Accepted for Optics Letters, 12th June 2017 Genetic algorithm-based control of birefringent filtering for self-tuning, self-pulsing fiber lasers R. I. Woodward and E. J. R. Kelleher Femtosecond Optics Group, Photon Science Section, Department of Physics, Blackett Laboratory, Imperial College London, London, UK Polarization-based filtering in fiber lasers is well-known to enable spectral tunability and a wide range of dynamical operating states. This effect is rarely exploited in practical systems, however, because optimization of cavity parameters is non-trivial and evolves due to environmental sensitivity. Here, we report a genetic algorithm-based approach, utilizing electronic control of the cavity transfer function, to autonomously achieve broad wavelength tuning and the generation of Q-switched pulses with variable repetition rate and duration. The practicalities and limitations of simultaneous spec- tral and temporal self-tuning from a simple fiber laser are discussed, paving the way to on-demand laser properties through algorithmic control and machine learning schemes. Fiber lasers are an important technology that contin- mation [5], and enabled tuning of both wavelength [6, 7] ues to enable new applications as device performance, and pulse duration [7] by exploiting the chirped pulse flexibility and reliability improve. Alongside research dynamics. pushing the frontiers of laser specifications in the labora- The use of polarization-based filtering techniques in tory, there is a need to develop tunable, turn-key systems practical systems has been limited, however, by two ma- for non-expert users, allowing precise control of temporal jor problems. Firstly, fiber birefringence can be modi- and spectral properties of the source. fied by its environment (i.e. thermally/mechanically in- Spectral tunability can be achieved by introducing a duced random fluctuations), thus optimum polarization bulk interference or birefringent filter, or diffraction grat- settings can drift, requiring regular readjustment. Ad- ing into the cavity. Free-space components, however, ditionally, the coupled and nonlinear dependence of the eliminate the alignment-free benefits of an all-fiber sys- output properties on cavity parameters that adjust tem- tem. A solution is to use an artificial birefringent fil- poral and spectral modulation result in a complex, time- ter, formed from the combined effect of dispersive lin- consuming optimization procedure to achieve a desired ear polarization rotation due to fiber birefringence and output [3, 7]. polarization-dependent loss [1]. This is analogous to a To address this, automated parameter control ap- Lyot filter, exhibiting a comb-like transmission function. proaches have been proposed, focused principally on Duration-tunable pulses can be generated by achieving stable fixed-wavelength mode-locking [8{12]. Q-switching (QS) and/or mode-locking using an Algorithms that simply search for optimum states, how- electrically-driven modulator. A conceptually simpler ever, struggle with the diversity of laser operating approach, however, is passive pulse generation ex- regimes that include multiple points of local maxima (in ploiting nonlinearity in fiber. Nonlinear polarization addition to the desired global maxima). A promising and rotation (NPR), for example, manifests itself through versatile solution to this problem is to employ machine an intensity-dependent change in the polarization state learning [13{17], broadly defined as system development of propagating light, yielding a power-dependent trans- to perform given functions without explicit instruction. mission when combined with a polarizer|i.e. forming Learning [14] and genetic algorithms (GAs) [15{17] have an effective saturable absorber (SA) through nonlinear recently been applied to fiber lasers to intelligently ex- birefringent filtering. The transfer function can be plore parameter space and locate global optima, e.g. sta- modified through polarization control, varying the ble single-pulse mode-locking [17]. modulation depth and saturation intensity, and enabling Here, we extend this approach by using a GA to auto- a range of pulsed behaviors. Despite progress in the mate self-tuning of a fiber laser to achieve user-specified development of new real SA materials [2], artificial SAs temporal and spectral properties, by harnessing birefrin- remain a robust approach to pulse generation, with gent filtering. Using automated polarization and pump arXiv:1702.06372v2 [physics.optics] 13 Jun 2017 a quasi-instantaneous response and without requiring power control, and designing appropriate fitness func- advanced material fabrication. tions, our system is able to self-tune its wavelength over Exploitation of linear and nonlinear polarization-based 55 nm and achieve self-Q-switching