Spatial Walk-off and Beam Quality in Nonlinear Frequency Conversion

Posted on 2010-03-15. Permanent link: http://www.rp-photonics.com/spotlight_2010_03_15.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Ref.: encyclopedia articles on spatial walk-off, critical phase matching, nonlinear frequency conversion and beam quality

It is well known that the phenomenon of spatial walk-off can degrade the beam quality in nonlinear frequency conversion processes. It occurs only in cases with critical phase matching. At least one of the involved waves has the extraordinary polarization direction, and such components will have intensity distributions which somehow “drift away” from the direction given by the wave vector. This phenomenon is a consequence of the anisotropy of the nonlinear crystal material.

The most common effect of that spatial walk-off is that the generated wave obtains a broader amplitude and intensity profile. This is the case, for example, for frequency doubling in LBO with the type-I scheme XY oo-e, where the harmonic wave (other than the pump wave) experiences walk-off. An interesting question is now whether or not that walk-off degrades the beam quality.

The widening of the harmonic beam as such does not necessarily lead to a degradation of beam quality, even in cases where it is substantial. While the beam waist becomes larger, the beam divergence is also reduced. This is essentially because we still have a “well-behaved” intensity profile, associated with flat or weakly curved wavefronts. In effect, the beam parameter product and thus the M² factor may remain more or less unchanged!

However, walk-off may indeed reduce the beam quality in situations where it leads to complicated intensity profiles. Typically, this occurs when we have both a strong walk-off and a strong conversion, involving strong pump depletion. The beam divergence may then not decrease as much as the beam radius increases, so that the beam quality is degraded.

Similar Effects Related to Temporal Walk-off

There is a similar effect in the case of temporal walk-off. Here, the product beam becomes temporally longer, but its optical bandwidth also becomes smaller, so that the time–bandwidth product may remain unchanged. However, temporal walk-off may also lead to complicated changes of pulse shape, and in that case the time–bandwidth product may be increased strongly.

Nonlinearities in Fiber Amplifier Modeling

Posted on 2010-03-09. Permanent link: http://www.rp-photonics.com/spotlight_2010_03_09.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Ref.: spotlight 2010-03-03; encyclopedia articles on nonlinearities, Brillouin scattering, Raman scattering, fiber amplifiers, laser modeling

I am often asked whether my fiber amplifier and laser modeling software RP Fiber Power can be used for modeling nonlinear effects. Strictly speaking, it can't, as it is not able to calculate the generation of power at new wavelengths through nonlinear effects, including the back-action (depletion) on the original wavelength components. What it can do, however, is to calculate the expected Raman and Brillouin gain. If the nonlinear gain is below the corresponding threshold value, you know that power extraction by these effects is negligible. If not, you know that the calculated powers are actually not realistic, because in reality the nonlinear effects would change the results.

In practice, it is very often fully sufficient to find out whether or not nonlinear effects become important. You do not need to know exactly what would happen in the strongly nonlinear regime, simply because you want to avoid operation in this regime anyway!

One might think that it would be not that difficult to fully take into account nonlinear effects in such a numerical model. After all, the corresponding equations are not necessarily very complicated. This reasoning is not valid, however – for several reasons:

• One would have to take into account the exact optical spectra of all involved waves, and these are often not known.
  For example, try to find out what the exact optical spectrum from a multimode seed laser diode is. The specs may indicate some bandwidth value of a few nanometers, but your chances to get anything like that in more precise form (exact spectral shape) or even guaranteed are very small, for understandable reasons. Such laser diodes may jump between different modes, strongly depending on the operation conditions (current, changes of current, any optical feedback, etc.) and minor details of the device. Nobody can know exactly what such a thing will feed into your amplifier. Therefore, it obviously makes little sense to try exact modeling such effects.
• Even if you have stable and exactly known spectra, you might have to numerically resolve many different wavelength channels, driving up the required computation time enormously. Although this is not a fundamental problem, it is a significant practical one.
• Different fiber nonlinearities often come together. For example, stimulated Raman scattering can be accompanied by strong four-wave mixing processes, depending on details of the chromatic dispersion, which the user then obviously also would have to provide to the software.
• Nonlinear effects often cause strong instabilities. This is particularly the case for Brillouin scattering: if significant back-scattering begins, this quickly depletes the forward signal wave, strongly reducing the Brillouin gain again. The nature of the resulting strong fluctuations depends on many tiny details (including Rayleigh scattering in the fiber) which nobody can tell you. Even if you knew them and the model could include them all, one would often have to simulate the temporal evolution and statistically process it.

Therefore, in many cases of interest such nonlinear modeling would be extremely difficult, and often at the same time not particularly useful. If anyone claims that his fiber amplifier software can do such things, you should be quite cautions.

Of course, there are cases where the modeling of strong nonlinear conversion processes makes sense. For example, fiber Raman lasers can be modeled with reasonable accuracy, even though it may be difficult to reliable predict the resulting optical spectrum. In the area of fiber amplifiers and lasers, I think it would not make much sense to include nonlinear conversion, and therefore such extensions are not planned for the RP Fiber Power software.

