# Laser fundamentals II: Laser transverse modes | MIT Video Demonstrations in Lasers and Optics

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the following content is provided under a Creative Commons license your support will help MIT OpenCourseWare continue to offer high quality educational resources for free to make a donation or view additional materials from hundreds of MIT courses visit MIT opencourseware at ocw.mit.edu in previous demonstrations we showed the laser beam to be very simple beam with a single spot in the transverse direction
00:30
now most lasers actually put out a beam like that just one spot in the transverse direction and the intensity distribution is Gaussian it has very nice properties and that's why it's a it's a very popular beam from a laser now a laser can also put out other intensity distribution because of the existence of transverse modes which means that the beam would look very
01:02
spotty sometimes it can look like a doughnut with with with darkness in the in the center you can also make it look like two spots three spots and make it look like a flower and so on all because of the existence of transverse modes now in this demonstration we got a special laser for you that can exhibit these transverse modes and the set up is is here we have our usual discharge tube
01:33
except in this case the board diameter is a little bit bigger than in previous demonstrations the the diameter here is of the order of two millimeters two-and-a-half millimeters or so while before the board diameter was about one and a half millimeters one mirror is attached to the discharge tube over here and and the other end of the discharge
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tube has a Brewster window so that we can place the second mirror over here the this mirror here is curved about 60 centimeters a radius of curvature and the mirror here is a flat one the transmission of the mirrors is very small and so that the the output light is not going to be as bright as we would like it but hopefully we'll be able to see the transverse modes the the beam
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then from the from the laser will come out over here and then we'll reflect it by this mirror and then this mirror into a lens here we expand the beam and then the expanded beam then will fall onto onto the screen over here so now let me turn on the laser and we count up to seven or eight seconds or so and here is his laser on and the the output then from the laser is its weak I know but
03:11
you might be able to to see it here's the output from the laser and then we're going to reflect it as I said before by this mirror this mirror to the lens and then on to on to the screen and now we'll have one camera look at the screen so we can look at the transverse mode and another camera can look at my hands adjusting one of the mirrors to change the the number of modes and the intensity distribution that you will see on the screen now here as you can see
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the the beam looks looks like a doughnut mode with with no field in the in the center and my hand you can see in the lower right hand corner adjusting the mirror mount now here I'm going to start now adjusting and then you can see that the the intense distribution are varies varies quite a bit here we are here you can see very complicated kind of pattern is another one with two dark spots single dark spot
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and here is like it looks like a flower nice pretty little patterns and these are all due to these transverse modes now what you're seeing here is a mix sure of transverse modes they're not necessarily pure ones that means just a single transverse modes by itself now here if I misaligned too much and get rid of most of them here is our lowest order mode which is called the zero zero mode now here is
04:47
the the normal kind of laser beam but in this particular laser setup I can generate all kinds of other intensity distribution due to the the other transverse modes that can be generated in this kind of setup with a large with a larger bore in the discharge tube it's very pretty as you can see now as I
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mentioned before in most lasers one wants to get rid of the these transverse modes so that we can only have the zero zero mode and when we come back we're going to show a method of eliminating the lazing of these transverse modes other than the lowest order one we're going to do this by placing a an aperture a small iris inside the laser cavity we have now placed an aperture
05:51
inside the laser cavity so as to get rid of all transverse modes except the lowest order one the zero zero mode the aperture is is over here when we're placing it in the space between the brewster window and and the second mirror so here's the aperture and then by by adjusting this knob here I can I can then change the size of the of the aperture in the meantime we've also
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covered this the laser tube here with with some white paper so that we don't have too much light to burn the camera so in case you don't see the discharge tube so well as before is because we've covered it up so now let's look at the at the now and see to see the transverse modes without without the the aperture stopped down here we are we see we see those transverse modes or mixture of
06:54
transverse modes now what I'm going to do is I'm going to now reduce the size of the aperture and let's see what happens here I am reducing it and you can see this me go back a little bit is some other modes and then when I stop it way down to about a millimeter or so you can see that I have now the lowest auto mode the zero zero mode okay let's do it again let me open it up again is the transverse mode and then I stop it down I get rid of all transverse
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modes except the lowest order in fact now I can even adjust the mirror I can adjust the mirror and and indeed I can't can move the spot around but I don't get any any transverse modes showing up so in summary then by putting a small aperture inside the laser cavity in choosing the diameter appropriately we can get rid of all transverse modes except for the lowest order model now
07:58
most commercial lasers either have an aperture like that inside the laser cavity or have the bore size of the of the laser amplifiers so chosen so that only the lowest order mode would lays and with very difficult to have the other transverse modes lasers and that's why most commercial lasers put out that lovely single spot beam now another interesting thing about transverse modes is that their frequencies are different
