we have been discussing about lasers in the
last couple of lectures and we have covered
almost everything to deal with continuous
lasers in this lecture will be doing the last
part of the lasers which are necessary for
our course which is going to be the pulsed
lasers so until now we have been focusing
on continuous lasers the principle of blazing
and all that now we are going to look at continuous
verses pulsed lasers
so what we have looked at as been excitation
of lasing atoms or molecules by using external
sources of light or radiation for example
flash lamps or another lasing the another
laser which is pumping ah by using electromagnetic
radiation or other things but basic idea has
been pumping the output of the laser light
can be a continuous wave as we have been discussing
if the pump is continuous or pulsed if the
pumping is pulsed now this is the second part
which are going to look at most of the cases
until now has been continuous and so ah the
pumping part in our case could be of various
kinds ah the pulsed lasers have very high
intensities because the laser intensity is
concentrated in a very short time duration
and that's one of the critical reasons ah
for studying this part because this is one
the which gives rise to non linear optical
properties ah so there are two waves are looking
into quantum computing and quantum related
aspects one is in the linear region which
is very easily possible with the continuous
lasers and principles that we are looking
at also under the condition where the photons
are very low in number which is low photon
count regions where would like to actually
have very low number of photons to be dealing
so that's one kind which you have almost done
now but the other kind where we would like
to deal with a lot of photons possibility
of having lot of them simultaneously so that
it can induce ah events or phenomena which
are not possible to be explain by under the
linear domain that's the part which you are
necessary to have short time pulses or other
kinds of things also for measuring time scales
which are very short and so this is the region
where we are now entering which is pulse laser
now linear optics is one of the things which
you have been looking at
so what is that's ah important for the continuous
verses ultra short pulses of light the continuous
beam for instance ah if you look at with time
is constant where is and it gives a spectrum
which is ideally a single frequency but we
know the details some very small band width
where as ah on the other hand ultra short
pulse again very short time window has say
ah constant frequency in the ideal case a
constant and a delta function which are basically
fourier transform pairs is what we have in
the ideal scenario but in reality this is
what we have we have the irradiance verses
time for a long pulse can be looked at at
a very narrow spectrum in the frequency band
and vice versa a very short pulse in time
corresponds to a very wide frequency or wave
energy band in the frequency spectra so by
using the ferial relation between the two
which is also the same as the uncertainty
principle states that the ah the two are transforms
each other in time verses frequency and so
what ever is long in one domain is short in
the other domain in the as we mentioned in
the last slide it's a sort of like the extreme
cases where we have continuous verses line
a line verses a continuous in reality it is
some width with respect to a very narrow width
again the short width with respect to a long
width that's what we are looking at
so the laser time band width relationship
therefore can be summarized in this slide
as we said for a continuous wave laser we
have roughly a single frequency which corresponds
to the delta function in wave length or frequency
and ah an ultrafast laser pulse is therefore
a coherent superposition of many monochromatic
light waves within a range of frequencies
that is inversely proportional to the duration
of the pulse so for instance ten femto second
ah pulse with femto second distinctive minus
fifteen seconds corresponds to say in wave
lengths ninety four nano meters around the
center frequency this is a titanium sapphire
laser so it as ah say eight hundred nanometers
center frequency and ah so that's how this
is a commercial laser and we will discuss
that in a minute so that's how ah the relation
works for the time and frequency and this
is known as a time band width relationship
which will be very useful when we are in this
domain or ultra short laser pulses
so ah what is the main difference here between
Let's say wide band source for instance light
bulbs which is also broad band but as we have
discussed many times over and over again ah
sources which are not going to have coherence
or anything it to stimulated emission i am
not going to be relevant in this picture so
a light bulb is the kind of scattering or
spontaneous emission process which is sort
of like eliminating mean ah but for a ultra
short laser pulse we need something which
is over hand so many some thing called a a
mode lock system ah so we have already shown
you spectral features where we have several
modes ah longitudinal modes present within
the mode of the laser being measured and so
within the profile of the laser and so ah
once we are talking about locking all the
modes ah what does it mean to how and how
do we go about doing that that's what we have
to look at
so in order to look at these pulses we have
to also ah recognize that they have to be
measured a very kind particular wave so the
laser pulse characteristics in these cases
