Відео

The two cases are a bit different. Terms with three unconjugated factors correspond to THG and are set to zero as we assume that phase matching is not satisfied for them anyways. Therefore, terms such as ba^2 are removed. For the same reason, b*(a*)^2 will be set to zero as it is just the complex conjugate of ba^2. The term b*|a|^2 = b*a*a is simply the complex conjugate of b|a|^2, which described XPM from a onto b. Note that we don't set these terms to zero. Rather, we just "absorb" b*|a|^2 into the c.c and do calculations with b|a|^2.

I am glad that you found it helpful! The GitHub repo where the book is located also contains its raw LaTeX files: github.com/OleKrarup123/NLSE-primer/tree/main I suggest that you clone the repo, copy the English LaTeX files into a new folder, translate them into Chinese, re-compile the book and then do a pull-request into my original repo. I personally used Overleaf to write the book, which was much more convenient than setting things up myself. I'd be very excited to see the book translated, so please let me know if you decide to proceed!

That's a good question! Here's how to think about it: Suppose you take turn launching three ideal CW lasers at 99THz, 100THz and 101THz, where each has zero linewidth into the same system causing THG. They will end up at 297THz, 300THz and 303THz respectively. You can see that the spacing between them started out being 1THz, which ultimately gets tripled to 3THz. This thought experiment shows that we generally expect the linewidth of a realistic laser to increase, but we should be careful about drawing conclusions about the exact amount from it, since nonlinear effects involve all its frequencies interacting with each other! In reality, each frequency in the spectrum does not simply get tripled. Rather, the spectrum undergoes a "triple convolution" with itself. Let's assume that you have a laser with a Gaussian lineshape that is undergoing SHG. Convolving two Gaussians simply results in adding their variances, so in terms of standard deviations, s: s_final = sqrt(s1^2+s2^2) = sqrt(2)s_initial, if s1=s2. Similarly, we would expect the final standard deviation for THG to be sqrt(3) higher than the initial one. Of course, this is only exactly true for a Gaussian lineshape (which is often more "Lorentzian" in practice), but it should be a good approximation. Here is a paper that explores something related to your question but for SHG: opg.optica.org/oe/fulltext.cfm?uri=oe-32-3-3266&id=545631 Check out the Q&A section of this article: www.rp-photonics.com/frequency_doubling.html This spec sheet for a commercial UV laser utilizing THG also indicates an approximate sqrt(3) increase in linewidth for the output compared to the input: www.sirah.com/wp-content/uploads/documents/THG.pdf

@@e-skills2120 By the way: Mathematically, we need to do a convolution, because in the time domain, the amount of THG field depends on E^3. From Fourier theory, we know that multiplying in the time domain is equivalent to doing convolutions in the frequency domain.

@@yourfavouriteta Thanks a lot for a clear and descriptive answer with reference. It was so kind of you, means a lot Once again thank you for the response

@@e-skills2120 You're welcome!

@@imperfect896 Thank you!

@@naymulhasan8559 You're welcome! Hope your defense went well!

It's already available via the link in the description :-) Would greatly appreciate your feedback!

@@yourfavouriteta Thanks! I took a quick look and feel like you should have a derivation of the NLSE somewhere (beginning or in appendix). I saw you mentioned Agrawal's book but it would nice to see your own derivation.

@@gedaliakoehler6992 I agonized over this, but decided to leave a full derivation out as it would take a lot of space. Felt it was more helpful to focus on the applications of the NLSE instead. But maybe I will add it as an appendix!

@@yourfavouriteta that makes sense. I think for completeness it would fit nicely in the appendix :)

@@optiondrone5468 Thank you very much!

Thank you!

@@hemantrajyora6965 The Stokes process involves a photon with energy E=hf exciting vibrations in a molecular bond that was initially static. Due to energy conservation, this must cause the enegy of the light to drop by an amount equal to the energy of the vibrating bond. In other words, the light loses optical energy, but the medium gains mechanical energy. Something similar happens in the anti-Stokes case; an already vibrating bond de-excites and loses energy, which is picked up by an incident photon.

@@yourfavouriteta Thank You for your valuable reply

@@hemantrajyora6965 You're welcome!

@@yourfavouriteta Can you explain the Anti stokes also Why molecule is already in excited state not static?

