Abstract

The operation of an intracavity frequency shifted feedback (FSF) laser exhibits a remarkable range of properties, some of which have been described previously. Here we report a more complete analysis of the dependence of the output power upon pump-laser power, based on simulations with an extended rate equation model and the use of phase space analysis. The effect of FSF is discussed in detail. The simulation of the operation of a titanium-sapphire laser with FSF reveals five separate regimes of operation, a superset of those observed in experiment. We predict the thresholds for each of these regimes for FSF-lasers with titanium-sapphire or neodymium doped crystals as gain medium.

© 2003 Optical Society of America

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References

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Appl. Phys. Lett. (1)

F. V. Kowalski, S. J. Shattil and P. D. Hale, �??Optical pulse generation with a frequency shifted feedback laser,�?? Appl. Phys. Lett. 53, 734-736 (1988)
[CrossRef]

Electron. Lett. (1)

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli and S. Wabnitz, �??Self-starting sliding-frequency fibre soliton laser,�?? Electron. Lett. 30, 321 (1994)
[CrossRef]

J. Lightwave Technol. (1)

H. Sabert and E. Brinkmeyer, �??Pulse generation in giber lasers with frequency shifted feedback,�?? J. Lightwave Technol. 12, 1360-1368 (1994)
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Quantum Electron. (3)

K. Nakamura, F. Abe, K. Kasahara, T. Hara, M. Sato and H. Ito, �??Spectral characteristics of an all solid-state frequency-shifted feedback laser,�?? IEEE J. Quantum Electron. 33, 103-111 (1997)
[CrossRef]

P. D. Hale and F. V. Kowalski, �??Output characterization of a frequency shifted feedback laser - Theory and experiment,�?? IEEE J. Quantum Electron. 26, 1845-1851 (1990)
[CrossRef]

C. C. Cutler, �??Spectrum and phase characteristics of an (apparently) broad-band continuous-wave mode-locked oscillator,�?? IEEE J. Quantum Electron. 28, 60-67 (1992)
[CrossRef]

Opt. Comm. (1)

G. Bonnet, S. Balle, T. Kraft and K. Bergmann, �??Dynamics and self-modelocking of a titanium-sapphire laser with intracavity frequency shifted feedback,�?? Opt. Comm. 123, 790-800 (1996)
[CrossRef]

Opt. Commum. (1)

M. J. Lim, C. I. Sukenik, T. H. Stievater, P. H. Bucksbaum and R. S. Conti, �??Improved design of a frequency shifted feedback diode laser for optical pumping at high magnetic field,�?? Opt. Commum. 147, 99-102 (1998)
[CrossRef]

Opt. Commun. (7)

D. T. Mugglin, A. D. Streater, S. Balle and K. Bergmann, �??Observation of white light-induced drift seperation of Rb isotropes,�?? Opt. Commun. 104, 165 (1993)
[CrossRef]

J. Martin, Y. Zhao, S. Balle, K. Bergmann and M. P. Fewell, �??Visible-wavelength diode laser with weak frequency-shifted optical feedback,�?? Opt. Commun. 112, 109-121 (1994)
[CrossRef]

S. Balle and K. Bergmann, �??Self-pulsing and instabilities in a unidirectional ring dye-laser with intracavity frequency-shift,�?? Opt. Commun. 116, 136-142 (1995)
[CrossRef]

I. C. M. Littler and K. Bergmann, �??Generation of multi-frequency laser emission using an active frequency shifted feedback cavity,�?? Opt. Commun. 88, 523-530 (1992)
[CrossRef]

M. W. Phillips, G. Y. Liang and J. R. M. Barr, �??Frequency comb generation and pulsed operation in a Nd-Ylf laser with frequency-shifted feedback,�?? Opt. Commun. 100, 473-478 (1993)
[CrossRef]

I. C. M. Littler, S. Balle and K. Bergmann, �??The cw modeless laser : Spectral control ; Performance data and buildup dynamics,�?? Opt. Commun. 88, 514-522 (1992)
[CrossRef]

S. Balle, I. C. M. Littler, K. Bergmann and F. V. Kowalski, �??Frequency shifted feedback dye laser operating at a small shift frequency,�?? Opt. Commun. 102, 166-174 (1993)
[CrossRef]

Opt. Lett. (1)

Optical Engineering (1)

F. V. Kowalski, S. Balle, I. C. M. Littler and K. Bergmann, �??Lasers with internal frequency-shifted feedback,�?? Optical Engineering 33, 1146-1151 (1994)
[CrossRef]

Z. Physik D (1)

I. C. M. Littler, H. M. Keller, U. Gaubatz and K. Bergmann, �??Velocity Control and Cooling Of an Atomic-Beam Using a Modeless Laser,�?? Z. Physik D 18, 307-308 (1991)
[CrossRef]

Supplementary Material (1)

» Media 1: MPG (217 KB)     

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Figures (13)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental layout of the FSF laser, showing cavity mirrors (M1 and M2), birefringent filter (B), etalon (E), laser crystal (LC) and acousto-optic frequency shifter (AOM). The output comes from the zero order light while the first order diffraction continues within the cavity

Fig. 2.
Fig. 2.

