Genetic Algorithm-Based Control of Birefringent Filtering for Self-Tuning, Self-Pulsing Fiber Lasers

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 spectral 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, the laser. All and other an in-line fiber newFortunately, generation GAs of parameter are ideally sets suitedis then generated to this task. by ‘breed- Briefly, isfiber low-birefringence polarizer. The polarizer’s (non-PM) fiber Corning pigtails SMF28. and subsequent Finally, ing’GAs from efficiently the previous perform generation, global where multivariate ‘parent selection’ optimization is a10% polarization-independent output coupler are constructed in-line from isolator high-birefringence is used, result- (i.e. probabilistic,using principles related from to the evolutionary parent’s score. biology ‘Mutation’ to find is applied param- ingpolarization-maintaining, in a total cavity length PM) of fiber, 21 m. ensuring a fixed output byeters randomly that maximize varying parameters a quality score, with a as small explained probability, in detail to polarization from the laser. All other fiber is low-birefringence preventfor this the context algorithm in Ref. converging [17]. The to local process optima. starts The withnew a (non-PM)To explain Corning the SMF28.operation Finally, of the a polarization-independent artificial birefringent filter, we use a simplified analysis [Fig. 1(b)] consider- generationpopulation is ofthen random tested and parameter the procedure sets, repeats, which areselectively each tri- in-line isolator is used, resulting in a total cavity length of 21 m. identifying and maintaining the best parameters, while rejecting ing the power transmission T of the polarizer, which alled and scored according to a fitness function. A new To explain the operation of the artificial birefringent filter, low-scoringgeneration sets. of parameter sets is then generated by ‘breed- blocks light (with >26 dB extinction) polarized in the We first demonstrate wavelength tuning, initially neglecting directionwe use a alignedsimplified with analysis the [Fig. fast-axis1(b)] considering of its PM the fiber power pig- ing’ from the previous generation, where ‘parent selec- transmission T of the polarizer, which blocks light (with >26 dB the temporal properties, to elucidate the GA evolution. The tion’ is probabilistic, relatedλ λ to the parent’s score. ‘Mu- tails.extinction) Light polarized in PM fiber in the after direction the aligned polarizer with remains the fast-axis lin- fitness function, F = 1 | − 0| , is used to score the spectrum tation’ is appliedλ by randomly− 0.5∆λ varying parameters with a earlyof its polarized PM fiber pigtails. in theLight fiber’s in slow PM fiber axis. after Non-PM the polarizer cav- (Fλ = 1 is optimal) measured on an optical spectrum analyzer ityremains fiber has linearly an polarizedintrinsicin birefringence the fiber’s slow orders axis. of Non-PM magni- (OSA),small probability, where λ is the to central prevent wavelength the algorithm (found using converging a peak to tudecavity lower fiber than has an PM intrinsic fiber, birefringence although stresses orders of from magnitude twist- detectionlocal optima. routine The on the new recorded generation data; if is no then peak testedfound, i.e. and no the inglower and than spooling PM fiber, non-PM although fiber stresses can from significantly twisting and increase spool- lasing,procedureFλ = repeats,0), λ0 is the identifying target wavelength, and maintaining and ∆λ = 70 thenm isbest this.ing non-PM The orthogonal fiber can significantly polarization increase mode this. axes The of the orthog- PM theparameters, estimated gain while bandwidth. rejecting low-scoring sets. onal polarization mode axes of the PM fibers form arbitrary The GA optimization procedure for a target wavelength of fibers form arbitrary angles θ1 and θ2 to the principal We first demonstrate wavelength tuning, initially ne- polarizationangles θ1 and axesθ2 to the of principalthe non-PM polarization fibers. axes Light of the launched non-PM 1550.0glecting nm isthe visualized temporal in Fig. properties,2: (a) shows to the elucidate 1st, 3rd and the 15th GA fibers. Light launched into non-PM fiber can excite both sup- generation results—the initial population of randomized|λ−λ0| param- into non-PM fiber can excite both supported polariza- evolution. The fitness function, Fλ = 1 , is used ported polarization modes, which couple and transfer power eters yields a random selection of laser wavelengths;− 0. subsequent5∆λ tionon propagation.modes, which This couple causes and a rotation transfer of power the polarization on propa- generationsto score the are spectrum formed from (F crossoverλ = 1 is of optimal) the ‘best’ measuredparameters on an optical spectrum analyzer (OSA), where λ is the cen- gation.state through This causes both a linear a rotation (∆φL = of2π theL∆n polarization/λ) and nonlinear state from the earlier generation, including a random mutation prob- through(∆φNL = both (2/3) aγLP linearcos 2θ1 (∆) phaseφL = shift 2πL between∆n/λ) the and two non- po- ability,tral wavelength resulting in (found the breeding using out a of peak ‘bad’ detection parameters routine that linearlarization (∆φ componentsNL = (2/3) [18γLP]; wherecos 2 theθ1) fiber phase has shift length betweenL, bire- yieldon the laser recorded wavelengths data; far if from no peak the target, found, and i.e. introducing no lasing, thefringence two polarization∆n, nonlinearity components parameter γ [18];, and the where instantaneous the fiber newFλ = parameters 0), λ0 is with the laser target wavelengths wavelength, closer and to the ∆ target.λ = 70 Af- nm hasoptical length powerL, is birefringenceP. An additional ∆n phase, nonlinearity shift term ∆ parameterφPC, vari- teris the several estimated generations, gain the bandwidth. algorithm converges to locate the γ,able and by the the user, instantaneous arises from opticalthe PC, which power permits is P . complete An ad- optimumThe GA PC and optimization pump power procedure settings that for yield a target the desired wave- traversal of the Poincaré sphere through the adjustable angles laserlength wavelength of 1550.0 [with nm is the visualized evolution ofin the Fig. best 2: and (a) averageshows the ditionalof four QWPs. phase Light shift launched term ∆ intoφPC the, variable0.2 m PM by input the fiber user, generation score shown in Fig.2(b)]. We executed the algorithm arisespigtail from of the the polarizer PC, which is not permitsnecessarily complete∼ aligned to traversal one of the of with1st, a 3rd range and of target15th wavelengths:generation results—the the tuning limits initial were found popula- theprincipal Poincar axes, sphere hence through birefringence the adjustable here also results angles in a of phase four totion be of1542.2 randomized to 1600.4 nm. parameters Within this yields range, a autonomous random selection self- QWPs.delay, which Light for launched simplicity isinto assumed the to0.2 be includedm PM input in ∆φ fiberand tuningof laser of thewavelengths; birefringent filtersubsequent was always generations successful, achievingare formed ∼ L pigtail∆φNL terms. of the After polarizer a cavity is round-trip, not necessarily any light aligned that is rotated to one on-demandfrom crossover wavelength of the selection ‘best’ parameters within 0.1 nm from of the the target earlier ofto the align principal with the polarizer’s axes, hence fast birefringence axis is attenuated, here giving also the re- [Fig.generation,2(b) inset]. including The factor a limiting random this mutation range is believed probability, to be results in a phase delay, which for simplicity is assumed sulting in the breeding out of ‘bad’ parameters that yield to be included in ∆φL and ∆φNL terms. After a cav- laser wavelengths far from the target, and introducing

2 Letter Optics Letters 3 Letter Optics Letters 3

Gene breeding & mutation Gene breeding & mutation (nm) 1540 1570 (kHz) 1 25 locate new optima Best in Generation (a)(a) (nm) 1540 1570 (b) (b) (kHz) 1 25 (a)(a) (b) (b) locate new optima Best in Generation 1 1 Gen. 1: Gen. 1: Generation initial initialrandom random Generation populationpopulation AverageAverage

