Transverse Modes

The diverse applications of laser beam sources require control of all properties of the light: from the wavelength spectrum to the temporal behavior to the spatial form. Structured light, i.e., light distributions whose properties vary as a function of space or time, are used for optical communication technologies, advanced imaging or innovative optical measurement methods, for example. These light distributions are sometimes transverse modes of a laser resonator, or they can be represented as a superposition of these modes. Complex light fields can therefore be generated directly in a resonator. In addition, the basis of transverse modes opens up the possibility of generating spatiotemporal dynamics, as the modes differ not only spatially but also spectrally. In so-called transverse mode-locking, this leads to beams that scan spatially at ultra-fast speeds.

Longitudinal to transversal conversion of mode-locked states

Simply put, both longitudinally and transversely mode-locked beams are merely phase-locked superpositions of optical fields of different frequencies. Their interference results in the characteristic ultrashort laser pulses and spatiotemporal oscillations, respectively. In the case of longitudinal mode locking, all fields have the same spatial form, whereas in the case of transverse mode coupling, the fields have different ones. This similarity allows to convert a state from one locking regime to the other.

Here, we have converted longitudinally mode-locked states into transversely mode-locked states. Thus, a beam modulated in intensity over time became a beam moving in space. The oscillation frequency results from the resonator geometry and was 80 MHz. This conversion scheme therefore enables ultra-fast beam movements - without any moving optics. In this scheme, different transverse mode-locked states can be generated in a controlled manner. This allows to directly control the beam dynamics during oscillation. Previously, control over the superimposed modes and their modes and phases was not possible at such a high level. See the publication by Michael.

Hermite-Laguerre conversion of mode-locked beams

The spatial light distributions of a laser can be represented both in radial coordinates (Laguerre-Gaussian modes) and in cartesian coordinates (Hermite-Gaussian modes). With a cylindrical lens telescope, these mode families can be converted into each other. Here, we have applied this concept to transversely mode-locked beams. 

The linear motions of a Hermite-Gaussian transversely mode-locked beam were converted into motions along a circular path (Laguerre-Gaussian). The ultrafast spatiotemporal dynamics (80 MHz) were retained. The radial symmetry results in an improved overlap with fiber modes, which could simplify the amplification and transport of transversely mode-locked beams. See the publication by Florian.

Active transverse mode-locking in a solid-state laser

With longitudinal mode-locking ultrashort pulses are generated, which is achieved by superimposing the longitudinal resonator modes with mutually fixed phase relationships. Similarly, coupling of the transverse modes can also be achieved by adjusting their relative phases, which leads to periodic spatiotemporal dynamics of the laser light distribution. The repetition frequency of the output pattern is directly dependent on the frequency spacing of the transverse modes and can reach up to several gigahertz. This periodic and spatial change of the light distribution can be used, for example, for fast spatial scanning of the laser output, which is of great interest for the realization of fast scanning microscopy. See the publication by Florian.

Selective excitation of higher-order transverse modes by spatial gain shaping

Higher-order transverse modes can be excited by spatially modulating amplitude or phase in a laser resonator. However, since these approaches require additional components within the resonator, they usually lead to increased losses and thus limit the maximum achievable resonator-internal power.

We showed that the excitation of transverse modes in solid-state lasers can also be achieved by means of resonator-external pump light shaping based on a "digital micromirror device" (DMD). The spatial shape of the pump light is adapted to a selected transverse mode, such that it experiences the greatest amplification and is selectively excited. In this way, almost 1000 Hermite-Gaussian modes were selectively generated. The spatial modulation of the pump light means that no internal resonator components were required. In addition, the use of the DMD enabled fully automatic control of the selective mode excitation. See the publication by Florian.