The challenge of guiding or deflecting a laser beam in a disturbed medium involves careful
consideration of various nonlinear interactions of light with air and their transient response. A
light filament provides a high intensity region in space that maintain its shape for propagation
lengths longer than the Rayleigh range. The possibility to use this light channel for coupling
optical, teraherz and radio frequency had been spurring researches in this field.
We present the contribution of transient nonlinear response of the medium on light propagation.
The nonlinear interaction of ultrashort pulses with air leaves a spatial distribution of ionized medium
that evolves into an equilibrium plasma. The light pulse has left the medium it ionized before the
plasma has reached equilibrium. Therefore, the reaction of the medium onto the filament involves
a transient evolution of the ensemble of ions and electrons that follow deterministic trajectories
under the influence of the light field. Other nonlinear interactions such as molecular alignment
also have a time dependent response. The relative influence of the plasma and molecular motion
is modified by focusing conditions. The standard focusing of light into air combines the nonlinear
Kerr focusing with the desired linear focusing of the optics. A focusing through a sharp pressure
gradient made by an aerodynamic window enhances the pointing stability of the laser beam. The
effect of transient response of the medium driven by nonlinear interaction of ultrashort pulse on
the guided beam will be discussed.
Frequency combs are revolutionizing metrology, providing a link between optical and RF fre-
quencies. The cavity of a mode-locked laser determines the wavelength of a particular comb
tooth, and the teeth spacing. It is demonstrated experimentally that the average tooth
spacing of a frequency comb can be tuned by tilting an etalon inserted in the cavity. This pro-
perty amounts to a control of the average group velocity of a pulse circulating in the resonator.
We have shown that a mode-locked laser in which two pulses circulate constitutes a
sensitive phase sensor. This is because any phase shift between the two pulses is converted
into a frequency shift, equal to the ratio of the phase shift to the cavity round-trip time at the phase
velocity. The two frequency combs issued from the laser are split in frequency, a split measured
as a beat note on a detector recording the interfering combs. A laser gyro is an example of such
an Intracavity Phase Interferometer. A structure with periodic discrete resonances matching
several teeth of the comb will, because of the dispersion associated with the resonances, decrease
or increase the beat note, since the split combs will see different cavity round-trip times. Such reso-
nant structures that applies to multiple teeth of the comb can be passive resonators (Fabry-Perot) in
transmission or reflection, narrow atomic two-photon resonances, phase matched frequency dou-
blers, etc. . . . Experimental demonstrations will be presented. No correlation is observed between
pulse velocity and beat note enhancement/reduction.
Possibility of creating a laser in the sky has been a hotly debated topic. Rather than a traditional laser with a cavity, what is generally understood is super-radiant emission, where a long and narrow gain volume produces coherent directional stimulated emission. Some filaments can provide the required geometry for an extended gain medium, necessary condition to create lasing in air. Ideal pulse parameters, including wavelength, duration energy and repetition rate will be discussed. Shadowgraphy is presented as a powerful method to analyze the shock wave created by the filament and its guiding-antiguiding properties. The best filaments to create a waveguide are not necessarily the same that will produce the optical excitation of air molecules leading to optical gain. The solution to ‘lasing in air” may reside in creating two color or “nested” filaments. It is shown that such combination can form a stable stationary waveguide.
The gain produced by 800 nm femtosecond filaments is analyzed in different conditions of pulse duration, energy and pressure. At certain wavelengths, lasing in the sky will be bet achieved at the low pressures found in the upper atmosphere. Time resolved high resolution spectroscopy of nitrogen plasma emission excited with 800 nm filament reveals the contribution of rotational wave packets in the nitrogen ion emission. The ultrashort 800nm pulse launches a wavepacket in all the occupied states of neutral and ionized molecule. As the states in B and X of the ion evolve with different phase and respond with opposite polarity to the applied field, the emission alternates between “P” and “R” branch across the accessible rotational manifold. The rovibrational transition can be retrieved back to understand the process by which optical gain is achieved.
A comprehensive modeling of the mode-locked laser is presented. The methodology, based for a large part on space-time analogy, applies to any cavity, but may be particularly important for short cavities with particular emphasis where very tight parameter control is essential. Unlike earlier models the beam deformation by nonlinear index in time and space is completely accounted for. It is shown that the mechanism responsible for starting mode-locking is not only Kerr lensing but also Kerr deflection. The problem of directionality in a ring laser is addressed. Will the operation be bidirectional, or unidirectional, and in the later case in which direction? It is suggested that this question can be addressed by considering the analogy between a ring laser and a quantum mechanical two level system. While it is generally taken for granted that multi-GHz combs can only be obtained by miniaturization of the laser, it is shown that a high frequency comb can be generated in a mode-locked laser by inserting a glass etalon.
Various models of filamentation in air are presented and the remaining theoretical challenges are pointed out. Means to extend the range of filaments are reviewed and proposed. Filaments offer promise of guiding electrical discharges over large gaps. Experiments of UV filament induced discharge are presented.
