Fundamentals of frequency combs: What they are and how they work

yes sir good morning and welcome to Caltech and we have a nice turnout today very pleased about that so as Michelle just said so we this week we have a workshop that we've been planning now for about nine months and the title of it is optical frequency combs for space applications our first speaker this morning who I'll introduce in just a moment will be giving us a really tutorial on what is a frequency comb so I think about a third of you in the audience are very familiar with frequency combs our workshop has been planned that way but there are quite a few of you that might be coming more from the application side and and we'll have some tutorials later in the in the morning that you'll probably be very familiar to you but the idea of this workshop of which this short course is kind of the kickoff is to bring together two very different communities the community of specialists that are studying frequency combs and really from the device side the manufacturing side and the physics side and the science side and to mingle that community together with the applications community that could potentially benefit from some of the remarkable properties of combs and so many of you probably are familiar with some of the things that have happened with combs in the last 15 years but there really are some truly remarkable metrology applications applications in other areas will hear about this morning that have completely new and have opened up because of the the properties of combs and so in the afternoon we'll be sort of focusing beginning to focus on the workshop part of it but this morning I want all of you to sit back and enjoy and learn a little bit about some areas hopefully that you you know will be new to you and so with that kind of a little bit of background I I want to introduce our first speaker Scott diddums we're very fortunate to have Scott involved both in the organization of the workshop but also as a speaker I really can't think of anyone who is you know would know more about frequency combs in terms of giving a great tutorial than Scott he has literally been involved in the subject from the very very beginning back fifteen sixteen years ago he was involved in the team at Jilla and this that actually built the first self reference frequency comb and and then has been involved angela in many many applications he was involved in the first demonstration with mercury ion clock which is the ion clocks using combs are going to be the next time standard and applications to microwaves the most stable microwave cyntha synthesizers are now based on combs Astro combs he's done at all and and so we're really very happy that he's here with us today just mentioned a few of the awards that Scott has received over the years okay so he is the recipient of the Department of Commerce gold and silver medals for revolutionising the way frequency is measured he was a presidential career award or early career award in science and engineering the peak ace awards for work on frequency combs he's a fellow of the optical society in the American Physical Society and in addition to being having a in addition to being a fellow at NIST and also leading the optical frequency measurements group there he also holds a joint or a joint professorship at the University of Colorado and so please let's give Scott a very warm welcome thank you very much Kari for the kind words so yeah it's a real pleasure to be here and to share with you a little bit about frequency combs and kind of a big picture like Carrie mentioned this morning session is going to be aimed on trying to get people to understand a common language and so the the presentation I will make today is tutorial in nature so those of you who are also experts are already experts in frequency combs you know I I've asked you two to help me try to think about these things in a new way particularly for applications that might make use of them so for those of you who don't know anything about frequency combs or are new to the subject feel free to you know if you've got a question in the middle that's just burning to ask say it you know let's let's talk now and there also be an opportunity afterward to have more questions so so let's get going I'm the goal of this is to try exactly as the title explains is to tell you you know what frequency cones are and how they work so the outline and that I will proceed on is shown here I first want to give you a little bit of background on how we got to where we are now like why frequency combs you know where did this technology even come from okay then then I'll discuss a little bit you know different ways and I call that the multiple faces of an optical frequency comb so there are different pictures that might be useful to start developing in your mind as to what a frequency comb is and then I the the bulk of the talk then will be talking about different classes of frequency combs and some of their basic operational principles and I'll talk about mode-locked lasers very new and exciting technology micro combs and I will just briefly have time to mention electro-optic frequency combs it's kind of interesting they they were some of the first combs that people were working on in the 90s and now there's some new ideas that brings about a resurgence where they have some interesting properties for various applications as well and then I'll just wrap up with some challenges and opportunities for the past so so that the frequency cone really came out of an effort in the precision spectroscopy the time and frequency community to build better clocks and this is this is kind of a long view of the progression of uncertainty and optical clocks so gown is better on this chart and this is the clock uncertainty and seconds per day as a function of year and so you know there were pendulum clocks back in the 1600s that kept time to maybe you know 10 second or second per day type scale and as history progressed there was a transition in about 1950 from mechanical clocks to atomic clocks so the first cesium clock was around 1950 introduced in in the NPL and in the UK and since then there's been this very rapid improvement in clocks based on the atomic technology down to where we start to now have optical clocks that are here at the bottom you know even falling off the chart it's hard to keep up with the progress so there's been in fact a kind of a Moore's law like improvement maybe many of you know the semiconductor kind of scaling of transistors on a chip about a one and a half decades per 10 years time keeping his not too far behind and in fact it's it's been something that has progressed as you see here extremely rapidly and and where it ends up you know no one quite knows one thing that has been true through this history is that that the frequency the fundamental frequency of the clock has increased as we go to higher and higher precision or better performance from kind of Hertz oscillators to tens of kilohertz with quartz the cesium clocks which are now the definition of the second or kind of 10 gigahertz and now optical clocks are in the in the 500 terahertz range so if we wanted to project where this is going perhaps it's going to be clocks that ticket peda Hertz in the future another interesting observation is that a very important one is that clocks have fueled some of the most important you know technical and you know sociological or developments that that really pushed our societies and our our world forward from you know enabling people to cross the Atlantic to you know scientific demonstrations of understanding you know that the Earth's rate is not constant so there's geophysics you know and there's