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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8773–8780
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Experimental evidence and theoretical modeling of two-photon absorption dynamics in the reduction of intensity noise of solid-state Er:Yb lasers

Abdelkrim El Amili, Gaël Kervella, and Mehdi Alouini  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8773-8780 (2013)
http://dx.doi.org/10.1364/OE.21.008773


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Abstract

A theoretical and experimental investigation of the intensity noise reduction induced by two-photon absorption in a Er,Yb:Glass laser is reported. The time response of the two-photon absorption mechanism is shown to play an important role on the behavior of the intensity noise spectrum of the laser. A model including an additional rate equation for the two-photon-absorption losses is developed and allows the experimental observations to be predicted.

© 2013 OSA

1. Introduction

2. Experimental setup and experimental observations

The experimental setup under consideration is depicted in Fig. 1. The laser used in this experiment is a single-frequency Er,Yb:Glass laser operating at 1560 nm. The laser is formed by a 4.9-cm-long planar-concave cavity. The active medium is a 1.5-mm-long phosphate glass codoped with Erbium and Ytterbium with concentrations of 1.08×1020 ions/cm3 and 20×1020 ions/cm3 respectively. The first side of the Er,Yb:Glass plate, which acts as the cavity input mirror, is coated for high reflectivity at 1550 nm (R> 99.9%) and high transmission (T= 95%) at the pump wavelength (975 nm). The cavity is closed by a 5-cm-radius of curvature mirror transmitting 0.5% of the intensity at 1560 nm. A 40-μm-thick Silicon (Si) plate is inserted into the laser cavity in order to induce the desired intensity dependent losses through two-photon absorption, this plate being perfectly transparent at 1560 nm. Moreover, this Si plate is left uncoated to act as an intracavity étalon enabling the laser to be single mode. The Si plate is mounted on a mechanical stage having three degrees of freedom, namely, one translation and two rotation axes. The rotation axes allow fine adjustment of the plate tilt in order to ensure perfect single mode and linearly polarized oscillation. The translation axis allows the Si plate to be translated along the optical axis of the resonator in order to change the photon density within the Si plate. Indeed, according to the plano-concave architecture of the optical resonator, and to the fact that its length is adjusted close to the limit of stability, the beam diameter on the Si plate increases when the plate is translated towards the output mirror. The active medium is pumped by a cw multimode fiber-coupled laser diode (from Jenoptik) operating at 975 nm. The pump power is fixed at 275 mW during data acquisition. The optical spectrum is continuously analyzed with a Fabry-Perot interferometer to check that the laser remains monomode without any mode hop during data acquisition. The laser intensity is measured using an InGaAs photodiode (Epitaxx Inc, 3.7 MHz bandwidth) and a homemade low noise amplification setup. Finally, the noise spectrum is recorded with an electrical spectrum analyzer (ESA) whose frequency range is 10 Hz–3.6 GHz.

Fig. 1 Experimental setup. O.I: optical isolator; BS: beam splitter. The arrow shows the direction of displacement of the two-photon absorber in order to change the effective cross-section of the TPA.

Figure 2 reproduces two RIN spectra recorded for two different situations: without (1) and with (2) the Si plate into the laser. In both cases the laser is ∼1.2 times above threshold. In accordance with the dynamics of class-B lasers, the RIN spectrum (1) exhibits a strong RO peak at about 40 kHz. By contrast, the RIN spectrum (2) shows that the insertion of the nonlinear absorber close to the active medium, i.e. where the laser photons density is important, leads to 33 dB reduction on the amplitude of the RO peak. Nevertheless, it is worthwhile to notice that the RO frequency is shifted toward high frequencies although the pumping rate is unchanged. Such a frequency shift cannot be predicted by the model proposed in [9

9. R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

]. This behavior in the intensity noise of the laser suggests that the time response of the TPA mechanism must be taken into account as it will be demonstrated in the following.

Fig. 2 RIN spectra of the laser without and with an intracavity two-photon absorber (Si plate). In this example, the insertion of the Si plate leads to a 33 dB reduction of the intensity noise at the relaxation oscillation frequency. ESA resolution bandwidth: 100 Hz; video bandwidth: 100 Hz.

