Utafiti huu unatengeneza laser cavity yenye energy management ili kushinda tatizo la low output energy linalopatikana katika pure-quartic soliton fiber lasers. Katika mfumo uliopendekezwa, mara tu pulse inapokuwa imeamplifyiwa katika erbium-doped fiber, %90 ya energy ndani ya cavity inatolewa kupitia main output coupler. Hivyo high-energy pulse inazuiwa kuzunguka kwa muda mrefu ndani ya fiber cavity, kukusanya excessive nonlinear phase, kuharibika spectrally au kugawanyika. Low-energy pulse inayobaki ndani ya cavity inazungushwa kwa uthabiti kupitia saturable absorber, spectral filter na single-mode fiber ili kujiandaa kwa amplification cycle inayofuata.

Watafiti walimodel laser kwa split-step Fourier method na kuchunguza effects za small-signal gain, spectral-filter bandwidth na nonlinear coefficient ya fiber kwenye pulse energy, peak power, duration na spectral width. Ilibainika kwamba kwa kila fixed gain value kuna filter bandwidth inayomaximize pulse energy. Wakati small-signal gain ilikuwa 40 dB, highest energy ilipatikana karibu na filter width ya 2,2 nm; gain ilipoongezwa hadi 80 dB, optimum width ilishuka hadi 0,6 nm. Lower nonlinear coefficient pia ilitoa higher pulse energy.

Katika optimum numerical design, small-signal gain ya 80 dB, filter bandwidth ya 0,6 nm na nonlinear coefficient ya 1 W^-1km^-1 zilichaguliwa. Katika main output coupler, energy ya 11,07 nJ, peak power ya 1180,2 W, pulse duration ya 8,78 ps na spectral width ya 0,47 nm katika 3 dB zilipatikana. Relative na initial operating point ya 3,46 nJ, energy hii ni roughly 3,2 times. Hata hivyo, energy increase haikupatikana kwa higher peak power, bali kupitia longer pulse yenye energy content kubwa zaidi; peak power ya optimized design ilikuwa roughly %7 lower kuliko initial example.

Findings zinategemea entirely idealized numerical model. Real fiber laser haikujengwa; pulse energy, spectrum au stability havikupimwa laboratory. Second- na third-order dispersions zilichukuliwa kuwa zero, na manufacturing tolerances pamoja na environmental effects hazikumodeliwa. Zaidi ya hayo, katika different sections za study, lengths za erbium-doped fiber na second single-mode fiber zinapingana. Kwa hiyo, results zinapaswa kutathminiwa si kama experimentally validated device performance, bali kama numerical preliminary design na parameter-selection guide kwa high-energy pure-quartic soliton lasers.

Pure-quartic soliton ni nini na main research problem ni nini?

Katika conventional soliton fiber lasers, stable propagation ya pulse inategemea balance kati ya second-order group-velocity dispersion na self-phase modulation inayotokana na Kerr nonlinearity. Katika pure-quartic solitons zilizochunguzwa katika study hii, balance hii inatengenezwa kati ya negative fourth-order dispersion na self-phase modulation badala ya second-order dispersion.

Kulingana na literature framework iliyoripotiwa na watafiti, pure-quartic solitons zina potential ya kubeba energy zaidi kuliko conventional second-order solitons. Hata hivyo, output energies za pure-quartic soliton fiber lasers zilizoonyeshwa hapo awali kwa kawaida zimebaki katika picojoule level. Kadiri energy inavyoongezeka, increase ya nonlinear phase inayokusanyika katika fiber, excessive spectral broadening, filter losses, pulse splitting na unstable dynamics zinapunguza energy inayoweza kupatikana.

Main question ya study ni hii: Ikiwa large fraction ya pulse energy inatolewa immediately baada ya amplification, je inawezekana kutoa high-energy output huku low-energy, stable pure-quartic soliton ikiendelea kuzunguka ndani ya cavity?

Energy-managed laser cavity imeundwaje?

Conceptual laser cavity iliyoonyeshwa katika Kielelezo 1 imepangwa kwa sequence ifuatayo:

Main logic ya energy management ni kutoruhusu highest-energy pulse kuzunguka katika entire fiber cavity. Baada ya pulse kuamplifyiwa katika EDF, sehemu yake kubwa inatolewa na OC₁. Hivyo main output energy inahifadhiwa, huku ndani ya cavity ikibaki only low-energy pulse inayohitajika kwa mode locking na stable regeneration.