@@hemantrajyora6965 Unless the glass is at absolute zero temperature, some of its molecular bonds will always vibrate a bit. Thus, the molecule can start at an excited vibrational state, get kicked up to a much higher one by the incident photon and emit a more energetic photon as the vibrational bond decays all the way down to the ground state.

@@soldieroftruth1976 You're welcome!

First of all, you should consider if this information is actually essential to whatever experiment you are trying to do. In this video, I don't actually need to know the which output has what polarization. For operating the EOM correctly to make pulses with a high extinction ratio, I just need to know that pure polarization along either the x- or y-axes is launched in regardless of its actual orientation. Assuming you do need to know, check the original packaging of the splitter if you have it. The spec sheet will often state which port is the "fast" axis and which one is the "slow" axis. If you don't have the original packaging, you can do the following: 1) Mount the input port PM fiber in such a way that it's "stress rods" are horizontal. Light polarized in the plane of the stress rods will be "slow" 2) Use a laser that you know is polarized in the horizontal plane and focus it onto the input PM fiber. 3) Measure which output port of the splitter has the most power. This will be the "slow" port. The other will be the fast port with polarization orthogonal to the "stress plane" of the PM fiber. 4) Make sure you label the ports on this device for future reference. 5) Repeat this process for all polarization splitters in your lab whose ports you are unsure of. Doing the last two steps whenever you build a setup for characterizing something is good experimental practice. My own research speed (and the speed of my lab mates) accelerated considerably when I took the time to thoroughly test and label equipment that was otherwise "floating around".

Vielen Dank!

@@deepakkushwaha8182 Thank you!

Here it is: doi.org/10.1364/OE.430682

@@jaskaransinghphull189 Another channel called Les' Lab has a series of videos with practical demonstrations of supercontinuum generation via the Raman effect: ua-cam.com/video/w1wSHizmbYg/v-deo.htmlsi=qNgap9bzzrOciDDK One of my recent videos also shows how to simulate SC numerically. Feel free to check those out if you haven't already.

@@SMITAJAISWAR-nc5lg You're welcome!

@@Terrar-fr1bk In the video, I do show how Group Delay Dispersion (i.e. Group Velocity Dispersion*distance=β2*dz) causes the pulse to broaden in the time domain, so I assume that you are referring to the impact of β1. You can watch my video on dispersion for an deeper explanation, but basically, β1 determines the arrival time at a distance, z, inside the medium of a pulse with a carrier frequency of ω0. Thus, we can replace the "actual" time, t, by T = t - β1z, which causes the term in the NLSE containing β1 to cancel out. Using T instead of t does not change the actual evolution of the pulse in either the temporal or spectral domains; only the arrival time.

@@Terrar-fr1bk See also this article: www.rp-photonics.com/group_delay_dispersion.html

@@yourfavouriteta Thank you for your answer! I might be confusing two different things, but I always interpreted the GDD as the first Taylor series expansion term of the propagation factor β around a center frequency ω0. It is essentially the inverse of the group velocity v_g. (Small derivation: beta(ω0 + Δω) = β0 + dβ/dω + d^2β/dω^2 + ...). With β1 = dβ/dω = 1/v_g, and β2 = d^2β/dω^2 = d/dω[1/v_g]. Here my understanding is that the GDD is the β1 term, and GVD is the β2 term. If we assume no GVD or higher order dispersion, that is β2 = 0, then we can still have β1 = 1/v_g, but v_g will be independent of the frequency ω. It will be some constant velocity. However, the phase velocity v_p and group velocity v_g don't necessarily have to be equal, so we can still get the optical packet propagating with group velocity v_g and the carrier wave inside it propagating with v_p. If we look at the spectrum of the pulse, it shouldn't matter how the carrier wave moves inside the packet, as long as the packet doesn't deform, so this is actually my understanding as to why they omit β1 in the equation, but I think you explained the same thing using the concept of 'retarded time' that everyone seems to mention in papers and yet nobody really explains it.