3. Theoretical model

To take into account the time response of the TPA mechanism, we propose to add to the usual rate equations of the laser a new rate equation driving the TPA process. We consider a single-frequency Er,Yb:Glass laser oscillating in cw regime and we assume a homogeneous gain medium described by a quasi-two-level scheme [10

10. P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm. 100, 311–321 (1993) [CrossRef] .

]. The intensity-dependent losses due to the TPA effect are first taken into account in the rate equation driving the laser intensity. However, unlike Ref. [9

9. R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

] these losses being time dependent, they are ruled by a third rate equation as follows:
dNdt=2σIN(wp+γ)N+(wpγ)NE,
(1)
dIdt=c2L2eσINγcIγTPAI,
(2)
dPTPAdt=αψIγPPTPA,
(3)
where γTPA = cPTPA/2L is the nonlinear loss rate and PTPA is the time-dependent losses induced by the TPA mechanism. N and NE are respectively the population inversion and the total Erbium ions (Er3+) population, γ and σ are respectively the population inversion relaxation rate and the emission cross-section of Er3+, wp is the pumping rate, I is the laser photon flux; e and L are respectively the optical lengths of the active medium and of the resonator, c is the velocity of the light. γc is the photon decay rate which includes both losses of the cold cavity and the slight linear losses of the nonlinear absorber. In the third rate equation which rules the time-dependent loss induced by the TPA mechanism, γP/2π is the inverse of the time response of the TPA mechanism, and αψ is the effective cross-section of TPA. This effective cross-section takes into account the photon density in the two-photon absorber which is, in general and in particular in our experiment, different from the photon density in the active medium. Thus, α is the ratio between the photon interaction areas in the active medium and in the two-photon absorber. Hence, considering that w0 and wTPA are respectively the beam radius in the active medium and in two-photon absorber α=w02/wTPA2.

It is worthwhile to notice that the usual quadratic dependence of the intensity decay due to TPA [11

11. R. W. Boyd, Nonlinear Optics (Academic Press, 2008), pp. 16.

] is recovered when considering together the second and third rate equations, PTPA and consequently γTPA being proportional to I.

Let us now consider the intensity noise of the laser which is conveniently described by the Relative Intensity Noise (RIN). The RIN level can be determined using a classical approach which is justified by the fact that, in our experiment, the noise level around the RO frequency is higher than the standard quantum noise limit. The parameters which can influence the laser intensity noise, in particular around the RO frequency, are the pump and the cavity loss fluctuations. Moreover, it was shown in [12

12. S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19–26 (1998) [CrossRef] .

] that the RIN spectrum behavior around the RO frequency can be predicted by computing the intensity transfer function of the laser induced by fluctuations of the cavity losses. This transfer function can be derived from the rate equations by introducing slight perturbations around the equilibrium state of the laser. Hence, small fluctuations of the cavity losses at frequency ω around the stationary value, i.e., γc = γ̄c + δγc exp(iωt), induce small fluctuations at the same frequency around the stationary values of the population inversion, i.e., N = + δN exp(iωt), of the intensity, i.e., I = Ī + δI exp(iωt), and of the TPA induced losses, i.e., PTPA = TPA + δPTPA exp(iωt). Injecting these expressions in the laser rate equations Eqs. (1)(3), leads to the normalized transfer function:
Hδγc(ω)=δI/I¯δγc/γ¯c=γ¯ciω+γ¯c(1N¯Nth)+γTPA(1γPiω+γP)+γ¯cN¯Nth2σI¯iω+2σ(I¯+Isat),
(4)
where Nth=Lecσγ¯c is the population inversion at threshold, and Isat=wp+γ2σ is the saturation intensity of the laser. The stationary values of the population inversion, of the intracavity intensity and of the TPA losses read:
N¯=12(αψIsat2eσγTPA+Nth+(αψIsat2eσγTPANth)2+4αψIsat2eσγTPAN0),
(5)
I¯=Isat(N0N1),
(6)
P¯TPA=αψγPI¯,
(7)
where N0=wp+γwpγNE is the unsaturated population inversion.

Equations (5)(6) clearly show that the insertion of a two-photon absorber leads to a nonlinear behavior of the population inversion and of the laser intensity. The transfer function in Eq. (4) predicts two kinds of behaviors depending on the time response of the TPA mechanism for a given TPA cross-section and a given intracavity intensity. Indeed, if the TPA time response is very short as compared to the time scale of the laser relaxation oscillations without TPA, then the two-photon absorber reacts instantaneously to the intensity fluctuations of the laser. Thus, the frequency of the RO peak remains constant whereas its level decreases as the intracavity intensity of the laser increases. By contrast, if the TPA time response becomes close to almost the tenth of the time constant of the laser relaxation oscillations without TPA, then the RO peak decreases as the intracavity intensity increases meanwhile its frequency shifts toward higher frequencies. It must be noted that in this case, the TPA process is less efficient in terms of noise reduction.

Our model in which a rate equation for the TPA losses is introduced is able to predict a frequency shift of the RO peak although the pumping rate of the laser is kept constant. In order to validate this model, we compare in the following its predictions with the experimental results.

4. Experimental validation of the model and discussion

The experimental setup is described in the first section of the paper. Here, we focus on how the RO peak behaves when the photon density in the Si plate is changed. Rather than changing the intracavity intensity which will be accompanied by a change of the laser parameters, we choose to modify the amount of nonlinear losses by modifying the effective cross-section of the TPA. As described previously, this can be achieved very easily by translating the Si plate along the propagation axis of the laser.