Energy kwenye OC₂ si simply one-tenth ya OC₁ output. Baada ya OC₁, pulse inapitia new losses katika saturable absorber, filter, fiber na second coupler. Katika initial operating point, OC₁ energy ilikuwa 3,46 nJ huku OC₂ energy ikiwa only 2,9 pJ; katika optimized design, values zilikuwa respectively 11,07 nJ na 9,5 pJ. Katika both cases, OC₂ energy ni roughly %0,086 ya main output.

Pulse propagation ilimodeliwaje?

Pulse propagation katika erbium-doped fiber ilimodeliwa kwa Ginzburg–Landau-type equation inayojumuisha gain na losses:

\[ \frac{\partial A}{\partial z}=-i\frac{\beta_2}{2}\frac{\partial^2A}{\partial t^2}+\frac{\beta_3}{6}\frac{\partial^3A}{\partial t^3}+i\frac{\beta_4}{24}\frac{\partial^4A}{\partial t^4}+\frac{g}{2}A-\frac{\alpha}{2}A+\frac{g}{2\Omega_g^2}\frac{\partial^2A}{\partial t^2}+i\gamma|A|^2A \]

Hapa \(A(z,t)\) ni slowly varying electric-field envelope katika reference frame inayosafiri na pulse; \(z\) ni position along fiber; \(t\) ni retarded time; \(\beta_2\), \(\beta_3\) na \(\beta_4\) ni second-, third- na fourth-order dispersion coefficients; \(g\) ni saturated gain; \(\alpha\) ni linear loss; \(\Omega_g\) ni gain bandwidth ya erbium-doped fiber; na \(\gamma\) ni Kerr nonlinear coefficient.

Final term ya equation, \(i\gamma|A|^2A\), inawakilisha intensity-dependent self-phase modulation. Ili kutenga pure-quartic soliton regime, simulations zilichukua \(\beta_2=0\) na \(\beta_3=0\). Hivyo main dispersion–nonlinearity balance iliwekwa kati ya negative \(\beta_4\) na Kerr effect.

Gain saturation ilihesabiwaje?

Gain ya erbium-doped fiber haikuchukuliwa constant; ilisaturate kulingana na pulse energy:

\[ g=\frac{g_0}{1+E_P/E_{\mathrm{sat}}} \]

\[ E_P=\int |A|^2\,dt \]

\(g_0\) inaonyesha small-signal gain; \(E_{\mathrm{sat}}\) gain-medium saturation energy; na \(E_P\) total pulse energy. Kadiri pulse energy inavyoongezeka, denominator inaongezeka na effective gain inapungua. Katika study, \(g_0\) ilibadilishwa kama model parameter inayowakilisha pump power badala ya directly measured pump power. Kwa hiyo, phrase “80 dB pump” haimaanishi physical pump-laser power katika watts, bali small-signal gain katika model.

Saturable-absorber model

Instantaneous transmittance ya mode-locking element ilitolewa kwa relation ifuatayo:

\[ T=1-\frac{\alpha_0}{1+I/I_{\mathrm{sat}}}-\alpha_{\mathrm{ns}} \]

\(T\) inaonyesha transmittance; \(\alpha_0\) modulation depth; \(I\) instantaneous pulse intensity; \(I_{\mathrm{sat}}\) saturation intensity; na \(\alpha_{\mathrm{ns}}\) nonsaturable loss. Values zilizotumika ni \(\alpha_0=%35\), \(I_{\mathrm{sat}}=1\) W/m² na \(\alpha_{\mathrm{ns}}=0,65\).

High-intensity pulse center inaona higher transmittance kuliko low-intensity wings. Katika simulations, effect hii ilichangia temporal reshaping ya pulse na formation ya shorter output.

Spectral-filter model

Band-pass filter ilimodeliwa kwa Gaussian transfer function:

\[ F(\omega)=\exp\left[-\frac{\omega^2}{2(\delta\omega)^2}\right] \]

Conversion kati ya filter width katika wavelength na angular-frequency width ilitolewa hivi:

\[ \delta\omega=2\pi c\frac{\delta\lambda}{1,665\lambda^2} \]

\(\omega\) inaonyesha angular-frequency offset kutoka center frequency; \(\delta\lambda\) filter bandwidth; \(c\) speed of light; na \(\lambda\) center wavelength ya filter.

