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 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 the
pumping part in our case could be of various kinds 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 for studying this part because this is one
the which gives rise to non linear optical properties 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 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 important for the continuous
verses ultra short pulses of light the continuous beam for instance 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 on the other hand ultra short
pulse again very short time window has say 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 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 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 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 say eight hundred nanometers
center frequency and so that's how this is a commercial laser and we will discuss
that in a minute so that's how 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 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 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 but for a ultra short laser pulse we need something which
is over hand so many some thing called a a mode lock system so we have already shown
you spectral features where we have several modes longitudinal modes present within
the mode of the laser being measured and so within the profile of the laser and so
once we are talking about locking all the modes 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 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 where as for 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 in this particular case the pulses just
separated at certain distances have been measured by delaying one pulse with respect to the
other and you can see how the interference pattern and fringes look like 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 which can be two types one is the field auto correlation which looks like this or
it could be intensity auto correlation where it looks like this square of what we are
looking at the field auto correlation so on and so forth
so the fourier transform an infinite train of pulses can be written in terms
of 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 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 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 so the overall function essentially
has a summation all this different modes which is quite difficult to certain 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 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 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 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 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 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 the phases are zero at time equal to zero but at other time whenever
they are in phase 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 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 one quick option is to actually use pulse pumping so instead of using a
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
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 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 which is set at forty five degree
so wave plate this is a roughly a quarter wave plate 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 under go a lambda by four shift when it ons to switch it otherwise it
remains it doesn't do anything to light coming through and that's how it's access
like a switch so 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 mode locking
yet we have been looking at the gain modulation process as have to do this now 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 which means that an absorber can keep on observing
until it gets saturated when it doesn't absorb any more so 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 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 again looking at
passive mode locking whenever we have high intensities spikes because of this
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 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 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 passively mode locked dye lasers yield pulses as short of
few hundred femtosecond they are limited by ability to saturate the absorbers so if
can have a fast absorber then all the combination of the process was possible to do this kind
of results so here some of the 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 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 even shorten pulse then that was one of the principles which were used
to get better shorter pulses so this is the one which was originally used to produce
very short pulses 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
many other important developments so the other approach were or other principle
which is really helped in terms of generating short pulses is the idea of the fact that
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 however they can be medium which can undergo
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 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 titanium being the active material in this sapphire
crystal where his non linear process of refractive index which is which at high
powers give rise to additional focusing effect which limits the the available zone
over which the 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 this is a type of saturable absorption which is used
for the case of 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 and so it gets lost and so only the high intensity beams survive
and finally produce the short pulses so here is a example how this modeling works
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
which is necessary for this kind of a short pulse of operation to happen so this
near infrared region which is what is been used it ranges laser from seven hundred
to about micron 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 amplifier system as i mentioned
before so 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
this is additional help with the help of dispersion compensation and then case of mode
locking we realize that only at a very short 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 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 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 or it could be something like a pump which already changing 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 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 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 short pulses which are then stretches which is
short of stretch because the group velocity dispersion 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
so this are the components of the ultra fast system shortening mechanism dispersion compensation
and the starting one was the process that we mentioned 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 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 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 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 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
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 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 use them for timed measurements or inducing
non linear process have all been looked into this lecture 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