The wavelength dependent measurement of the relaxation oscillation frequency in a laser oscillator allows the study of the three- and four-level nature of the active material. Accordingly we present a tunable thulium doped fiber laser that covers the transition from three- to four-level operation at 2025 nm, characterized by the vanishing occupation of the terminal laser level. The laser is tunable from 1864nm to 2075nm with a linewidth below 0.3 nm. A maximum output power of 3.8W at 1930nm was achieved with a slope efficiency of 33.6% and an absorbed pump power of 17.5W. Absorption and emission cross sections were derived over the tuning range by an intracavity measurement method.
©2008 Optical Society of America
Rare-earth doped silica fibers are widely used in many cavity configurations and with different operation regimes. Setup of new and optimization of existing laser designs requires the knowledge of basic properties of the actual active material. These are normally gained by spectroscopic measurements and calculations and can be used to predict gain, lasing threshold, noise properties and other parameters of interest. However, these measurements are often complex, involving cut back measurements, and scaling of the derived spectra for the absorption and emission cross sections tends to be problematic especially for the emission cross section. An alternative approach is the intracavity method for deriving the cross sections based on the measurement of relaxation oscillations in a tunable laser . The relaxation oscillation frequency is directly linked to the absorption and emission cross section. Moreover, the wavelength dependent change in the transition properties of a laser from three-level to four-level operation can be directly derived. The knowledge of the transition character of a laser is required for modeling its output characteristics. In fiber lasers the transition character especially defines, if reabsorption effects have to be considered, which influence the transient laser behavior. Whereas amplitude instabilities due to reabsorption effects should be avoided in high stability lasers they may be necessary as starting mechanisms in mode locked lasers. The intracavity measurements have been reported for tunable fiber lasers based on Er3+, Nd3+ and Yb3+ [1–3].
Nowadays, Tm3+ doped silica fibers have gained increasing interest, expanding the accessible wavelength range of rare earth doped fiber lasers to the 2µm wavelength region. High power lasers have been demonstrated as well as short pulsed lasers and amplifiers [4–7].
In this paper we report on the intracavity measurement of the transition nature of a widely tunable, Tm3+-doped fiber ring oscillator and derive the absorption and emission cross section of the fiber without the use of complex spectroscopic measurements. The measurement allows to distinguish between three- and four-level operation of the system and is easy to perform in order to obtain basic transition parameters directly from the operating laser.
2. Experimental setup
The setup of the unidirectional ring-cavity is shown in Fig. 1. It consisted of a fiber section with a length of 4.22m and a free space propagation section of 0.46m length. The fiber section was divided into 2.78m of active fiber and 0.64m and 0.8m long passive fibers. Both fibers are double clad large mode area fibers with a pump core of 250µm diameter, and a signal core of 25µm diameter with a numerical aperture of 0.46 and 0.10, respectively. The active thulium-doped fiber has a nominal absorption of 5 dB/m at the pump wavelength of 793nm corresponding to a pump light absorption of 96 %. Both fiber ends were angle polished to avoid Fresnel back reflections. The complete length of the active fiber was water cooled to reduce thermal influences on the stability of the laser. An optical isolator ensured unidirectional operation and additional wave-plates adjusted the polarization between the fiber and the input polarizer of the isolator acting as a variable output coupler. The wavelength selection of the laser was provided by a blazed grating with 600 lines/mm, used near Littrow-angle. With the half wave plate in front of it, the polarization state was adjusted for optimized diffraction efficiency. The pump light was delivered via the end facet of the fiber, contra directional to its operation direction. A dichroic mirror was applied for the separation of pump- and laser light. The pump diode was a fiber coupled module operated at 793nm with a fiber diameter of 200µm and a numerical aperture of 0.22. The maximum launched pump power was 17.5W.
3. Operation of the thulium-doped fiber laser
In Fig. 2(a) the output power of the laser system versus pump power is shown for different wavelengths. A maximum output power of 3.8W with a slope efficiency of 33.6% was generated at 1930 nm. For longer wavelengths the slope efficiency decreased, due to the reduced emission cross section of thulium in silica fibers. For shorter wavelengths the laser threshold increased due to reabsorption losses caused by the increasing absorption cross section and therefore higher optimum output coupling ratio.