Mode-locked fiber lasers are the most promising lasers for intracavity phase interferometry,<sup>1</sup> because they offer the possibility to have two orthogonally polarized pulses circulating independently in the cavity. The saturable absorbers based on polarization maintaining tapered fiber coated with carbon nanotubes are developed and analyzed for minimum coupling between the slow and fast axis of the fiber.
Passively mode-locked bidirectional operation of a ring diode pumped Nd:YVO<sub>4</sub> laser with optimized resonator design
is reported. Beat note with frequency between 140 Hz and 300 Hz between two counter propagating beams was observed
and its origin is explained as a result of phase modulation of the laser beam via nonlinear index of refraction n<sub>2</sub> of
Nd:YVO<sub>4</sub> which was calculated.
We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the
frequency and amplitude of the modulation to determine the conditions for cavity self-stabilization and
enhanced gyroscopic sensitivity. We find an enhancement in the sensitivity of a laser gyroscope to rotation
for normal dispersion, while anomalous dispersion can be used to self-stabilize an optical cavity. Our results
indicate that atomic media, even coherent superpositions in multilevel atoms, are of limited use for these
applications, because the amplitude and phase filters work against one another, i.e., decreasing the
modulation frequency increases its amplitude and vice-versa. On the other hand, for optical resonators the
dispersion reversal associated with critical coupling enables the amplitude and phase filters to work together.
We find that for over-coupled resonators, the absorption and normal dispersion on-resonance increase the
contrast and frequency of the beat-note, respectively, resulting in a substantial enhancement of the
gyroscopic response. Under-coupled resonators can be used to stabilize the frequency of a laser cavity, but
result in a concomitant increase in amplitude fluctuations. As a more ideal solution we propose the use of a
variety of coupled-resonator-induced transparency that is accompanied by anomalous dispersion.
Various solid state lasers such as Cr:LISAF, Yb:YAG, Nd:Vanadate, Ti:sapphire and Nd:YAG have in common a long lifetime of the laser level, which results in a tendency to Q-switching rather than pure mode-locking. These lasers are being used in a linear or ring cavity for intracavity sensing applications (displacements, rotation, electric and magnetic fields), and for applications in spectroscopy. The requirements for these applications are that the pulses be centered at a specific wavelength, and be of a specific pulse duration. Multiple Quantum Wells (MQW) typically used for ultrashort pulse generation have often a high defect concentration which causes losses incompatible with the large number of intracavity elements required by the applications. We have established for all these lasers a composition curve for the MQW, that enables one to tune to a specific wavelength. These saturable absorbers have excellent optical quality both in reflection and transmission.
The approach to prevent Q-switching has generally been to use very low loss modulation (single quantum wells). With a large number of intracavity elements, a larger loss modulation is desirable, hence the use of multiple QW (4 to 100). We have successfully demonstrated stable continuous model-locked operation by using passive energy limiters in the cavity. Two-photon generated carriers induce lensing in the cavity, resulting in power dependent losses through an aperture in the cavity. We show that the attenuation is proportional to the square of pulse intensity, resulting in a steep energy limiter. We demonstrate theoretically and experimentally that the presence of two intracavity pulses required for sensor applications can be satisfied with multiple quantum wells appropriately positioned in the cavity. Examples of applications include rotation sensors (ring cavity) or acceleration sensors (linear cavity), magnetic filed sensor, displacement sensors.
In a mode-locked laser, a wave packet of light of transverse dimension of the order of a mm, and longitudinal dimension of only a few micron, travels back and forth in a resonator of the order of one or two meter. It is difficult to conceive why a light bullet, six orders of magnitude shorter than the cavity, would care whether its central wavelength would fit as a sub-multiple of the cavity length. As the length of the resonator changes constantly because of vibrations, thermal drifts, the “central wavelength” of the intracavity fs pulse should also change constantly to follow the cavity resonances. We present evidence that this is indeed the case, and that the micron long wave packet traveling in the cavity does indeed keep record of cavity motion, with subwavelength accuracy. Applications range from distance measurements with a spatial resolution of 0.01 pm, and fs temporal resolution, to inertial navigation (measurement of acceleration and rotation). Stabilization of the mode-locked laser can enhance the resolution of these measurements by at least three orders of magnitude.
The feasibility of ultrafast (10 THz) communication by time multiplexing using femtosecond pulses is discussed. Such a system calls for stable mode-locked sources in frequency and repetition rate, that can be synchronized with sub fs jitter. Preliminary experiments and theory show this goal to be achievable.
There are numerous applications that require stabilization of mode-locked lasers. Mode-locked ring laser sensors have been demonstrated to have a sensitivity to rotation of the order of the rotation of the earth, and sensitivity to optical path changes of less than 0.01 Angstrom. These performances could be enhanced by several order of magnitude through stabilization. Stabilized and accurate femtosecond pulse trains have also applications in ultrafast communication, where there is a need to synchronize with subfemtosecond jitter independent sources.
We have demonstrated stabilization on a short time scale of both the repetition rate and the average frequency of a mode-locked laser, using an ultra-low expansion quartz reference cavity. We will discuss techniques to extend the short term stabilization to long time scales, by locking the laser to atomic lines.