Abstract

The response of an Er/Yb-codoped waveguide ring laser to a sinusoidally modulated pump power is studied. Experimentally, resonance peaks are observed and their dependences on the average pump power and the modulation index are analyzed. For high modulation indexes bistable behaviour is found. Numerically, a good agreement is obtained for the resonance peak frequencies by using a straightforward approximate model and assuming a dependence on the average pump power of the macroscopic Yb⇒Er energy-transfer coefficient. This dependence can be related to these mechanisms’ performance for high doping and pump levels when examined in a microscopic statistical formalism.

© 2007 Optical Society of America

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  1. N C. Becker, T. Oesselke, J. Pandavenes, R. Ricken, K. Rockhausen, G, Schreiber, W. Sohler, H. Suche, R. Wessel, S. Balsamo, I. Montrosset and D. Sciancalepore, "Advanced Ti:LiNbO3 waveguide lasers," IEEE J. Select. Top. Quantum Electron. 6, 101-110 (2000).
    [CrossRef]
  2. J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt and R. Sauerbrey, "Energy transfer and upconversion in erbium-ytterbium-doped fluoride phosphate glasses," Appl. Phys. B 74, 233-236 (2002).
    [CrossRef]
  3. D. Khoptyar, S. Sergeyev and B. Jaskorzynska, "Homogeneous upconversion in Er-doped fibers under steady state excitation: analytical model and its Monte Carlo verification," J. Opt. Soc. Am. B 22, 582-590 (2005).
    [CrossRef]
  4. J. A. Lázaro, J. A. Vallés and M. A. Rebolledo, "Determination of emission and absorption cross-sections of Er3+ in LiNbO3 waveguides from transversal fluorescence spectra," Pure App. Opt. 7, 1363-71 (1998).
    [CrossRef]
  5. J. A. Vallés, J.A. Lázaro and M.A. Rebolledo, "Analysis of Competing Mechanisms in Transitions Between Excited States in Er-Doped Integrated Waveguides," IEEE J. Quantum Electron. 38, 318-323 (2002)
    [CrossRef]
  6. J. A. Vallés, M. A. Rebolledo and J. Cortés, "Full characterization of packaged Er-Yb-codoped phosphate glass waveguides," IEEE J. Quantum Electron. 42, 152-159 (2006).
    [CrossRef]
  7. J. A. Vallés, M. Á. Rebolledo and J. Used, "New characterization dynamic methods for Er/Yb codoped phosphate glass waveguides," Proc. SPIE,  6183, 61830F (2006).
    [CrossRef]
  8. I. J. Sola, J. C. Martín and J. M. Álvarez, "Non linear response of a unidirectional erbium-doped fiber ring laser to a sinusoidally modulated pump power," Opt. Commun. 212, 359-369 (2002).
    [CrossRef]
  9. J. A. Lázaro, M. A. Rebolledo and J. A. Vallés, "Modeling, Characterization and Experimental/Numerical comparison of signal and fluorescence amplification in Ti:Er:LiNbO3 waveguides," IEEE J. Quantum Electron. 37, 1460-1468 (2001).
    [CrossRef]

2006 (2)

J. A. Vallés, M. A. Rebolledo and J. Cortés, "Full characterization of packaged Er-Yb-codoped phosphate glass waveguides," IEEE J. Quantum Electron. 42, 152-159 (2006).
[CrossRef]

J. A. Vallés, M. Á. Rebolledo and J. Used, "New characterization dynamic methods for Er/Yb codoped phosphate glass waveguides," Proc. SPIE,  6183, 61830F (2006).
[CrossRef]

2005 (1)

2002 (3)

J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt and R. Sauerbrey, "Energy transfer and upconversion in erbium-ytterbium-doped fluoride phosphate glasses," Appl. Phys. B 74, 233-236 (2002).
[CrossRef]

I. J. Sola, J. C. Martín and J. M. Álvarez, "Non linear response of a unidirectional erbium-doped fiber ring laser to a sinusoidally modulated pump power," Opt. Commun. 212, 359-369 (2002).
[CrossRef]

J. A. Vallés, J.A. Lázaro and M.A. Rebolledo, "Analysis of Competing Mechanisms in Transitions Between Excited States in Er-Doped Integrated Waveguides," IEEE J. Quantum Electron. 38, 318-323 (2002)
[CrossRef]

2001 (1)

J. A. Lázaro, M. A. Rebolledo and J. A. Vallés, "Modeling, Characterization and Experimental/Numerical comparison of signal and fluorescence amplification in Ti:Er:LiNbO3 waveguides," IEEE J. Quantum Electron. 37, 1460-1468 (2001).
[CrossRef]

2000 (1)