Filter inatengeneza effects mbili zinazopingana. Inasaidia stable low-energy pulse ku-form tena kwa kudhibiti spectrum, lakini pia inaongeza cavity loss kwa kuondoa energy components outside filter. Bandwidth inayomaximize pulse energy inatokana na balance ya effects hizi mbili.

Main values zilizotumika katika numerical model

• Center wavelength: 1569 nm.
• Initial pulse: Gaussian pulse yenye duration ya 100 fs na peak power ya 100 W.
• SMF fourth-order dispersion: \(-22,8\) ps⁴/km.
• EDF fourth-order dispersion: \(-25,5\) ps⁴/km.
• SMF nonlinear coefficient: 1,7 W^-1km^-1.
• EDF nonlinear coefficient: 1,4 W^-1km^-1.
• EDF gain bandwidth: 15 nm.
• Total laser-cavity length: 6 m.
• Reported total fourth-order dispersion: \(-0,141\) ps⁴.
• Gain saturation energy: 900 pJ.
• Main output coupler: inatoa %90 ya cavity energy.

Field iliyopatikana mwisho wa kila cavity round ilitumika kama initial field ya round inayofuata. Process iliendelea hadi field kufikia self-consistent steady state. Differential equation ilisolveiwa kwa split-step Fourier method. Watafiti wamesema kwamba kutumia white noise kama initial condition kulitoa same final result, ingawa rounds zaidi zilihitajika kwa convergence.

Reporting inconsistency katika fiber lengths

Katika methods section ya study, fiber lengths zimeripotiwa kwa njia mbili tofauti. Katika first parameter list, EDF length ni 1,5 m, SMF₁ length ni 1 m na SMF₂ length ni 3,5 m. Katika later results section, EDF imeandikwa 3,5 m, SMF₁ 1 m na SMF₂ 1,5 m.

Reported total fourth-order dispersion ya \(-0,141\) ps⁴ inalingana approximately na first length set:

\[ (-22,8)(0,0045)+(-25,5)(0,0015)=-0,14085\ \mathrm{ps}^4 \]

Second length set ikitumika, total inakuwa roughly \(-0,14625\) ps⁴. Calculation hii inadokeza kwamba first set inaweza kuwa intended value; hata hivyo, kwa sababu study haitoi explicit correction, hii ni inference tu based on numbers ndani ya text. Length inconsistency ni important reporting issue kwa independent reconstruction ya model.

Ni pulse gani ilipatikana katika initial operating point?

Katika first detailed operating point, small-signal gain ya 40 dB, filter bandwidth ya 2,0 nm na initial nonlinear coefficients za fibers zilitumika. Katika OC₁ output, results zifuatazo zilipatikana:

• Pulse energy: 3,46 nJ.
• Peak power: 1269,6 W.
• Pulse duration: 2,53 ps.
• 3 dB spectral width: 1,67 nm.

Pulse profile ilikuwa smooth, bell-shaped na moderately linearly chirped. Low-energy soliton iliyofuatiliwa kwenye OC₂ ilionyesha energy ya 2,9 pJ, peak power ya 1,07 W, duration ya 2,56 ps na spectral width ya 1,4 nm.

Temporal profile ya OC₂ pulse inaendana na `sech²` function. Watafiti waliichukulia hii kama indicator kwamba low-energy pulse inayobaki ndani ya cavity inasambaa stably kama soliton.

Spectrum, duration na energy vinabadilikaje ndani ya cavity?

Intracavity maps tatu katika Kielelezo 2 zinaonyesha mechanism ya energy management:

1. Kadiri pulse inavyoamplifyiwa ndani ya EDF, energy na peak power zake zinaongezeka.
2. Spectrum inapanuka kwa sababu ya self-phase modulation.
3. OC₁ inatoa %90 ya amplified energy.
4. Low-energy pulse inayobaki ndani ya cavity inare-shapeiwa na kukandamizwa katika time domain na SA.
5. Spectral filter inasuppress edges za broadened spectrum na kupunguza spectral width.
6. Pulse inasafiri kupitia SMF₂ katika low-energy, stable state na kufikia gain cycle inayofuata.

