P. Peterson

CW theory of a laser diode-pumped two-manifold solid state laser

Abstract We develop a general plane wave theory for cw diode-pumped solid state lasers which is valid for arbitrary saturation and outcoupling. Our model is based on the steady state rate equations for a two-manifold system coupled to the growth of the laser field and the depletion of the pump. This model is entirely analytic and predicts: a linear photon flux conservation law; the modification to Beers law pump depletion due to outcoupling, and its influence on the pump threshold; optimal crystal lengths and outcouplings as functions of temperature. We give some examples which show optimal lengths and reflectivities for Tm:YAG.

Diode-pumped Tm: YAG solid-state lasers with indirect and direct manifold pumping

We study the continuous-wave (cw) characteristics of both two-manifold and three-manifold Tm: YAG laser pumped at λp ≈ 1.8 µm or λp = 0.785 µm and lasing at λ1 = 2.02 µm. The three-manifold rate equations are adiabatically reduced to their two-manifold form. For each pumping scheme, the steady-state rate equations are combined with the cw differential equations for the forward- and reverse-lasing fields and the pump-depletion differential equation. These three coupled cw differential equations are solved analytically. This gives the linear flux-conservation law between the input pump and the laser output, the minimum crystal length, and optimal output couplings. We show that the major difference between these two pumping schemes is due to the different pump effective absorption cross sections and not the two-for-one cross relaxation. Our example shows that the minimum intensity threshold and optimal crystal length are smaller for pumping at λtp = 0.785 µm than pumping at λp ≈ 1.8 µm.

Modeling of Yb:YAG tuning curves

Abstract We simulate Yb:YAG laser tuning curves using analytic equations for a two manifold laser. Our simulations agree with experiment.

Extraction efficiency and thermal lensing in Tm: YAG lasers

We model and compare with experiment the threshold, extraction efficiency and temperature effects in Tm:YAG lasers. In particular, we are concerned with high pump powers where lasing can cease abruptly. We simulate the pump depletion equation with the forward and reverse lasing equations combined with the CW rate equations which include cross-relaxation. The resonator is single-pass, end-pumped Fabry-Perot. Consequently, the equations must be solved numerically with a shooter. Our simulation of these equations gives the z-dependence of the intensities, of the populations and of the heat source. Heating is created by nonradiative decay from the two upper manifolds and by the cross-relaxation energy deficit. This leads to thermal lensing as a function of incident pump power which causes lasing shut-off as the resonator becomes unstable. Our simulations for the slope efficiency, threshold and laser shut-off agree with experiment. Additionally, we show that for pump powers in the range of 15–20 W the core temperature rise is about 40 K and the thermal focal length is in the range 5–6 cm.

Back-reflection pumping versus contradirectional pumping in upconversion solid state lasers

Abstract We show that a change from contradirectional pumping to back-reflection pumping in upconversion lasers can reduce the threshold by 50%, increase the slope efficiency by 87%, and increase the laser output power by a factor of two to six depending on the pump powers. Our predictions are anchored to an upconversion Pr 3+ ZBLAN fiber laser experiment to within 10%.

Cw theory of a diode pumped solid state laser in a resonant pump cavity

Abstract We develop the cw extraction equations for diode pumped solid state lasers when the pumping field is also constrained by a resonant cavity. That is, both the pump and the laser fields are described by forward and reverse fields and two point boundary conditions. Our model includes depleted pump with direct-manifold pumping characterized by the pump photon connecting the two manifolds from which lasing occurs. We derive the condition for minimum threshold pumping and show that it occurs when the reflected pump field vanishes. We compare the optimal crystal lengths, thresholds, and laser output rates for resonant pumping with their single pass pump counterparts. We show that with the recirculating pump the laser output can be at least ten times larger than the single pass output for the parameters chosen.

Periodic response of the Bloch equations to a pulse train; an application to mesospheric sodium

Abstract The post-transient response of the Bloch equations subject to a periodic pulse train is investigated. This is accomplished by representing all time-dependent variables in their Fourier series with time independent expansion coefficients. Inserting these expansions into the Bloch equations results in a matrix equation which is easily solved. In order to check the validity of this code a square pulse analytic piecewise solution is developed for the relaxation times much longer than the pulse width. Several comparative examples are given for scattering in mesospheric sodium when it is approximated as a two-level atom with short pulse gaussian and square wave envelopes.

Modelling of excited state absorption and upconversion in erbium germanosilicate continuous wave fibre lasers

The effects of upconversion and pump excited state absorption (ESA) on a three-manifold continuous wave (CW) laser are investigated by solving the laser and pump differential equations subject to two-point boundary conditions. This technique is applied to erbium germanosilicate fibre lasers in low-finesse cavities. First, the three-manifold laser problem in a low-finesse cavity is solved analytically, without ESA and upconversion. This shows that the finite value of the upper pump manifold decay rate causes the extracted power to saturate, and it also shows that pump threshold is strongly influenced by the cavity reflectivity. Next, upconversion and ESA are included. This leads to a study of the extracted power and pump threshold as functions of fibre length and outcoupling. This simulation is numerical and is successfully anchored to experiment.

Modelling of Threshold and Extraction Efficiency in Pr3+ ZBLAN Upconversion Fibre Lasers Using Two-Photon Pumping

We model the steady-state threshold and extracted power of a two-photon incoherently pumped upconversion fibre laser. Our threshold analysis is entirely analytic, and along with this derivation we obtain an analytic threshold cutback formula. This takes a particularly simple form when the ground state pump absorption follows exponential absorption. We also numerically simulate the extracted laser power. The experiment which we simulate is upconversion in Pr3+ doped ZBLAN fibre lasing at 491 nm and pumped with 1017 nm and 835 nm diode lasers. Our formulas and simulations are mutually consistent and agree with the experiment to within 10%.

Periodic response of the Bloch equations to a phase modulated pulse train; an application to mesospheric sodium

Abstract The periodic response is compared of the Bloch equations with a phase modulated pulse train to the response with an unmodulated pulse train. The starting equations are the Bloch equations with complex Rabi frequencies. The used analytic methods rely on decomposing all time dependent variables in their Fourier series periodic in the pulse train period. This leads to a complex matrix equation for the expansion coefficients. The obtained results for a quadratically chirped phase show about a five fold increase in scattering for chirped over unmodulated pulse trains. This is for a gaussian pulse train with period T>50 ns, pulse width tp = 2 ns, intensity of I = 10 W cm 2 , and a quadratic chirp of α = 1.5 × 1018S-2.