N C. Becker, T. Oesselke, J. Pandavenes, R. Ricken, K. Rockhausen, G, Schreiber, W. Sohler, H. Suche, R. Wessel, S. Balsamo, I. Montrosset and D. Sciancalepore, "Advanced Ti:LiNbO3 waveguide lasers," IEEE J. Select. Top. Quantum Electron. 6, 101-110 (2000).
[CrossRef]

1998 (1)

J. A. Lázaro, J. A. Vallés and M. A. Rebolledo, "Determination of emission and absorption cross-sections of Er3+ in LiNbO3 waveguides from transversal fluorescence spectra," Pure App. Opt. 7, 1363-71 (1998).
[CrossRef]

Álvarez, J. M.

I. J. Sola, J. C. Martín and J. M. Álvarez, "Non linear response of a unidirectional erbium-doped fiber ring laser to a sinusoidally modulated pump power," Opt. Commun. 212, 359-369 (2002).
[CrossRef]

Becker, N C.

N C. Becker, T. Oesselke, J. Pandavenes, R. Ricken, K. Rockhausen, G, Schreiber, W. Sohler, H. Suche, R. Wessel, S. Balsamo, I. Montrosset and D. Sciancalepore, "Advanced Ti:LiNbO3 waveguide lasers," IEEE J. Select. Top. Quantum Electron. 6, 101-110 (2000).
[CrossRef]

Cortés, J.

J. A. Vallés, M. A. Rebolledo and J. Cortés, "Full characterization of packaged Er-Yb-codoped phosphate glass waveguides," IEEE J. Quantum Electron. 42, 152-159 (2006).
[CrossRef]

Ebendorff-Heidepriem, H.

J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt and R. Sauerbrey, "Energy transfer and upconversion in erbium-ytterbium-doped fluoride phosphate glasses," Appl. Phys. B 74, 233-236 (2002).
[CrossRef]

Ehrt, D.

J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt and R. Sauerbrey, "Energy transfer and upconversion in erbium-ytterbium-doped fluoride phosphate glasses," Appl. Phys. B 74, 233-236 (2002).
[CrossRef]

Jaskorzynska, B.

Khoptyar, D.

Lázaro, J. A.

J. A. Lázaro, M. A. Rebolledo and J. A. Vallés, "Modeling, Characterization and Experimental/Numerical comparison of signal and fluorescence amplification in Ti:Er:LiNbO3 waveguides," IEEE J. Quantum Electron. 37, 1460-1468 (2001).
[CrossRef]

J. A. Lázaro, J. A. Vallés and M. A. Rebolledo, "Determination of emission and absorption cross-sections of Er3+ in LiNbO3 waveguides from transversal fluorescence spectra," Pure App. Opt. 7, 1363-71 (1998).
[CrossRef]

Lázaro, J.A.

J. A. Vallés, J.A. Lázaro and M.A. Rebolledo, "Analysis of Competing Mechanisms in Transitions Between Excited States in Er-Doped Integrated Waveguides," IEEE J. Quantum Electron. 38, 318-323 (2002)
[CrossRef]

Martín, J. C.

I. J. Sola, J. C. Martín and J. M. Álvarez, "Non linear response of a unidirectional erbium-doped fiber ring laser to a sinusoidally modulated pump power," Opt. Commun. 212, 359-369 (2002).
[CrossRef]

Oesselke, T.

N C. Becker, T. Oesselke, J. Pandavenes, R. Ricken, K. Rockhausen, G, Schreiber, W. Sohler, H. Suche, R. Wessel, S. Balsamo, I. Montrosset and D. Sciancalepore, "Advanced Ti:LiNbO3 waveguide lasers," IEEE J. Select. Top. Quantum Electron. 6, 101-110 (2000).
[CrossRef]

Pandavenes, J.

N C. Becker, T. Oesselke, J. Pandavenes, R. Ricken, K. Rockhausen, G, Schreiber, W. Sohler, H. Suche, R. Wessel, S. Balsamo, I. Montrosset and D. Sciancalepore, "Advanced Ti:LiNbO3 waveguide lasers," IEEE J. Select. Top. Quantum Electron. 6, 101-110 (2000).
[CrossRef]

Philipps, J. F.

J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt and R. Sauerbrey, "Energy transfer and upconversion in erbium-ytterbium-doped fluoride phosphate glasses," Appl. Phys. B 74, 233-236 (2002).
[CrossRef]

Rebolledo, M. A.

