Abstract

An analytic expression for the phase noise spectrum is estimated when two arbitrary longitudinal modes are selected for beating from the output of an actively modelocked laser. A separate experiment confirmed the theory qualitatively. It was found that two-mode beating posseses more phase noise than the beating involving the entire mode spectrum, especially at low offset frequency, even though two mode beating noise is decoupled from the RF oscillator noise to the first order.

© 2005 Optical Society of America

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References

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  1. A. Nirmalathas, C. Lim, D. Novak, R. B. Waterhouse, and D. Castleford, “The merging of photonic and radio technologies,” Conference Proceedings. OECC/IOOC 2001 Conference. Incorporating ACOFT, 2001, 227–230, (2001).
  2. A. S. Bhushan, P. Kelkar, and B. Jalali, “30 Gsamples/s time-stretch analog-to-digital converter,” Electron. Lett. 36, 1526–1527 (2000).
    [Crossref]
  3. B. K. Mathason and P. J. Delfyett, “Pulsed injection locking dynamics of passively mode-locked external-cavity semiconductor laser systems for all-optical clock recovery,” J. Lightwave Technol. 18, 1111–1120 (2000).
    [Crossref]
  4. R.T. Logan, “Photonic radio-frequency synthesizer,” Proc. SPIE 2844, 312–317 (1996).
    [Crossref]
  5. T. Yilmaz, C.M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14, 1608–1610 (2002).
    [Crossref]
  6. D. R. Hjelme and A. R. Mickelson, “Theory of Timing Jitter in Actively Mode-Locked Lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
    [Crossref]
  7. P. T. Ho, “Phase and Amplitude Fluctuations in a Mode-Locked Laser,” IEEE J. Quantum Electron. 21, 1806–1813 (1985).
    [Crossref]
  8. D. von der Linde, “Characterization of the Noise in Continuously Operating Mode-Locked Lasers,” Appl. Phys. B. 39, 201–217 (1986).
    [Crossref]

2002 (1)

T. Yilmaz, C.M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14, 1608–1610 (2002).
[Crossref]

2000 (2)

1996 (1)

R.T. Logan, “Photonic radio-frequency synthesizer,” Proc. SPIE 2844, 312–317 (1996).
[Crossref]

1992 (1)

D. R. Hjelme and A. R. Mickelson, “Theory of Timing Jitter in Actively Mode-Locked Lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
[Crossref]

1986 (1)

D. von der Linde, “Characterization of the Noise in Continuously Operating Mode-Locked Lasers,” Appl. Phys. B. 39, 201–217 (1986).
[Crossref]

1985 (1)

P. T. Ho, “Phase and Amplitude Fluctuations in a Mode-Locked Laser,” IEEE J. Quantum Electron. 21, 1806–1813 (1985).
[Crossref]

Abeles, J. H.

T. Yilmaz, C.M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14, 1608–1610 (2002).
[Crossref]

Bhushan, A. S.

A. S. Bhushan, P. Kelkar, and B. Jalali, “30 Gsamples/s time-stretch analog-to-digital converter,” Electron. Lett. 36, 1526–1527 (2000).
[Crossref]

Castleford, D.

A. Nirmalathas, C. Lim, D. Novak, R. B. Waterhouse, and D. Castleford, “The merging of photonic and radio technologies,” Conference Proceedings. OECC/IOOC 2001 Conference. Incorporating ACOFT, 2001, 227–230, (2001).

Delfyett, P. J.

T. Yilmaz, C.M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14, 1608–1610 (2002).
[Crossref]

B. K. Mathason and P. J. Delfyett, “Pulsed injection locking dynamics of passively mode-locked external-cavity semiconductor laser systems for all-optical clock recovery,” J. Lightwave Technol. 18, 1111–1120 (2000).
[Crossref]

DePriest, C.M.

T. Yilmaz, C.M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14, 1608–1610 (2002).
[Crossref]

Hjelme, D. R.

D. R. Hjelme and A. R. Mickelson, “Theory of Timing Jitter in Actively Mode-Locked Lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
[Crossref]

Ho, P. T.

P. T. Ho, “Phase and Amplitude Fluctuations in a Mode-Locked Laser,” IEEE J. Quantum Electron. 21, 1806–1813 (1985).
[Crossref]

Jalali, B.

A. S. Bhushan, P. Kelkar, and B. Jalali, “30 Gsamples/s time-stretch analog-to-digital converter,” Electron. Lett. 36, 1526–1527 (2000).
[Crossref]

Kelkar, P.

A. S. Bhushan, P. Kelkar, and B. Jalali, “30 Gsamples/s time-stretch analog-to-digital converter,” Electron. Lett. 36, 1526–1527 (2000).
[Crossref]

Lim, C.

A. Nirmalathas, C. Lim, D. Novak, R. B. Waterhouse, and D. Castleford, “The merging of photonic and radio technologies,” Conference Proceedings. OECC/IOOC 2001 Conference. Incorporating ACOFT, 2001, 227–230, (2001).

Logan, R.T.

R.T. Logan, “Photonic radio-frequency synthesizer,” Proc. SPIE 2844, 312–317 (1996).
[Crossref]

Mathason, B. K.

Mickelson, A. R.

D. R. Hjelme and A. R. Mickelson, “Theory of Timing Jitter in Actively Mode-Locked Lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
[Crossref]

Nirmalathas, A.

