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Using a short linear cavity composed of a section of highly ytterbium-doped fiber surrounded by two fiber Bragg gratings, dual-frequency switching is achieved by tuning the pump power of the laser. The dual-frequency switching is generated by the thermal effects of the absorbed pump in the ytterbium-doped fiber. At each frequency, the laser shows single-longitudinal-mode behavior. In each single-mode regime, the optical signal-to-noise ratio of the laser is greater than 50 dB. The dual-frequency, switchable, fiber laser can be designed for various applications by the careful selection of the two gratings.
©2007 Optical Society of America
1. Introduction
Fiber lasers have compact volume, high beam quality, high output power, good thermal management, and low noise floor [1–4]; therefore, in many applications they are considered to be superior alternatives to solid-state and semiconductor lasers. In recent years, multiple-frequency fiber lasers have attracted significant interest [5–11] for their use in sensing [12], instrumental testing [13], and optical communications [14,15].
Frequency-switchable fiber lasers [16–20] have been proven to play an important role in wavelength-routing wavelength-division-multiplexer (WDM) networks. Although much effort has been focused on semiconductor lasers [21], fiber lasers are considered to be desirable candidates as switchable sources for photonic networks. Multiple-frequency switchable fiber lasers have been realized by designing different thresholds at various wavelengths [16] or by changing the polarization of the various lasing modes [17–20]. Such systems require overlapping multiple cavities or polarization controllers. In this paper, dual-frequency switching is demonstrated in a single linear, fiber-laser cavity without any polarization-controlling component. The laser frequency switching is caused by the pump-induced thermal effects of the two fiber Bragg gratings (FBGs), and can therefore be controlled by current tuning of the pump laser. This phenomenon can be used to design dual-frequency switchable fiber lasers by carefully aligning the spectra of the two gratings along a short linear cavity.
2. Switchable dual-frequency laser configuration
In the switchable dual-frequency laser shown in Fig. 1, a 1.5-cm section of highly ytterbium-doped silica fiber was spliced between two FBGs. The pump absorption rate of the active fiber is 1700 dB/m. The polarization maintaining (PM) FBG has two reflection peaks with 0.3-nm spacing due to the different modal average index along the orthogonal fast and slow axes. Both of the reflection bands have 3-dB bandwidths of 0.06 nm and exhibit a peak reflectivity of 55% at the corresponding wavelengths. The single-mode (SM) FBG has a center wavelength of 1029.3 nm and a peak reflectivity of 99%. The transmission spectra of the PM FBG and SM FBG are measured with an unpolarized amplified spontaneous emission (ASE) source and are shown in Fig. 2. The spectra of the SM and PM FBGs overlap at room temperature. A WDM is used to couple the 976-nm pump light into the active gain medium.
Fig. 1. Setup of the dual-frequency fiber laser. PM is the power meter, OSA is the optical spectrum analyzer, and FP is the Febry–Parot scanning spectrometer.
The laser output characteristics were measured from the transmission end of the PM FBG with a power meter, a Fabry–Perot (FP) scanning spectrometer, and an optical spectrum analyzer (OSA). In the measurement, the FP spectrometer had a 1-mm cavity length, corresponding to a free spectral range of 150 GHz. With the finesse of 150, the FP cavity had a frequency resolution of 1 GHz. Since the 2-cm laser cavity dictates a 5-GHz mode spacing, the FP spectrometer can resolve all longitudinal modes of the laser resonator.
3. Experimental results
Ytterbium can be treated as a homogeneously broadened medium, nominally permitting only one laser frequency above threshold; however, polarization hole burning and spatial hole burning in the linear cavity enable the laser to work in the dual-frequency regime [22]. In the configuration of Fig. 1, the laser shows stable dual-frequency output, with an optical signal-to-noise ratio (OSNR) greater than 60 dB [23].
The pump current–output power characteristics of the dual-frequency laser are shown in Fig. 3. The available output power was measured to be 16.5 mW. The maximum pump power in the experiment was 270 mW at 850 mA. The rollover of the curve is due to the thermal effects, as will be explained in Sec. 4. The single-longitudinal-mode property of each frequency was verified in previous reports [23,24].
Dual-frequency switching can be achieved by tuning the power of the pump laser. The laser output measured with the OSA and FP spectrometer are shown in the movies of Figs. 4 and 5, respectively. Switching between the two frequencies is clearly observable in both movies.
Fig. 5. Movie of the measured output spectrum on the FP spectrometer at different pump levels. [Media 2]
The peak power at each lasing wavelength as a function of the pump current is displayed in Fig. 6. This figure shows that the pump current can be selected to generate either single-frequency or dual-frequency output. The laser emits equal powers at two lasing peaks when the pump current is 250 mA, 430 mA, or 640 mA. The output-power ratio of the two lasing wavelengths differs at other pump currents. In the single-frequency working regime, at pump currents of 100 mA, 310 mA, 490 mA, and 850 mA, the OSNR of the laser is greater than 50 dB. Additionally, the power rms variation is <0.9% and the peak-to-valley wavelength deviation is <0.02 nm over a 2-h period [24]. In the dual-frequency working regime, the relative peak-power variation between two lasing peaks is less than 0.05% for a typical diode pump controller [23].