astrophysics and understanding that the spin down rates of millisecond pulsars which imply they're shedding gravitational waves you know down to GPS time where where maybe we we get a little bit of the flavor of the Moore's law scaling you know there's probably a billion smartphones in the world right now that have GPS receivers and you know that are guiding us that we're being guided by clocks that are that are orbiting us right now so there's there's much interesting physics and science and I hope that these are some of the things that we want to try to to work together to crystallize you know what might be the the next are new interesting developments that that the technologies that we will talk about will enable so so this this idea of using higher frequencies that's really been the drive for optical clocks or atomic timekeeping and there's a very simple scaling that if you if you want to think of a second as being ticks on a ruler and if we divide up the second into in the case of a microwave frequency may be 10 billion subdivisions in the case of an optical frequency we might be a hundred thousand times more precise just by the nature of the fact that the frequency of the optical light is is about a hundred thousand times higher than the microwave so so this was something that that one of our speakers I don't see him here yet John Hall later in the week it's really interesting in the in the late 60s early 70s he already made lasers that were much more stable than microwave standards or microwave clocks but there was there was no way to count or control or measure those optical frequencies and that was really a hard problem for about two or three decades that no one had a good solution to until the late 1990s and that is really where the frequency comb entered in as a tool to measure and count optical frequencies so in the context of optical clocks how does that work let me just briefly explain that is an optical clock is a clock that ticks at the frequency of a laser it's actually the light wave the crest and valley of that electromagnetic wave that are the the pendulum if you would of the clock and maybe this this laser is first stabilized to to an isolated cavity it provides kind of a short-term reference atoms then with the atomic residence in the optical domain or even the near UV provide the the the stable long-term accuracy of this clock and now as I showed in the previous slide the levels kind of it part in 10 to the 18 remarkable type of precision so the last piece to come along was what I mentioned this counter in the readout and that is really the laser frequency comb it's a way of counting and measuring optical cycles at least that's and I wanted to just make this point clear is that's that's the the the way this field evolved is starting with this tool as a counter for optical clocks but as I hope to show and I think Nate Newbury in the next talk will explain even better is that now there's a wide range of applications that make use of this same basic technology okay so let's let's talk about you know kind of what I call the multiple faces of a frequency comb well maybe the simplest picture is a frequency comb is just a ruler for light frequencies you know think of a ruler and cross out the millimeters or centimeters and put optical Hertz on there and that can be an absolute ruler traced to the definition of the second or of the Hertz in in a frequency comb this shows up as some broad optical spectrum and if you can zoom in there there's you know millions of little teeth the teeth of the optical comb the ticks on the ruler well the Fourier transform properties tell us that if you have this in the frequency domain then in the time domain you have a perfectly spaced train of optical pulses and and properties of this pulse train are of course related for example that the spacing of the teeth and the in the optical domain is inversely proportional to are inversely related to the time separation of the pulses and the bandwidth of the optical spectrum the total bandwidth is related to the shortness of the pulses so these are these are simple pictures that one might develop another picture that I really like is it is that the the comb is an optical clockwork it's a set of gears okay and I think this is a real powerful picture because it conveys the idea that that a frequency comb is like a synthesizer it's a tool that that if you can amass and build together the right set of gears you can synthesize frequencies you know not only in the optical domain but in the microwave domain as well so it has incredible uncertainty the teeth if you will on these gears are perfectly spaced and can be perfectly measured and controlled and it can connect optical frequencies as shown here maybe these two new one and new two and it also provides this this down conversion and this is the the clock type application of allowing us to count optical frequencies relative to some microwave reference or transition okay so that's that's maybe a few pictures that you can have in your mind as to what an optical frequency comb has or what it looks like so now now let's shift gears and get a little more concrete and and talk about actual you know things that are you know how do you realize these these simpler pictures so first I'll discuss mode-locked lasers so mode-locked laser is a type of laser that produces short pulses and here I've shown a simple kind of bowtie cavity there's maybe some laser gain inside the cavity that's excited by in this case another optical source and inside this cavity is something that's like a bullet or maybe it's even a better picture as a pancake of light that's just circling around in this cavity and each round-trip there's maybe a partially transmissive mirror and a little bit leaks out okay so this is kind of a simple lazy picture of a laser if if one was able to stop that with a femtosecond scale camera and take a picture this is what you would see is that from pulse to pulse here's the the short bullet of light and each pulse that comes out first of all they're they're exactly spaced by a number related to the round-trip time in this cavity but an interesting fact is that the the envelope and the carrier there's you know there's some slip if you will from pulse to pulse where the the carrier advances with respect to the envelope and this is simply because the group velocity and the phase velocity inside this cavity are slightly different we come back now to then this is again two of these phases of the comb I already described to you in the frequency domain the Fourier transform of this is again our optical frequency comb but now we get a real key piece here that's related to this carrier envelope phase slip and that is that these teeth are not pure harmonics of the rate at which pulses come out but rather are offset if you extrapolate back to zero there's an offset frequency and that offset frequency is exactly related to this carrier envelope phase shift so now we can write with these this little bit of knowledge we can write the optical frequencies of this comb exactly as an integer times this mode spacing plus a common offset and that that's really the key concept and and the the equation that is most important to remember there's a nice image that maybe for some of you who haven't seen how this the group and phase velocity relate so here's a picture of a pulse evolving in a laser cavity so maybe this is a high reflector now we got a linear cavity and here's the output coupler in each round-trip some light comes out and as you can see that in the cavity where there's a dispersive medium this carrier envelope phase is evolving once we're out in free space it stops evolving or at least maybe