The Photonics Spotlight
The Photonics Spotlight – associated with the Encyclopedia of Laser Physics and Technology – is a “blog” (web log) with the purpose of highlighting interesting news and useful information in the area of photonics, particularly laser technology and applications. The content can be related to particularly interesting scientific papers or to other forms of publications, reporting for example cute new techniques, special achievements, or useful hints.
Note that the Spotlight articles (as well as those of the Encyclopedia) are citable. Permanent links are given for each article.
This blog is operated by Dr. Rüdiger Paschotta of RP Photonics Consulting. Comments and suggestions are welcome. The news items are definitely not available for advertising, but advertisers can order banners on the right column of this page.
You can read this content in various ways:
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Make a bookmark to remember this page.
(Disadvantage: you may still forget to come back.)
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And here are the articles:
Beam Quality Limit for Multimode Fibers
Posted on 2013-11-12 as a part of the Photonics Spotlight.
Permanent link: http://www.rp-photonics.com/spotlight_2013_11_12.html
- How good does the beam quality of my light source have to be – for example in terms of the M2 factor – for efficient launching into the fiber?
- What will be the beam quality of the light coming out of the fiber?
Surprisingly, it is not so easy to find helpful and reliable advice on such essential things in the Internet or in textbooks, but this is what I will try to provide in the following.
Clearly, the input light to the fiber should essentially be limited to the region of the fiber core; we don't want to launch light into the cladding. In addition, the angular distribution needs to be limited according to the numerical aperture of the fiber. Can we now calculate the maximum M2 factor of the fiber input or output from these two conditions?
Strictly speaking, we can't – basically because these two values do not determine the details of the beam intensity profile. However, one may assume that the optical power is well spread over all the guided modes of the fiber. For that case, one can show that the M2 factor of the output can be well estimated by the equation
where rcore is the core radius, NA the numerical aperture, and λ the vacuum wavelength. (In case you don't see the equation, please make sure that images are displayed.) I have confirmed this with some numerical tests.
As the high-order modes contribute more to a high M2 value than the low-order ones, reality might be worse than according to the equation, if one preferentially launches into high-order modes. However, that is unlikely in typical practical cases. One will then usually not obtain more than the calculated limit, or even less.
The maximum M2 factor of the input light (for efficient launching) can be estimated with the same equation, but again, it is an estimate, which is often very reasonable, but not a strict limit.
The figure below shows the intensity profile of a monochromatic beam from a numerical simulation, where the power is well spread over all guided modes.
Note that much smoother intensity profiles are possible for polychromatic light, where different wavelength components have similar intensity patterns as shown above, but the minima and maxima of different components largely average out. That averaging effect has not impact on the beam quality, however.
Will the Output Beam Quality be the same as that of the Input?
From a simple picture, one might expect that the M2 value for the output of the fiber should be the same as for the input. That is not always true, however:
- If some of the launched light is “stripped off” by the fiber, i.e., lost in the cladding, the output beam quality might be better. The fiber then acts as a kind of spatial filter.
- If you launch primarily into low-order modes, using a light source with good beam quality, you may also get that good beam quality from the fiber end. However, there might also be some mode mixing in the fiber, e.g. as a result of bending. That may shuffle light into higher-order modes, leading to a higher M2 value.
- If you do not illuminate the whole area of the fiber core at the input, you will nevertheless get light from essentially the whole core area at the output. The increased beam area together with the usually not decreased beam divergence leads to a higher M2 value.
How About Few-mode Fibers and Single-mode Fibers?
In the latter case, the angular distribution for the guided mode normally remains well below the limit calculated from the numerical aperture. In other words, one can construct light beams which would reasonably well fulfill the condition of a maximum angular spread, and nevertheless cannot be efficiently launched into the fiber.
A nice example is that of a TEM10 beam, which is well aligned to the fiber and has a reasonable beam radius. Although only some small fraction of its angular distribution is outside the limit set by the fiber's NA, the launch efficiency is zero. That already follows from symmetry reasons: the overlap with the single guided fiber mode is zero, since that mode is radially symmetric, whereas the TEM10 beam is anti-symmetric. Curiously, some of the light can be launched if the center of the TEM10 beam is somewhat offset against the fiber axis – although that misalignment surely does not modify the angular distribution.
