## Energy-transfer efficiency in the Er/Yb-codoped waveguide ring laser under sinusoidally modulated pump

Optics Express, Vol. 15, Issue 25, pp. 16767-16772 (2007)

http://dx.doi.org/10.1364/OE.15.016767

Acrobat PDF (251 KB)

### 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

## 1. Introduction

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:LiNbO_{3} 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 Er^{3+} in LiNbO_{3} 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]

## 2. Experimental

### 2.1 Set up

^{2}, the distance from the waveguide axis to the glass surface is 7 µm and the refractive index change at the peak of the index profile is approximately 0.04. The buried waveguide was fabricated by Teem Photonics

^{™}using a two-step ion exchange process in a phosphate glass codoped with Er/Yb ions (Er

^{3+}and Yb

^{3+}concentrations are

*n*=2.0×1026 ions/m

_{Er}^{3}and

*n*=2.2×10

_{Yb}^{26}ions/m

^{3}, respectively). The waveguide is pigtailed in order to allow an efficient input/output coupling of the optical powers.

_{l}, and finally, to close the ring configuration, a variable coupler was arranged.

### 2.2 Measurements

*l*=30,04±0.03 m and the ring transmission coefficient was measured to be T=0.33 for λ

_{l}=1534 nm. In order to carry out the measurements, the intensity current which feeds the pump laser was sinusoidally modulated. The pump laser output power was confirmed to be linear with regard to the modulated current and, accordingly, can be written as:

*P*(

_{p}*t*)=

*P*[1+

_{av}*m*cos(2

*πf*)], where

_{e}t*P*is the pump power average value,

_{av}*m*is the modulation index and

*f*is the excitation frequency. The ring laser output signal detection was performed by a PIN photodiode connected to a digital oscilloscope, and the maximum voltage difference in a time period (from now on the peak to peak laser power amplitude) was stored.

_{e}*f*for several values of

_{e}*P*and for a constant modulation index,

_{av}*m*=0.2. In Fig. 2(a), it can be noticed how as

*P*increases the resonance peaks shift towards higher frequency values and also how the discontinuity in the left wing of the curves progressively vanishes.

_{av}*m*, while the average pump power was adjusted in order to obtain a fully modulated laser signal. Therefore, the experimental variation range for

*m*(0–0.45) is, in practice, limited by the threshold pump power (137 mW) and the maximum available pump power at the waveguide input end (356 mW for a 900 mA-drive current). In Fig. 2(b), the ascending sense sweeps are represented for 4 values of the modulation factor. Besides, for high modulation indexes other resonance peaks show up (see Fig. 2(b)). According to ref. 8, the reason for the appearance of these amplitude peaks is that as the modulation index increases, the ring laser system favours the development of signal harmonics that fall within the bandwidth around the natural frequency of the system.

## 3. Theoretical

### 3.1. Model

*n*,

_{1}*n*,

_{2}*n*and

_{3}*n*are the population densities of the ytterbium levels

_{4}^{2}F

_{7/2}and

^{2}F

_{5/2}and of the erbium levels

^{4}I

_{15/2}and

^{4}I

_{13/2}, respectively) and the equations that describe the propagation of the optical powers along the laser ring (only the pump power and the counterpropagating fluorescence power at the laser wavelength are considered). In order to suppress the transversal coordinates dependence, this model uses the overlapping factors formalism [9

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:LiNbO_{3} waveguides,” IEEE J. Quantum Electron. **37**, 1460–1468 (2001). [CrossRef]

*n*+

_{1}*n*=

_{2}*n*and

_{Yb}*n*+

_{3}*n*=

_{4}*n*, the equations that describe the temporal evolution of the relative population densities,

_{Er}*n*=

_{2r}*n*/

_{2}*n*and

_{Yb}*n*=

_{4r}*n*/

_{4}*n*, and of the laser power,

_{Er}*P*, in our system are:

_{l}*A*represents the spontaneous radiative relaxation rate between the

_{ij}*ith*and

*jth*levels,

*C*is the homogeneous upconversion coefficient,

_{44}*C*is the non radiative Yb⇒Er energy transfer coefficient, σ

_{23}*is the cross section corresponding to the transition between the*

_{ij}*ith*and

*jth*levels, α

_{i}are the scattering losses at the laser wavelength,

*ν*is the frequency of the optical signals and the label

_{γ}*γ*is

*p*for the pump and

*l*for the laser, L is the waveguide length,

*D*=

*nl*is the passive ring optical path,

*n*being the refractive index, and T is the ring transmission coefficient. Moreover,