Before inserting TPA effects into the laser, we have characterized it by replacing the Si plate by a silica étalon which introduces almost the same linear losses. In this case the only unknown parameter of the model is the intrinsic intracavity losses, which is adjusted using the experimental intensity-versus-pump characteristic and also by checking that the experimental and theoretical RIN spectra fit together. When the Si plate is inserted back into the laser close to the output mirror, it turns out that the laser threshold remains the same and that the RIN spectra are also the same as compared to that obtained with the silica étalon. Consequently, the TPA effect can be neglected when the Si plate is close to the output mirror, namely, where the laser beam is sufficiently wide. When the Si plate is moved closer to the active medium, the only unknown parameters are now the effective TPA cross-section and its lifetime.

Figure 3 reproduces the experimental RIN spectra (in gray color level) recorded for different positions of the Si plate from the active medium, that is, for different photon densities. The theoretical transfer functions are also represented in this figure. The laser parameters that we use in the model are given in the caption Fig. 3. The experimental RIN spectra of Fig. 3 clearly show that the noise power peak shifts towards higher frequencies meanwhile its level decreases when the Si plate is moved closer to the active medium. We have checked that both laser wavelength (observed with the optical spectrum analyzer) and laser frequency (observed with the Fabry-Perot interferometer) remain constant when moving the TPA plate. More importantly, we have verified that the laser threshold and the pumping rate are not affected by moving the plate inside the cavity, proving that (i) the frequency shift of the RO is only ruled by the TPA process and that (ii) the losses induced by the TPA process are very small (in the order of 10−5 according our the model). As depicted in Fig. 3, the theoretical model is able to predict the noise power peak shift towards higher frequencies. Moreover, the theoretical transfer functions match very well the corresponding experimental RIN spectra. Furthermore, we found that the lifetime of the TPA process in our Si plate must be adjusted once at 3 μs whatever the photon density. This high lifetime value is not so surprising since the carrier’s recombination lifetime in silicon semiconductors can be in the range of a few ms to a few ns depending on the crystal purity and whether it is doped or not [13

13. J. G. Fossum and D. S. Lee, “A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon,” Solid-State Electron. 25, 741–747 (1982) [CrossRef] .

15

15. J. A. del Alamo and R. M. Swanson, “Modelling of minority-carrier transport in heavily doped silicon emitters,” Solid-State Electron. 30, 1127–1136 (1987) [CrossRef] .

]. These results confirm the fact that the TPA induced losses cannot be considered as instantaneous and that the carrier recombination lifetime must be taken into account when sizing a TPA assisted low noise solid-state laser.

Fig. 3 RIN spectra of the laser with a Si plate. Each spectrum is recorded for different positions z from the active medium of the TPA plate. The full lines in red are the theoretical transfer functions. The numerical values of the laser parameters used in the calculation are: NE = 1.08 × 1020 cm−3; γ = 154 s−1; e = 0.15 cm; L = 5 cm; σ = 6 × 10−21 cm2; γc = 2.2 × 108 s−1; α(z1)ψ = 6.4 × 10−22 cm2; α(z2)ψ = 2.7 × 10−22 cm2; α(z3)ψ = 1.7×10−22 cm2; α(z4)ψ = 6.9×10−23 cm2; α(z5)ψ = 6.7×10−23 cm2. ESA resolution bandwidth: 100 Hz; video bandwidth: 100 Hz.

Fig. 4 RIN spectra of the laser with a GaAs plate. Each spectrum is recorded for different positions z from the active medium of the TPA plate. The full lines in red are the theoretical transfer functions. The numerical values of the laser parameters used are the same as those in Fig. 3 except γc = 1.56 × 108 s−1; α(z1)ψ = 1.7 × 10−19 cm2; α(z2)ψ = 7.5 × 10−20 cm2; α(z3)ψ = 5.5 × 10−20 cm2. ESA resolution bandwidth: 100 Hz; video bandwidth: 100 Hz.

5. Conclusion

Acknowledgments

The authors acknowledge Goulc’hen Loas and Cyril Hamel for technical support. This research was partially funded by the Délégation Générale de l’Armement. Gaël Kervella is now with Alcatel-Thales 3–5 lab.

References and links

1.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er,Yb: Glass laser eigenstates for RF photonics applications,” IEEE Photon. Tech. Lett. 13, 367–369 (2001) [CrossRef] .

2.

D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev. 141, 306–322 (1966) [CrossRef] .

3.

S. Taccheo, P. Laporta, O. Svelto, and G. de Geronimo, “Intensity noise reduction in a single-frequency ytterbium-codoped erbium laser,” Opt. Lett. 21, 1747–1749 (1996) [CrossRef] [PubMed] .