are done in typically two ways one is to note
the spectral width which is comes from monochromatic
and so for example in this particular commercial
laser that we are discussing eight hundred
or seven ninety nanometers into frequency
we have a band width which is associated to
the measurement made in the spectrometer monochrometer
ah where as for ah in time with pulses which
are so short it is not possible to measure
directly so see the measured by using a auto
correlating system are cross correlating system
but generally the first principle is to use
an interferometric way of measuring a correlation
between the pulse and itself and that's one
of the ways it is measured and you can see
ah in this particular case the pulses just
separated at certain distances have been measured
ah by delaying one pulse with respect to the
other and you can see how the interference
pattern and fringes look like ah if you make
a square measurements with the detector actually
does it squaring of the system then you can
pick up the difference between the two fields
and so it could be interferometric auto correlation
or ah which can be two types one is the field
auto correlation which looks like this or
it could be intensity auto correlation where
ah it looks like this square of what we are
looking at the field auto correlation so on
and so forth
so ah the fourier transform an infinite ah
train of pulses ah can be written in terms
of ah how it looks like where the single pulse
and the time between the pulses the convolution
theorem can be used and what we can look at
is that there is a frequency band over which
this different frequency components can be
appear in the fourier domain train of pulses
results from a single pulse bouncing back
and forth inside the laser cavity of round
trip time t the spacing between the frequencies
called laser modes and that is the one which
is given as two pi over the round trip time
t so that's why the delta nu which is separation
between this pulses on this modes ah which
we are looking at which is this so thats generally
what is the situation which is happening is
that we have these round trip times within
which the pulse is rattling around the sorry
the light is been rattling around the within
the amplifying cavity and that's what we a
measuring when we look at the pulses which
are coming out
so ah mode locked pulse train therefore as
this field which as this profile where a train
of short pulse is which is particular for
the as we just mentioned this is what we have
just looked at we have non mode locked pulse
train then we have a random phase for each
mode and ah so the overall ah function essentially
has a summation all this different modes which
is quite difficult to certain ah they can
be all over the place so there is a they can
beating all kinds of a all of this does not
happen when you are looking at and the mode
lock condition when the phases are all the
same so the basic idea about the non mode
lock verses mode lock is that the phase distribution
is fixed for the mode lock pulse train
so here is the pictorial output we are looking
at locking the phases of the laser modes yields
an ultra short pulse and that is the mode
locking so if you have random phases of all
laser modes this ah like this radiance with
time similar to what we have in case of light
bulb also so the phases are all random where
as when ah when they are all one kind they
are all in phase with each other then the
period of time and when they are all in phase
gives rise to the time over which all the
lock phases are there so all this other unlocked
phase conditions are ah not possible to be
seen only the ultra short period of time over
which all the phases are in all the laser
pulse laser is in time is in phase is the
one which looked at so this is the ultra short
pulse during which all the phases are the
same
so here is how it looks like then there is
all this are different modes that will coming
out from the laser is a resonator round trip
time and as the modes get get to have the
same phase and they they overlap and they
get amplified more and more at this points
with respect to the time where they are not
in phase and so they randomly are all over
the place so statistically so they average
out ah where is the amplified once at the
once which are happening exactly at the laser
round trip time and we get the lock mode at
those places so you can actually go ahead
and do numerical simulation of mode locking
going to see how ha you can have different
ah time frames and these modes appear exactly
locked at a period of time and you can have
the very short period of time over which all
the modes are equivalent the rest of the time
they are not there so if you have for instance
you can do it for simple eight modes and you
can do a simulations and here it is doing
an example case where ah the phases are zero
at time equal to zero but at other time whenever
they are in phase ah have a fixed phase between
all of them then they come together and for
a very short period of time and that's the
ultra short pulses for me and if they are
always random and there is no time possible
where they will all get amplified simultaneously
to give rise to their short period
so ultra fast lasers often a thousands of
modes so a generic ultra short pulse laser
ah as a broad band gains media a pulse shortening
device and two or more mirrors that's typically
the case this pulse shortening device is known
as a mode locker so there are many pulse shortening
device which has been proposed and over the
