Design of Q-Switched laser; Methods of Q switching,

Theory of Mode locking, Methods of mode locking.

LASER FUNDAMENTALS BY W T SILFVAST

Chapter 13: Pages 439-450, 451-460

Principles of LASER BY O Svelto

Chapter 08: Pages 311-320,

Also see
MODE LOCKING- https://youtu.be/xfBgwlhtt40
on You Tube
 MODE LOCKING

Mode locking is a technique in optics by which a

laser can be made to produce pulses of light of
extremely short duration (i.e. ultrashort pulses),
on the order of picoseconds (10−12 s) or
femtoseconds (10−15 s).

A laser operated in this way is sometimes referred

to as a femtosecond laser,
General concept:

• The basis of the technique is to induce a

fixed phase relationship between the longitudinal modes of
the laser's resonant cavity.
• Constructive interference between these modes can cause
the laser light to be produced as a train of pulses. The laser
is then said to be "phase-locked" or "mode-locked".
• The pulse repetition rate is determined by the resonator's
round-trip time and the number of pulses. ...
• The pulse duration is usually far shorter than the round-trip
time.
• the basic mechanisms leading to mode locking can usually
be much more easily understood in the time domain
Mode locking structure
 It is instructive to consider the synthesis of a periodic pulse train by superposition of
sinusoidal oscillations with equally spaced frequencies, corresponding to different
axial resonator modes in a mode-locked laser. The larger the number of frequency
components involved, the shorter can be the duration of the generated pulses relative
to the round-trip time.

Fig. Synthesis of a periodic pulse train (red curve) by adding seven oscillations with slightly
different but equidistant frequencies (blue curves). The vertical lines indicate points in
time where all the oscillations add up in phase.
 Fig. Temporal evolution of the intracavity field in a laser, once with a fixed phase
relationship between the modes (mode-locked state), once with random phases.

The blue curve shows a pulse train with a fixed phase relationship, so that
at regular temporal positions (e.g. at t = 0) the electric fields of all
frequency components add up to a maximum of the total field strength.
The red curve shows the electric field for the same strength of all frequency
components, but with random relative phases.
Figure: Five waves are added on top of each other,
such that at a given time all the crests coincide.
Generally, the pulses last for a much shorter
time than a round trip in the cavity. They are
limited by the Fourier transform of the
spectrum emitted by the laser: the wider the
spectrum, the shorter the pulse.
 Experimental consideration/Geometry/Setup
Mode locking is the most important technique for generating pulses with picosecond and
femtosecond durations. When a laser is mode locked, one or sometimes several pulses are
circulating in the laser resonator. The case of a single pulse is most common. Each time
the pulse hits the output coupler mirror, a part of its energy is emitted, so the laser output is a
regular pulse train. The gain medium replenishes the pulse energy in each roundtrip.

 The pulse repetition rate is determined by the resonator's round-trip time and the number of pulses.
 For example, a 10-ns round-trip time for a single pulse leads to 100 MHz. Typical values are between 50
MHz and 500 MHz, but miniature lasers can reach repetition rates on the order of 100 GHz, whereas
some lasers with very long resonators have repetition rates below 10 MHz.
 The pulse duration is usually far shorter than the round-trip time. In steady-state operation, the duration is
determined by an interplay of various effects that the pulses experience in each resonator round-trip.
Typical pulse durations are between 30 fs and 30 ps, but values down to ≈5 fs have been achieved with
Ti:sapphire lasers.
 Due to the high pulse repetition rate, the pulse energy cannot be very high; it is typically between a few
picojoules and hundreds of nanojoules.
 The method used to obtain these operating conditions consists in using a rapid
light modulator that can chop the light in the cavity into periods of exactly the
same length as a round trip. Thus, only those photons allowed to pass through
the modulator in its on-state will be amplified and will always find the modulator
in this state after each round trip. The other photons elsewhere in the cavity will
be subject to losses when they travel through the modulator

Figure shows only a single pulse travelling in the cavity. However, a pulse train can be seen leaving the laser, generated each time
the pulse hits the output mirror. The pulse repetition period corresponds to the cavity round-trip time (typically several
nanoseconds).

The average power of a mode-locked laser is of the same order of magnitude as that of
continuous-wave lasers. In fact, in contrast to Q-switched lasers, these can also reach a
steady state like continuous-wave lasers. The fundamental difference is that the
stimulated photons are condensed in a packet rather than spread all around the cavity.
During one round trip, only one laser pulse is emitted via the output mirror. The pulse
energy is thus equal to the average power multiplied by the duration of a round trip.
Generally, these energies are of the order of several nanojoules.
 Methods of Mode Locking

• Active Mode Locking

• Passive Mode-Locking
• Hybrid Mode-Locking
• Mode Locking by Residual Cavity Fields
• Fourier Domain Mode Locking
 Active Mode Locking
Active mode locking involves the periodic modulation of
the resonator losses or alternatively of the round-trip
phase change. That can be achieved in different ways, for
example

 with an acousto-optic,
 an electro-optic modulator,
 a Mach–Zehnder integrated-optic modulator, or
 a semiconductor electroabsorption modulator.
In an actively mode-locked laser, as shown below, mode locking is achieved with a
modulator (for example, electro-optic type), which modulates the resonator losses in exact
synchronism with the resonator round-trips. The modulator is often placed near an end of
the resonator.

Figure: Schematic setup of an actively mode-locked laser.

The circulating pulse goes through the modulator at times where the
losses are smallest, and the slightly higher losses in the pulse wings
slightly shorten the pulses.
After thousands of round-trips, a steady state is reached where this shortening effect is balanced by
pulsebroadening effects (for example, the limited gain bandwidth or chromatic dispersion).
The pulse duration of actively mode-locked solid-state lasers is typically a few tens of picoseconds.
This means that the pulse bandwidth is far smaller than the gain bandwidth of the laser medium.
 Applications
• Nuclear fusion (inertial confinement fusion).
• Nonlinear optics, such as second-harmonic generation, parametric down-conversion, optical
parametric oscillators, and generation of terahertz radiation.
• Optical data storage uses lasers, and the emerging technology of 3D optical data
storage generally relies on nonlinear photochemistry. For this reason, many examples use
mode-locked lasers, since they can offer a very high repetition rate of ultrashort pulses.
• Femtosecond laser nanomachining – the short pulses can be used to nanomachine in many
types of materials. An example of pico- and femtosecond micromachining is drilling the silicon
jet surface of inkjet printers.
• Two-photon microscopy.
• Used in modern refractive surgery. Corneal surgery . Femtosecond lasers can be used to create
bubbles in the cornea. A line of bubbles can be used to create a cut in the cornea, replacing
the microkeratome, e.g. for the creation of a flap in LASIK surgery (this is sometimes referred
to as Intralasik or all-laser surgery). Bubbles can also be created in multiple layers so that a
piece of corneal tissue between these layers can be removed (a procedure known as small
incision lenticule extraction).
• A laser technique has been developed that renders the surface of metals deep black. A
femtosecond laser pulse deforms the surface of the metal, forming nanostructures. The
immensely increased surface area can absorb virtually all the light that falls on it, thus
rendering it deep black. This is one type of black gold[3]
• Photonic sampling, using the high accuracy of lasers over electronic clocks to decrease the
sampling error in electronic ADCs.
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