The tuning behavior is depicted in Fig. 2(b). The whole tuning range spanned from 1864nm to 2075nm at an absorbed pump power of 17.5W. In the wavelength range between 1880nm to 2060nm the laser generated an output power of more than 2W. The wavelength was measured by using a grating monochromator with a spectral resolution of 0.3 nm. Therefore the measured line width was limited by this resolution over the whole tuning range. An example spectrum is shown in Fig. 3 for a wavelength of 1942.25 nm. The lineshape is caused by the asymmetric transmission function of the monochromator (The actual spectral linewidth could not be measured with the equipment available at 1.95µm wavelength).
4. Three- and four-level operation
The characterization of the transition properties of a rare earth doped fiber laser can be performed by a detailed analysis of the wavelength dependence of the relaxation oscillations. Regarding the rate equations for a three-level system, the small-signal analytical solution reveals an expression for the relaxation oscillation frequency ω relax [1, 3]:
Here N is the total number of active ions per volume, c is the speed of light. η is the fraction of the optical path length of the active fiber to the total cavity length and σ Abs and σ Em are the absorption and emission cross section respectively. τ c and τ f are the cavity and fluorescence lifetimes, respectively. r=R/R Th is the pumping rate normalized to the pumping rate at laser threshold. In the three-level case, the relaxation oscillation frequency depends on the wavelength due to the fractional thermal occupation of the lower laser level, whereas the second term in the first set of parenthesis in Eq. (2) vanishes in the four-level case (σ Abs→0), leading to the well known relation ω 2 relax=(τ c τ f)-1(r-1).
The result for ω 2 relax versus pumping rate (r-1) is given in Fig. 4(a). It shows a linear dependence for all operating wavelengths of the laser. The slope efficiency of the curves decreases towards longer wavelengths due to the decreasing influence of the thermal population of the terminal laser level. The corresponding wavelength dependence is shown in Fig. 4(b). Above 2025nm the values become independent from the wavelength, indicating that the terminal level of the laser transition is not populated and the laser can be characterized as a four-level system for longer wavelengths.
5. Absorption and emission cross sections
In the four-level limit Eq. (2) simplifies to the relation ω 2 relax/(r-1)=1/(τ c τ s) and allows the calculation of the cavity lifetime τ c. The fluorescent lifetime τ f was measured with a decay experiment to τ f=420µs, which is in good agreement with values published elsewhere (see Fig. 5(a)) [8–12]. This results in a cavity lifetime of τ c=5.3 ns. The doping concentration N=2.4 ·1026m-3 was only given roughly by the fiber manufacturer and therefore is the main source of errors.
Inserting these values into Eq. (2) reveals the wavelength dependent absorption cross section that in turn allows the calculation of the emission cross section using Eq. (1). The resulting spectra are shown in Fig. 5(b). The peak emission cross section of 5.8·10-25m2 at 1880nm is in good agreement with the values reported in [9, 10], but almost twice the value reported in [8,12]. Main advantage of the presented method is its simplicity compared with spectroscopic measurement method. It allows to achieve cross sections for the fiber operating in the laser. The results obtained will be used to further improve the laser design for higher efficiency and optimized tuning range.
In summary, the relaxation oscillation dynamics of a thulium-doped fiber-ring laser was characterized over a wide spectral range. The laser was tunable from 1864nm to 2075nm with a line width below 0.3 nm. At an absorbed pump power of 17.5W the maximum output power was 3.8W at 1930 nm. To the best of our knowledge, this is the highest output power obtained so far with a thulium doped fiber laser in a unidirectional ring cavity setup.
The laser relaxation oscillations revealed a strong wavelength dependence caused by the change of the transition character from a three-level system below 2025nm to a four-level nature at longer wavelengths. Using the relaxation measurement, absorption and emission cross sections were derived, avoiding external measurements and cut back methods. The change in the transient dynamics as well as the characteristics of the spectral shape of the cross sections has to be taken into account carefully for the development of pulsed and stable continuous wave thulium-doped fiber lasers as well.
References and links
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