Katika energy graph, sharpest drop inatokea kwenye position ya OC₁. Hii inaonyesha kwamba system haipati high output energy kwa kuaccumulate high energy ndani ya cavity, bali kwa kutoa energy haraka baada ya amplification katika kila round.

Small-signal gain iliathirije?

Watafiti walibadilisha \(g_0\) kati ya 30–80 dB. Katika OC₁ results, kadiri gain ilivyoongezeka:

• Pulse energy iliongezeka monotonically.
• Peak power iliongezeka.
• Spectrum ilipanuka.
• Pulse duration ilipungua.

Higher small-signal gain ilitoa stronger amplification ndani ya EDF na kuongeza self-phase modulation. Increased nonlinear phase ilipanua spectrum huku ikifanya pulse iwe narrower katika time domain na kuongeza peak power.

OC₂ behavior ilikuwa tofauti. Gain ilipokuwa chini ya 50 dB, spectrum ilibaki narrow, kwa hiyo filter effect ilikuwa limited na energy ya low-energy output iliongezeka pamoja na gain. Gain ilipozidi kuongezeka, spectrum ilipanuka, energy iliyokatwa na filter ikaongezeka, na energy pamoja na peak power kwenye OC₂ zikaanza kushuka.

Kulingana na study, stable single-pulse propagation haikudumishwa chini ya 30 dB au juu ya 80 dB. Stability limits hizi zinatumika only kwa cavity, initial condition, filter na model parameters zilizotumika.

Kwa nini filter bandwidth ina optimum value?

Wakati small-signal gain ilikuwa 40 dB, filter bandwidth iliscaniwa kati ya 0,2–3,2 nm. Kadiri filter ilivyopanuka:

• Output spectrum iliendelea kupanuka.
• Pulse duration ilipungua.
• Peak power iliongezeka.
• Pulse energy kwanza iliongezeka, kisha ikapungua.

Katika filter width ya 2,2 nm, highest energy ilipatikana kuwa roughly 3,47 nJ. Narrow filter inakata large part ya spectrum na kutengeneza substantial cavity loss. Filter ikiwa too wide, spectral shaping inakuwa weak, pulse inakusanya nonlinear phase zaidi na kudumisha high-energy stable state kunakuwa more difficult.

Optimum point inawakilisha balance kati ya filter loss, pulse duration, peak power, self-phase modulation na stable soliton regeneration. Highest-energy point si lazima iwe same na shortest-pulse au highest-peak-power point.

Kwa nini optimum filter inakuwa narrower kadiri pump inavyoongezeka?

Same scan iliporudiwa kwa \(g_0=80\) dB, filter bandwidth inayolingana na maximum energy ilishuka hadi 0,6 nm. Higher gain inaweza kufidia more effectively energy loss inayosababishwa na narrow filter. Kwa hiyo, katika high gain, stronger spectral confinement inaweza kutumika huku high pulse energy ikiendelea kudumishwa.

Result hii haitoi single universal filter rule. Optimum bandwidth inabadilika pamoja na gain, total dispersion, nonlinear coefficient, saturable absorber na coupling ratios.

Effect ya nonlinear coefficient

Nonlinear coefficient ilibadilishwa kati ya 1–7 W^-1km^-1. Katika OC₁ output, kadiri coefficient ilivyoongezeka:

• Pulse energy ilipungua.
• Spectral width iliongezeka.
• Pulse duration ilipungua.
• Peak power kwanza iliongezeka, kisha ikapungua.

Stronger Kerr effect ilitengeneza more nonlinear phase, kupanua spectrum na kukandamiza pulse. Mwanzoni, decrease ya pulse duration iliongeza peak power. Coefficient ilipozidi kuongezeka, cutting ya broad spectrum na filter iliongeza energy loss; energy loss ilipozidi gain kutoka pulse compression, peak power pia ilianza kushuka.

Katika OC₂ output, peak power ilipungua continuously pamoja na nonlinear coefficient. Kwa kuwa main energy ilitolewa kwenye OC₁, spectral broadening ya remaining low-energy pulse ilifanya filter loss kuwa more pronounced.

Study inapendekeza lower nonlinear coefficient kwa high energy. Hata hivyo, \(\gamma\) si numerical setting tu; inategemea effective mode area ya fiber, material na wavelength. Kwa hiyo watafiti walibainisha kwamba coefficient inapaswa kuchaguliwa ndani ya experimentally realizable range.