J. A. Vallés, M. A. Rebolledo and J. Cortés, "Full characterization of packaged Er-Yb-codoped phosphate glass waveguides," IEEE J. Quantum Electron. 42, 152-159 (2006).
[CrossRef]

J. A. Lázaro, M. A. Rebolledo and J. A. Vallés, "Modeling, Characterization and Experimental/Numerical comparison of signal and fluorescence amplification in Ti:Er:LiNbO3 waveguides," IEEE J. Quantum Electron. 37, 1460-1468 (2001).
[CrossRef]

J. A. Lázaro, J. A. Vallés and M. A. Rebolledo, "Determination of emission and absorption cross-sections of Er3+ in LiNbO3 waveguides from transversal fluorescence spectra," Pure App. Opt. 7, 1363-71 (1998).
[CrossRef]

Rebolledo, M. Á.

J. A. Vallés, M. Á. Rebolledo and J. Used, "New characterization dynamic methods for Er/Yb codoped phosphate glass waveguides," Proc. SPIE,  6183, 61830F (2006).
[CrossRef]

Rebolledo, M.A.

J. A. Vallés, J.A. Lázaro and M.A. Rebolledo, "Analysis of Competing Mechanisms in Transitions Between Excited States in Er-Doped Integrated Waveguides," IEEE J. Quantum Electron. 38, 318-323 (2002)
[CrossRef]

Ricken, R.

N C. Becker, T. Oesselke, J. Pandavenes, R. Ricken, K. Rockhausen, G, Schreiber, W. Sohler, H. Suche, R. Wessel, S. Balsamo, I. Montrosset and D. Sciancalepore, "Advanced Ti:LiNbO3 waveguide lasers," IEEE J. Select. Top. Quantum Electron. 6, 101-110 (2000).
[CrossRef]

Rockhausen, K.

N C. Becker, T. Oesselke, J. Pandavenes, R. Ricken, K. Rockhausen, G, Schreiber, W. Sohler, H. Suche, R. Wessel, S. Balsamo, I. Montrosset and D. Sciancalepore, "Advanced Ti:LiNbO3 waveguide lasers," IEEE J. Select. Top. Quantum Electron. 6, 101-110 (2000).
[CrossRef]

Sauerbrey, R.

J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt and R. Sauerbrey, "Energy transfer and upconversion in erbium-ytterbium-doped fluoride phosphate glasses," Appl. Phys. B 74, 233-236 (2002).
[CrossRef]

Sergeyev, S.

Sola, I. J.

I. J. Sola, J. C. Martín and J. M. Álvarez, "Non linear response of a unidirectional erbium-doped fiber ring laser to a sinusoidally modulated pump power," Opt. Commun. 212, 359-369 (2002).
[CrossRef]

Töpfer, T.

J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt and R. Sauerbrey, "Energy transfer and upconversion in erbium-ytterbium-doped fluoride phosphate glasses," Appl. Phys. B 74, 233-236 (2002).
[CrossRef]

Used, J.

J. A. Vallés, M. Á. Rebolledo and J. Used, "New characterization dynamic methods for Er/Yb codoped phosphate glass waveguides," Proc. SPIE,  6183, 61830F (2006).
[CrossRef]

Vallés, J. A.

J. A. Vallés, M. Á. Rebolledo and J. Used, "New characterization dynamic methods for Er/Yb codoped phosphate glass waveguides," Proc. SPIE,  6183, 61830F (2006).
[CrossRef]

J. A. Vallés, M. A. Rebolledo and J. Cortés, "Full characterization of packaged Er-Yb-codoped phosphate glass waveguides," IEEE J. Quantum Electron. 42, 152-159 (2006).
[CrossRef]

J. A. Vallés, J.A. Lázaro and M.A. Rebolledo, "Analysis of Competing Mechanisms in Transitions Between Excited States in Er-Doped Integrated Waveguides," IEEE J. Quantum Electron. 38, 318-323 (2002)
[CrossRef]

J. A. Lázaro, M. A. Rebolledo and J. A. Vallés, "Modeling, Characterization and Experimental/Numerical comparison of signal and fluorescence amplification in Ti:Er:LiNbO3 waveguides," IEEE J. Quantum Electron. 37, 1460-1468 (2001).
[CrossRef]

J. A. Lázaro, J. A. Vallés and M. A. Rebolledo, "Determination of emission and absorption cross-sections of Er3+ in LiNbO3 waveguides from transversal fluorescence spectra," Pure App. Opt. 7, 1363-71 (1998).
[CrossRef]

Appl. Phys. B (1)

J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt and R. Sauerbrey, "Energy transfer and upconversion in erbium-ytterbium-doped fluoride phosphate glasses," Appl. Phys. B 74, 233-236 (2002).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. A. Vallés, J.A. Lázaro and M.A. Rebolledo, "Analysis of Competing Mechanisms in Transitions Between Excited States in Er-Doped Integrated Waveguides," IEEE J. Quantum Electron. 38, 318-323 (2002)
[CrossRef]