You may also gradually increase the core diameter and/or the NA, and suddenly you will reach a point where a substantial part of the power of the TEM10 beam can be launched into the fiber core.
So the wave optics details become more subtle for single-mode and few-mode fibers, even though simple estimates as provided above generally work well for fibers with many modes, where we nearly have a continuum of modes.
Fiber Optics Tutorial
You find such things and more in our tutorial on fiber optics, in particular in its section 4 on multimode fibers. I have worked hard to provide more substance, particularly concerning the physics, than the dozens of other fiber optics tutorials which you can find in the Internet.
I hope you will agree that our newsletter and our tutorials provide useful high-quality information, and that you can recommend them to your colleagues – possible also using your website and social media.
Simulation of a Q-switched Nd:YAG Laser:
Numerical Beam Propagation Reveals What Happens, Analytical Reasoning Explains It
Posted on 2013-09-24 as a part of the Photonics Spotlight.
Permanent link: http://www.rp-photonics.com/spotlight_2013_09_24.html
Laser modeling is often based on certain assumptions, which might not always be well fulfilled in practice. This is particularly the case for analytical models, which often require more assumptions in order to keep the problem manageable. Purely numerical simulations are better in this respect. Here, I present a nice example for that.
In simulations of laser performance, we often assume that we get a certain beam size – for example, the size of the fundamental resonator mode. For most bulk lasers with stable transverse single-mode operation, this is a well fulfilled assumption. I wondered, however, whether gain guiding in a Q-switched laser might have a significant effect. After all, the laser gain is often pretty high in such a laser, so that gain guiding might pull the beam size away from that of the fundamental mode – presumably to a smaller value. As strong gain saturation then sets in, the gain guiding effect changes during pulse formation, making things somewhat complicated.
The way to check such things is, of course, to numerically simulate the pulse formation – not just the dynamics of the optical power, but of the full beam profile. The new version V5 of our RP Fiber Power software is a great tool for such things, even though it has actually be designed for fiber lasers and amplifiers, not for bulk lasers. One simply defines the refractive index profile and the gain profile for the bulk laser resonator, just as if it were a piece of fiber. In that case, it doesn't form a waveguide, except if one also includes thermal lensing, which I didn't do here in order to focus on gain guiding. (It is one of the nice feature of numerical tests that you can easily eliminate effects which you are not interested in at the moment.)
The results first came out pretty much as one might expect them. A nice pulse was generated, when a weak seed beam was injected into the resonator after pumping the crystal. (One might also simulate the start-up from quantum noise, but here I started up with a clean seed beam as I was interested only in what happens when the powers get large and gain saturation sets in.) Here is the evolution of output power and beam radius:
As expected, I saw some moderate fluctuations of beam size:
The beam, starting with a Gaussian beam fitting the resonator mode (without gain guiding), quickly adapted to a somewhat smaller size due to the gain guiding. (Nevertheless, the second-moment-based beam radius actually gets somewhat larger due to wings of the profile.) When the pulse maximum was reached after 13 resonator round-trips, the beam got larger and finally settled at a size close to the resonator mode size.
Then I did the same again for modified values of the resonator length. There was an air gap of initially 20 mm between the laser crystal and the right end mirror. When this was increased up to 30 mm, the mode size hardly changed at all. Therefore, nobody would have been surprised to see that for 30 mm air gap width one gets quite the same as before. However, for a spacing of just 25 mm – not for 23 or 27 mm – something strange happened:
One can see that now the beam shrinks substantially during the pulse build-up, and later evolves into a kind of donut shape. Although that shape is rather pronounced, it would be difficult to detect experimentally, as that requires a time-resolved measurement. (The temporarily integrated beam profile, weighted with the optical power, does not show much – just a certain deviation from a Gaussian beam profile.) If one would put a photodiode at different portions of the beam, one would find different temporal pulse shapes and durations.
