Fig. 1. Experimental scheme for intracavity dispersion measurement using a mode-locked femtosecond laser. The frequency locking error signal is obtained via frequency modulation generated by the electro-optic modulator (EOM), with the light detected in cavity reflection and after spectral selection. The cavity transmission spectrum is recorded to determine the cavity FSR.

Fig. 2. Principle of intracavity dispersion measurement using a mode-locked laser. (a) Cavity transmission spectra obtained with two different values of the laser f _rep. The peak at 830 nm is the result of locking the average frequency of the selected comb to the cavity modes there. (b) The inverted parabola indicates the cavity FSR versus wavelength, due to the net cavity dispersion. Different settings of the laser f _rep, as shown by straight horizontal lines, allow different sections of cavity modes to become overlapped with the frequency comb, resulting in changes in the cavity transmission. The shaded area between f _rep1 and the cavity FSR curve illustrates that the integral of the difference between these two curves over the frequency interval separating the two transmission peaks is zero (see Eq. (1)). (c) Cartoon showing the walk-off effect between the frequency comb and the non-uniformly spaced cavity modes. Near the locking frequency, the detuning between the laser f _rep and the cavity FSR cause the optical comb modes to walk-off from the cavity modes. Away from the locking region, the frequency-dependent cavity FSR causes the optical comb to realign with the cavity modes such that the m ^th comb component is once again resonant with the m ^th cavity mode.

Fig. 3. (a) Cavity-based measurement of the GDD of zero-GDD mirrors used as an input coupler. Three independent measurements are shown. The design theory curve is shown as a dashed line. (b) Cavity-based measurement of the GDD of zero-(open circles) and negative-GDD (filled circles) high reflectors. Data from three independent measurements are shown for the zero-GDD mirror and a single data set is shown for the negative-GDD mirror. Also included are the design curves for both types of mirrors. Due to the sensitivity on layer thickness of the GTI structure, the range obtained from 20 theoretical curves corresponding to a 0.5% RMS variation in the layer thickness is shown. .

Fig. 4. Cavity-based measurement of the dispersion of air versus theory. The theory curve is derived using the Sellmeier equation for the air refractive index and multiplying it by the cavity length. This curve illustrates that the disagreement between the measurement method and theory across the entire spectrum is less than 1 fs².