 [ 1 τ p + 2 i ( ω L - ω 0 ) - ω μ 2 ( χ i - i χ r ) ] × A ^ ( t ) + G ^ ( t ) + g ^ ( t ) + ( 1 τ pe ) 1 / 2 f e ( t ) + κ exp ( i ϕ m ) r ^ ( t - τ ) ,
d N c ( t ) d t = P - N c ( t ) τ sp - ω μ 2 χ i A ^ A ^ - ω μ 2 χ i + Γ p ( t ) + Γ sp ( t ) + Γ ( t ) ,
r ^ ( t ) = - f ^ e ( t ) + 1 / τ pe A ^ ( t ) ,
P Δ r ( Ω ) = 4 A 3 2 1 + C i + α C r 2 τ pe D 2 ( 4 k T q 2 R s + N c 0 τ sp ) + ( Ω 2 + A 1 2 ) 1 + C i 2 τ pe τ p 0 D 2 + 2 n sp ( Ω 2 + A 1 2 ) τ p τ pe D 2 C r 2 + | 1 - ( i Ω - A 1 ) ( 1 + C i ) τ pe D | 2 + ( 2 n sp - 1 ) 1 + C i 2 τ p τ pe D 2 | ( i Ω - A 1 ) - 2 A 0 A 3 ( 1 + α C r 1 + C i ) | 2 .
C i ( Ω ) = { [ 1 - exp ( - i Ω τ ) ] / ( i Ω τ ) } κ 0 τ cos ( ϕ 0 ) , C r ( Ω ) = - { [ 1 - exp ( - i Ω τ ) ] / ( i Ω τ ) } κ 0 τ sin ( ϕ 0 ) , D ( Ω ) = i Ω ( i Ω - A 1 ) [ ( 1 + C i ) 2 + C r 2 ] - A 2 A 3 ( 1 + C i + α C r ) , A 1 = - ( 1 / τ sp + 1 / τ st ) , A 2 = - 2 A 0 E cv / n sp , A 3 = 1 / ( 2 A 0 τ st ) ,

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