Experiments on the Generation of Higher-Order Hermite-Gaussian Pulses From an FM Mode-Locked Laser

We experimentally generated higher-order Hermite-Gaussian (HG) pulses from an FM mode-locked laser that had a specific optical filter
$F_{HG{\mathrm {m}}}(\omega)$
characterized by a Bessel function
$J_{n}\mathit {(M_{PM}})$
and
$A_{HG{\mathrm {m}}}(\omega)$
and
$A_{HG\mathrm {m}}(\omega +n\Omega _{m})$
with n =
$- \infty \sim $
+
$\infty $
. Here,
$M_{PM}$
is the phase-modulation index and
$A_{HG\mathrm {m}}(\omega)$
was the Fourier transformed spectrum of the
$m$
th HG pulse
$a_{HG\mathrm {m}}(t)$
in the time domain and
$\Omega _{m}$
was the fixed angular phase-modulation frequency. The laser we constructed was a 10 GHz polarization-maintained FM mode-locked erbium fiber laser emitting at a wavelength of
$1.56 \mu \text{m}$
, which included a liquid crystal on silicon (LCoS) optical device to implement the specific filter function needed to generate HG pulses. We successfully generated
${m}$
= 0
$\sim $
7th HG pulses with pulse widths of 10
$\sim $
50 ps. For the generation of
${m}$
= 1, 3, 5,...odd-numbered HG waveforms, the corresponding
$F_{HG\mathrm {m}}(\omega)$
has no center frequency mode. Since these waveforms are odd functions in the time domain, their spectral profiles are given entirely by imaginary components with the same shape as those in the time domain. For the generation of
${m}$
= 0, 2, 4,...even-numbered HG waveforms, the corresponding
$F_{HG\mathrm {m}}(\omega)$
has a center frequency component. Since these waveforms are even functions in the time domain, their spectral profiles are given entirely by real-value components with the same shape as those in the time domain. Finally, we generated
${m}$
= 1
$\sim $
3 dark and bright higher-order HG pulses by introducing a CW amplitude offset. To generate these pulses, a new bandwidth-limiting filter was installed since these pulses have a rectangular pulse component, which creates many high-frequency sidebands.