It is the advantage of the cholesteric phase that its pitch and thereby the
wavelength of the emitted laser light can be tuned by various external stimuli
(usually the temperature). Lasers relying on a cholesteric feedback medium have
usually a very narrow linewidth and their emission is circularly polarized. With this
concept, rather small lasers can be constructed [97, 98]. They are usually pumped
by pulsed solid-state lasers although, after first attempts [99], continuous pump
conditions were recently successfully established [100]. Lasing has been mostly
observed from low molar mass cholesteric mixtures because they show excellent
alignment. The state of the art is reviewed in [98, 101, 102].
The key concept of cholesteric laser is best explained by the density of optical
modes or density of states (DOS) [97] known from the physics of solid state
lasers. The cholesteric phase provides resonance through its periodic structure.
Light propagation only occurs for allowed (or cavity) modes, whose number is
proportional to the density of states [103]. Inside the photonic band gap of a
cholesteric phase, the DOS is equal to zero and emission is suppressed but enhanced
at the band-edges [104]. Here, the photon velocity decreases to zero while the
photon dwell time increases to infinity because of multiple reflections from the
periodical structure. The details of lasing depend now on the width of the band-gap,
which is mostly determined by the birefringence Δn and by the orientation of the
fluorescent dyes parallel or perpendicular to the director. The stimulated emission
of the gain material in a DFB laser at frequencies where the DOS reaches its
maxima can be considered as a standing wave. For one of the standing waves
(in-phase), the polarization direction is always parallel to the director (Fig. 14,
right) and feels the extraordinary refractive index of the liquid crystal. It has a lower
energy, which corresponds to the low energy band-edge. For cholesteric materials
with a wide band-gap resulting from a large Δn, the threshold for the low energy
band-edge is considerably lower than at the other band-edge, where the polarization
direction is perpendicular to the director (out-of-phase standing wave; Fig. 14, left).
Lasing may thus be found first at the low energy band-edge, but at sufficient high
pumping power it becomes possible at both edges [105].
In addition to band-edge lasing, defect mode lasing is possible [97]. A defect in
the photonic structure creates fine bands of allowed transmissions inside the
photonic band gap. A defect may result from an isotropic or anisotropic layer
between adjacent cholesteric layers, but also from phase shifts [106], particle
stabilized defects [107], deformation of the cholesteric helix [108] or local
polymerization [109]. The threshold of such defect modes are low and can be as
low as a few nanojoules per pulse [110].
2.4.2 Crosslinked Polymeric Cholesterics as Lasing Material
Today’s challenge is the search for robust cholesteric materials with a low threshold
value for lasing, but a high tolerance for pumping. As mentioned above, lasing from
cholesteric structures is mostly the domain of low molar mass liquid crystals. That
is because it is essential to obtain a monodomain, which is as defect-free as
Optical Properties of Assemblies of Molecules and Nanoparticles
89
wavelength of the emitted laser light can be tuned by various external stimuli
(usually the temperature). Lasers relying on a cholesteric feedback medium have
usually a very narrow linewidth and their emission is circularly polarized. With this
concept, rather small lasers can be constructed [97, 98]. They are usually pumped
by pulsed solid-state lasers although, after first attempts [99], continuous pump
conditions were recently successfully established [100]. Lasing has been mostly
observed from low molar mass cholesteric mixtures because they show excellent
alignment. The state of the art is reviewed in [98, 101, 102].
The key concept of cholesteric laser is best explained by the density of optical
modes or density of states (DOS) [97] known from the physics of solid state
lasers. The cholesteric phase provides resonance through its periodic structure.
Light propagation only occurs for allowed (or cavity) modes, whose number is
proportional to the density of states [103]. Inside the photonic band gap of a
cholesteric phase, the DOS is equal to zero and emission is suppressed but enhanced
at the band-edges [104]. Here, the photon velocity decreases to zero while the
photon dwell time increases to infinity because of multiple reflections from the
periodical structure. The details of lasing depend now on the width of the band-gap,
which is mostly determined by the birefringence Δn and by the orientation of the
fluorescent dyes parallel or perpendicular to the director. The stimulated emission
of the gain material in a DFB laser at frequencies where the DOS reaches its
maxima can be considered as a standing wave. For one of the standing waves
(in-phase), the polarization direction is always parallel to the director (Fig. 14,
right) and feels the extraordinary refractive index of the liquid crystal. It has a lower
energy, which corresponds to the low energy band-edge. For cholesteric materials
with a wide band-gap resulting from a large Δn, the threshold for the low energy
band-edge is considerably lower than at the other band-edge, where the polarization
direction is perpendicular to the director (out-of-phase standing wave; Fig. 14, left).
Lasing may thus be found first at the low energy band-edge, but at sufficient high
pumping power it becomes possible at both edges [105].
In addition to band-edge lasing, defect mode lasing is possible [97]. A defect in
the photonic structure creates fine bands of allowed transmissions inside the
photonic band gap. A defect may result from an isotropic or anisotropic layer
between adjacent cholesteric layers, but also from phase shifts [106], particle
stabilized defects [107], deformation of the cholesteric helix [108] or local
polymerization [109]. The threshold of such defect modes are low and can be as
low as a few nanojoules per pulse [110].
2.4.2 Crosslinked Polymeric Cholesterics as Lasing Material
Today’s challenge is the search for robust cholesteric materials with a low threshold
value for lasing, but a high tolerance for pumping. As mentioned above, lasing from
cholesteric structures is mostly the domain of low molar mass liquid crystals. That
is because it is essential to obtain a monodomain, which is as defect-free as
Optical Properties of Assemblies of Molecules and Nanoparticles
89