Fig. 6. Measured laser power as a function of pump current. Each curve represents a different frequency.
4. Modeling and simulations
The switching phenomenon demonstrated in this laser is achieved via pump-induced thermal effects. The absorption of pump light in the active fiber leads to asymmetric heating in the laser cavity, which causes the reflection spectra of the FBGs to shift with respect to each other [25]. The round-trip net gain at each of the two lasing peaks will thus be altered in the laser cavity. The lasing thresholds of the two lasing peaks are therefore changed, leading to differential laser gain and output.
To model this phenomenon, the axial distribution of absorbed pump power is calculated along the active fiber, from which the temperature is calculated along the entire fiber laser cavity. After the temperature distribution is calculated, the spectra of the two FBGs are calculated using the temperature profile in the FBGs with the transfer matrix method [26]. The gain thresholds at the two lasing wavelengths are thus derived at different pump levels and phenomenologically describe the dual-frequency switching in this laser cavity.
To obtain the absorbed pump power along the fiber, a simulation is carried out using an iteration method [27]. Similar to erbium-doped fiber lasers, ytterbium-doped fiber lasers can be modeled as a quasi-two-level system [28]. In this case, the distribution of pump power, lasing signal power, and ASE power can be described in the steady-state (i.e., cw) regime by [27]:
where Pp(z) is the pump power; P ±(z,λ) is the signal, PT(z,λ) is P +(z,λ) + P -(z,λ), and ASE power per unit wavelength traveling in the forward (+) or backward (-) direction; A is the fiber-core cross section; Γp/S is the overlap factor of the pump/signal with the doping ions; α p/s is the scattering coefficient at the pump/signal wavelength; N is the total population density and N 2 is the upper-state population density; σe(λ) and σa(λ) are the emission and absorption cross-sections, respectively, whose values are taken from previous work [29]; and τ is the upper-state spontaneous lifetime, measured as 0.17 ms for this highly ytterbium-doped fiber. The spontaneously emitted power P 0(λ) per unit wavelength is defined as
Equations (1)–(3) are solved numerically with a spectral bandwidth of 0.05 nm using the finite-difference method. This bandwidth provides sufficient resolution to model the observed laser behavior. The boundary conditions at the two FBG’s are
where λ 1 and λ 2 are the peak reflection wavelengths of the PM FBG, corresponding to the lasing peaks. Since the FBG bandwidths are very small, the reflection spectra can be approximated as
where R PM is the PM FBG peak reflectivity and R SM is the SM FBG peak reflectivity. When Eqs. (1)–(3) are solved using Eqs. (4)–(6) and the parameters from Table I, the total signal power converges at an error of less than 10-5. The results are displayed in Fig. 7, which shows the pump power attenuation along the fiber due to the absorption by the ytterbium ions.
Table I. Parameters used for the laser pump simulation.
The temperature distribution in the laser is described with the following heat-conduction equation [30]:
where pν(r,z) is the pump power absorbed per unit volume, η is the conversion efficiency of the absorbed pump into heat, and k is the thermal conductivity. Due to the relative sizes of the core and cladding, pν can be simplified by assuming the pump power is uniformly absorbed across the core as [30]
The boundary condition at the fiber–air interface is [30]
where h is the heat-transfer coefficient, b is the cladding radius of the active fiber, and T 0 is the ambient environmental temperature. Assuming azimuthal symmetry, Eqs. (7)–(9) are solved in both the active and passive sections of the fiber with the parameters from Table II using the finite-difference method [31]. The resu ltant steady-state temperature distribution along the fiber is shown in Fig. 8. Due to the single-end pump geometry, the heat generation is higher on the PM FBG end of the laser; therefore, the temperature rise and thermal gradient in the PM FBG are larger than those of the SM FBG, becoming very pronounced at higher pump powers.
Table II. Parameters used for the thermal calculation.