years so ah one quick option is to actually
use pulse pumping so instead of using a ah
pulse shortening device if you already have
a pulse pumping device then pumping a laser
medium with a short flash lamp yields a short
pulse flash lamp pulse is a short as one micro
second can exists unfortunately this yields
a pulse as long as the excited state lifetime
of the lasing media which can be considerably
longer than the pulse pump it's so that is
one of the issues here since the solid state
laser media have lifetimes in the microseconds
range it yields pulse of microseconds to milliseconds
long so ah
so this is typically how it looks like these
are long and potentially complex pulse is
that come out from partially from a laser
which is being pumped with a pulse laser so
this is based on the pulse pumping idea there
is no mode locking device inside the laser
in this case is another approach which is
known as q switching q is a typically known
as the quality factor and so this is what
it is done in case of laser like this is a
q switching involves preventing the laser
from lasing until the flash lamp is finished
the flashing and abruptly allowing the laser
to lase the pulse length in this case is limited
by how fast we can switch and the round trip
time of the laser and yields pulse of ten
to hundred nanoseconds long so this is basically
based on the idea that you are building up
cavity within the ah building of the gain
within the cavity and then at a certain point
of time we just let the let the system switch
so that the the output can go up output can
go and then you get the pulse so it's a switching
system this is the switching so how do we
switch a laser for example q switching involves
preventing a laser until we are ready a typical
q switching a pockel cell which switches in
a nanoseconds from a quarter wave plate to
nothing so pockel cell is a basically a wave
plate ah which is set at forty five degree
so wave plate this is a roughly a quarter
wave plate ah which is placed and so light
becomes circular in it's first pass and then
in horizontal on the next and is rejected
by the polarizer in this particular case
so basically when ever we have this lambda
over four so it goes through first time it
becomes circular it comes through here and
then it's a having opposite polarization of
the incident when i am so reject and it comes
out so the wave plate is respect to that after
switching light is unaffected by the pockels
cell and hence it is passed by the polarizer
so the pockel cell is something which makes
the material ah under go a lambda by four
shift when it ons to switch it otherwise it
remains ah it doesn't do anything to light
coming through and that's how it's access
like a switch so ah so that is the basic idea
behind q switching now there are different
waves of looking at mode locking so until
now we have not looked at ah mode locking
yet we have been looking at the gain modulation
process as have to do this now ah passive
mode locking there can be two different kinds
one is the passive mode locking and the other
one is the active mode locking so in case
of passive mode locking the idea is to use
something called saturable absorber ah which
means that an absorber can keep on observing
until it gets saturated when it doesn't absorb
any more so ah like an sponge an absorbing
medium can only absorb so much high intensity
spikes burn through low intensity light is
absorbed
so it's like a it's its an intensity getting
in that sense beyond a that intensity just
Let's it go so that is ah passive mode locking
principle for example so here is the effect
away saturable absorber first imagine raster
scanning pulse by time for instance so with
the passive mode locking we can almost act
it like a gate so for example here is the
case which is shown of a saturable absorber
so Let's consider the that we are looking
at the pulse at every point of time but we
see the that the week pulses are suppressed
and the strong pulse shortens and gets amplified
after many round trips even a slightly saturable
absorber can yield very short pulse so that
is one way we are looking at how you can generate
a short pulse like this ah again looking at
ah passive mode locking ah whenever we have
high intensities spikes because of this ah
principle of letting the system go through
this idea of intensity which can be only high
intensity which can go through and when there
is a spikes where the laser can output and
the so the gain goes through a dip and again
goes up goes to a point reaches the maxima
and then again it goes to through ah the saturable
point where it can get out of the system and
it keeps on going so this is basically the
principle of creating a short pulse this was
actually one of the first ones which you are
used for producing very short pulses it can
have different effects when you have a slow
saturable absorber verses a fast saturable
absorber if the absorber responds slowly more
slowly than the pulse only the leading edge
will experience pulse shortening ah this is
which is the most common scenario unless the
pulse is many peaker seconds long the gain
saturation essentially shortens the pulse
trailing edge and so the leading edge becomes
faster and reducing gain is available for
for trailing edge of the pulse and for the
later pulses and so there is this particular
over all curve that you can look at have this
initial loss verses gain and you can see that
basically the peak pulse is getting amplified
more and more where the mode locking is going
to be achieved and tails are getting at innovated
