Phase noise properties of supercontinuum generation in all-normal dispersion fibers

TL;DR

The paper investigates phase-noise properties of supercontinuum generation in polarization-maintaining all-normal-dispersion (PM-ANDi) fibers, focusing on intrapulse coherence and energy-induced phase fluctuations. Experimentally, Fourier-transform spectral interferometry is used with a Mach-Zehnder arrangement to quantify spectral-phase stability across $450$--$1700$ nm while varying seed energy, deriving spectrally-resolved intensity-to-phase transfer coefficients $\kappa(\lambda)$ that show an inverse-wavelength trend. A generalized nonlinear Schrödinger equation model including self-steepening and Raman effects reproduces the observed $\kappa(\lambda)$ and a very low phase-noise floor of about $10$–$15$ mrad RMS across the spectrum, with coherence preserved up to seed energies around $20$ nJ and degrading beyond $25$–$30$ nJ due to other nonlinearities such as ionization. The results demonstrate deterministic SCG in PM-ANDi fibers with minimal intrinsic spectral phase noise and reveal a significant, predictable intensity-to-phase coupling that can be tailored via dispersion engineering for applications in CEP metrology and ultra-stable broadband light sources.

Abstract

The spectral coherence properties of supercontinuum generation in polarization-maintaining all-normal dispersion fibers are investigated. Stochastic phase noise induced by energy fluctuations, along with spectrally-resolved intensity-to-phase transfer coefficients, are quantitatively analyzed, confirming the high coherence of the generated supercontinuum. Our results show that the nonlinear process is fundamentally deterministic with ultra-low spectral phase noise, yet exhibits significant intensity-to-phase coupling.

Figures (5)

• Figure 1: (a) Experimental setup. BS1 : 1030 nm 50/50 beamsplitter, BS2: 600-1500 nm 50/50 beamsplitter, $\lambda$/2: half wave plate, TFP: thin film polarizer, L1: f = 3.14 mm, L2: achromat f = 8 mm, F 1 F2 : $~$12 cm NL-PM-1050-NEG NKT Photonics fiber, SP : Spectrometer. (b) Spectral intensity profile in log-scale as a function of laser input energy (reference arm, slow axis).
• Figure 2: (a,c) Spectrograms for the short- and long-wavelength spectral ranges, obtained from 1000 single-shot measurements. (b,d) Phase standard deviation ($\sigma$, solid lines) as a function of wavelength (left y-scale), measured along the two fiber's eigen-axis (blue : slow axis, red : fast axis). The dashed lines show the noise model $\sigma_\text{meas}$, according to Eq. \ref{['eq:3']} (blue : slow axis, red : fast axis). The shaded area indicate the experimental SNR for both axis (right y-scale).
• Figure 3: Phase standard deviation as a function of seed pulse energy of the test arm, in the short (a) and long (b) wavelength ranges. The energy in the reference arm is 15 nJ.
• Figure 4: Phase standard deviation in the short wavelength range at high input energy. The seed energy is increased simultaneously in both arms.
• Figure 5: (a,b) Spectrograms measured over 10000 single shot measurements with time-varying input energy in one arm. The fiber slow axis is selected in the two arms. (c) Retrieved phase for selected wavelengths (1300 nm, 1200 nm, 890 nm, 710 nm - from top to bottom). The curves are artificially offset. (d) Experimental intensity-to-phase coupling coefficient $\kappa(\lambda)$ (rad$/\%$) as a function of wavelength (blue for the short wavelength range and red for the long-wavelength range). The gray-shaded region indicates the experimental deviation, evaluated from three successive measurements. The black solid line is the result of the numerical simulation.