ParentParent selection selection by by Gen. 3:Gen. 3: fitnessfitness ranking ranking yields yields algorithm finds algorithm finds convergeconverge towards towards optima optima improvedimproved parameters parameters de dpeepnednsd st srotrnognlgyly CCoonnssttaanntt ccoonttours Fitness (a.u.) Fitness (a.u.) uponupon QWP1, QWP1, dependdepend onon changeschanges in weaklyweakly upon upon power power bothboth QWP1QWP1 && powerpower Gen. 15:Gen. 15: (c)(c) ( µ(sµ)s) 1 1 3030 (d) (d) FitnessFitness 0 11 1550.01550.0 nm located nm located & & convergenceconvergence complete complete 1540 1540 15701570 16001600 0 0 WavelengthWavelength (nm) (nm) Optimum 15401540156015601580158016001600 1 1 5 5 10 10 1515 WavelengthWavelength (nm) (nm) GenerationsGenerations 0-0.9 W 0-0.9 W Pump Power Pump Power

FIG.Fig. 2. 2.GA-based GA-based wavelength wavelength self-tuning: self-tuning: (a) visualization(a) visualization Compound fitness Fig. 2. GA-based wavelength self-tuning: (a) visualization Compound fitness score, targeting ofof spectra spectra for each parameter parameter set set in in generations generations 1,3 1, and 3 and 15 15 score, targeting of spectra for each parameter set in generations 1, 3 and 15 QWP1 Angle 1550 nm & 15 kHz QWP1 Angle ...... Null Data 1550 nm & 15 kHz (b)(b) fitness evolution evolution showing showing convergence convergence towards towards optimum optimum 0- rad ...... Null Data pulse train (b) fitness evolution showing convergence towards optimum 0- rad pulse train (inset:(inset:(inset: self-tuned self-tuned spectra spectra spectra showing showing showing tuning tuning tuning range). range). range). Fig. 3. Maps of laser characteristics with respect to QWP1 an- Fig. 3. Maps of laser characteristics with respect to QWP1 an- FIG.gle (x-axis: 3. Maps 0 to ofπ laserrad) and characteristics pump power with (y-axis: respect 0 to 0.9 to W):QWP1 (a) insertion losses in fixed fiber components (e.g. isolator/WDMs), gleangle (x-axis: (x-axis: 0 to π 0rad) to π andrad) pump and power pump (y-axis: power 0 (y-axis: to 0.9 W): 0 (a) to insertion losses in fixed fiber components (e.g. isolator/WDMs), wavelength; (b) Q-switched repetition rate; (c) pulse duration; newwhich parameters are specified with for operation laser wavelengths around 1560 closer nm. to the tar- wavelength;0.9 W): (a) (b) wavelength; Q-switched (b) repetition Q-switched rate; repetition (c) pulse duration; rate; (c) which are specified for operation around 1560 nm. (d) score with targets: 1550 nm & 15 kHz. get.The After choice several of GA generations, parameters (generation the algorithm size, converges crossover (d)pulse score duration; with targets: (d) score 1550with nm & targets: 15 kHz. 1550 nm & 15 kHz. Thetorate locate choice etc. [19 the of]) defines optimum GA parameters the PC accuracy and (generation pump and convergence power size, settings crossover rate of that the rate etc. [19]) defines the accuracy and convergence rate of the yieldsystem—i.e. the desired the time laser taken wavelength to locate the [with desired the state.evolution Empir- of self-pulsation over a 25 kHz repetition rate range. system—i.e.theically, best we and the achieved time average taken good generation to performance locate the score desired using shown a state. generation in Fig. Empir- 2(b)]. size self-pulsation over a 25 kHz repetition rate range. ically, we achieved good performance using a generation size measured,Fig.3 highlights and when that pulsing, various combinations the pulse duration of laser and proper- rep- Weof 20, executed crossover the rate algorithm of 90%, and with mutation a range rate of of 20%target (which wave- is tiesFig. can3 highlights be accessed—e.g. that various a contour combinations of constant of repetition laser proper- rate of 20, crossover rate of 90%, and mutation rate of 20% (which is etition rate are measured using a photodetector and oscil- lengths:linearly damped the tuning as the limitsaverage were score foundapproaches to be 1). For1542.2 parent to ties15 can kHz be accessed—e.g.in Fig.3(b) corresponds a contour to aof region constant in Fig. repetition3(a) where rate linearly damped as the average score approaches 1). For parent loscope.