Comparison of Output Performance of Tunable Lasers with Two Different External Cavities

Based on the simplified model of the tunable fiber laser system, the tuning performance of the laser was analyzed. Two kinds of tunable setups were established, which are the configurations with an external cavity and the configuration of the Littrow cavity. The tuning output characteristics experimentally were analyzed by means of setups. The simulation gives the output efficiency of two tunable lasers as 40% and 30%. In the experiment, the measured slope efficiency of the two lasers was 24% and 18.3%, and the tunable range of the two lasers was 32 nm and 40nm, respectively. Both lasers could achieve laser output with good beam quality.


Introduction
e ber laser is widely used in many elds, including optical communication, industrial manufacturing, and ber sensing systems [1][2][3][4], which require that the output beam of the laser can be tuned to one or more speci c wavelengths. erefore, tunable ber lasers have become important optical devices. A tunable external cavity ber laser can achieve tunable wavelengths by tuning the optical element [5,6]. Various external cavity tunable ber lasers system with the grating have been reported, which include the con guration with an output coupled mirror in an external cavity (the laser is called con guration); and the con guration with a Littrow cavity (the laser is called con guration); the maximum continuous tunable range can be up to several tens of nanometers; and the linewidth of the output beam is e ectively narrowed [7][8][9][10][11]. However, when we compare the external cavity tunable lasers with di erent con gurations, the output performances of lasers are di erent. Most researchers only reported their experimental results in tunable lasers but did not carry out a theoretical and experimental comparison of the performance between the di erent external cavity tunable lasers.
In this study, two kinds of tunable lasers with di erent external cavity con gurations are studied. First, the output e ect of the two lasers is analyzed theoretically. en, using a di raction grating with a di raction e ciency of 70% as a wavelength selector, we build two experimental systems of the external cavity tunable ber lasers and compare their experimental results. e results show that con guration 1 can realize the tunable range of 32 nm with the maximum output power of 560 mW and for con guration 2, can achieve the maximum output power of 427 mW with the tunable range of 40 nm. Both two tunable ber lasers can produce single-mode output with a beam quality factor (M 2 ) < 1.35. show the schematic diagram of con gurations 1 and 2, respectively. According to the generation principle of laser, the system can be simpli ed, as shown in Figure 2 [12].

Theoretical Analysis
In Figure 2, the inserted devices in con guration 1 are the collimating lens and grating and those in con guration 2 are the collimating lens and DM2. Assuming the length of the gain ber is L, that of the resonator is L′, launched pump power is P in p , and the output power is P out . According to the framework shown in Figure 2, if the transmissivity of the front-cavity mirror to the pump light equals 1, then the following equations can be obtained [12]: where K(λ) is the di raction e ciency of a blazed grating, and η(λ) is the coupling e ciency that the signal light is coupled back into the ber core. For K(λ), it can be derived as where K 0 is a constant with respect to the grating structure, d is the grating period, b is the lateral size of the di ractive facet, m is the di raction order, and θ is the blazed angle. If d 2.43 μm, b 5 μm, λ c 1550 nm, K 0 0.70, and m 1, the di raction e ciency of the grating at di erent wavelengths could be obtained, as shown in Figure 3. It can be seen that the di raction e ciency of the grating gradually increases from 1500 nm to 1545 nm, the di raction eciency gradually decreases from 1545 nm to 1600 nm, the highest di raction e ciency is 0.70 at 1545 nm, and the lower di raction e ciency is 0.598 at 1600 nm.
In the tuning performance analysis, another parameter of η must be used. For the parameter, Bochove has carried out the derivation [9], which can be written as where θ 0 λ/πw 0 is the far-eld divergence angle of the Gaussian mode eld, σ is the coupling bandwidth, and ω x and ω y are the wavefront curvature parameters, which are [13] Figure 1: Schematic diagram of tunable ber laser (a). Con guration 1 (b). Con guration 2.

Gain fibers
Inserted devices…(R 4 ) Figure 2: e framework of a simpli ed tunable ber laser system.

International Journal of Optics
where Z R is the Rayleigh length of the mode eld, ε is a defocus value, X is the transverse distance of the emitter from the system axis, Y is the emitter lateral o set out of the array plane, α and β are the parameters determined by transform lens, α 3 and β 1.33 [13]. If Y = 0, θ x,y = 0, and ε = 0, for di erent focal lengths of transformed lenses, the coupling e ciency at di erent transverse distances from the system axis can be obtained according to Equation (3), as shown in Figure 4. It can be seen that when the transverse distance increases, the coupling e ciency of the laser decreases gradually, and the coupling e ciency gradually increases with the increase of the focal length of the transform lens.