Optimized high-energy design

Parameter scans zilitoa design strategy ifuatayo:

1. Kutumia high small-signal gain upande wa juu wa stable range.
2. Kuchagua optimum na narrower spectral filter inayolingana na gain hiyo.
3. Kutumia low nonlinear coefficient inayoweza kufikiwa experimentally.

Final parameters ni hizi:

• \(g_0=80\) dB,
• SFBW = 0,6 nm,
• \(\gamma=1\) W^-1km^-1.

Relative na initial operating point ya 3,46 nJ, energy iliongezeka roughly %220. Kwa upande mwingine, pulse duration iliongezeka kutoka 2,53 ps hadi 8,78 ps na peak power ikashuka kutoka 1269,6 W hadi 1180,2 W. Comparison hii inaonyesha wazi kwamba optimization iliincrease total pulse energy, si peak power.

Katika optimized state, durations na spectral widths kwenye OC₁ na OC₂ kuwa same inaonyesha kwamba shape ya remaining pulse baada ya main energy extraction inarestabilize ndani ya cavity. Hata hivyo, energies za outputs mbili zinatofautiana kwa roughly orders tatu.

Kwa nini spectral sidebands zilitoweka?

Katika conventional pure-quartic solitons, phase matching kati ya soliton na dispersive waves inaweza kutengeneza spectral sidebands. Katika optimized energy-managed state, spectrum ilionekana relatively smooth. Watafiti waliihusisha hii na narrow spectral filter kuvuruga spectral components zinazohitajika kwa phase matching.

Ili kutest interpretation hii, filter iliondolewa kutoka cavity. Ili kudumisha single-pulse stability, small-signal gain ilipunguzwa katika same experiment kutoka 80 dB hadi 30 dB. Bila filter, clear symmetric sidebands zilijitokeza katika spectrum.

Comparison hii inaunga mkono strongly role ya filter katika sideband suppression. Hata hivyo, kwa sababu gain pia ilibadilishwa wakati filter iliondolewa, experiment si single-variable ablation. Kwa hiyo, claim kwamba sideband change inatokana na filter pekee haijaonyeshwa kwa fully controlled numerical comparison. Stronger validation ingehitaji parameter pair ambapo filtered na unfiltered designs zinaweza kufanya kazi stably kwa same gain, au direct calculation ya phase-matching terms.

Study inaunga mkono nini?

• Kutoa high fraction ya energy immediately baada ya amplification kuliwezesha high-energy output na low-energy stable cavity pulse kuwepo pamoja ndani ya model.
• Kadiri small-signal gain ilivyoongezeka, pulse energy katika main output iliongezeka.
• Kwa kila gain value, filter bandwidth inayomaximize energy ilipatikana.
• Kadiri gain ilivyoongezeka, optimum filter ikawa narrower.
• Lower nonlinear coefficient ilitoa higher pulse energy ndani ya same model limits.
• Chini ya selected optimum parameters, stable single pulse ya 11,07 nJ ilipatikana numerically.
• Sidebands kurudi baada ya filter kuondolewa kuliunga mkono role ya filter katika formation ya smooth spectrum.

Study haithibitishi nini?

• Energy ya 11,07 nJ haijapimwa katika real laser.
• Haijaonyeshwa kwamba proposed cavity ni robust kwa environmental temperature, mechanical vibration na polarization changes.
• Haijaonyeshwa kwamba second- na third-order dispersion zinaweza kuwekwa exactly zero katika real fiber system.
• Haijaelezwa jinsi small-signal gain ya 80 dB itakavyopatikana kwa specific pump power, gain fiber na experimental setup.
• Haijaelezwa jinsi effective nonlinear coefficient ya 1 W^-1km^-1 itatengenezwa simultaneously katika all cavity components.
• Filter-sideband suppression mechanism haijathibitishwa kwa single-variable test katika same gain.
• Long-term stability, timing jitter, amplitude noise au pulse-to-pulse energy variation hazijahesabiwa.
• Haijaonyeshwa kwamba results zinatumika kwa same way kwa different center wavelengths, fiber types au cavity lengths.

Methodological value kwa Uturuki

Nchini Uturuki, fiber lasers ni important research area kwa precision processing, micromachining, biomedical imaging, spectroscopy, optical communications na defense systems. Directly transferable aspect ya study kwa Uturuki si kwamba 11,07 nJ ni ready-made device recipe; ni design approach inayotenganisha high energy na intracavity stability.