∼ The laser threshold is 0.2 W. For many QWP1 1600.4selection nm. during Within breeding, this we range, use a autonomous‘rank selection’ self-tuning algorithm, 15the kHz wavelength in Fig.3(b) varies corresponds over 10 nm. to∼ aThis region shows in Fig. that3(a) by where adjust- selection during breeding, we use a ‘rank selection’ algorithm, ∼settings above threshold∼ stable QS is observed, with the ofin the contrast birefringent to our previous filter GA was work always to find successful, mode-locking achiev- [17] theing wavelength just the power varies and over QWP1,10 nm. a 15 This kHz shows pulse trainthat by could adjust- be in contrast to our previous GA work to find mode-locking [17] pulse properties determined∼ by the pump power and po- ingwhere on-demand ‘roulettewheel wavelength selection’ selection was chosen. within Roulette 0.1 nmwheel of the ingachieved just the at power any target and wavelength QWP1, a 15 in kHz this pulserange. train An important could be whereselection ‘roulette assigns wheel the selection’ selection was probability chosen. based Roulette on a wheel param- larization phase bias. Increasing the pump power during target [Fig. 2(b) inset]. The factor limiting this range is achievedquestion, at therefore, any target is can wavelength we arbitrarily in this select range. wavelength, An important pulse selectioneter set’s assigns score, the favourable selection for probability identifying based small on mode-locked a param- question,QSduration operation therefore, and repetition with is can fixed ratewe waveplates arbitrarily within the select full results tuning wavelength, in range? a linear pulse in- eterbelievedstates set’s score, within to favourable be a wideinsertion parameter for losses identifying space in fixed of small non-lasing, fiber mode-locked components CW and crease in repetition rate [Fig. 3(b)] and decrease in pulse (e.g. isolator/WDMs), which are specified for operation durationWe explore and repetition the potential rate within for this the self-tunability full tuning range? using a GA statesQS within regimes a wide exhibiting parameter high performance space of non-lasing, contrast. RankCW and selec- durationwithWe aexplore compound [Fig. the 3(c)]. potential fitness Thisfunction for is this expectedthat self-tunability assigns as a score a QS using according pulse a GA is QSaround regimestion, however, 1560 exhibiting nm. chooses high parameters performance based contrast. on their Rank position selec- in emitted once sufficient stored energy in the cavity is accu- withto both a compound the wavelength fitness and function pulse repetitionthat assigns rate: a scoreFtotal according= 0.5Fλ + tion,the however,The fitness-sorted choice chooses of list parameters GAof all parameter parameters based sets. on (generationtheir This position enhances insize, the mulated; thus, higher pump power enables increased rep- to0.5 bothFf . the The wavelength effect of this and function pulse in repetition identifying rate: a targetFtotal operating= 0.5Fλ + thecrossover fitness-sortedcontrast between rate list etc. similarly of [19]) all parameter defines scoring the parameter sets. accuracy This sets,enhances and and conver- is the thus 0.5etitionregimeF . The rates (arbitrarily effect and of this shorter chosen function pulses. to bein identifyingλ0 Pulse= 1550 properties anm target wavelength, operating are also contrastgencebetter between rate suited of forsimilarly the implementing system—i.e. scoring parameter on-demand time taken sets, tunability to and locate is thus over the a f regimeaffectedf0 = (arbitrarily15 bykHz the repetition QWP chosen angle rate) to be is asλ illustrated this= adjusts1550 bynm applying ∆ wavelength,φPC in it the to continuous range. 