*η*are the overlapping factors between the

_{iγ}*ith*level population density and the

*P*intensity modal distributions, and

_{γ}*R*are the overlapping factors between

_{ij}*ith*and

*jth*levels population density distributions. Finally,

*h*is Planck constant and

*c*is the speed of light in vacuum. All the values of the parameters have been taken from Ref. 6., and the overlapping factors have been computed for laser steady state regime and for the average pump power, and have been assumed to remain constant when the pump power is modulated. Since no analytical solution is achievable for the system of equations (1–3) we have to proceed numerically. Switch off initial conditions are assumed for the first frequency of the series and the laser response is calculated by solving the above equations by the fourth order Runge-Kutta method. Then,

*f*is varied over the whole range of interest and for each frequency the end values of the preceding

_{e}*f*are taken as initial conditions. The difference in the initial conditions allows that the laser response for a given frequency may differ, depending on whether the modulation frequency is swept in ascending or descending sense.

_{e}### 3.2. Results

*C*

_{23}is necessary. Besides, in Ref. 3, where a statistical microscopic formalism is used to describe homogeneous upconversion and migration in an erbium doped silica fiber, it is concluded that for high density and high pump levels the concentration-dependent inter-atomic energy-transfer interactions are more efficient than what the usual macroscopic models describe. Therefore, it seems reasonable to keep on using the more simple macroscopic formalism while introducing a pump-power dependent Yb⇒Er energy transfer coefficient that comprises the increasing efficiency of this mechanism for high pump levels. The value of this effective coefficient,

*C*

_{23}, is referred to the value of the non radiative Yb⇒Er energy transfer coefficient determined in Ref. 6 in steady state regime,

*C*

^{o}

_{23}=1.8×10

^{-23}m

^{3}/s, through an average pump-power dependent energy-transfer factor,

*f*

_{23}=

*f*(

*P*), so that

_{av}*C*

_{23}=

*f*

_{23}

*C*

^{o}

_{23}. We checked, as it is indicated in Ref. 7 for the laser transient parameters analysis, that the influence of the value of

*C*

_{44}on the resonance peaks frequencies is, in practice, negligible.

*f*

_{23}. From Fig. 4 it is clear that, as

*P*increases, in order to numerically fit the experimental results, higher values of

_{av}*f*

_{23}are required.

*f*

_{23}that fit the resonance peak frequencies measured as a function of

*P*for m=0.2 (see Fig. 2(a)), and used them to compute the resonance peak frequency dependence on the modulation factor

_{av}*m*(some of the measured resonance curves are shown in Fig. 2(b)). In Fig. 5 the experimental values are plotted together with the numerical results using the best-fit

*f*

_{23}values.

*m*values the numerical and the experimental results start to separate.

## 4. Conclusions

## Acknowledgements

## References and links

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:LiNbO |

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 |

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 |

4. | J. A. Lázaro, J. A. Vallés, and M. A. Rebolledo,, “Determination of emission and absorption cross-sections of Er |

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. |

6. | J. A. Vallés, M. A. Rebolledo, and J. Cortés, “Full characterization of packaged Er-Yb-codoped phosphate glass waveguides,” IEEE J. Quantum Electron. |

7. | J. A. Vallés, M. Á. Rebolledo, and J. Used, “New characterization dynamic methods for Er/Yb codoped phosphate glass waveguides,” Proc. SPIE , |

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. |

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:LiNbO |

**OCIS Codes**

(130.3130) Integrated optics : Integrated optics materials

(140.3560) Lasers and laser optics : Lasers, ring

(140.4480) Lasers and laser optics : Optical amplifiers

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: July 23, 2007

Revised Manuscript: November 12, 2007

Manuscript Accepted: November 12, 2007

Published: December 3, 2007

**Citation**

J. A. Vallés, M. Á. Rebolledo, J. Cortés, and J. Used, "Energy-transfer efficiency in the Er/Yb-codoped waveguide ring laser under sinusoidally modulated pump," Opt. Express **15**, 16767-16772 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16767

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### References

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

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