Relevant Parameters.
In the theoretical analysis, if the used gain ber is Er 3+ /Yb 3+ codoped double-clad ber with a ber length of 4 m. e relevant parameters include the spectrum absorption-emission cross-sections (σ Era and σ Ere ) of Er 3+ , as shown in Figure 5 [14].
According to the parameters of the ber given by the Nufern Company, the core diameter of the ber is 25 μm, the clad diameter is 300 μm, and the coating diameter is 450 μm. In addition, the concentration of Er3+ and Yb3+ doped in the ber is 4.8 × 10 25 m −3 and 3.7 × 10 26 m −3 , respectively, and the lifetime of Er3+ is 11 × 10 −3 s. Assuming the wavelength of the pump is 980 nm, the transition crosssections σ Er13 2.0 × 10 −25 m 2 and σ Yb65 5.0 × 10 −25 m 2 . Other relevant parameters involved are given in Table 1 [15,16].

Simulation Results.
Assuming the tunable range is 1500-1600 nm, the tuning step is 5 nm, Y 0, θ x,y 0, ε 0, and R 1 0.90, and the power of the tuning laser at di erent wavelengths was calculated, as shown in Figure 6.
For con guration 1, maximum output power is 800 mW, at a wavelength of 1547 nm, the minimum power is 210 mW at 1600 nm, and the calculated maximum output e ciency is 40%. Furthermore, the laser output power increases gradually in the range of 1500-1547 nm, and the output power gradually decreases in the range of 1547-1600 nm. For con guration 2, the maximum power is 600 mW at 1555 nm, the minimum power is 345 mW at 1500 nm, and the maximum output e ciency is 30%. e output power of the laser changes greatly at di erent wavelengths. e reason is that the di raction e ciency of    International Journal of Optics the grating at di erent wavelengths is di erent, and the absorption-emission cross-section of the optical ber at di erent wavelengths is di erent. e di erence in output e ciency between the two con gurations is mainly caused by the di erence in feedback intensity (R 3 ) at the backend of the external cavity. As the increase of the backend feedback intensity, the output e ciency gradually decreases [12].

Experimental Setup.
In two kinds of laser con gurations, the pump was provided by a laser diode with a central wavelength of 976 nm through a coupled system. e maximum power coupled into the ber was 3.0 W. e ber used was LMA Er 3+ /Yb 3+ codoped double-clad ber named PLMA-EYDF-25P/300-HE with a length of 4 m, whose core had a diameter of 25 μm with a numerical aperture (NA) of 0.09. e absorption coe cient was 2.9 dB/m at 980 nm. A dichroic mirror (DM1, high transmission to pump, and high re ectivity to signal light) was placed at the input end of the ber, which served as the front-cavity mirror of the resonator.
e output end of the ber was angle cleaved to suppress Fresnel re ection. A collimating lens (f 50 mm) was placed at the output end of the ber. e experimental setups are shown in Figure 7.
For con guration 1, the rst-order di racted beam of the grating was incident on the outcoupling mirror (OCM), which has a re ectivity of 15% to provide feedback for laser oscillating and achieve laser output. For con guration 2, to improve the conversion e ciency and output power of the ber laser, DM2 (high transmission to signal light and high re ectivity to pump) is placed behind the collimating lens. e grating was placed according to the Littrow angle, the rst-order di racted beam was re ected back, and the zeroth-order di racted beam was used as the output beam.
In addition, the grating has a frequency of 1200 lines/ mm with a blazing wavelength of 1550 nm, and the rstorder di raction e ciency of the grating can reach 70%. e laser beam quality was measured using a beam quality analyzer (M2MS BP209-IR), and the spectral performance was analyzed by an optical spectra analyzer (model: MS9710B).

Comparison of Tunable Ranges.
First, using con guration 1, the experiment was carried out. When the coupled pump power was 3 W, the tuned laser at the range of 32 nm from 1532 nm to 1564 nm was achieved, as shown in Figure 8(a). For each spectrum of the tuned laser, the measured 3 dB linewidth was less than 0.08 nm. e suppression of the ASE background was better than 46 dB. Next, the experiment of con guration 2 was conducted, as shown in Figure 8  measured maximum tuning range is 40 nm from 1530 nm to 1570 nm. For each spectrum of the tuned laser, the measured 3 dB linewidth was less than 0.1 nm. e suppression of the ASE background was better than 41 dB.
Compared to Figures 8(a) and 8(b), the tunable range of con guration 2 is wider than that of con guration 1. is is because the backend of the external cavity of con guration 1 is OCM, which has low feedback for the signal light. According to the curve in Figure 6, for con guration 1, the weak feedback signal light cannot induce a more population of Er 3+ transitions. For con guration 2, the backend of the external cavity is the grating, which has higher feedback for the signal light, and the higher feedback intensity can induce more population of Er 3+ to nish the energy level transition, realizing the tuned laser output in a wider band.
Furthermore, we also compared the tuning range of the simulation and the experiment. It can be found that the tuning range in the experiment is narrower than that in simulation. is is because the oscillation threshold of two con gurations is di erent at di erent wavelengths; it can also be found in Figure 9 (Section 3.2.2). However, the oscillation threshold is set to a small constant in the simulation, which makes laser oscillation be produced at lower power, resulting in a wider tuning range.