so the combination of saturable absorption
and saturable gain yields short pulses in
the when the absorption is slower and the
pulse this is one of the idea and so this
was first applied for dye lasers where the
gain media so it is a dye laser was the advantage
of using it for a dye laser was because that
the dye laser had the capability of a very
broad spectral condition so this is one of
the things which would mention about dye lasers
they had a very wide absorptions and that's
the advantage of using this ah passively mode
locked dye lasers yield pulses as short of
few hundred femtosecond they are limited by
ability to saturate the absorbers so if ah
can have a fast absorber ah then all the combination
of the process was possible to do this kind
of results
so here some of the ah dye laser are used
for producing the initial short pulse lasers
in fact the nobel prize which went to suhail
he is no more for demonstrating the first
very short time dynamics was incidentally
using these kinds of lasers dye lasers ah
which were able to go down to very short pulses
and this is essentially the first of it's
which are used which was a ring dye laser
where the pulse were made to collide and higher
intensity of the saturable absorber is what
was being used so it's called a colliding
pulse mode lock laser where two pulses colliding
resulted in ah even shorten pulse then that
was one of the principles which were used
to ah get better shorter pulses so ah this
is the one which was originally used to produce
very short pulses ah sub fifty femto seconds
for the first time which were then shorten
further to produce the real fast dynamics
measurements which were finally led to ah
many other important developments
so ah the other approach were or other principle
which is really helped in terms of generating
short pulses is the idea of the fact that
ah many materials the actually behave like
lens so lens can be something which as which
is due to the phase delay can be seen the
beam varies with the distance that we know
and that's how we get the lens effect of that
ah however they can be medium which can undergo
ah the length is constant but it's a reflective
index varies with the the distance and that
can also act like a lens both cases quadratic
variation of phase with distance yields a
lens and so this is the second principle of
this has been a seen of late to be given rise
to a lot of ah mode locking principle and
that's the kerr lens principle which is used
in solid state laser so today which gives
rise to this phenomena of producing short
pulses and this is the mechanism which is
used in the most popular laser up today which
is title titanium sapphire laser ah titanium
being the active material in this sapphire
crystal where ah his non linear ah process
of refractive index which is which at high
powers give rise to ah additional focusing
effect which limits the ah the available zone
over which the ah system can keep on going
back and forth
so it's sort of likes works like a very short
aperture and losses are too high for low intensity
c w mode to lase but not for high intensity
from second lasers so this acts like a very
sharp aperture like which only the peak of
the intensity can go through producing a very
short pulse so it's a type of satural absorption
in some sense we have pulse at experience
additional focusing due to high intensity
and the non linear reflective index then we
align the laser for this extra focusing then
a high intensity beam would have a better
overlap with the gain medium and ah this is
a type of saturable absorption which is used
ah for the case of ah titanium sapphire laser
and this additional focusing optics can arrange
for perfect overlap of high intensity beam
back into the ti sapphire crystal and that's
what has been used for this particular purpose
the low intensity beam unfortunately does
not have the advantage ah and so it gets lost
and so only the high intensity beams survive
and finally ah produce the short pulses
so here is a example how this modeling works
ah for a such able absorption being generating
through kerr lens and so this is the model
of the idea as to how it happens and mode
locked laser is seen which as a wide band
width and a short pulse so it's a currently
as i mentioned ti sapphire is the currently
the work horse laser for most of the ultra
fast community emitting pulses as short as
a few femtoseconds and average power in excess
of a watt and more it as it is wide band width
ah which is necessary ah for this kind of
a short pulse of operation to happen so this
near infrared region which is what is been
used ah it ranges laser from seven hundred
to about micron ah it has a very nice life
time also of the excess state which Let's
say two remain inverted for a quite a while
it's four level ah amplifier system as i mentioned
before so ah what we have learnt here is that
so here is the principles that we have learnt
here we have the components of the laser system
is like this what we are trying to do in this
process is we are going to lock the cavity
modes in such a ways that only for a brief
period of time they overlap to get the maximum
gain which is locking mechanism and this is
ah this is additional help with the help of
dispersion compensation and then case of mode
locking we realize that only at a very short
ah point of time in phased locked phases for
all the pulses giving rise to short pulse
otherwise they are random and therefore they
go away the band width ah results in this
point over which the pulses will be wide and
as with the narrow spectrum it will start