0 betterdesired suited state. for implementing Empirically, weon-demand achieved tunability good performance over a fbirefringentthe= reduced15 kHz 2D repetitionfilter, parameter which rate) space varies is illustrated (of the pump intensity-dependent- power by applying and QWP1), it to We now consider temporal properties. To highlight the di- 0 continuoususing a range. generation size of 20, crossover rate of 90%, and thelossresulting reduced function. in 2D the parameter fitness To target map space Fig. autonomous3(d), (of pump highlighting power control the and optimum of QWP1), a QS Wemutationversity now of consider possible rate of temporal output20% (which states properties. and is linearly the To dependence highlight damped theon as input di- the operation region for these properties. parameters, we measure a two-dimensional slice of the five- resultingoutput inwith the on-demand fitness map Fig. repetition3(d), highlighting rate (excluding the optimum wave- versityaverage of possible score approaches output states 1). and For the parent dependence selection on input during operationlengthSelf-tuning tuning), region from for we these randomized redefine properties. the initial GA parameters fitness functiontowards the as parameters,dimensional we measure parameter a space: two-dimensional three QWPs sliceare fixed, of the while five- the breeding, we use a ‘rank selection’ algorithm, in contrast target λ0 =|f−1550f0| nm and f0 = 15 kHz is demonstrated by pump power is swept from 0 to 0.9 W and one QWP (hereafter, FfSelf-tuning= 1 from, randomized with measured initial repetition parameters frequency towards thef dimensional parameter space: three QWPs are fixed, while the running the compoundf0 fitness-function-based GA. Within the tocalled our QWP1) previous is swept GA work through to find 180 mode-locking[Fig.3(a)-(c)]. At [17] each us- target λ0 −= 1550 nm and f0 = 15 kHz is demonstrated by pump power is swept from 0 to 0.9 W and◦ one QWP (hereafter, andfirst targetgeneration,f0, achieving a range of non-lasing, self-tuning, CW self-pulsation and QS states over (with a ingpoint, ‘roulette the wavelength wheel selection’.is measured,and Roulette when pulsing, wheel selectionthe pulse running the compound fitness-function-based GA. Within the called QWP1) is swept through 180 [Fig.3(a)-(c)]. At each 25widely kHz varying repetition pulse rate repetition range. rates) are observed, as expected assignsduration the and selection repetition rate probability are measured◦ based using on a photodetectora parameter first generation, a range of non-lasing, CW and QS states (with point, the wavelength is measured, and when pulsing, the pulse fromFig. the 3 broad highlights parameter that space various (Fig. combinations3), giving a low of aver- laser set’sand oscilloscope. score, favourable The laser for threshold identifying is 0.2 smallW. For mode-locked many QWP1 widely varying pulse repetition rates) are observed, as expected duration and repetition rate are measured using a photodetector age score. The algorithm maintains the ’good’ parameters settings above threshold stable QS is observed,∼ with the pulse fromproperties the broad can parameter be accessed—e.g. space (Fig. a3), contour giving a of low constant aver- states within a wide parameter space of non-lasing, CW and breeds/mutates them to identify improved performance— and oscilloscope.properties determined The laser threshold by the pump is 0.2 powerW. For and many polarization QWP1 repetition rate 15 kHz in Fig. 3(b) corresponds to a and QS regimes exhibiting high∼ performance contrast. ageshown score. by the The increase algorithm∼ in the maintains ‘Best in Generation’, the ’good’ which parameters leads to settingsphase above bias. threshold Increasing stable the pump QS ispower observed, during with QS the operation pulse region in Fig. 3(a) where the wavelength varies over Rank selection, however, chooses parameters based on andconvergence breeds/mutates to optimal them performance to identify over improved numerous performance— generations propertieswith fixed determined waveplates by results the pump in a linearpower increase and polarization in repetition 10 nm. This shows that by adjusting just the power their position in the fitness-sorted list of all parameter shown∼[Figs.4 by(a)-(b)]. the increase The routine in the is ‘Best re-executed, in Generation’, each time which following leads ato phaserate bias. [Fig. Increasing3(b)] and