​@@Terrar-fr1bk You're getting closer, but your picture is still not quite accurate. The "group delay" (or as I like to call it for maximum clarity: The "pulse delay") is related to β1 by T_g = d(β(ω)*L)/dω|_ω0=L*β1. It is essentially the time delay experienced by any pulse with a certain carrier frequency propagating through a *particular* fiber. Note that it is measured in units of [time]. The value v_g = 1/β1 is also called the "group velocity" (though I think that "pulse velocity" would be a better phrase). "Group delay dispersion" is related to the derivative of β1 by D_2 = dT_g/dω|_ω0 = L*dβ1/dω|_ω0 = L*β2. It is essentially a measure of how much the frequencies surrounding the carrier frequency, ω0, get delayed relative to each other and thus how much the pulse *broadens* in the time domain when propagating through a *particular* fiber. Note that it is measured in units of [time^2]. The value, β2, is called the "group velocity dispersion" and essentially tells you "how much more the pulse broadens for every additional meter we extend the medium". Thus, the difference between GDD and GVD (as the terms are commonly used) is like the difference between "mass" and "density". We can talk about the mass (GDD) of a *particular object* and the density (GVD) of a *type of material*. Just as the density tells us how much more mass we will get if we add additional volume to the object, GVD tells us how much more GDD we will get if we add additional length to our fiber. Please do let me know if you have further questions!

@@mhd-em6yt You're welcome!

@@asim4050 Thank you, I definitely will!

I am not much of an expert in the electronics used for controlling laser diodes. In my research, I would usually place DFB laser diodes in mounting blocks like this one (www.newport.com/p/LDM-4984-BTB) and hook it up to a current/temperature controller like this (www.newport.com/p/LDC-3724C-120V). I can't say whether they will be helpful to you, but here are some links that seem promising: beamq.com/dfb-laser-driver-board-power-supply-with-temperature-control-p-2193.html electronics.stackexchange.com/questions/266386/help-designing-a-circuit-to-drive-a-1550nm-dfb-ld-and-use-it-to-modulate-an-rf-s

@@AmJo11015 You're welcome! I find that answering viewer questions always gives me a much deeper understanding. In this case, the main take-away was the run-time analysis.

@@samil26 That sounds like very exciting work! It would be cool to see what your MATLAB code is capable of.

@@yourfavouriteta Your comment encourages me to record a video to tell about it :D

@@samil26 Please do! I recommend the free OBS Studio for recording and I have heard good things about DaVinci Resolve for editing (also free).

That sounds like exciting work!

@@mishuk2008 Thank you!

As an electronics Luddite, I quite appreciate your videos as well! :-)

In this video, I don't use a clock at all. I just wanted to demonstrate that two interfering lasers create a sinusoidal signal and that their frequency difference can be measured. The phases of the two laser signals don't matter in this case, though they can be relevant in other situations. Can you explain in a bit more detail what kind of setup you are working on and what you are trying to achieve?

@@yourfavouriteta thanks for response. I'm having a train of optical pulses at 100 MHz repetition rate. We have DCA infinium 86100C with 40 GHz module. The pulse source doesn't have any clock output dedicated. I want to measure that pulse train over the DCA. It is showing nothing without the clock signal.

@@dixitkumar9050 Hmm, have you tried triggering on the pulses themselves? I mean if they are detected by a photodiode connected to Channel 1 on the oscilloscope, you should be able to set the scope to trigger when a certain voltage on Channel 1 is exceeded.

@@yourfavouriteta I tried it while having a doubt whether it would work or not. Should I send the pulses to the photodiode and split some part of it to use as a clock?

@@dixitkumar9050 Maybe it would be good to take a step back and try to get the oscilloscope to trigger on an electrical pulse train from a function generator (I assume your lab has one). Just plug the output of the generator directly into channel 1 of oscilloscope and verify that you can get it to trigger on that signal. If that works you should be able to get the oscilloscope to trigger directly on the pulse train as well. If your experiment involves measuring a change in the arrival time of the pulses due to some effect, you can split the pulse train into two branches. Sending branch 1 to Channel 1 and triggering on that while applying the effect to branch 2 and sending that to Channel 2 should allow you to measure the time delay.

Thank you!

Thank you! Using an approximation, It is possible to capture the impact of the Raman effect without having a fs time step. For a pulse that's much longer than the Raman response time, the magnitude of the effect in the NLSE basically depends only on the derivative of the pulse power w.r.t. time. Introducing the term T_R*A*d|A|^2/dT (where T_R is the average duration of the Raman response function) in the NLSE can thus capture the impact for long pulses. You might want to do this if, for example, you have a very high power pulse with a duration of ~100ps. The high power means that Raman could be significant, but the 100ps duration means that using a 1fs time step (i.e. using 100.000 points just to cover the pulse itself) could be too computationally expensive. The derivative term allows you to use a much larger time step and still get the expected red-shift at the peak of the pulse. I might actually make a quick video about this, since it's an interesting example of physical insight leading to a more efficient way of doing things. My code does support using the derivative approximation. Just specify "raman_model = 'approximate' " when defining the fiber.