there's only a constant shift and so that a subsequent pulse that comes out we'll see it here in just a second has different carrier envelope phase relative to the first one and it's this periodic slipping of the phase relative the envelope that again is related to that offset frequency so let's tie this back in another way you know many of you know about cavities you know or even acoustics right is acoustics is all about cavities as well and so a frequency comb is you can simply think of it as being composed of the multiple resonances and these would be standing wave modes of an optical cavity so here I'm depicting two mirrors and these are just the plucked guitar string modes or the the lowest order standing wave modes that when locked in phase add up to give a short pulse at the output each round-trip and it's indeed these these modes and I show them displaced in space this way just so I can make the point that it's these discrete modes that are the modes of the frequency column so how does that work okay so some of you who might already be saying well look I know something about modes and cavities and they aren't perfectly harmonically related and even in an optical instrument or an acoustic instrument they they aren't always harmonics of each other at least it's hard to get them that way so so there's must be something else going on here or something that that really forces those to be uniform and you're absolutely right and and what it is relates to kind of the fundamental way in which mode-locked lasers operate mode-locked lasers you know not in addition to a cavity and some gain source they require this this balance of dispersion control and phase modulation and coupled with some sort of power dependent gain or loss and I won't say a lot about that but that's the mechanism that after introduces the mode locking but the important point to take away on this slide is that if you drew a simple cavity like this you would write down that the ideal mode spacing is just the speed of light divided by twice the cavity length well because you actually have air in there or the coatings on the on them the mirrors are not perfectly non dispersive the actual modes you know at one end of the frequency spectrum there may be a little more closely spaced at the other end of the spectrum they're a little more widely spaced from this see over to L so this dispersion means that the cavity modes are not evenly spaced however and this is the really important thing is that there's a nonlinear phase shift or phase modulation in the mode lock laser that compensates or corrects for this such that these modes can all be locked in phase and become perfectly uniformly spaced and this is a concept and I describe it here for mode-locked lasers but a little later I'll talk about micro resonator combs and there's actually a very similar type of operation that that occurs there as well so just the basic physics again to reiterate what's going on there is there's a balance between dispersion and non-linearity that makes this perfect frequency column okay so let's show a few examples of what these devices look like if you've never seen a comb maybe it's interesting to know that that at least with titanium sapphire you can make a tiny one here's this little bowtie cavity I showed before and this this one is just 3 centimeters roundtrip such that it makes a 10 gigahertz frequency comb other ones out with titanium sapphire can can make directly from the from the cavity very broad spectrum active spanning spectrum k in fact and here's the envelope but again if you zoomed in they're spaced by a gigahertz in this case would be this this fine-tooth comb hi sapphire is is kind of the the Cadillac of laser material or you know at least in in the u.s. maybe we say it's a Cadillac it's it's it's really exceptional laser material for making very short pulse lasers it has the drawback that it isn't so efficient and it requires quite a bit of green pump energy to make it work I wouldn't say that that this type of technology is is ruled out for for applications outside the lab but it has some particular engineering challenges I think that would have to be overcome another type of G is based on on erbium doped fiber and you can make frequency combs out of these as well and erbium doped fiber laser and one nice thing about this technology is that it leverages kind of the multi-billion dollar telecom industry and all the components you know that that operate in the 1550 nanometer region of the spectrum so so these types of lasers operate in some cases that the quietest ones on this property of nonlinear polarization rotation I won't go into the details describing that but they can be very compact you know integrated piece of fiber and from these devices you can also get and I'll tell you a little bit more about this octave spectrum and why that keeps coming up but you can get very broad spectra of these after you've additionally broadened them in some nonlinear fiber my colleague Nate Newbury who will speak after the break has he and his his colleagues at NIST have developed a very robust polarization maintaining erbium fiber and this is you know I realized those might be some specific words for for people who are outside the laser community but essentially these these lasers can now be made to be kind of a single piece of fiber integrated fiber no air gaps just all continuous fiber all the way out to amplifiers and nonlinear optics that are required for their frequency control and Nate and colleagues have shown that you can put this type of laser in the back of a van and drive it around the hills behind our lab in Boulder the the good news are I think a really exciting piece of news is that not only are these things happening at National Labs but Ronald Holt sparse who runs the as president of Menlo Systems will tell you about our can tell you about similar technology that is now available to even by so these are quite quite robust and becoming more and more widespread type of lasers that people are able to use outside the lab I want to mention one other technology and just highlight you know you can put different ions in silica fiber instead of erbium let's put your terbium and you can build lasers out of you terbium fiber I think the interesting the most interesting thing and the point I want to make about you terbium fiber lasers is that they're incredibly scalable you know right now people have gone up to near a hundred watts of 100 femtosecond pulses using this you terbium fiber technology in fact yeah I think you can get even with your terbium what people will tell you in the laser field is the amount of power you can get out is essentially limited by the pump power and so you start running out of laser diodes to pump this material before you run out of actual power that the system could support so just before the the meeting Deborah Fisher who's sitting here in front said well what's what do you mean by optical frequency combs so I want to address that comment right now and I think you know to be fair that's that's a very good question is I think when we started this workshop we didn't really we said optical frequency comb mainly because that was where we had this work had started it started an optical domain maybe in the near-infrared 1.5 micron I think really the key thing is that by optical we mean it's laser based and you know whether those lasers operate you know say in this region here say 500 to a thousand s titanium sapphire these are the three materials I just told you about the ytterbium kind of in the around 1 micron erbium fiber centered around 1550 you know maybe we call these all optical but the point i'd like to make in this slide is that