J. A. Vallés, M. A. Rebolledo and J. Cortés, "Full characterization of packaged Er-Yb-codoped phosphate glass waveguides," IEEE J. Quantum Electron. 42, 152-159 (2006).
[CrossRef]

J. A. Lázaro, M. A. Rebolledo and J. A. Vallés, "Modeling, Characterization and Experimental/Numerical comparison of signal and fluorescence amplification in Ti:Er:LiNbO3 waveguides," IEEE J. Quantum Electron. 37, 1460-1468 (2001).
[CrossRef]

IEEE J. Select. Top. Quantum Electron. (1)

N C. Becker, T. Oesselke, J. Pandavenes, R. Ricken, K. Rockhausen, G, Schreiber, W. Sohler, H. Suche, R. Wessel, S. Balsamo, I. Montrosset and D. Sciancalepore, "Advanced Ti:LiNbO3 waveguide lasers," IEEE J. Select. Top. Quantum Electron. 6, 101-110 (2000).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

I. J. Sola, J. C. Martín and J. M. Álvarez, "Non linear response of a unidirectional erbium-doped fiber ring laser to a sinusoidally modulated pump power," Opt. Commun. 212, 359-369 (2002).
[CrossRef]

Proc. SPIE (1)

J. A. Vallés, M. Á. Rebolledo and J. Used, "New characterization dynamic methods for Er/Yb codoped phosphate glass waveguides," Proc. SPIE,  6183, 61830F (2006).
[CrossRef]

Pure App. Opt. (1)

J. A. Lázaro, J. A. Vallés and M. A. Rebolledo, "Determination of emission and absorption cross-sections of Er3+ in LiNbO3 waveguides from transversal fluorescence spectra," Pure App. Opt. 7, 1363-71 (1998).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Er/Yb-codoped waveguide ring laser scheme.

Fig. 2.
Fig. 2.

Experimental peak to peak laser power amplitude vs. pump power excitation frequency: (a) for 5 Pav values and m=0.2 and (b) for 4 modulation index values and fully modulated laser signal. The laser wavelength is 1534 nm and the sweeps are in ascending sense.

Fig. 3.
Fig. 3.

Experimental laser output amplitude versus pump power modulation frequency, for m=0.45, λl=1534 nm and Pav=249 mW. The frequency is swept in ascending (∘) and descending (□) orders.

Fig. 4.
Fig. 4.

Experimental resonance peak frequencies (∘) versus average pump power for m=0.2 and λl=1534 nm. The numerical curves are for 4 values (1, 5, 10 and 20) of the Yb⇒Er energy-transfer factor, f 23.

Fig. 5.
Fig. 5.

Experimental (∘) and numerical (□) resonance peak frequencies for λl=1534 versus the modulation index.

Equations (9)

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d n 2 r ( t ) dt = T 1 ( t ) + T 2 ( t ) n 2 r ( t ) + T 3 n 2 r ( t ) n 4 r ( t )
d n 4 r ( t ) dt = S 1 ( t ) + S 2 ( t ) n 4 r ( t ) + S 3 P l ( t ) + S 4 P l ( t ) n 4 r ( t ) + S 5 n 4 r 2 ( t ) + S 6 n 2 r ( t ) + S 7 n 2 r ( t ) n 4 r ( t )
d P l ( t ) dt = P l ( t ) ( R 1 + R 2 n 4 r ( t ) ) ,
T 1 = σ 12 ( ν p ) η 1 , p h ν p P p ( t ) , T 2 = ( A 21 + σ 12 ( ν p ) η 1 , p h ν p P p ( t ) + σ 21 ( ν p ) η 2 , p h ν p P p ( t ) + R 23 C 23 n Er ) ,
T 3 = R 23 C 23 n Er
S 1 = σ 35 ( ν p ) η 3 , p h ν p P p ( t ) , S 2 = ( σ 35 ( ν p ) η 3 , p h ν p P p ( t ) + A 43 ) , S 3 = σ 34 ( ν l ) η 3 , l h ν l ,
S 4 = ( σ 34 ( ν l ) η 3 , l h ν l + σ 43 ( ν l ) η 4 , l h ν l ) , S 5 = R 44 C 44 n Er ,
S 6 = R 23 C 23 n Yb , S 7 = R 23 C 23 n Yb ,
R 1 = c [ ln ( T ) ( σ 34 ( ν l ) η 3 , l n Er + α l ) L ] D + L , R 2 = cL ( σ 34 ( ν l ) η 3 , l + σ 43 ( ν l ) η 4 , l ) n Er D + L ,

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