@@yourfavouriteta Thank you. I will try this out. Waiting for the video!

It's an XTM-50 filter from EXFO. Being able to tune both the bandwidth and center frequency is super convenient. I think that they cost around USD8.000; not unusual for a specialized piece of research equipment.

Thank you. Do you recommend another cheaper tunable filter?

@@Lephysicien1993 Hmm it depends on what specs you need; range, bandwidth etc. The cheapest option would probably be to build a temperature stabilized box with an FBG in it; takes some time to tune and has a fixed bandwidth, which is inconvenient, but otherwise pretty simple. Found some FP filters here in the USD2000 range: wdmquest.com/collections/tunable-optical-filter

@@yourfavouriteta I made a Phi-OTDR system with a 3 MHz laser at 1550 nm based on the article "A Distributed Optical Fibre Dynamic Strain Sensor Based on Phase-OTDR" by A. Masoudi, M. Belal, and T. P. Newson. The system is based on an MZI interferometer. However, what I see on the oscilloscope are two pulses: one corresponding to Fresnel reflection at the end of the fiber and another within the fiber i think at X=0m (which I don't understand the origin of).The problem is that I don't see the same results you obtained; I don't even see the backscattering trace like an OTDR trace. Do you have any suggestions?

@@Lephysicien1993 The detection scheme in that paper is more advanced than the one I present in my video, which may explain why you get a different signal than me. I recommend trying to build my more basic setup before attempting to recreate the one in the paper. In my experience, mastering the basics early always pays off in the long run. One thing you may want to verify is the duration of the pulses you use and the repetition rate. First of all, the temporal duration, D, of the pulse should be such that Dc/2<<L, where L is the length of the medium. Otherwise, the resolution will be bad. Additionally, the time between two pulses, T, should satisfy Tc/2<L to allow the first pulse to completely exit the medium before the 2nd one arrives.

You're welcome!

I am happy that you find them useful! Many of the concepts I explain only really clicked for me in the process of producing these tutorials, so I highly recommend making a few about your own field of research!

Thank you! My code also works for PIC. At the moment, only single mode behavior is supported, so be aware at which frequency your waveguide become multimode; results may be invalid beyond this limit!

Since the fission requires the pulse to have a certain peak power and duration, you could in principle create a very short pulse that is highly attenuated. Then, by gradually reducing the attenuation and thus boosting the power, you will eventually make it bright enough for soliton fission to occur.

@@yourfavouriteta makes sense, but how would one reduce the attenuation when the pulse is already on its way? altering the properties of the cable?

@@GeoffryGifari You could generate the pulses externally, launch them into a variable attenuator and then into the fiber. Simply reduce the attenuation to boost the power of the pulse. Alternatively you could generate low power fs pulses, send them into an amplifier, whose gain can be adjusted and then into the fiber. Otherwise, just change the power of the pulses by changing the amount of current supplied to the laser that generates them.

It depends a bit on what you mean by "soliton". The fission products that arise when Raman is present have stable power envelopes, but constantly reduce their own frequency; they are "solitonic" if you only care about the power envelope, but not if you also care about the spectrum. Another way to view the evolution is to think of an intense field going through a fiber with γ>0 and β2<0 as "one basic sech soliton with N=γPT^2/|β2| = 1 plus a bunch of extra field piled on top". Then, the fission process can be though of as all the additional field "peeling away" until only the basic soliton is left. This is of course a rather cartoonish way to think about it, but I believe it can be helpful.

by this i mean, would a separation between multiple aolitona develop?

​@@GeoffryGifari The animations in the beginning of the video essentially show "The power you would measure over time if the pulse had propagated through a fiber with a length of z". For example, if you pause the video when z=2.62m and consider the "Raman graph" in the lower left corner, it is telling you the following: "Imagine taking a 2.62m long piece of fiber with a certain negative β2 value and a certain nonlinear parameter. If you launch a sech pulse with (whatever duration and peak power I was using) into this fiber and observe the light coming out the other end, you will first see a small amount of light at both high and low frequencies, then a short, moderately large flash at a lower frequency and finally (500fs later) a very intense, very brief flash at a much lower frequency. " If we could track the propagation of this pulse through an actual fiber (imagine looking at the stretched out fiber from the outside), we would see a flash of light at a single color propagate through the first meter, whereupon two short sub-pulses are created and begin trailing behind the main pulse.