with target pulse filtering in all-fiber cavities has enabled wide tunability properties in a 25 kHz repetition rate and 30 µs dura- over a range of output properties, including: >75 nm tion range. We explore the feasibility of simultaneous mode-locked tuning range [3], multiwavelength operation wavelength and repetition rate tunability and discuss the with up to 25 distinct wavelengths simultaneously [4]; practicalities and limitations of self-tuning laser technol- and temporal states from CW to Q-switching and mode- ogy. locking. More recent applications of birefringent filtering A ring fiber laser design is used [Fig. 1(a)], includ- in all-normal dispersion lasers have stabilized pulse for- ing a 2.3 m length of erbium-ytterbium co-doped double- Letter Optics Letters 2 Non-PM Fiber Erbium powerity round-trip, transmission any function light that [18]: is rotated to align with the (a) Isolator Fiber PM Fiber polarizer's fast axis is attenuated, giving the power trans- 2 2 2 2 missionT = cos functionθ1 cos θ2 [18]:+ sin θ1 sin θ2 Electronic WDM 1 10% Inline + sin 2θ sin 2θ 2cos(∆φ 2 + ∆φ + ∆φ ). (1) Polarization 2 2 2 1 2 L NL PC Coupler Polarizer Controller T = cos θ1 cos θ2 + sin θ1 sin θ2 1 The+ finalsin cosine 2θ1 sin term 2θ2 indicatescos(∆φL that+ ∆ theφNL birefringent+ ∆φPC filter): (1) Tap Coupler Pump transmission2 is periodic with wavelength due to ∆φ . We also Output Diode L Diagnostics Genetic Algorithm note that spectral filtering is introduced by weak wavelength- dependenceThe final of cosine both γ termand indicates∆n. Importantly, that the the birefringent transmitted fil- θ 1 θ2 ter transmission is periodic with wavelength due to ∆φ . (b) wavelengths can be tuned by adjusting the PC (i.e. ∆φPC). In L Birefringent Fiber PC combinationSpectral filtering with the is dynamic also introduced gain profile by of weak the erbium wavelength- fiber ΔΦL & ΔΦNL ΔΦPC amplifierdependence [3], the of birefringent both γ and filter ∆ definesn. Importantly, the laser wavelength. the trans- from linear & nonlinear tunable to Tomitted achieve wavelengths pulsation, the can phase be bias tuned∆φPC byis adjusting set such that the the PC polarizer phase delay phase bias polarizer linear(i.e. ∆ transmissionφPC ). In combination (i.e. for CW light) with is the low, dynamic while the gain filter pro- permits a higher transmission for light of greater intensity, con- FIG.Fig. 1. 1. Self-tuning laser laser cavity: cavity: (a) (a) schematic; schematic; (b) simplified(b) simplified file of the erbium fiber amplifier [3], the birefringent filter illustration of phase delays arising from fiber birefringence. trolleddefines by the∆φNL laser. The wavelength. modulation depth, Toachieve non-saturable pulsation, loss and the illustration of phase delays arising from fiber birefringence. saturation intensity of this artificial SA can thus be adjusted by thephase phase bias bias. ∆φPC is set such that the linear transmis- sionTypically, (i.e. for the CWidentification light) is of low,system while parameters the filter (here, permits the 4 a higher transmission for light of greater intensity, con- cladrange. fiber, We pumped explore the at feasibility 965 nm, of an simultaneous electronic polarization wavelength PC waveplate angles and pump power) to achieve on-demand controllerand repetition (PC) rate consisting tunability and of four discuss stepper-motor-driven the practicalities and outputtrolled properties by ∆φNL is. a non-trivial The modulation optimization. depth, Fortunately, non-saturable GAs quarterlimitations waveplates of self-tuning (QWPs) laser technology. formed of fiber loops with areloss ideally and saturation suited to this intensity task. Briefly, of this GAs artificial efficiently SA perform can thus globalbe adjusted multivariate by the optimization phase bias. using principles from evolu- stress-inducedA ring fiber laser birefringence, design is used and [Fig. an1(a)], in-line including fiber a 2.3 polar- m izer. The polarizer's fiber pigtails and subsequent 10% tionaryThe biology identification to find parameters of system that parameters maximize a quality (here, score, the 4 length of erbium-ytterbium co-doped double-clad fiber, pumped as explained in greater detail for this context in Ref. [17]. The pro- outputat 965 nm, coupler an electronic are constructed polarization controller from high-birefringence (PC) consisting of PC waveplate angles and pump power) to achieve on- cessdemand starts output with a population properties of randomis a non-trivial parameter optimization. sets, which (i.e.four stepper-motor-driven polarization-maintaining, quarter waveplates PM) fiber, (QWPs) ensuring formed a are each trialled and scored according to a fitness function. A fixedof fiber output loops polarization with stress-induced from birefringence,