based on these types of systems we can expand to the ultraviolet or even to the mid and far infrared using other nonlinear optical tricks either either harmonic generation where we have take the second or third or fourth harmonic of of light Center to say at one micron or difference frequency generation where we had take two sections of this comb and subtract their frequencies in a nonlinear optical process and that puts us out say in the in the 2 to 10 micron regions so I think for the for the context of this workshop it's very important not to limit ourselves just to these ideas and these materials in fact there are other materials and systems that people are talking about and I think you'll hear some about that later today that that are directly producing combs say out in the mid infrared so so back to this picture I had offered earlier about a frequency comb being a gear or a clockwork I want to just spend a few minutes telling you okay so that that maybe gives a nice picture you can have in your mind but but how does that actually work right I just showed you that we're actually talking about mode-locked lasers you know how how do these gears actually connect and work together let me say a few words about that well they're in a frequency comb I'd already told you there's a very simple expression for describing the frequencies of the teeth of that comb right there's the nth tooth is is just an end times the mode spacing or the repetition rate of this comb plus a constant offset so to to make this gear work hole to a mesh the gears to connect the gears we have to be able to measure and control these two frequencies that the offset frequency and this repetition rate so usually the offset frequency is the tricky one that's the one that that came last and this is measured and controlled by a technique we call self referencing and and here we need an octave span spectrum to do this easily the repetition rate or the mode spacing is is you know it's more of a microwave or a radio frequency that we can usually easily measure detect it's just the rate at which these pulses come out of the laser and that might be you know a gigahertz or or a hundred megahertz for mode-locked lasers usually we can we can measure that more directly and in some of the the cases however I'll talk about micro combs in just a few minutes that frequency can be higher and and that therefore it can be more challenging so we can either connect it to a microwave source or measure it or relative to a microwave source or in some cases relative to a CW laser and the next slide I'll describe how that works so so here's the picture of the comb again I put it on its side you'll see why I do it that way just a minute so each of these teeth of the comb you can think of as a CW laser okay and these I have to break the axis here because there's a lot of cycles in a second they're just streaming out of this this laser frequency comb and we can label them as I've done here so if we have a comb that spans an octave and that's a very important point and we keep coming back to that because that gives us access to this offset frequency we can take light on the red side of the spectrum and use a nonlinear optical material to double its frequency and interfere it with light on the blue side of the spectrum and from this interference we get directly this offset frequency okay if we want to to then control the mode spacing the way we do this whenever we have an optical clock is we take another continuous-wave laser and this laser i I label with the frequency nu 0 r nu not that that that would be the frequency of say the atomic transition in the clock we can take that laser and interfere it with one mode from the frequency comb and then feedback that is to control the the mode spacing of this comb such that these crests and valleys we make what we call a phase lock that the this mode is forced to block in march step with this reference laser now I had explained a few slides back that these modes of this comb are all already phase locked together tightly phase locked by this nonlinear mode locking mechanism so that if we can control one mode then we actually gain control of all of them such that their their superposition of these modes adds up to be this short pulse each round-trip okay so this controlling of a single mode relative to a CW laser now fixes the rate at which the pulses come out the offset frequency fixes this slip of the carrier relative or the slip of the envelope relative of the phase each time here I drew it for simplicity that the offset frequency was zero so each pulse is identical so that shows how we can go from an optical reference to coherently synthesize a pulse train in my gear picture that would be engaging a gear at a high frequency right up in the optical domain and using the comb to divide down to a microwave rate but but it's fully reversible we can in measure this repetition rate and engage or control the comb there and multiply up to produce coherent optical frequencies or optical frequency that are coherent with the microwave source so that's a bit of a technical picture but I just wanted to give you an idea of how this gear work actually actually operates so I'd already discussed that that having very broad spectrum portent here's one case this is the first case of how these broad spectral were first produced and that was with what's called nonlinear micro structured optical fiber and this is technology from 2000 or so it completely changed the game in this frequency comb business and I mention it now though because the the properties of those optical fibers are exactly the same as more advanced materials that people are using now and let me let me say a few words about that so this isn't a piece of optical fiber it's glass or silica fiber and you can see there's some sort of honeycomb-like structure that if you zoom in there there's an arranged arrangement of air holes around a defect or a little strand of silica there in the center and this would be the the place where the light would be guided down the center of this fiber now the important aspect of this fiber is are the construction in this way is that first of all the the confinement this this group of air holes packed around this this defect the confinement of the light is very tight in fact the the diameter here might be only a micron or so in diameter so you you restrict the light to propagate in a small volume it pushes the intensity up it turns on nonlinear optical effects the other feature that is not immediately obvious here is that the arrangement of these air holes forms something like a photonic bandgap and in such a structure you can you can tailor the dispersive properties or the waveguide properties of this longitudinal wave guide such that the dispersion is drastically changed from that of standard silica to something you know in principle whatever you would design it to be and that that's shown here is that in in a standard optical fiber and this is the dispersion in some units this would be the dispersion of silica and these microstructure fibers you can move the dispersion from something that's that's very anomalous down to something that is is normal or near zero at 800 nanometers in this case or slightly anomalous excuse me it'd be from from very normal excuse me I had to said that wrong down to something around 800 nanometers its anomalous so so this engineering if you would of the waveguide allows us to to change the dispersion properties of this waveguide and the combination of this dispersion engineering and the tight confinement of light allows you to generate these very broad super continuous spectrums so here's a picture of an input spectrum from in