decrease the pump in pulsepower duration during [Fig.QS operation3(c)]. This and QWP1, a 15 kHz pulse train could be achieved at sets. This enhances the contrast between similarly scor- convergencedifferent evolution to optimal due performance to the probabilistic over numerous process and generations random- withis fixed expected waveplates as a QS results pulse is in emitted a linear once increase sufficient in repetition stored en- ing parameter sets, and is thus better suited for imple- [Figs.anyized4 target(a)-(b)]. initial conditions, wavelength The routine but is in demonstrating re-executed, this range. each reliability The time tuning following by always range a rateergy [Fig.3 in(b)] the and cavity decrease is accumulated; in pulse duration thus, higher [Fig.3 pump(c)]. This power differenthere,converging however, evolution on the by due generation varying to the probabilistic of only a 1550 two nm process parameters wavelength, and random- 15 is kHz lim- is expectedmentingenables increasedas on-demand a QS pulse repetition tunability is emitted rates and once over shorter sufficient a continuous pulses. stored Pulse range. en-prop- izeditedpulse initial compared train—as conditions,characterized to the but full demonstrating performance in Figs.4(c)-(e). reliability range The that pulses by always can are be ergyerties inWe the noware cavity also consider affected is accumulated; temporal by the QWP properties. thus, angle higher as this To pump adjusts highlight power∆φ thein PC convergingachievedmeasured through on to havethe generation 5.9 varyingµs duration ofall a five 1550 and parameters nm the wavelength, electrical [e.g. spectrum 15 30 kHz nm enablesdiversitytheincreased birefringent of possible repetition filter, which output rates varies and states shorter the and intensity-dependent-loss pulses. the dependence Pulse prop- on pulsewavelengthshows train—as a high range peak-to-background characterized in Fig. 3(a) in Figs. contrast compared4(c)-(e). of 40 to The dB 58 at pulses nmthe funda- range are ertiesinputfunction. are also parameters, affected To target by we autonomous the measure QWP angle control a two-dimensional as this of adjustsa QS output∆φ slice within of PC measuredinmental Fig. 2]. repetition to An have important 5.9 frequencyµs duration question, of the and pulse therefore, the train, electrical indicating is can spectrum we good ar- thethe birefringenton-demand five-dimensional filter, repetition which rate parameter varies (excluding the intensity-dependent-loss space: wavelength three tuning),QWPs weare showsbitrarilystability. a high Theselect peak-to-background 4.7 wavelength, mW output is pulse linearly contrast duration polarized of 40 dB and with at repetition the a funda- 19 dB function. To target autonomous control of a QSf outputf0 with fixed,redefine while the GA the fitness pump function power asisF sweptf = 1 from| − 0| , withto 0.9 mea- W mentalextinction repetition ratio, corresponding frequency of the to 0.31pulseµJ train, pulse indicating energy. We good also on-demand repetition rate (excluding wavelength− f tuning),0 we rate within the full tuning range? andsured one repetition QWP (hereafter, frequency f calledand target QWP1)f0, achieving is swept self-tuning, through stability.note that The when 4.7 mW the outputlaser is is intentionally linearly polarized disturbed with mechani- a 19 dB ◦ f f0 We explore the potential for this self-tunability using redefine180 the[Fig. GA 3(a)-(c)]. fitness function At each as Ff point,= 1 the| − wavelength| , with mea- is extinction ratio, corresponding to 0.31 µJ pulse energy. We also − f0 sured repetition frequency f and target f0, achieving self-tuning, note that when the laser is intentionally disturbed mechani- 3 Letter Optics Letters 4