Local research groups zinaweza kuendeleza method hii kwa njia zifuatazo:

• Kuongeza measured second-, third- na fourth-order dispersion values za real fibers kwenye model.
• Kuunganisha pump power ya gain fiber, population inversion na spectral gain profile na physical model.
• Kuoptimize filter width na center wavelength ndani ya real optical-filter tolerances.
• Badala ya kuchukua OC₁ coupling ratio kuwa fixed %90, kuioptimize pamoja na energy, stability na efficiency.
• Kuzingatia polarization, additional losses, splices, component dispersion na environmental fluctuations.
• Baada ya numerical design, kujenga erbium-doped fiber-laser prototype na kupima energy, spectrum, duration na noise experimentally.

Study haichukui nafasi ya stages hizi. Lakini inatoa useful preliminary-design framework inayoonyesha parameters zipi zinahitaji kutunewa pamoja na kwa nini kuongeza pump power pekee haitoshi.

Mbinu na Matokeo ya Utafiti

Technical summary ya research design

Comparison ya initial na optimized design

Trends kutoka parameter scans

Main results zilizoonyeshwa na figures

• Kielelezo 1: Kinaonyesha energy-managed cavity structure yenye output couplers mbili na main energy extraction immediately after EDF.
• Kielelezo 2: Kinaonyesha outputs mbili katika 40 dB na 2 nm operating point, spectrum-time evolution na sudden energy drop kwenye OC₁.
• Kielelezo 3: Kinaonyesha kwamba gain ikiongezeka, OC₁ energy na peak power zinaongezeka, duration inapungua na spectrum inapanuka.
• Kielelezo 4: Kinaonyesha kwamba katika 80 dB gain, baada ya high energy kutolewa kupitia OC₁, OC₂ pulse inabaki katika `sech²` form.
• Kielelezo 5: Kinaonyesha kwamba katika 40 dB gain, energy maximum iko around 2,2 nm.
• Kielelezo 6: Kinaonyesha kwamba katika 80 dB gain, optimum filter width inashift hadi 0,6 nm.
• Kielelezo 7: Kinaonyesha stable evolution ya low-energy cavity pulse around optimum filter.
• Kielelezo 8: Kinaonyesha kwamba energy inapungua na spectrum inapanuka kadiri nonlinear coefficient inavyoongezeka.
• Kielelezo 9: Kinaonyesha stable intracavity evolution katika low nonlinear coefficient.
• Kielelezo 10: Kinaonyesha OC₁ na OC₂ pulses na spectra za optimized design.
• Kielelezo 11: Kinaonyesha amplification, %90 energy extraction, filtering na low-energy stable circulation katika single cavity round ya optimized design.
• Kielelezo 12: Kinaonyesha clear symmetric sidebands zilizotokea baada ya filter kuondolewa.

Strengths za study

• Gain, filter na nonlinearity zimescaniwa separately ili kutenganisha effects za design decisions.
• Si final pulse pekee, bali spectrum, duration na energy evolution ndani ya cavity zimechunguzwa pamoja.
• Main high-energy output na low-energy soliton inayobaki katika cavity zimeripotiwa separately.
• Imeonyeshwa numerically kwamba optimum filter width inategemea gain.
• Filtered na unfiltered spectra zimelinganishwa ili kuchunguza sideband mechanism.
• Imeelezwa kwamba optimized parameters zilichaguliwa ndani ya experimentally accessible ranges.
• Kwa kuwa pulse duration, energy, peak power na spectral width zimeripotiwa pamoja, physical nature ya energy increase inaweza kutathminiwa.

Methodological na reproducibility limitations

• Hakuna physical prototype au experimental validation.
• Second- na third-order dispersions zimechukuliwa ideally kuwa zero.
• EDF na SMF₂ lengths zimeripotiwa reversed katika sections mbili.
• Numerical time window, sample count, spatial step na convergence tolerance hazijaripotiwa.
• Number ya cavity rounds zinazohitajika kufikia steady state haijaripotiwa.
• Parameter scans hazitoi uncertainty analysis, repeated runs au sensitivity ranges.
• Small-signal gain haijaconvertiwa kuwa physical pump power.
• Haiko clear kama final nonlinear coefficient ilitumika separately kwa SMF na EDF au jointly.
• Numerical value ya linear-loss coefficient haijatolewa.
• Splice losses zimepuuzwa na quantitative effect yake haijatestwa.
• Polarization, birefringence, Raman scattering, amplified spontaneous emission na component tolerances hazikumodeliwa.
• Kwa sababu gain pia ilibadilishwa katika filter-removal test, sideband mechanism haikutestwa kwa single-variable comparison.
• Data na simulation code hazijashareiwa katika open archive.