this early days a titanium sapphire laser and the output spanning you know many hundreds of nanometers more than an octave and this is this octave is precisely what's needed for this self-referencing it also as you might imagine it gives you light at a lot of different colors and maybe those are useful for other types of measurements here's here's a picture of kind of a family of spectra from different laser systems ty sapphire erbium fiber and you terbium systems that show kind of the different types of octave spanning spectra that are achievable you know the blue is PI sapphire at 10 gigahertz here I'd showed this spectra earlier the gray one is 1 gigahertz ty sapphire that's directly emitting a very broad spectra red is what one typically obtains from say ytterbium fiber with one of these not ytterbium lasers with one of these non-linear fibers and the green is what can be attained with erbium fiber you'll notice that these units here might be relevant power per mode you know as the repetition rate goes up here's 10 gigahertz we can have you know even hundreds of micro watts to approaching a mill a lot promote as the repetition rate goes down that energy of course has to be divided among many more modes so the power promote is lower so that's something that that will play into different applications of these combs let me just you know very concrete example show you how this offset frequency is measured so let's imagine we had for example this spectrum here this green one we could take light at the the red end of the spectrum we send it through a nonlinear crystal and we make a little bit of light around one micron and we heterodyne it with that light and this is this is how you would actually lay that out in the lab in kind of just there's of course more sophisticated ways to lay that out but I just wanted to point out very simple you you generate the broad spectrum you take the infrared portion you frequency double and you combine with the visible portion and if you put that on to a photo detector this is what you would see you would first of all see the the harmonics of the repetition rate there's still pulsed light hitting this photo detector but in between you would see this offset frequency and replicas of it because we are heterodyning a comb against a comb if you will so you get many different replicas of it here in the microwave spectrum so there's just you know somewhat for the record there's been a variety of different systems that have been self referenced and frequency controlled in this manner starting with titanium sapphire down to now more recently through Liam fiber and this is even a few years old so there's probably a couple extras that I've missed and I think the point I want to perhaps one of the important points to make from this is first of all I tried to estimate kind of and give you an idea of what the I call electrical to optical efficiency is that's actually the wall plug efficiency so that includes some assumed losses for power supplies and things like that but but if you just want to throw out rough numbers the most efficient systems are actually at this point are you terbium two to three percent erbium is is as close maybe a little less efficient you know this here's what i mentioned earlier that for example titanium sapphire is is significantly less efficient so those those kind of factors might play into things as we think about applications as we think about what what would it take to put something this in a remote site or even in space you mean as I explained in the previous slide so yeah yeah that's the see if I can go back here so that the the question was by beating the comb against another comb what useful information comes out so so I think Nathan Newbury will describe to you some types of measurements that you can make by heterodyning two independent combs okay two separate frequency combs and I'll let him talk about that in this case the what I wanted to try to tell you is that this is this is kind of a self beating of the comb okay so we take the light from the infrared portion of the comb and we convert it to green light and we head or dine it with the green light that already existed there so it's kind of like taking the two parts of the comb and folding it over and heterodyning against itself and I could write for you after an the break that the simple math that shows that when you do that you directly obtain this offset frequency that is what is the global offset or shift of the frequency comb from being pure harmonics of the repetition rate let's let's chat a little bit more afterwards I can draw some more pictures to explain that okay so how's the time looking this oh it's right there oh gosh I got lots of time 24 minutes okay good so so I'm going to shift gears a little bit and I spent a lot of time talking about mode-locked lasers that's the more established technology and now I'm going to shift it a bit and talk about micro combs and you know some of the things that we like to try and make analogies between these two different kinds of and there are some good analogies for example this general statement I already made that that you have to have a balance of non-linearity and dispersion in these types of systems but some of some of the analogies don't apply so we have to be a little bit careful but but the basic picture of the comb still applies for the micro combs and it's really just a different way of generating them and by the way there they'll be for those involved in the workshop there'll be much more discussion about micro combs and many of experts in this field will be you know presenting ideas in their work as well so so here's here's kind of a you know a global picture of where the micro comb fits in into this you know if I if you go back to my very first slides where I said well where does the frequency comb idea come from so so here's where the micro comb fits into that if if you went back you know 30 years or 40 years at a place like NIST or some other National Lab I people were trying to make something that was like a frequency comb I mentioned that that people already knew in the late 60s early 70s that a laser could be much more stable and could be a much better metrology tool than a microwave oscillator but no one knew how to to connect that or to measure those optical cycles coming by that kind of a femtosecond rate okay so people made something that was called a frequency chain and I could tell you more about that in the break if you wanted there is this revolution around the year 2000 where you know something that was kind of a hundred square meters was taken down to a square meter and now you know the the commercial versions are even smaller than that kind of a laptop notebook size okay so this was a significant reduction in space and and not only that but it actually could work you know and could work everywhere or you know you know and now you can buy these things so so the the vision for the future and this is where micro combs fit in is that well there's new ideas and new technologies that could allow us to take you know what is kind of a breadboard or you know here I say it's a square meter you know maybe it's a it's a square foot but it could go down another factor of a thousand to ten thousand in size by using technologies related to micro resonators and integrated photonics so this could I think have the impact of enabling frequency combs to operate in practically any environment you know chip scale devices they could be very inexpensive and mass-produced as I'll tell you some of the technologies here are you know basically the same technologies that people use to make computer chips so they could be lithographically patterned and