A. Nirmalathas, C. Lim, D. Novak, R. B. Waterhouse, and D. Castleford, “The merging of photonic and radio technologies,” Conference Proceedings. OECC/IOOC 2001 Conference. Incorporating ACOFT, 2001, 227–230, (2001).

Novak, D.

A. Nirmalathas, C. Lim, D. Novak, R. B. Waterhouse, and D. Castleford, “The merging of photonic and radio technologies,” Conference Proceedings. OECC/IOOC 2001 Conference. Incorporating ACOFT, 2001, 227–230, (2001).

Turpin, T.

T. Yilmaz, C.M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14, 1608–1610 (2002).
[Crossref]

von der Linde, D.

D. von der Linde, “Characterization of the Noise in Continuously Operating Mode-Locked Lasers,” Appl. Phys. B. 39, 201–217 (1986).
[Crossref]

Waterhouse, R. B.

A. Nirmalathas, C. Lim, D. Novak, R. B. Waterhouse, and D. Castleford, “The merging of photonic and radio technologies,” Conference Proceedings. OECC/IOOC 2001 Conference. Incorporating ACOFT, 2001, 227–230, (2001).

Yilmaz, T.

T. Yilmaz, C.M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14, 1608–1610 (2002).
[Crossref]

Appl. Phys. B. (1)

D. von der Linde, “Characterization of the Noise in Continuously Operating Mode-Locked Lasers,” Appl. Phys. B. 39, 201–217 (1986).
[Crossref]

Electron. Lett. (1)

A. S. Bhushan, P. Kelkar, and B. Jalali, “30 Gsamples/s time-stretch analog-to-digital converter,” Electron. Lett. 36, 1526–1527 (2000).
[Crossref]

IEEE J. Quantum Electron. (2)

D. R. Hjelme and A. R. Mickelson, “Theory of Timing Jitter in Actively Mode-Locked Lasers,” IEEE J. Quantum Electron. 28, 1594–1606 (1992).
[Crossref]

P. T. Ho, “Phase and Amplitude Fluctuations in a Mode-Locked Laser,” IEEE J. Quantum Electron. 21, 1806–1813 (1985).
[Crossref]

IEEE Photon. Technol. Lett. (1)

T. Yilmaz, C.M. DePriest, T. Turpin, J. H. Abeles, and P. J. Delfyett, “Toward a photonic arbitrary waveform generator using a modelocked external cavity semiconductor laser,” IEEE Photon. Technol. Lett. 14, 1608–1610 (2002).
[Crossref]

J. Lightwave Technol. (1)

Proc. SPIE (1)

R.T. Logan, “Photonic radio-frequency synthesizer,” Proc. SPIE 2844, 312–317 (1996).
[Crossref]

Other (1)

A. Nirmalathas, C. Lim, D. Novak, R. B. Waterhouse, and D. Castleford, “The merging of photonic and radio technologies,” Conference Proceedings. OECC/IOOC 2001 Conference. Incorporating ACOFT, 2001, 227–230, (2001).

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Figures (2)

Fig. 1.
Fig. 1.

Optical intensity spectra for the entire modes (a), two selected modes (b).

Fig. 2.
Fig. 2.

Single sideband phase noise measurement for both full-mode and two-mode beating cases. (Dotted lines are the theory for lower limit, upper limit and fitted two-mode beat noise with C=5×10-5.)

Tables (1)

Tables Icon

Table 1. Parameters used in the noise calculation.

Equations (13)

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E n = E n ( 0 ) · e i θ n , θ n 1
θ n ( t ) θ ( t , x ) = p = 0 A p ( t ) · H p ( x )
I ( t ) = I o k , l exp [ ( k 2 + l 2 ) N 2 ] · exp [ i l ω m · ( t + 1 ω m l ( θ n θ m ) ) ]
I ( t ) = I o 2 π N l exp [ l 2 N 2 ] · exp [ i l ω m · { t + J ( t ) } ]
J ( t ) = 2 ω m N p = 0 A p ( t ) z H p ( z )
z H p ( z ) = k [ exp ( k 2 2 N 2 ) · z H p ( z ) ] k exp ( k 2 2 N 2 )
I ( t ) = I o exp [ ( k 2 + 1 ) N 2 ] · exp [ i ω m · ( t + 1 ω m ( θ n θ n 1 ) ) ]
J ( t ) = 1 ω m p = 0 A p ( t ) ( H p ( n ) H p ( n 1 ) )
J ( t ) = 1 ω m A 0 ( t )
J ( t ) = [ 1 ω m A 0 ( t ) ] · C + [ 2 ω m N p = 0 A p ( t ) z H p ( z ) ] · ( 1 C )
L ( f ) = 2 Δ ω st · l 2 N ( γ N 2 ) 2 ( γ N 2 ) 2 4 π 2 f 2 + ( γ N 2 ) 2 { 1 + N 2 2 ( Δ ω γ N 2 ) 2 ( 2 γ N 2 ) 2 4 π 2 f 2 + ( 2 γ N 2 ) 2 + γ / N 2 ( 2 2 / N ) ( Δ ω st γ N 2 ) S ϕ ( f ) }
L ( f ) = 2 Δ ω st N ( γ N 2 ) 2 ( γ N 2 ) 2 4 π 2 f 2 { 1 + N 2 Δ ω 2 4 π 2 f 2 + ( γ N 2 ) 2 }
S ϕ ( f ) = S 0 ( 1 + ( f 0 f ) β ) f 1 2 f 2 + f 1 2

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