Statistical assessment

Kwa sababu study inategemea deterministic numerical simulations, significance tests zinazotumiwa katika clinical au experimental studies hazikutumika. Standard deviation, confidence interval au repeated-run distributions hazijaripotiwa kwa parameter points. Imeelezwa kwamba white-noise initialization pia ilifikia same stable result, lakini quantitative results za different noise seeds hazijatolewa.

Kwa hiyo, result ya 11,07 nJ si mean au uncertainty interval; ni single steady-solution value iliyopatikana chini ya selected parameters na numerical-solution settings.

Maelezo ya Chanzo na Mbinu

• Jina kamili la asili la study: Optimal design of an energy-managed pure-quartic soliton fiber laser
• Waandishi na mpangilio: Ruohan Wang; Qian Zhang; Xingliang Li; Mengmeng Han; Shumin Zhang
• Equal contribution au equal first authorship: Haijaelezwa.
• Corresponding author: Shumin Zhang
• Corresponding-author email: zhangsm@hebtu.edu.cn
• Corresponding-author ORCID: 0000-0002-3037-9854
• Institution: Hebei Key Laboratory of Photophysics Research and Application, College of Physics, Hebei Normal University, Shijiazhuang 050024, China
• DOI: 10.2139/ssrn.6944938
• Publication platform: SSRN
• Platform operator: Elsevier
• Peer-reviewed journal: Hakuna accepted au published peer-reviewed journal name iliyoelezwa.
• Publication date: 15 Juni 2026
• Source type: Preprint ya numerical fiber-laser modeling na parametric-optimization research
• Peer-review status: Study haijapitia peer review.
• Official SSRN link:SSRN study page
• DOI link:10.2139/ssrn.6944938

Kuna older SSRN record yenye same author list na same results za 11,07 nJ, 1180,2 W na 8,78 ps, yenye title “Optimal Design of Energy-Managed Pure-quartic Soliton Fiber Laser Based” na DOI 10.2139/ssrn.6765665. Kwa sababu version relationship kati ya records hizi mbili haijaelezwa katika text, 10.2139/ssrn.6944938, ambayo inalingana na footer ya uploaded file na current title, inapaswa kutumika katika bibliographic citation.

Author contributions zimetolewa katika study hivi: Ruohan Wang — conceptualization, methodology na writing; Qian Zhang — data curation na software; Xingliang Li — validation na software; Mengmeng Han — validation na software; Shumin Zhang — supervision, review na editing.

Research ilifadhiliwa na Natural Science Foundation of Hebei Province chini ya support number F2026205023. Waandishi wametangaza kwamba hakuna known financial conflict of interest au personal relationship inayoweza kuathiri study.

Data na simulation outputs zinazounda msingi wa results hazijachapishwa katika open data repository. Waandishi wameeleza kwamba data inaweza kutolewa upon reasonable request. Hakuna open link iliyotolewa kwa source code ya split-step Fourier solution au full numerical configuration files.

Maelezo haya ya Kituruki yameandaliwa kwa kuchunguza full text ya study, five main equations, laser-cavity schematic, twelve figures, pulse na spectrum maps, gain-filter-nonlinearity scans, energy evolutions na optimized-design results. Scientific content inategemea only study iliyochunguzwa. External sources zilitumika only kwa bibliographic verification ya title, authors, institution, corresponding author, DOI, SSRN record na publication status.

Result ya 11,07 nJ ya study si experimental laser measurement. Result ilipatikana katika numerical model ambapo second- na third-order dispersion zilichukuliwa kuwa zero, splice losses negligible na components ideal. Kwa physical implementation, real fiber dispersions zinahitaji kupimwa, pump-gain relationship kuanzishwa, filter na coupler tolerances kuongezwa kwenye model, prototype kutengenezwa na long-term pulse stability kuthibitishwa experimentally.