用於光學同調斷層掃描的摻鈦藍寶石晶體光纖之FDML雷射動態建模

Abstract

傅立葉域鎖模雷射(FDML)是高速光學同調斷層掃描(OCT)的重要進展，可在不犧牲光譜解析度的前提下實現超高速成像。我們建立一套基於摻鈦藍寶石晶體光纖之 FDML 雷射的時域模擬，評估其作為下一代 OCT 寬頻波長掃描光源之可行性。結合摻鈦藍寶石具備的寬增益頻寬與極快恢復時間，以及晶體光纖優異的散熱管理，本研究構建完整數值模型，納入增益動態與非線性傳播。 本研究之核心為模組化腔體模型： (1) 摻鈦藍寶石增益介質以含飽和增益與頻譜濾波之Ginzburg–Landau Equation描述；(2) 被動腔體光纖，以相似方程納入色散與自相位調變；(3) 掃頻濾波器元件，於共動座標系中以動態高斯帶通濾波器實作。此架構可物理地解析增益整形、頻譜濾波與非線性傳播之交互作用。 我們先對腔內元件（繞射光柵、法布里–佩羅濾波器、聲光調變器, AOM）進行特性建模，並模擬連續波（CW）與掃頻運作。傳播以分步傅立葉法（SSFM）求解，並由放大自發輻射（ASE）啟動以呈現自啟動行為，同時連結小信號增益係數與實際泵浦功率。 另引入共動掃頻濾波器與失諧策略 Δf：同時調變掃頻角頻率ω₀與濾波器中心頻率，以改善既有 FDML 模型之穩定性限制。我們重現典型 FDML 行為：漸進式自啟動、脈衝與掃頻同步，以及無失諧時可達廣頻光譜展演；引入失諧後，則觀察到頻寬縮減、振盪包絡與相位調變等現象。結果顯示，FDML摻鈦藍寶石雷射的動態輸出並非持續單一波長掃描，而是時域局部化脈衝，每個脈衝具狹窄瞬時線寬，並與掃頻濾波器同步；時間平均後呈現寬頻輸出，然任一時刻僅釋出狹窄頻段，為 FDML 之典型特徵。 綜上，本研究建立泵浦功率、增益閾值、失諧量與光譜輸出之定量關聯，並提供經驗證之模擬框架，可支援以摻鈦藍寶石增益介質開發超寬頻 FDML 雷射之設計與最佳化。

Fourier Domain Mode-Locked (FDML) lasers represent a key advancement for high-speed Optical Coherence Tomography (OCT), enabling ultrafast imaging without sacrificing spectral resolution. In this work, we develop a time-domain simulation of an FDML laser based on a Ti:sapphire crystal fiber, aiming to explore its potential as a broadband, wavelength-swept light source for next-generation OCT systems. Leveraging the broad gain bandwidth and ultrafast recovery time of Ti:sapphire, as well as the thermal management advantages of a crystal fiber geometry, we construct a complete numerical model that incorporates both gain dynamics and nonlinear field propagation. A central innovation of this study is the modular architecture of the simulation, in which the FDML cavity is modeled through three distinct components: (1) a Ti:sapphire gain medium, governed by a Ginzburg–Landau equation with saturable gain and spectral bandwidth filtering; (2) a passive cavity fiber, described by a similar equation incorporating dispersion and self-phase modulation; and (3) a lumped sweeping filter element, implemented in a co-moving frame via a dynamically tuned Gaussian bandpass filter. This framework enables physically interpretable modeling of the interplay between gain shaping, spectral filtering, and nonlinear propagation. We first characterize the gain medium and cavity elements—including diffraction gratings, Fabry–Perot filters, and acousto-optic modulators—and simulate both continuous-wave and wavelength-swept laser regimes. The propagation is solved using a Split-Step Fourier Method with noise self-starting from amplified spontaneous emission (ASE) and realistic values for gain saturation and dispersion. Another key contribution of this work is the implementation of a co-moving sweeping filter and a new detuning strategy: by modulating both the sweeping frequency ω₀ and the filter’s spectral center with a detuning factor Δf, we resolve stability limitations encountered in earlier FDML models. Linking our small-signal gain coefficient to realistic pump power, our simulation reproduces typical FDML behavior: including gradual self-starting, pulse synchronization to the sweep, and broadband spectral evolution up to 74 THz in the non-detuned case. Upon introducing detuning, we observe a reduction in bandwidth, oscillatory signal envelopes, and phase modulation, in agreement with theoretical expectations and prior experimental observations. Based on our simulation results, the dynamic spectral output of the FDML Ti:sapphire laser does not correspond to a continuously swept single-wavelength output. Instead, the laser exhibits time-localized pulses, each containing a narrow instantaneous linewidth (~0.5-0.8 GHz), synchronized with the sweeping filter. This confirms a pulsation-like behavior in both time and frequency domains, consistent with experimentally observed FDML laser dynamics. The output spectrum appears broadband when averaged over time, but at any given moment, only a narrow portion of the spectrum is emitted, a hallmark of FDML operation. These results establish a quantitative link between pump power, gain threshold, detuning, and spectral output, and provide a validated simulation framework for the design of ultra-broadband FDML lasers using Ti:sapphire gain media.