The thermal distribution in the PM and SM FBGs will chirp the two gratings and shift their central wavelengths. The PM FBG has a peak reflectivity of 55% and a grating length of 5 mm, giving a coupling coefficient of κ PM = 1.6 cm-1. The SM FBG has a peak reflectivity of 99% and a grating length of 4 mm, yielding a coupling coefficient of κ SM = 7.1 cm-1. The coefficient of thermal expansion of the active silica fiber is 5 × 10-7/°C [32]. Starting with these parameters, the FBG spectra with different thermal distributions are calculated with the transfer matrix method [26]. In this method, the chirped gratings are segmented into many sections, each having a uniform period of ʌ = ʌ0 (1 + C TE∆T), where Λ0 is the grating period at room temperature, C TE is the coefficient of thermal expansion, and ∆T is the grating temperature rise. Each section is described with a fundamental transfer matrix in the following form:
The matrix elements are derived from standard coupled mode theory for a uniform grating and are given by [26]
where γ 2 j = κ 2 j-(∆βj)2 , ∆βj = β-βjB, βjB = π/Λj, β = 2π/λ, ϕj =ϕ j-1 + 2βjB L j-1, Lj is the length of the jth section, and kj is the coupling strength of the grating. The total transfer matrix describing the chirped grating can be written as
and the reflection spectrum of the grating is [26]
The reflection spectrum of each FBG is calculated using Eqs. (10)–(16) and the calculated temperature distributions shown in Fig. 8. The movie in Fig. 9 shows the chirped PM and SM FBG spectra under different pump levels from 0 mW to 270 mW (pump current from 0 mA to 850 mA). The SM FBG is only minimally affected by the pump-induced heating, while the PM FBG is substantially thermally chirped. The lasing wavelength shift is less than 0.01 nm as the pump current is increased. Assuming that the gain curve in the measured wavelength region is uniform, the gain threshold is determined by the reflectivities of the two FBG’s and can be described by the simple equation
The laser wavelengths are therefore determined by the product of the reflection spectra of the two FBGs. The result of generating this product from the spectra is shown in Fig. 9. As the pump power is increased, the induced temperature rise causes the spectrum of the PM FBG to shift with respect to that of the SM FBG. As the peaks of the PM FBG shift, their overlap with the structured spectrum of the SM FBG also changes, creating threshold conditions for each peak that vary with pump current. The gain thresholds at the two peaks (along the fast and slow axes) are calculated according to Eq. (17 ). Figure 10 shows the threshold-gain difference between the two spectra peaks along the two polarization axes. When the gain difference is near zero, the two modes have equivalent threshold gain and the two lasing modes generate equal power. When the gain difference is not zero, differential output power is produced. For example, when the pump current is 160 mA, having the differential gain threshold shown in Fig. 10, the two wavelengths operate with output powers having 10-dB mode discrimination, as can be seen in Fig. 6. Furthermore, the calculated multiple switching currents at 250 mA, 430 mA, and 640 mA are in excellent agreement with the switching currents measured in Fig. 6. As the pump current is increased, the spectrum of the PM grating shows a pronounced shift to the longer wavelength, while the SM grating shows only a minor shift. The overlap of the PM FBG spectrum with the side lobes and the center reflection band of the SM FBG spectrum are crucial for having multiple switch points in this dual-frequency-switching phenomenon. This can be verified by observing the shifting of the PM FBG peaks across the side lobes and nulls of the SM FBG in Fig. 9. Additionally, the walk-off of the two spectra generates the total output power rollover observed experimentally in Fig. 3. If the temperature difference between the two FBG’s becomes large enough, the output power will be zero.
Fig. 10. Calculated threshold gain discrimination between the fast and slow axes as a function of the pump current.
5. Discussions and conclusions
Given the grating detuning mechanism, the dual-frequency switching can be induced thermally without changing the pump current. Holding the pump power constant at 270 mW, the temperature of the PM FBG is varied between 25°C and 35°C. Under these conditions, the laser output spectra measured with the FP spectrometer and OSA are shown in the movies of Figs. 11 and 12, respectively. While both the pump power and the temperature varied in the pump-induced switching experiment, the temperature variation alone generates the dual-frequency switching in this experiment; therefore, the thermal chirp of the gratings is not the main contributor of the dual-frequency switching.
The dual-frequency-switching DBR fiber laser can be designed according to the application. The side lobes of the SM FBG can have high reflectivities as the product of the grating coupling coefficient κ and the grating length L becomes large. To achieve the dual-frequency switching from the fiber laser with a temperature rise, the left reflection peak of the narrowband PM FBG should be overlapped with the left side lobe of the SM FBG, the other reflection peak of the PM FBG should be overlapped with the right edge of the SM FBG center reflection band. Alternatively, to achieve the dual-frequency switching with a temperature reduction, the right reflection peak of the narrowband PM FBG should be overlapped with the right side lobe of the SM FBG, the other PM FBG reflection peak should be overlapped with the left edge of the SM FBG center reflection band. Note that ambient temperature changes will affect both gratings similarly and no switching will occur, unless one of the gratings is temperature controlled. In either case, thermally induced spectral overlap variation will generate dual-frequency switching from the carefully designed DBR fiber laser.
Fig. 11. Movie of the measured output spectrum on FP spectrometer at different PM FBG temperatures. [Media 4]
It is also important to note that the complexities due to the spectral side lobes of the FBG are not required if only a single switching point is desired. Overlapping one peak of the PM FBG with the SM FBG will generate a single-frequency output. By thermally tuning the PM FBG to make the other peak overlap with the SM FBG, the former peak walks out of the SM FBG reflection band, and a single switching point can be realized to achieve dual-frequency switching.
In conclusion, using a short linear cavity composed of a section of highly ytterbium-doped fiber surrounded by two FBG’s, dual-frequency switching is achieved by tuning the pump power of the laser. The dual-frequency switching is generated by the thermal effects of the absorbed pump in the ytterbium-doped fiber. At each frequency, the laser shows single-longitudinal-mode behavior. In each single-mode regime, the OSNR of the laser is greater than 50 dB. The dual-frequency, switchable, fiber laser can be designed for various applications by careful selection of the two gratings.
This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52–92SF19460, the University of Rochester, and the New York State Energy Research and Development Authority. The support of DOE does not constitute an endorsement by DOE of the views expressed in this article.
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