The theoretically determined slope efficiency and threshold pump power for continuous wave (CW) operation of a Tm-doped silica fiber laser are presented. The associated rate equations are solved using standard techniques and, in conjunction with the published and our measured spectroscopic parameters as input, the model was used to examine the fiber laser output for a variety of fiber and pump configurations. After good agreement was achieved between the model calculations and the published experimental measurements, the model was used to examine the relative performance of the fiber laser when the pump wavelength was varied over the /sup 3/F/sub 4/, /sup 3/H/sub 5/, and /sup 3/H/sub 4/ absorption bands of Tm/sup 3+/. The calculated maximum slope efficiencies were determined to be /spl sim/40, /spl sim/57, and /spl sim/84%, respectively, for each of the /sup 3/F/sub 4/, /sup 3/H/sub 5/, and /sup 3/H/sub 4/ absorption band pump schemes and the threshold pump power over the range of pump schemes was determined to vary by only 28%. The model was further used to analyze the fiber laser output when the fiber length, Tm/sup 3+/ concentration and /sup 3/H/sub 4/ energy level lifetime were varied and the consequences on the operation of the fiber laser with these variations are discussed.

Theoretical modeling of Tm-doped silica fiber lasers

In this paper, Topological insulator (TI) Bi2Se3 as a saturable absorber (SA) is exploited to Q-switch fiber lasers at 2 μm wavelength for the first time. Few-layer TI:Bi 2Se 3 nanosheets in CS-HAc solution are prepared by the liquid-phase exfoliation method, and the thin 2-D structure with the thickness of 3-5 layers is well characterized. The open-aperture Z-scan experiment shows that the few-layer TI:Bi 2Se 3 has the saturable optical intensity of 41 MW/cm 2 at 800 nm and the modulation depth of 3.7%. The optical deposition technique is used to efficiently assemble the TI:Bi 2Se 3 nanosheets in the solution onto a fiber ferrule, therefore constructing a fiber-compatible TI-based SA (FC-TISA). By further inserting the FC-TISA into a diode-pumped Tm 3+-doped double-clad fiber laser (TM-DCFL), stable Q-switching operation at 1.98 μm is successfully achieved with the shortest pulse width of 4.18 μs and the tunable repetition rate from 8.4 to 26.8 kHz. In particular, the TM-DCFL can deliver large-energy Q-switched pulses with the pulse energy as high as 313 nJ (corresponding to average output power of 8.4 mW). Our results suggest that TI-based SA is suitable for pulsed laser operation in the eye-safe region of 2 μm, and potentially develops as an ultra-broadband photonics device.

Topological-Insulator Passively Q-Switched Double-Clad Fiber Laser at 2 $\mu$ m Wavelength

An analytical model for two-, three-, and four-level system rare-earth-doped fiber amplifiers and lasers is presented. The theory is applicable to dopants such as erbium, neodymium, thulium; praseodymium, and ytterbium. Fiber-amplifier gain is expressed in terms of attenuation coefficients, intrinsic saturation powers, and cross-saturation powers at the pump and signal wavelengths. These parameters can be directly determined from one- and two-beam fiber-transmission measurements. System-independent formulas are given for the slopes and thresholds of ring and linear fiber lasers. Good agreement between theory and experiment has been shown for erbium-doped fiber amplifiers and lasers and thulium-doped fiber lasers. Because of the finite-pump-level lifetime, three- and four-level models predict a flattening of the fiber laser slope at higher pumping powers when the fiber is shorter than the optimum length. Approximate system-independent solutions are also given for fiber amplifiers with excited-state absorption at either the pump or signal wavelengths. A novel technique, requiring only one tunable light source, is proposed for finding the best pump wavelength when pump ESA is present. The two-level analytical model recently developed for erbium-doped fibers is a special case of this theory. >

Analytical model for rare-earth-doped fiber amplifiers and lasers

Spectroscopic measurements and analysis of energy transfer processes for Tm3+ singly- and Tm 3+ Ho 3+ doubly-doped glasses pumped with 790 nm diode laser have been performed. The emission cross-sections and the net gain have been determined from the measured absorption spectra for both the ions on the basis of principle of reciprocity. Tm3+ singly-doped fluorozircoaluminate glass, which has a higher fluorescence efficiency at 1.82 μm and a longer upper state lifetime, is a material suitable for Tm laser compared with oxide glasses. The quantum efficiency of Ho3+ fluorescence of 5I75I8 at 2.05 μm for the Tm 3+ Ho 3+ doubly-doped glass is dominated by three energy transfer processes: Tm3+Tm3+ cross-relaxation, net Tm3+Ho3+ energy transfer, and energy transfer upconversion. The first process allows pumping efficiency to approach 2, and the second one contributes to population of the upper 5I7 laser level, while the final process gives rise to a sublinear increase in upper state population with pump power. Optimum doping levels for laser performance are easily predicted based on spectroscopic measurements and are found to be 2–8Tm3+ (1020/cm3) for Tm3+ singly-doped and 2–8Tm3+/0.3–1Ho3+ (1020/cm3) for Tm3+/Ho3+ doubly-doped systems, respectively.

Spectroscopic properties and energy transfers in Tm3+ singly- and Tm3+Ho3+ doubly-doped glasses

Tm-doped ZBLAN and Tm-doped silica glass are compared spectroscopically and the fiber lasing of the Tm 3
F
4 →3
H
6 transition around 1.9 μm in ZBLAN and silica fibers is compared. The spectroscopy of these materials indicates that Tm:ZBLAN possesses advantages over Tm:silica glass due to the lower phonon energies. The phonon energy in these glass hosts influences both the pump manifold lifetime, the Tm 3
H
4, and the upper laser manifold lifetime, the Tm 3
F
4. The maximum phonon energy in Tm:ZBLAN, ∼500 cm-1 , compared to Tm:silica, ∼1100 cm-1, leads to better Tm–Tm self quenching towards populating the Tm 3
F
4, as well as better Tm 3
F
4→3
H
6 quantum efficiency. A spectroscopic analysis using the Judd–Ofelt theory and measured lifetimes are used to assess the merits of Tm:ZBLAN over Tm:silica as a fiber laser material. Diode-pumped fiber lasing experiments show that Tm:ZBLAN possesses advantages over Tm:silica that are believed to be due to a lower phonon energy. Data is presented for launched pump energy versus laser energy, fiber length versus slope efficiency, and output mirror reflectivity versus slope efficiency. Tm:ZBLAN is demonstrated to possess higher slope efficiencies and lower thresholds, than Tm:silicate. A grating tuned Tm:ZBLAN laser is also demonstrated for tunable operation between 1.893 μm and 1.955 μm.

Comparison of Tm:ZBLAN and Tm:Silica fiber lasers; Spectroscopy and tunable pulsed laser operation around 1.9 μm

A tunable Q-switched thulium-doped single-mode silica fiber laser is presented for the first time. Its performance is analyzed as a function of pulse repetition rate and pumping power. The optimization of laser parameters resulted in 4 W/1 30 ns, 1 .92-jrm wavelength pulses generated at a 4-kHz repetition rate. From the measured values of small- signal attenuation and intrinsic saturation power, the thulium ion param- eters at the pump and signal wavelength are derived and used in the- oretical modeling of the laser. The moderate power required from the Ti:sapphire pump laser used in the experiment suggests that similar re- suIts can be obtained using a laser diode pump.

Xing Pan

Papers

Q-switched thulium-doped fiber laser