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from one another and that depends on the again the length of the cavity and the curvature of the mirrors so when we come back we're going to have the spectrum analyzer setup so we can look at the frequencies of the various transverse modes we're now ready to look at the frequencies or the spectrum of the transverse modes of this laser using a scanning fabry-perot interferometer
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acting as an optical spectrum analyzer and here's the setup the output of the laser now we take the output from the other end from the other mirror we're going to reflect it by this mirror here this mirror here onto the scanning fabry-perot interferometer the length of the cavity is about 10 centimeters which means that the free spectral range will be about one and a half gigahertz the output of the scanning fabry-perot interferometer then goes onto the scope display to display the the frequencies
09:37
of the of the laser now we're going to look at the intensity of the of the beam or the transverse intensity distribution of the beam showing the various transverse modes and at the same time we're going to look at the spectrum of the laser light as measured by the scanning fabry-perot interferometer now here on the screen now we see on top we see the the intense distribution of the
10:11
laser the transverse intensity distribution and below we see the corresponding spectrum what I've done here is I've stopped down the aperture so that we only have the lowest order mode the zero zero mode oscillating and on the scope we see three or four modes due to the longitudinal modes in the in the laser oscillating in the in the laser and of course the number of longitudinal modes will depend on the
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width of the gain medium the laser is about 40 centimeters long which means that the mode spacings are about is about 375 megahertz and that's why we get three and sometimes four modes oscillating within the bandwidth of the amplifier which is one and a half gigahertz and just for fun what I'm going to do is tap on on the mirror gently to shake the cavity and you can see the contour of the of the bandwidth of the amplifier
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which is about as I said before around one-and-a-half gigahertz so when I'm not shaking the cavity too much then we see the the modes longitudinal modes stable and and quite clearly the so now what I'm going to do is open up the aperture introduce some high order modes so what I'd like you to do look at the picture above and and then at the same time look at the spectrum so I'm just slowly going to bring in now you can see already here
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even though still looks like it appears to be just the lowest auto mode but it isn't because if you look at the spectrum you see that we have introduced some new frequencies and these new frequencies are associated with the transverse modes and now oscillating and I can I can go further now and open up the aperture some more here we are so now you can definitely see a number of higher-order modes and look at the frequencies now there's lots of them and they again they're within the bandwidth of the of the amplifier there's one
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thing nice about having a lot of transverse modes is that you can have a lot more power coming out from the laser because you have more modes oscillating so here I'll do it again I'm going to reduce the aperture size and to get the lowest auto mode oscillating so again they just get the longitudinal modes of the zero zero mode and now I will introduce the transverse mode again to show that that they have their
12:50
longitudinal mode frequencies are different from the from the zero zero mode so far I've only been able to show you a mixture of transverse modes in fact the only isolated mode that I was able to show you was the lowest order one the zero zero mode by itself and then I showed you a mixture of transverse modes now in the next demonstration I'm going to use a little trick to isolate a single high
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order transverse mode so that we can look at it and then we can also look at its spectrum now in order to isolate one high order transverse mode I'm going to use a very thin wire the wire will place along the vertical direction inside the laser cavity and in this way we'll be able to prevent the lowest auto mode the
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zero zero mode from oscillating because we'll place the wire right in the center of the zero zero mode so it's providing a lot of diffraction loss for it but for the next high order mode the the to spot mode so-called one zero zero one depending on how you count these modes then one will be able to to oscillate if the wire is thin enough because this wire is going to be placed right where the field is zero now to make that clearer I'm going to show to you on the
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screen before I do this I'm going to show you where the wire is placed the wire is placed in a holder here and the wire is about 50 microns wide and you placed vertically inside the laser cavity I have an adjustment here I can move the wire in and out or is in a horizontal direction and also I have another adjustment here that rotates the the orientation of the wire from let's say vertical to to horizontal now let's go look at the screen and see what sort
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of transverse mode I've been able to isolate now here on the screen you see that I've isolated the the next transverse mode it's called either 0 1 or 1 0 depending on how you count these modes and this consists of essentially two two spots with zero field in between and remember I use the vertical wire right in the center of the
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of the mode so that this particular transverse mode doesn't need any in the middle and and therefore can oscillate with the wire in place but most of the other modes like the lowest order mode and so on cannot oscillate with this wire in there because that provides too much diffraction loss that's why we've been able to isolate this this one particular mode like this now if we look on the output of the spectrum analyzer as shown
15:58
on this on the oscilloscope below you can see that we have two and sometimes three three modes are that correspond to the longitudinal frequencies of this transverse mode just like in the case of the zero zero mode just clean single transverse modes now what I'm going to do now is adjust the the wire or translate it horizontally so that I can
16:27
bring in other modes so now I'm going to move it a little bit now you can see I brought the what we call the zero two mode it's a little faint but that's what I'm able to do right now and you can see on the scope below that again it's clean mode but of course the the intensity is is weak now let me go in the in the other direction back again here we bring in the zero one mode and now let me go further