Comparison of Output Power.
In the experiment, the measurements of the laser output power of the two congurations at di erent coupled pump power were made, as shown in Figure 9. When the coupled pump power was 3 W, the maximum laser output of 501 mW at 1546 nm was achieved by con guration 1 with a slope e ciency of 24%. For con guration 2, the maximum output power is 409 mW at 1550 nm with a slope e ciency of 18.3%.
e output e ciency of the tuned output laser in the experiment is lower than that in the simulation. is is because the anglecleaved facet of the ber is not polished, and the lenses used in this experiment do not have an antire ection coating of a 1550 nm band, which reduces the e ciency of the lasers. In addition, with the increase of the pump power, the output laser power increases approximately linearly, and saturation gain does not occur, which means that the pump power can be continuously increased to obtain higher output power.
Furthermore, the output power of the tunable laser at di erent wavelengths is measured, which is shown in Figure 10. It can be seen that the wavelength of maximum power in the experiment is slightly di erent from that in the calculation because of the di erent lengths of the resonators. e output power of con guration 1 is higher than that of con guration 2; this is because considering all external e slope e ciency when the tuning wavelength is 1546 nm for con guration 1 and 1550 nm for con guration 2. International Journal of Optics cavity loss factors, the total feedback level of rst-order di raction light is over 50% in con guration 2, and the grating di raction e ciency of zero-order light is 25%, which lead to a lower outcoupling ratio of the resonator, and cause large cavity loss and limit the e ective increase of the output power and slope e ciency of the tunable ber laser. However, in con guration 1, the feedback intensity of the external cavity is about 15%, which causes a higher outcoupling ratio and increases the e ciency of the resonator. Furthermore, the slope e ciency and output power of the laser can be improved by reducing the external cavity loss and adopting the backward output con guration [15].

Comparison of Beam Quality.
When the wavelength of the output laser was 1548 nm, the output beam quality factor(M 2 ) of the two lasers was measured, as shown in Figure 11. For con guration 1, the measured M x 2 is 1.22, and for con guration 2, M x 2 1.31. Compared with the ideal Gaussian beam, the beam quality is degraded; this is due to the aberration of the transform lens and the etching error of the grating. Figure 12 shows the measurement results of the M 2 in the tuning range. e M 2 of con guration 1 is kept at the range of 1.22-1.26, and M 2 of the con guration 2 is kept in the range of 1.31-1.34. e output beam quality of con guration 1 is better than that of con guration 2; the reason is that the direction of propagation of the output beams is normal to the OCM [17] in con guration 1, which causes the divergence angle to be smaller than that in con guration 2. In addition, the lower NA of the Er 3+ -Yb 3+ codoped doubleclad ber also makes it easier to achieve laser output with good beam quality. Furthermore, with relatively simple modi cations to the cavity design (with a shorter focallength collimating lens or a di raction grating with a larger pitch), it should be possible to improve the beam quality M 2 to <1.1 [18][19][20][21].

Conclusion
In this study, according to the principle of laser generation, we simplify the two external cavity tunable systems into a ber laser system. Based on the rate equation of Er/Yb codoped ber laser and the established boundary conditions, the changes of the output powers with the wavelength were analyzed. e result shows that assuming the pump power is 2 W, the maximum tuning power of con guration 1 is 800 mW at 1545 nm. e maximum tuning power of conguration 2 is 600 mW at 1555 nm. Furthermore, the experimental setups of two kinds of external cavity tunable ber lasers were also built, and their di erences in output e ects of them were compared and analyzed. For con guration 1, the measured maximum output power is 501 mW with a maximum slope e ciency of 24%, the tuning range is 32 nm from 1532 to 1564 nm, and M 2 is kept in the range of 1.22-1.24; the suppression of the signal background caused by ASE was better than 46 dB. For con guration 2, the maximum output power is 409 mW with a slope e ciency of 18.3%, the tuning range is 40 nm from 1530 to 1570 nm, and M 2 is kept in the range of 1.31-1.33. e suppression of the signal background caused by ASE was better than 41 dB. e backend feedback (R 3 ) of the resonator has a great in uence  on the tunable range and output power. is research can provide potential value for the DWDM and fiber sensing system.

Data Availability
e (DATA TYPE) data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.