printed and fabricated in that way you know and as they get smaller and less expensive perhaps they could just be widespread or you know so that they could go into a variety of sensing or communication and or navigation instrumentation so so what is a micro comb and how does it work I like this play on words it's it's a kind of a tiny revolution and this these are some ideas that were hatched here in Pasadena actually an in group of professor of Ajala and Malachy at that time at JPL not OE waves you know but but really gained a foothold in the laboratory of Tobias Kippenberger and around the year 2006 and and the idea is to make a frequency comb with a little micro resonator and here I'll show you more concrete pictures in a minute but the idea is that that one would couple light into the periphery of this micro resonator and the light would circle or circulate around and around here and you could go from a continuous wave just a single frequency of light into a comb and the way that happens is via a nonlinear optical process called for wave mixing you can think of this in a photon picture as two photons that compose this input light as adding up and then breaking apart being you know spontaneously generating in a photon of higher frequency and lower frequency and those would be your first plus and minus side bands here for example so energy is conserved momentum is conserved by a phase matching around this and the line spacing of this comb is given by kind of the resonator diameter so there were some really nice examples of this and in the work of to be a skipping Berg now at the Federal Polytechnic Institute in our university analyst on Alex kaiidas group in Cornell and and Maliki and colleagues at OE waves now and these are just some examples of combs that could be produced in this way and so you see the the input light the residual input light and then this broad optical spectrum that can be produced and so something is maybe to take note of here is that now we're talking maybe in some cases of comb spacing up to you know 850 gigahertz or gonna terahertz no or down to 25 gigahertz but that's determined by the size of this device and these devices are kind of millimeter to micron scale so so just by nature of the fact that the devices are small the mode spacing is going to be large so so one thing that we've learned in the intervening years is that a beautiful comb like that it may look regularly spaced but it's possible that it's not at all useful for metrology or this clockwork it's too noisy so so there's really an important emphasis on understanding and controlling the noise processes in these micro combs that's that's critical it's related to that is kind of asking yourself and it was one of the pictures of the faces of the frequency comb I described you earlier as is what's okay if that's the frequency domain picture what's going on in a time domain so in some cases these these combs can produce short pulses just like a mode lock laser in other cases they aren't necessarily short pulses so here here's real devices so kind of a gallery and it's a rapidly growing field and you know lots of different materials and technologies are coming on line daily if not monthly so I probably missed something but I just wanted to give a kind of a snapshot gallery of different devices ranging from you know waveguide integrated silicon nitride to devices that are for example this silica pore OIG's and wedges are devices that are produced here at Caltech the the crystalline resonators is the work of Bowie waves and has been picked in other places at NIST we've we've developed some quartz type resonators and then there's even materials like diamond and aluminum nitride that have their own interesting properties for making frequency combs are making these resonators that can be used for frequency combs so so a lot of different systems you know and a lot of different technologies that go in there some of the common key properties are that we like for making frequency combs in these devices is that they have high Q that means that light that gets trapped in a resonance and and some of these resonators it's very clear you could imagine the light it's like a car going around the racetrack right some of these others it's maybe not as clear for example where is the resonator here it's this little bulge and look and it's a Whispering Gallery type resonator and the light is you know maybe you want to think of it it's totally internally reflected as it bounces around the periphery the circumference of this resonator so some of these it's it's more to better define what the cavity is some it's you know you have to get used to this concept of the Whispering Gallery mode to really understand that but but what's common to many of these or all of these is that you'd like to have high Q and in the crystalline devices it can be up to 10 to the 10 or so you know in in silica it's it's maybe a billion or a few hundred million some of the the more integrated devices nitride and aluminum nitride it's lower numbers but still the high Q the ability to store light in these resonances and resonators is important the small mode volume means that we can confine the light tightly and nonlinear optics can turn on with low powers okay I already mentioned that that kind of the mode spacing is given by the round-trip time around one of these devices controllable dispersion I had introduced this idea in the context of the microstructure fiber where you could play with the the waveguide properties by adjusting the diameter the pitch the spacing of these air holes you can do similar things with with these types of resonators by adjusting what the the actual shape of the waveguide looks like and that turns out to be very important is to control the dispersed and and in some cases you know you can see that these can be integrated into you know a chip scale package some more more obviously so than others I think you you know we'll hear more about these at least those who are participating in the workshop in the next few days like I said some from some of the real experts and pioneers in the field so so let me come back to the the kind of comb generation principle in these micro resonators and distinguish it from what happens in a conventional mode lock laser so so here on the right let's start there with a mode lock laser it's just a different picture of what I showed you before but it has kind of these these main components it has some gain medium and here would be energy coming into the game medium pump light for example that green light maybe in the case of this high sapphire laser or diode laser it could even be electrically excited gain but this this laser cavity has dispersion so something some balance of dispersion and mind you what also is occurring in this game medium is the nonlinear phase shift I mentioned it's very important and some satchel absorption something that that favors the operation at at high peak power rather than low average power so in contrast a micro comb has no storage no energy storage in the game medium it's just a transparent dielectric material that has a nonlinear response and we call that Chi 3 that's a response of that that leads to this four wave mixing so there there's no energy storage in the game that's a big difference there is the dispersion so we have the dispersion in the non-linearity in this system and the other interesting distinction is that that here the pump comes from the outside here the pump is actually an integral part of the of the comb and the cavity so just to revisit the picture I showed you a few slides earlier you know you can have the pump coming in and you can have this four wave mixing process where