(a)Best in Generation (b) Generation Average a GA with a compound fitness function that assigns a 1 1 Finally, we critically discuss the potential of intelligently au- score according to both the wavelength and pulse repeti- tomated birefringent filtering for the development of self-tuning tion rate: Ftotal = 0.5Fλ + 0.5Ff . The effect of this func- fiber lasers. For optimization of a single characteristic, the pro- Single Run Single Run tion in identifying a target operating regime (arbitrarily 0 Ensemble Mean 0 Ensemble Mean posed solution performs well: >55 nm tunability was demon- Fitness (a.u.) Fitness (a.u.) chosen to be λ0 = 1550 nm wavelength, f0 = 15 kHz 0 5 10 15 0 5 10 15 strated, without user intervention or active monitoring of the repetition rate) is illustrated by applying it to the re- (c)Generations (d) Generations environment (e.g. temperature compensation). This could enable reliable automated wavelength tuning of lasers, including duced 2D parameter space (of pump power and QWP1), 0 1 pulsed sources (mode-locked or Q-switched) using real SAs. For resulting in the fitness map Fig. 3(d), highlighting the 1550.0 nm 5.9 µs multi-characteristic tuning, however, the intrinsic coupling of optimum operation region for these properties. 30 temporal and spectral properties and finite spectral gain present Self-tuning (from randomized initial conditions, in- 0 500 µs 60 0 limitations to the achievable tuning ranges: when demanding a cluding all five parameters) towards the target λ0 = Intensity (a.u.)

Intensity (a.u. dB) 1530 1560 1590 15 0 15 30 15 kHz repetition rate, our tuning range was limited to 20 nm. 1550 nm and f0 = 15 kHz is demonstrated by running the ∼ (e)Wavelength (nm) (f) Time (µs) Introducing additional degrees of freedom and electronically compound ﬁtness-function-based GA. Within the ﬁrst controlled components is thus an interesting topic for future 0 40 dB 1.0 generation, a range of non-lasing, CW and QS states 15.0 kHz work. Compared to alternative approaches, such as in-line ac-

(with widely varying repetition rates) are observed, as 30 Signal 0.5 tive modulators, automated passive filtering to achieve tuning expected from the broad parameter space (Fig. 3), giving of laser output characteristics represents a novel and potentially Background 0.0 a low average score. The algorithm maintains the ’good’ 60 Fitness (a.u.) simpler/economical route forwards. We note that miniaturized Intensity (a.u.) parameters and breeds/mutates them to identify im- 10 15 20 1540 1560 1580 1600 low-cost optical diagnostics are an area of active research and de- Frequency (kHz) Target Wavelength (nm) proved performance—shown by the increase in the ‘Best velopment; thus, the inclusion of real-time monitoring systems in Generation’, which leads to convergence to optimal in laser devices will enable further progress in this area. FIG.Fig. 4. 4.Self-tuning Self-tuning laser characteristics, with with targets targetsλ =λ0 = In conclusion, we have demonstrated the first self-tuning performance over numerous generations [Figs. 4(a)-(b)]. 0 15501550.0.0 nm and f00 ==15 kHz: kHz: evolution evolution of of (a) (a) ’best’ ’best’ and and (b) (b) self-Q-switching fiber laser using a genetic algorithm to control The routine is re-executed, each time following a different ’average’’average’ fitness; fitness; performance performance with the the self-optimized self-optimized param- param- intracavity birefringent filtering. Self-tuning is possible in the evolution due to the probabilistic process and random- eters,eters, (c) (c) optical optical spectrum, spectrum, (d) (d) pulse pulse, (inset: (e) pulse RF spectrum; train), (e) (f) presence of an unregulated environment which has to date pro- ized initial conditions, but demonstrating reliability by optimumelectrical achieved spectrum; fitness (f) optimum with 15 achieved kHz target fitness repetition at a 15 kHz rate hibited the practical application of artificial saturable absorbers always converging on the generation of a 1550 nm wave- andconstant variable target target repetitionλ. rate, and variable target wavelength. without complex active thermal and mechanical stabilization. length, 15 kHz pulse train—as characterized in Figs. 4(c)- Extending the autonomous tuning range of on-demand laser (e). The pulses exhibit a 5.9 µs duration and the electri- properties is a future challenge; yet, we believe there is great cal spectrum shows a high peak-to-background