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get the wire sort of out of the way of the of the cavity now you can see that I'm bringing in other transverse modes difficult to tell from the intensity distribution just look like a blob but below the frequencies you can see I'm bringing in other other modes and here I'll go further and and that's what it is now let's get me go back to the to
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the 1 0 mode Here I am one zero mode and then over here which is the the to zero or zero to depending as you say how you count how you count them and now I'm back to the to the mixture of transverse mode now the the frequencies of the transverse modes depend on the length of the cavity and the curvature of the mirrors and on the
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certain conditions for example in the case of a confocal cavity where the Rays of curvature of the mirrors are identical and equal to the spacing in the cavity you can get a you can get all the even modes under the zero zero mode and all the odd modes are halfway in between and for a plane another example is for a plane mirror cavity all the
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modes the frequencies of almost all transverse modes are degenerate are identical but if you're not controlling you're not playing plane then you can expect modes transverse modes all over the place so so far I've shown you that by using a simple thin wire placed in a vertical direction inside the laser cavity we were able to isolate one of the transverse modes the 0 1 or 1 0 mode
19:11
that's the one with the two spots side-by-side now if I took this Y are not placed it along the horizontal direction inside the cavity I would be able to isolate the other transverse mode that has the two spots one on top of the other similarly if I place the Y 45 degrees I would have the two spots inclined at 45 degrees just in case you don't believe me I'm going to do this
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right now so let's look at the screen while I rotate the the wire by a few degrees at a time and then and then pick it up pick up the horizontal position of you I as you can see the two modes are beginning to get inclined I'll do it some more here we are it's almost 45 degrees or so following the orientation of the wire so
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here we are we see the two modes now are inclined at an angle close to 45 degrees now lets me see if I adjust the position of the wire the translational position of the of the wire let's see what happens to the next high order mode where here we are the 0 2 or 2 0 you can see that's that one is also inclined at the same angle as the 0 1 mode now let
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me go back to that one and back to this one and indeed you can see that I have a pure mode because the spectrum below shows that I have only the longitudinal modes associated with with 1 1 transverse 1 transfer small now in in practice I could place all kinds of structures inside the laser cavity and isolate almost any transverse mode I
21:18
want make it complicated but but in principle it can be done now in this next demonstration we're going to have some fun we're going to start with the laser oscillating in the 0 1 or 1 0 transverse mode then I'm going to take a knife edge or a razor blade like this and I'm going to place it inside the
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laser cavity to block only one of the spots one of the lobes of this transverse mode and see if the laser can still oscillate on just one one one lo all right so I'm going to take this then this knife edge I'm going to place it here inside the laser cavity and as I'm doing it maybe we can look at the screen and here we are we have the the 1
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0 0 1 mode then I'm going to bring this knife edge OOP close here we are and now it's not interrupting anything but now I'm going to move it in to cut one of the one of the lobes out all right so I'm going to do it slowly whoop too fast now I'm going to slow it again now what you can see that as soon as I get close
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to the two these lobes the entire mode drops out or stops lazy I cannot just have the laser oscillate only in one of the one of the lobes and this shows that indeed this is a transverse mode of the of the laser because I cannot separate them they they go together I cannot just have one and not not the up now what's going to happen if I take this knife
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edge and place it outside the laser cavity and try to block one of the modes when the mode has already left the cap so this is interesting question so I'm going to take it out from here and then I'll place it outside the laser cavity and then we'll see what happens then here we are outside the laser cavity now I'm going to put the knife edge over here let me first adjust it so I'm close
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to the beam OOP right about here okay now let's look at the transverse mode as I cut with this knife edge I cut into into the transverse mode so here we are you see above the transverse mode now let me start coming in with an my age and let's see what happens so what you see happens is that we get rid of one lobe and the other lobe is there if I cut in some more you see the starts
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to distort a little bit starts to get bigger let me go back is by itself and then here is here is with the knife edge outside the beam altogether and we have the the transverse mode by itself again let's do it again I come in I can cut one side lobe and it still some intensity left and then I was in it cutting some more you can see that
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the the other lobe gets wider all right so that's very very interesting when I did it inside the cavity the mode actually just got extinguished it could not lace but when I did it outside I still have light propagating even though I cut one of the lobes out now to to actually calculate what happens to the intensity distribution or the field
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distribution when I do that is little complicated because it's not it's not just that I remove one of the one of the loads it's a lot of diffraction issues that one has to consider and just like any complicated problem we leave it as an exercise to the viewer to calculate what actually happens to the field distribution when I place a knife-edge in the beam when it's outside the laser cavity you