the pump generates sidebands like this there's also the possibility for non where you would take two sidebands and mix them together and this is just you can just add and subtract the energy in these simple vector pictures here and you could generate two new side bands so so that's a very different mechanism for generating a comb then this laser-based our mode lock laser based system and here again I just highlight some of those features that I had I just mentioned so there's there's very beautiful nonlinear optics very simple nonlinear optics in some ways that that goes into the generation of these micro combs so so let me just just back up again and because motivate what I'm gonna say in the next slide is that one would start with a pump wave and and okay we aren't using a cavity made of discrete components now we've got to think back to a cavity that's just a continuous resonator but that cavity has resonances okay and so the the the frequency at which we couple the light into the cavity is quite important so in this slide I'm gonna try to explain that a little bit is that this the the resonance the optical resonance that you a couple the light into this cavity actually becomes distorted due to the non-linearity in the cavity and so maybe at low power one would see this as actually being something that looks much more like a Lorentzian that the more familiar type cavity resonance that you'd have in an optical cavity but because we have high circulating power and this non-linearity as the as the power goes up the index of the material goes up and the resonance shifts so as we bring the pump into resonance the resonance actually moves away from the pump frequency a little bit and so you have to keep moving the if you want to come to the resonant peak you have to move the pump laser with the resonance as it moves this is you know called a kerr nonlinear cavity and it's described by this simple equation which has only three or four parameters it has the strength of the field that's the electric squared so that's the power this term describes dispersion this is the the power of the the pump and importantly it describes detuning are where the the pump sits relative to this cavity resonance so so there's a very simple equation that describes this but the behavior can be quite complicated and and this is an example of the types of combs that are generated for example if you take the pump laser that's the center frequency here and scan it into the resonance and we call this upper upper um the the upper level of this this by stable type resonance and you can see that you get as you as you ramp up the power you you start with a very sparse comb and then the comb can fill in and can fill in completely the the characteristic though on this upper branch is that the the combs generally tend to be noisy and one would ideally like to jump to this lower branch or the other side of the resonator resonance where one can have these these very low noise cavity solitons generated and this is this is something that is you know just now being understood in this field and how to to repeatedly and you know efficiently generate single solitons or our low noise micro comb States is something that's actually a very active topic of research right now and there there are some clear paths but but there are some paths that aren't so clear I should say and and you know we'll have some there's lots of experts and even people here in carries group and and the other speakers who you know can tell you more about the details of doing that but I just wanted to point out that that it's a very simple system in some sense but there's some very complicated and intricate nonlinear optics that needs to be you know carefully manipulated and carefully what are on say it once you have to have a very careful way of landing in these single soliton low noise States if you can do that or if you can achieve low noise Micro combs and and I should just add one other statement is that there's a not all of the micro comb spectra that we've seen are our single solitons that's maybe the the most kind of simple final solution here is a single solid tom but in other cases one can have multiple solitons in in the cavity or still different configurations that are still low noise but don't have this this unique kind of hyperbolic secant spectra here but with those kind of spectra what I just wanted to point out that that even with an imperfect total understanding we've still been able to demonstrate ability to control the frequency of these these types of micro combs in particular to control the mode spacing okay so remember if we're gonna use the comb as gears we have to not only measure and control this offset frequency and I'll get to that in just a minute but we have to control the mode spacing so these are some ideas that that we have introduced are used to control the mode spacing and and interestingly kind of at the level of a part in 10 to the 15 at a second so if we can make a low noise comb in a micro resonator we can we can control it at these interesting levels here so one one an idea is to just apply mechanical pressure and squeeze the micro resonator so this I like this picture not only because it shows how we implement that there's a piezo electric device that's squeezing this glass rod but it also shows you how in a laboratory setup we can couple into these resonators there's a there's a tapered fiber a piece of optical fiber that brings light up and just barely touches the resonator and that's how light is coupled in in other cases we can and this is approach that's useful when the mode spacing or the resonator is very small the mode spacing is large we can introduce using electro optic techniques combs you know kind of inside the parametric comb is the blue one and then after the comb we introduce an electro optic modulator to kind of link in this case the 143 gigahertz comb teeth it's a challenging number to measure electronically but if we can kind of subdivide it using an electro optic technique we can get down to a way of controlling and measuring this 143 gigahertz or even larger I'll show you an example in a few minutes these larger mode spacings and again thereby control the spacing of the of the micro comb itself yeah yeah that's a good question if I if I back oh yeah the question was what's the major noise source that we're working against the the the major noise source is that this parametric gain is very broadband and it can turn on in all of the resonate resonances in uncorrelated manner maybe this is one way to think about it is that is that you can generate you introduce light into one resonance and you try to get this nice cascading of the energy out sometimes the energy that cascades out it falls at a frequency that is not exactly harmonically related to the mode spectrum so it's it's you know in a simple way are as simple simple terms this is really the the main noise process that were we're fighting against are trying to control is to figure out a way to get these combs to to really all phase lock together all the individual elements because kind of their natural tendency is to just go all on their own all the different teeth the question was what kind of mode spacing one could get with micro combs I just back up that you know it's it depends a lot on the devices you know these types of devices are you know anywhere from 10 ish gigahertz or even a few gigahertz you know up to kind of terahertz so it it actually is quite complimentary to laser combs with a laser comb it's hard to get a mode spacing much above a gigahertz so with the micro coma it it turns on kind of at the few gigahertz or 10 gigahertz range up to hundreds of gigahertz or even