getting broader the pulse will get more locked
and you will get a broader and broader spectrum
and finally when all the pulses are the shortest
possible you get the maximally broadest spectrum
this is the broadest spectrum for the shortest
possible pass that's the basic idea behind
this ah principle of ultra short pulses that
what we have learnt is this is the band width
to a looking at it and this is the time width
you re looking and what we have found is delta
nu delta t is constant so expect what we do
when w have a short pulse we have a long band
of the pulses you know we have looked into
the different mode lock mechanism an active
verses passive the active ones actively modulate
the gain in the medium ah or it could be something
like a pump which already ah changing ah pulsed
there is a synchronous pump mode locking the
other one is use to acousto optic modulator
which is a loss modulation which kind does
that the other one which is ah these are active
the other cases the passive mode locking which
is a saturable absorber like dye solid state
and the optical kerr effect that we have mentioned
so the outputs are of this different kinds
which mean mention c w verses c w mode lock
q switched q switched mode lock and four possibility
exits the kerr lens one one we discuss in
detail because thus the one which as which
is been used in detail now days the kerr medium
is our a sapphire crystal that we used in
titanium sapphire for instance and the high
intensity ultra short pulses are the ones
which are which survived in this process the
focus pulse is going through high intensity
profile only the ultra short pulses survive
the rest the intensity dependent refractive
index one which helps in this process it creates
specially self focusing condition as well
as the temporally self forced focusing condition
which is due to pulse shortening due to group
velocity dispersion and this is the last modulation
ah saturable placement of kerr medium and
a hard aperture which is coming due to the
intensity dependent refractivity index
so here is the cartoon which shows the refractive
index depends on the intensity of light self
phased modulation due to temporal intensity
due to transversal mode profile and in as
it goes through it produces this ah short
pulses which are then ah stretches which is
short of stretch because the group velocity
dispersion ah which is provide due to process
and one can have it short by using other process
compensating for the group velocity dispersion
because it's a linear process and we can get
a short of six femtoseconds five femtoseconds
in this kind of process so the compensator
can be simple as a present compensator can
basically go through the wave length tuning
mark this is the band width part where we
essentially making sure it can be compensated
so it goes through this prism systems where
the amount of linear frequency are compensated
by by this process ah
so this are the components of the ultra fast
system shortening mechanism dispersion compensation
and the starting one was the process that
we mentioned ah it can also have many other
process like saturable absorber cavity perturbation
and all that in a ti sapphire laser which
is one which is most important today is it
has a typical cavity as shown here which is
inside and oscillated which is then compensated
with the help of prism pair the dispersion
and it is applied for many different cases
so in the output coupler comes through the
laser ah the it it can be further amplified
by using the of linear gain were it is done
is the oscillator is put through a linear
stretching device which makes a longer a pulse
it is done put through an amplifier where
it is again amplified in this process then
a compressor within decompress which again
compresses the system ah of the amplified
pulse to get even higher intense pulses so
here is the typical chirped pulse amplification
principle that we have of today oscillator
which produces the short pulse initial short
pulse which goes through an chirping process
to ah stretch it and then the low power safe
for amplification goes though amplifiers and
then high energy pulse is have done to amplifier
then second grading pair reverses the dispersion
of the first pair so this is the first part
which which lengthens pulse then the second
pair is eventually compresses it and it results
finally in a high intensity ultra short pulses
so femtosecond pulse can be amplified to petawatt
powers this are o intense that it electrons
can be rapidly stripped from atoms so we have
used principles where we have also ah use
the idea that the modulation of light induces
the beam narrowing and all this principles
where used for model as just we mentioned
as we mention modulation directly or externally
by using different principles and typical
ah external modulation was to use the c w
laser light modulation which are also done
in fibers and other kinds of optical sources
the femtosecond lasers thus amplified can
be ah taken out to petwatt powers which can
be so intense that strip electrons rapidly
from atoms with this i am going to end this
lecture because whatever we wanted to do in
terms of lasers in their being a continuous
source for the kinds of operation that we
are interested or a source we can actually
ah use them for timed measurements or inducing
non linear process have all been looked into
this lecture ah with this we end this entire
look into then lasers and their required ideas
behind it and the next lecture on will be
using them for further applications into quantum
computing
thank you