Stationary spectrum of photon density ρ(v) versus v-v 0 (in GHz) as solid line (units on right axis, in Hz-1) and effective gain G(v) versus v-v 0 (in GHz) as a dashed line (units on left axis, in µs-1) (a) for laser without FSF, (b) for FSF laser.

Fig. 3.
Fig. 3.

Construction of a bifurcation diagram. (a) Time history: Pout (in W) vs. time (in µs), for Pin =8 W, showing pulsations, (b) phase space trajectory : Pout (in W) vs. out (in W/µs) for Pin =8 W, showing a limit-cycle. The dashed line is the Poincaré section at out =0, (c) bifurcation diagram of Pout (in W) vs. Pin (in W) with dP/dtout =0.

Fig. 4.
Fig. 4.

Contour plot of photon density M versus frequency v-v 0 (in GHz) and time t (in µs) for input power of 3.9 W, showing time evolution of the spectrum. (a) without FSF and (b) with FSF, where the spectrum is shifted by about 16.5 GHz away from v 0.

Fig. 5.
Fig. 5.

Contour plots of the photon number M(v, t) versus frequency v-v 0 (in GHz) and time t (in µs) for different pump power values Pin : (a) 4.0 W, (b) 4.5 W, (c) 8.0 W, (d) 9.87 W, (e) 12.5 W, (e) 15.0 W.

Fig. 6.
Fig. 6.

(217 kB) Animated plot of photon number M(v, t) (upper frame) and effective gain G (lower frame) versus frequency v-v 0 for one pulsation cycle within the dual-frequency-scenario at Pin =9.87W (see section 4.2.2).

Fig. 7.
Fig. 7.

Plot of the inversion (in 1013) versus time (in µs) for different values of pump power. Frames (a) – (f) are for the same values of Pin as in Fig. 5.

Fig. 8.
Fig. 8.

Time averaged output power out (in W) versus pump power Pin (in W) for (a) laser without FSF and (b) laser with FSF. The insets show details of the threshold region.

Fig. 9.
Fig. 9.

Frames (a) – (d) show plots of output power Pout (in W) versus time t (in µs) for different values of pump power Pin near a transition from one regime into another:(a) 8.615W (regime ③), (b) 9.7 W (regime ③), (c) 13.2 W (regime ④), (d) 13.3 W (regime ⑤). Frame (e) shows limit cycles, Pout (in W) vs. out (in W/µs), for each of these cases, illustrating the shrinking of the phase-space trajectory to a point with increasing pump power.

Fig. 10.
Fig. 10.

Bifurcation diagram of Pout (in W) vs. Pin (in W) with out =0 calculated for dt=τRT /10 and observing Pout after 900 µs. Triangles" laser without FSF; Dots: laser with FSF.

Fig. 11.
Fig. 11.

Contour plot of photon density versus frequency v (in GHz) and time t (in µs) for an input power of 14.0 W after switching off the spontaneous emission at t=100µs. Vertical cuts show the evolution of the spectrum of the FSF laser.

Fig. 12.
Fig. 12.

Bifurcation diagrams of Pout (in W) vs. Pin (in W) with out =0 calculated for dt=τRT /10 and observing Pout after 900 µs. The spontaneously emission is either modeled normal or randomly.

Fig. 13.
Fig. 13.

Bifurcation diagrams of Pout (in W) vs. Pin (in W) with out =0 for neodymium doped crystals without intracavity etalon

Tables (3)

Tables Icon

Table 1. Parameters used in the simulation studies. All data are taken either from [7] or www.casix.com

Tables Icon

Table 2. Operation regimes for FSF lasers having an intracavity etalon with a 200 GHz bandwidth. The error is ±2 for the last digit. Items marked n.o. were not observed in simulation.

Tables Icon

Table 3. Operation regimes for FSF lasers without an intracavity etalon. The error is ±0.025 W. Items marked n.o. were not observed in simulation. The Ti:Sa FSF laser does not operate without the gain bandwidth restriction by an etalon.

Equations (10)

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δ ρ i , j δ t = B i N j ρ i , j γ i τ R T ρ i , j + A i N j
γ cav ( v ) = ln [ ε T et al ( v ) 2 ]
T et al = ( 1 R ) 2 v [ ( 1 RV ) 2 + 4 RV sin 2 ( π i n + π 2 ) ] 1
δ N j δ t = η λ P P in hc γ sp N j N j i I B i ρ i , j δ v
A i = B i τ RT = σ i c τ RT v mode
s i , j = A i N j δ v δ t
b ( k ) = ( S j k ) p k ( 1 p ) S j k
P out ( t j ) = hc λ v out τ RT i ρ i , j δ v .
P ¯ out = 1 N j P out ( t j )
G i , j = B i N j γ i

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