@@yourfavouriteta ah i see

@@GeoffryGifari. Glad I was able to clarify. Great questions btw! :-)

I agree :-)

You're welcome!

In reality, two things would change. First, The values of the dispersion coefficients, β2, β3, ..., would change because they are the 2nd, 3rd, ... derivatives of β(ω) = n(ω)ω/c w.r.t. ω evaluated at the carrier frequency of the pulse. This will change how the pulse evolves in the time domain and whether phase matching is satisfied. If the carrier frequency of the pulse is initially close to a frequency, where β2=0, the new β2 value at twice the frequency is very unlikely to also be close to 0, so most likely the generated spectrum will be narrower. Secondly, the impact of self-steepening is reduced. In the GNLSE, the term describing this effect is significant when the time derivative of A|A|^2 is large compared to the carrier frequency. Thus, doubling the frequency cuts this term in half. If we assume that the dispersion coeffs are miraculously unchanged, the effect of increasing the carrier frequency by an amount so large that self steepening becomes negligible can be seen in the video when I switch self steepening on/off. Lastly, if the carrier frequency is doubled in my code, only self steepening is affected because the dispersion coeffs are entered into a list independently of the carrier frequency. In reality, the two are of course linked, but doing it this way gives the user more flexibility in investigating the impact of dispersion.

Thank you! Please let me know if you need any help with the code.

Your video was the first thing I thought of when I saw this video. 😀

@@yourfavouriteta Code is great, had to tweak the directory path line to get it to run on Linux, but that is all, it works just great! When I get time, I will throw some other parameters at it. It looks like a really nice intuitive way to poke at things without hours of setup!

@@LesLaboratory Awesome, I am happy to hear that you got it to work! My intention was to make it accessible and flexible, so the user can quickly begin to play around with the parameters. I recommend trying to re-create basic effects like self-phase modulation first to familiarize yourself, but I am sure you will figure it out. Otherwise, let me know if you need help!

If only one had all the time in the world :-) My next video will be on supercontinuum generation, so stay tuned!

To clarify, the betas in that equation are spatial frequencies evaluated at four different temporal frequencies. For example, β_u = β(ω_u), which has units of 1/m. They are emphatically NOT group-velocity-dispersion values (i.e. 2nd derivatives of β w.r.t. ω), which have units of s^2/m.

@@yourfavouriteta This is the phase mismatch equation for degenerate FWM 2𝛽𝑝(𝜔𝑝) − 𝛽𝑠(𝜔𝑠 ) + 𝛽𝑖 (𝜔𝑖 ) − 2𝛾𝑃 = 0, IMPLYING balancing GVD, if these betas are the frequencies as u mentioned what is their relation to the respective GVDs? Because after all we are balancing GVDs for PUMP, SIGNAL AND IDLER.

@@muneebfarooq3882 At 11:30 in the video, I explain that 2β(ωb)-β(ωa)-β(ωu) is approximately equal to -Δω^2 * β2(ωb) = -Δω^2 * GVD(ωb) when the difference between three temporal frequencies, ωb, ωa, ωu is small. Note again that "β_b" in my derivation is "the spatial frequency in the medium of an EM wave with a temporal frequency of ω_b". Meanwhile, β_2 = GVD = 2nd derivative of the spatial frequency, β(ω), w.r.t. ω. The point is that phase matching ***in general*** depends on whether the temporal frequencies that are interacting via the nonlinearity (in this case ωb, ωa and ωu) have the correct spatial frequencies and powers for 2β(ωb)-β(ωa)-β(ωu) - 2γP = 0 to be satisfied. In the ***special case***, where the difference between the temporal frequencies is small, this is equivalent to asking if Δω^2 * GVD + 2γP~0.

@@yourfavouriteta that is right but I think this approximation works only in the linear dispersion regime.

@@muneebfarooq3882 Well, the range of Δω values where the approximation works depends on how quickly β changes as a function of ω. If β changes a lot, using the full expression is better.

Good luck!