Apparently, the laser resonator is substantially more sensitive to the gain guiding effect for that particular resonator length – but why is that? The explanation is far from obvious. A resonator design analysis (done with the RP Resonator software) shows that just for 25 mm air gap size, the Gouy phase shift of the resonator per round trip becomes 1.59 rad, which is close to π/2 (= 1.57 rad). A consequence of that is that the TEM40 and TEM22 modes have resonance frequencies which coincide with resonances of the TEM00 fundamental mode. At this point, some resonant mode coupling can occur, which has a strong impact on the beam profiles (see R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions”, Opt. Express 14 (13), 6069 (2006)).
This example shows that substantial effects, which might impact performance and also applications of the laser beam, could easily stay hidden with analytical simulations, requiring assumptions such as a constant beam size. Moreover, even in experiments one would probably not recognize what is going on – maybe only that the performance is not quite as good as expected. It would then be very hard to find out what's the matter.
By the way, I wouldn't say that the numerical approach is always better – ideally, you are able to use both approaches. In our example case, numerical modeling brings up interesting details, but only analytical considerations (see the cited paper) can well explain them.
You can read a more comprehensive description of the model and some technical details on the page with the detailed case study for the Q-switched laser.
Frequency Doubling and the Reverse Process
Posted on 2013-08-26 as a part of the Photonics Spotlight.
Permanent link: http://www.rp-photonics.com/spotlight_2013_08_26.html
Years ago, in a Ph. D. viva I heard the following interesting question:
A degenerate optical parametric oscillator (OPO) converts green light at 532 nm, for example, into infrared light at 1064 nm. This is just the opposite of what a frequency doubler, pumped with a 1064-nm laser, does. How can it be that the OPO works only above a certain threshold power, whereas the frequency doubler has no threshold? After all, isn't one process just the time-reserved version of the other process?
The Ph. D. candidate who got that question was taken by surprise. A colleague of him, who was a listener on that day and had his viva a few weeks later, then got the same question and failed as well. I wondered whether the professor asking the question actually knew the answer himself!
Anyway, the answer is not that difficult to find, although one may easily miss one detail and therefore require some time. Consider what exactly is the time-reserved process of frequency doubling. The frequency doubler has an input at 1064 nm and only partially converts that to 532 nm; some of the 1064-nm light exits the crystal unconverted. So the time-reversed process requires two inputs: one at 532 nm, but also one at 1064 nm! If you really do that properly, you can convert all the light back to 1064 nm – not only above some threshold.
Here, another interesting question arises. How can the crystal “know” whether it is supposed to transfer optical power from the fundamental to the harmonic wave, or vice versa? If you heard rumors that it is the relative phase between the two beams, you may (or should!) wonder how one can compare phases of beams with different optical frequencies – doesn't that phase difference change substantially within attoseconds!? Well, we have to look at the physics occurring in the nonlinear crystal. The fundamental wave generates a nonlinear polarization wave, having twice the optical frequency – i.e., the frequency of the harmonic wave. That polarization wave now interacts with the existing harmonic wave, and the relative phase between these two is what determines the direction of power transfer. How, the phase of the nonlinear polarization at the second harmonic is twice the phase of the fundamental wave. The relevant phase difference is thus not that between fundamental and harmonic, but rather twice the fundamental phase minus the harmonic phase.
That relative phase is also affected by the phase mismatch. So if we don't have proper phase matching of our process, the relative phase changes such that after some short distance the direction of energy transfer is reversed. That's why phase matching is essential for efficient nonlinear power conversion.
Even with perfect phase matching, a frequency doubler can run into back-conversion when operated at too high intensities: if the fundamental wave is fully depleted at some point, back-conversion will take place after that point. Note that for a Gaussian beam profile, for example, that will occur before the conversion of the wings of the beam profile is complete. For that reason, 90% conversion is not possible with Gaussian beams – at least in a single pass. With resonant frequency doubling, such a limit wouldn't apply; here, the single-pass conversion doesn't need to be high for complete overall conversion.
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- 2013-06-13: Two New Photonics Newsletters
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