contrast larizationcally, causing controller, the performance for example, to change after randomly, the output the GA cou- can potential for artificial intelligence in the control of laser systems, of 40 dB at the fundamental repetition frequency of the plerquickly would relocate allow the controlnew optimum over system the polarization parameters to state restore of not least by harnessing linear and nonlinear polarization effects. the desired output properties (similar to Ref. [17]). pulse train, indicating good stability. The 4.7 mW out- light launched into the non-PM fiber [15]. Additionally, To explore the limits of this approach, we repeated the opti- put is linearly polarized with a 19 dB extinction ratio, >75 nm of spectral tunability was demonstrated by in- Funding Information mization process targeting 15 kHz pulse train generation over EPSRC & Royal Academy of Engineering Fellowships. corresponding to 0.31 µJ pulse energy. We also note that troducinga range of wavelengths.a variable attenuator The optimal into converged a laser cavityfitness values allow- when the laser is intentionally disturbed, causing the per- ingas a adjustment function of target of the wavelength threshold are and shown thus in the Fig. population4(f). Unity formance to change randomly, the GA quickly relocates inversion,fitness is not modifying achieved across the the spectral full range, gain highlighting shape [3]—this that the Acknowledgements new optimum parameters to restore the desired output couldtarget also properties be included were not as found a GA in control all cases. variable Consistently, to extend high We thank J. R. Taylor, R. T. Murray and T. H. Runcorn for fruitful properties (similar to Ref. [17]). theperforming tuningregimes range. are The observed automated between tunability 1550 and in 1570 wave- nm, discussions and M Squared Lasers for loan of an IceBloc DDTC. To explore the limits of this approach, we repeated the lengthwith achieved and repetition optimal scores rate suggest exceeding that 0.96. applications Outside of this such region, however, the maximum score, despite numerous iterations optimization process targeting 15 kHz pulse train gen- as laser spectroscopy and photoacoustic imaging could REFERENCES eration over a range of wavelengths. The optimal con- beof exploredthe self-tuning to exploit process, such is lower—indicating a Q-switched fiber the target laser laser [20]. verged fitness values as a function of target wavelength wavelengthFinally, we and critically repetition ratediscuss could the not potential be mutually of satisfied; intelli- 1. P. Humphrey and J. Bowers, IEEE Photon. Technol. Lett. 5, 32 (1993). 2. R. I. Woodward and E. J. R. Kelleher, Appl. Sci. 5, 1440 (2015). are shown in Fig. 4(f). 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4 and potentially simpler/economical route forwards. We potential for artificial intelligence in the control of laser note that miniaturized low-cost optical diagnostics are systems, not least by harnessing linear and nonlinear po- an area of active research and development; thus, the in- larization effects. clusion of real-time monitoring systems in laser devices will enable further progress in this area. In conclusion, we have demonstrated the first self- Acknowledgements tuning self-Q-switching fiber laser using a genetic algorithm to control intracavity birefringent filtering. Self- We thank J. R. Taylor, R. T. Murray and T. H. tuning is possible in the presence of an unregulated envi- Runcorn for fruitful discussions and M Squared Lasers ronment which has to date prohibited the practical appli- for loan of an IceBloc DDTC. We acknowledge support cation of artificial saturable absorbers without complex through EPSRC (RIW) & Royal Academy of Engineering active thermal and mechanical stabilization. Extending (EJRK) Fellowships. the autonomous tuning range of on-demand laser prop- All data underlying the results presented in this Letter erties is a future challenge; yet, we believe there is great are freely available upon request from the authors.

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