Fig. 1. Principles of continuously tunable femtosecond fiber laser. (a) Phase-matching curves for FOCR generation for different fiber pitch dimensions, allowing for FOCR generation at different wavelengths in the visible range from a pump pulse of 1035 nm central wavelength. Circles indicate phase-matched FOCR wavelengths in the limit of weak pump power, while squares indicates the phase-matching points for a typical peak power of 100 kW. Inset: representative image of a PCF structure. (b) Peak power evolution of the pump pulse (left) and simulated spectrum (right) along a tapered PCF for FOCR generation at 580 nm from a transform-limited Gaussian input pump pulse at 1035 nm. FOCR is generated around the point of maximum soliton compression of the pump pulse in the fiber, as indicated by the green arrow. (c) Illustration of continuous FOCR tunability in a tapered PCF by a combination of power and pulse duration control of a fixed-wavelength pump pulse. Such control of the pump pulse determines the point of maximum pump pulse compression, which is the FOCR generation point within the taper, as shown in (a). The FOCR wavelength, in its turn, is defined by the local dispersion of the tapered PCF at this generation point, according to the pump-to-FOCR phase-matching condition such as shown in (a). (d) Average visible wavelength for numerically simulated FOCR spectra, as a function of pump pulse energy and duration. Well-defined FOCR peaks appear close to the FOCR generation threshold, whereas for increasing pulse energy/decreasing duration, continuum formation ensues. Circles are the experimental results. The error bars represent the uncertainty in deconvolution factor of the pulse duration from the measured autocorrelation, as explained in the Appendix A.2.

Fig. 2. Experimental setup. Simplified schematic of the tunable femtosecond Cherenkov fiber laser. By adjusting the power and compression settings, or the power alone, of a fixed-wavelength pump pulse provided by a standard mode-locked fiber laser, the output FOCR wavelength from a PCF taper is continuously tuned in a wide spectral range. Inset: the designed (solid line) and its practical realization (dots) of a PCF taper profile.

Fig. 3. Characterization of a widely tunable femtosecond fiber laser. (a) Simulated and experimentally measured spectra of tunable FOCR. (b) The far-field images of the output light. (c) Left: the measured autocorrelation curves of FOCR signals. Right: the autocorrelation FWHM calculation (dashed line) and measurement (dots) of the generated FOCR pulses, and of the pump pulses (squares).

Fig. 4. Output power, conversion efficiency, and noise as a function of laser emission wavelength. (a) Generated FOCR output power (blue dots) and its conversion efficiency (red squares). (b) The SNR of FOCR signals (dots) and of a standard ps-SC source spectrally sliced to 10 nm bandwidth (FWHM) by optical bandpass filters (dashed line).

Fig. 5. Representative image of the PCF. Λ is the PCF fiber pitch.

Fig. 6. Experimental setup of the tunable FOCR laser. OSC, pump oscillator; AMP, pump amplifier; ISO, pump isolator; G, grating; M, high reflection mirror; HWP, half-wave plate; PBS, polarization beam splitter; FM, flip mirror; AC, autocorrelator; PM, photometer; OSA, optical spectrum analyzer; DM, dichroic mirror; F, optical bandpass filter; ESA, electrical spectrum analyzer with photodiode. Inset: typical spectrum of the pump laser output.

Fig. 7. Examples of different designs (solid line) and their practical realizations (dots) for PCF tapers.

Fig. 8. Dispersion curves for three different Λ values of the PCF structure shown in the inset.

Fig. 9. Simulations of FOCR generation in linear and nonlinear taper profiles. (a), (c) Spectrum and (b), (d) temporal power profile versus propagation distance z in a (a), (b) linear and (c), (d) nonlinear taper profile, with taper and input pulse parameters as described in the text. Both spectral density (pJ/THz) and power (W) is plotted logarithmically. See also Visualization 1 and Visualization 2 for simulations of FOCR generation in linear and nonlinear taper profiles, respectively.

Fig. 10. Simulated tunable FOCR spectral profiles and temporal pulses. Selected (a) spectral profiles and (b) temporal pulses obtained after short-pass filtering the spectrum at 750 nm as simulated in the nonlinear taper structure when varying pump power and duration. The temporal pulses have been artificially shifted along the time axis for better viewing.

Fig. 11. Optical pump power response profile dependent on the electronic control of pump power.

Fig. 12. Noise measurements of the FOCR pulses dependent on the output wavelength. (a) The RIN spectra of the FOCR pulses versus the FOCR wavelength. (b) The SNR of FOCR dependent on the wavelength (red circles) and the corresponding output power (black squares).

Fig. 13. Noise measurements of the FOCR pulses after bandpass optical filters. (a) FOCR spectra with and without bandpass optical filters. The power of unfiltered FOCR is 1.3 mW. (b) The RIN spectra of FOCR measured with and without bandpass optical filters. (c) Spectrum of FOCR output (black dashed line) and SNR measured with bandpass filters at different spectral positions (red circles). The SNR of the spectrally unfiltered FOCR is 931.

Fig. 14. Noise measurements of the FOCR pulses dependent on the output power. (a) Noise spectra of the FOCR pulses versus output power at FOCR wavelength of 560 nm. (b) The SNR of FOCR dependent on the output power.