a terahertz so another technique that that we've been experimenting with is to in addresses just what Deborah had asked is is you know maybe we can seed this parametric oscillator with a little bit of light that we already have controlled and so instead of sending in pump light at just one frequency we can modulate a little bit of light and put on some side bands that would be close to matching the natural oscillation frequency of the micro cavity and thereby enforce its behavior it's it's low noise behavior on on a uniform grid and I won't say much more about that I guess the main point I wanted to raise here is that is that we do have techniques to control the mode spacing of these micro combs at at significant levels of significantly low noise okay but what about the offset frequency and the next slides will just walk you through you know some very recent experiments that ourselves and and other groups the group of Tobias Kippenberger have been employing to try to measure the offset frequency of a micro comb so I have to admit that that I in these slides it will diverge from being micro at least for the moment we'll come back to it with a path that we think could could make a self reference micro comb but for a for a moment I'm going to have to diverge and there's there's kind of a generation of the micro home there's some nonlinear broadening our I'm sorry some some face control and amplification and then nonlinear broadening and let me just show you quickly kind of how that works we can generate a micro comb and this is one that that I'm eluded to earlier that it's we we can make a low noise micro comb but it this is some sort of a multi soliton like state that doesn't have a single smooth spectra but the comb in fact is phase-locked and we verified that so this can be a low noise comb we have to do some spectral shaping and amplification that's showing the the field at different places and finally we get to an high intensity short pulse that can then be used in a nonlinear optical fiber to generate this coveted octave spanning spectrum so we can do this with a micro comb and in fact can measure the offset frequencies so again back to the the question that was asked earlier what we actually do is we take light from this side and we frequency double and we heterodyne against light at this side and if you zoom in here and and this line looks a little fuzzy and that's because if you zoom in you actually see with the relatively low resolution spectrometer that was used to make this measurement you see the actual optical modes and you can measure the offset frequency here it's it's the spacing of the modes between the doubled and the original comb light and if you put that on a photo detector you actually see this offset frequency of the comb and that and the good news is that it can be quite narrow and and low noise and controlled so I won't I told you I was gonna mention electro-optic combs just one brief word about that yo-yo those in the workshop will hear more about this from Scott path but I wanted to just mention that that you know not only did we learn the nonlinear optics here that enabled this but but this is a way of starting with a CW laser without a micro resonator to grow up octave spanning combs so I apologize I won't have time to go into that now but I wanted to now just wrap up by coming back to this idea of you know I showed you a way we can self-reference this but this is you know here's the micro and this is all pretty macro so it teaches us something to understand how these micro combs work and how they can be controlled but we we would like to think ahead of a root you know how could that all be integrated and and here's one possibility and this is something that ourselves and people at Caltech and and Santa Barbara and in Europe are working on together and the idea is to to you know the goal is to ultimately have this octave spanning self-reference comb on a chip the challenges is the power constraints how do we do this with with low power and with basic nonlinear optics the idea from the goat gear picture is we're gonna have a dual reduction gear I see the red light blinking huh okay so I'll talk fast here but um we're gonna first go from 200 terahertz the optical frequency down to a terahertz and then to 15 gigahertz eventually so it's it's kind of a nested gear approach where we're gonna use different technologies silicon nitride to make this the terahertz comb and silica to make this 15 gigahertz cone so let me just say a few words about this this terahertz comb generator it here's a min of the kind of rings that are calling card extreme of Austin at NIST in Gaithersburg is made and some of the important things that we have to understand about that is how to control the dispersion and how that dispersion couples to the non-linearity to make spectra that start to become octave spanning so these are models okay and calculations have to talk quickly here at the end just to run over this but to show that now for the first time in this terahertz comb generator with what I think the most exciting point is it starts to be a relatively modest amount of power just a few hundred millivolts we can make this octave and comb and moreover the it this power required scales as the quality factor of this resonator so we think there's good reason to believe this be even a factor of four or five lower so I think you know where this is going I think with micro combs there really is a vision that all of this could be integrated on a kind of chip and with not only with electronics and pump lasers and active components but the full gear work if you would the clockwork that would enable the optical to microwave conversion okay I will just wrap up quickly I think I'll skip that slide you know what I've described to you is is combs that are useful for clocks or at least I started there but there are numerous many applications of frequency combs and and our next speaker a new variable we'll go into that I just wanted to point out that you know maybe some of these applications best use a mode lock laser comb maybe some of them use a micro comb and that will be interesting things to debate and discuss with everyone here finally just some some last slide on challenges and opportunities there really are gaps in our knowledge you even heard me not say not be able to say you know so sharply how it is that we can make low noise states in a micro comb because this is we know paths to do this but there's still incomplete knowledge there and so we need to learn about that fiber combs in many cases that the technology is mature but it still employs some empirical recipes you know that the technology of all of these devices is complex we need improve robustness space worthiness if it's going to fly there's a lot to be understood about materials and systems not only for the nonlinear optics you know for generating new colors in the mid-infrared or you know new materials are coming online you know what's going to be the best platform to achieve different wave lengths to achieve combs and different wavelength regions there's of course the question of integration and then matching the the technology to the application so I will stop there I want to thank there these are at least a snapshot of some of the people who work with me and Boulder a lot of contributions there and also for material I presented from colleagues you know here at Caltech and around the world who we work with so I apologize for taking a few extra minutes but we'll stop now and thank you for your attention and happy to answer any questions you

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Length: 68min 38sec (4118 seconds)

Published: Tue Nov 10 2015