4.

J. Zhang, H. Ma, C. Xie, and K. Peng, “Suppression of intensity noise of a laser-diode-pumped single-frequency Nd:YVO4 laser by optoelectronic control,” Appl. Opt. 42, 1068–1074 (2003) [CrossRef] [PubMed] .

5.

G. Baili, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Shot-noise-limited operation of a monomode high-cavity-finesse semiconductor laser for microwave photonics applications,” Opt. Lett. 32, 650–652 (2007) [CrossRef] [PubMed] .

6.

M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett. 95, 033509 (2009) [CrossRef] .

7.

H. Statz, G. A. deMars, and C. L. Tang, “Problem of spike elimination in lasers,” J. Appl. Phys. 36, 1510–1514 (1965) [CrossRef] .

8.

J. F. Pinto and L. Esterowitz, “Suppression of spiking behavior in flash-pumped 2–μm lasers,” IEEE. J. Quant. Elec. 30, 167–169 (1967) [CrossRef] .

9.

R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

10.

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm. 100, 311–321 (1993) [CrossRef] .

11.

R. W. Boyd, Nonlinear Optics (Academic Press, 2008), pp. 16.

12.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B 66, 19–26 (1998) [CrossRef] .

13.

J. G. Fossum and D. S. Lee, “A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon,” Solid-State Electron. 25, 741–747 (1982) [CrossRef] .

14.

R. J. Van Overstraeten and R. P. Mertens, “Heavy doping effects in Si,” Solid-State Electron. 30, 1077–1087 (1987) [CrossRef] .

15.

J. A. del Alamo and R. M. Swanson, “Modelling of minority-carrier transport in heavily doped silicon emitters,” Solid-State Electron. 30, 1127–1136 (1987) [CrossRef] .

OCIS Codes
(140.3500) Lasers and laser optics : Lasers, erbium
(140.3570) Lasers and laser optics : Lasers, single-mode
(140.3580) Lasers and laser optics : Lasers, solid-state
(270.2500) Quantum optics : Fluctuations, relaxations, and noise
(270.3430) Quantum optics : Laser theory
(270.4180) Quantum optics : Multiphoton processes

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: February 13, 2013
Revised Manuscript: March 24, 2013
Manuscript Accepted: March 24, 2013
Published: April 2, 2013

Citation
Abdelkrim El Amili, Gaël Kervella, and Mehdi Alouini, "Experimental evidence and theoretical modeling of two-photon absorption dynamics in the reduction of intensity noise of solid-state Er:Yb lasers," Opt. Express 21, 8773-8780 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8773


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References

  1. M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er,Yb: Glass laser eigenstates for RF photonics applications,” IEEE Photon. Tech. Lett.13, 367–369 (2001). [CrossRef]
  2. D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev.141, 306–322 (1966). [CrossRef]
  3. S. Taccheo, P. Laporta, O. Svelto, and G. de Geronimo, “Intensity noise reduction in a single-frequency ytterbium-codoped erbium laser,” Opt. Lett.21, 1747–1749 (1996). [CrossRef] [PubMed]
  4. J. Zhang, H. Ma, C. Xie, and K. Peng, “Suppression of intensity noise of a laser-diode-pumped single-frequency Nd:YVO4 laser by optoelectronic control,” Appl. Opt.42, 1068–1074 (2003). [CrossRef] [PubMed]
  5. G. Baili, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Shot-noise-limited operation of a monomode high-cavity-finesse semiconductor laser for microwave photonics applications,” Opt. Lett.32, 650–652 (2007). [CrossRef] [PubMed]
  6. M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009). [CrossRef]
  7. H. Statz, G. A. deMars, and C. L. Tang, “Problem of spike elimination in lasers,” J. Appl. Phys.36, 1510–1514 (1965). [CrossRef]
  8. J. F. Pinto and L. Esterowitz, “Suppression of spiking behavior in flash-pumped 2–μm lasers,” IEEE. J. Quant. Elec.30, 167–169 (1967). [CrossRef]
  9. R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).
  10. P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm.100, 311–321 (1993). [CrossRef]
  11. R. W. Boyd, Nonlinear Optics (Academic Press, 2008), pp. 16.
  12. S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B66, 19–26 (1998). [CrossRef]
  13. J. G. Fossum and D. S. Lee, “A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon,” Solid-State Electron.25, 741–747 (1982). [CrossRef]
  14. R. J. Van Overstraeten and R. P. Mertens, “Heavy doping effects in Si,” Solid-State Electron.30, 1077–1087 (1987). [CrossRef]
  15. J. A. del Alamo and R. M. Swanson, “Modelling of minority-carrier transport in heavily doped silicon emitters,” Solid-State Electron.30, 1127–1136 (1987). [CrossRef]

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