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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: th-cam.com/video/w1wSHizmbYg/w-d-xo.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!

Thank you!

Check out this browser-based tool from Octave Photonics: www.octavephotonics.com/nlse I plan on doing a comparison of various implementations (including my own) at some point, so viewers can choose one that works for them.

@@yourfavouriteta Thank you. I have not used NLSE or any nonlinear based optical simulations in the past. I used linear computational photonics tools like TMM and FDTD on NanoHub before. Plasmonics and biosensing are also an interesting domain that I think worth focusing on.

@@maz3808 You're welcome!

You're welcome!

No problem!

Check out this explanation: en.m.wikipedia.org/wiki/Distributed_Bragg_reflector_laser#:~:text=A%20distributed%20Bragg%20reflector%20laser,proven%20to%20be%20commercially%20viable.

@@yourfavouriteta Thank you! Really appreciate it.

@@mishuk2008 No problem!

You're welcome!

Thank you!

Thank you! Other viewers have advised me to slow down in future videos, which I will try to do.

I am happy that you found it useful! The interesting thing is that the B-field outside is 0 no matter the current in the solenoid, but nevertheless the interference pattern changes when the current is increased, which hints that A is the field affecting the particle! An "equivalent" experiment would be to send the particle through both one path with zero electric potential and one with a high electric potential (but somehow no E-field!) and let it interfere with itself. If Wikipedia is to be believed, this latter experiment has apparently not been performed yet!

Yes, you are overall correct in both cases. When β2 is positive and nonlinearity is present, "Optical Wave Breaking" can occur. Essentially, SPM makes the leading edge of the pulse "more red" and β2>0 implies that red light moves faster than blue light. Similarly, the trailing edge will become "more blue". In total, this causes the pulse to spread out quickly. Check out my video on this phenomenon! If, additionally, the loss coefficient, α, is positive (i.e. the pulse experienced gain!) we can form "Similaritons", with parabolic shapes and linear chirps. I also have a video on this. With regards to the β2<0 case, SPM will still make the leading edge of the pulse red and the trailing part blue, but now blue light moves fast and red light is slow. Thus, if the peak power and shape of the pulse is exactly right, we get a "fundamental soliton" that retains its shape as it propagates. If you increase the power further, you will eventually get higher order solitons that "oscillate" with distance. And of course, I also have a video about that :-)

Hey, my email is: yourfavouriteta@gmail.com You can also find an up-to-date version of the code here: github.com/OleKrarup123/NLSE-vector-solver/blob/main/ssfm_functions.py The main function at the end of the code should work as is. Feel free to experiment with it and email me if you need help!

Thank you very much! I will try my best to slow down in future recordings and will see if I can improve the audio quality.

Many viewers have expressed something similar. I will try to slow down in future videos!

I am glad you found it useful! What part of the audio do you find to be bad and do you have any suggestions for fixing it?

Interesting idea! Makes sense that if one diode is more sensitive to external noise, "smearing" could occur in the spectrum.