Thresholds for Nonlinear Effects in Fiber Amplifiers

Posted on 2010-03-03. Permanent link: http://www.rp-photonics.com/spotlight_2010_03_03.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Ref.: encyclopedia articles on nonlinearities, Brillouin scattering, Raman scattering, fiber amplifiers, laser threshold

Comparing with bulk lasers, fiber lasers and fiber amplifiers exhibit a much higher tendency for unwanted nonlinear effects, because they typically use a much longer solid medium, and this with a rather small effective mode area. Frequently, one calculates a “threshold” for the onset of such effects, even though they normally do not exhibit a threshold which is as well-defined as a laser threshold. It is instructive to think a little more on this.

Unwanted Power Extraction by Stimulated Raman Scattering

Stimulated Raman scattering (SRS) in a fiber amplifier generates some amount of Raman gain in the region of somewhat longer wavelengths. For simplicity, let us assume that these wavelengths are clearly separated from the spectral region of the amplified signal light (which is sometimes not the case, for example in pulse compression experiments). Although there is no input signal in that longer-wavelength region with nonlinear gain, some significant power can be extracted here. In a semiclassical model, this can be explained as follows: even with no classical input signal, there are vacuum fluctuations (vacuum noise) entering the device, which can be amplified to macroscopic power levels. This can occur in two directions: co-propagating with the signal and counter-propagating. If the Raman gain gets too high (for example, well above 40 dB), much of the original signal power may be transferred into this longer-wavelength region, and the amplifier performance is degraded severely.

Such unwanted power extraction does not really set in at a well-defined threshold power. However, the extracted power rises exponentially. Let us assume that at some signal power level we get only 1% of the power removed by SRS, and that the SRS gain is 40 dB here. If we now increase the signal power level by only 10%, the extracted power rises by 4 dB, i.e., to ∼2.3% of the signal power. So we have something one may call a “soft threshold” in terms of the allowable signal power. For amplification of pulses, what counts is of course the peak power.

Similar Effects from Stimulated Brillouin Scattering

With stimulated Brillouin scattering, similar effects can occur, but with some important differences:

• The gain occurs only in backward direction. (Only in relatively exotic situations, some small level of forward Brillouin scattering can be observed.)
• The gain bandwidth is much smaller – of the order of 50 MHz, to be compared with hundreds of GHz for Raman scattering. Therefore, significant power extraction can occur only once the Brillouin gain gets to the order of 70 dB.
• If the optical bandwidth of the signal exceeds the Brillouin gain bandwidth, the Brillouin gain spectrum is “smeared” out, so that the peak gain is reduced and the effective Brillouin threshold becomes higher accordingly. For that reason, stimulated Raman scattering is often the dominating problem, despite the smaller intrinsic nonlinear gain.

Fighting Against Nonlinearities

Reducing nonlinear effects is often a central issue in the design of active fiber devices, in particular of fiber amplifiers for short pulse amplification. A good thing is to increase the effective mode area of the fiber, but there are limits to that, assuming that you need transverse single-mode performance for high beam quality. Making devices shorter by using higher doping concentrations may also be useful, but there are limits to the acceptable doping concentration and also to the heat load per unit length. On the materials side, there is not much one can do: silica fibers already have a fairly low nonlinearity, and one may only avoid the excessive use of certain dopants in the fiber core. Sometimes, one needs to increase the signal bandwidth in order to avoid problems with Brillouin scattering. Another approach is to broaden the Brillouin gain spectrum via longitudinal or transverse variations of the Brillouin frequency shift. That may be worth a Spotlight article at some later time.

New Scientific Paper: Timing Jitter and Phase Noise of Mode-locked Fiber Lasers

Posted on 2010-02-26. Permanent link: http://www.rp-photonics.com/spotlight_2010_02_26.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Ref.: R. Paschotta, “Timing jitter and phase noise of mode-locked fiber lasers”, Opt. Express 18 (5), 5041 (2010)

(See also: spotlight article of 2009-08-22)

My latest scientific paper just appeared in the open-access journal Optics Express. I believe that this work will get a lot of attention, as it significantly expands the knowledge on the noise properties of mode-locked fiber lasers.

The noise performance of simple soliton mode-locked fiber lasers has been well understood for many years already; it has been investigated in 1993 (H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers”, IEEE J. Quantum Electron. 29 (3), 983 (1993)), using soliton perturbation theory. Unfortunately, soliton fiber lasers have a fairly limited pulse energy, and mainly for that reason their quantum-noise limited timing jitter is much higher than for bulk lasers, for example. The achievable performance is still quite good, but clearly not the last word.

In recent years, several schemes for mode-locked fiber lasers with substantially higher pulse energies have been developed – most notably, stretched-pulse lasers and wavebreaking-free lasers, the latter often realized with all-normal chromatic dispersion in the resonator. The Haus/Mecozzi analysis is clearly not applicable here, as the assumptions of soliton perturbation theory are not fulfilled. I myself have developed a much more general theoretical treatment (R. Paschotta, Appl. Phys. B 79, 163 (2004)), which can be applied to various mode-locked lasers including most bulk lasers. Still, for the fairly complicated pulse-forming mechanisms in the stretched-pulse and wavebreaking-free fiber lasers, it was not clear whether the application of these results would be valid. Therefore, I decided to investigate several cases using a numerical model as described in R. Paschotta, 79, 153 (2004). The main results are:

• For stretched-pulse lasers, the timing jitter is only slightly higher than estimated from the equations of the simple analytical model when inserting the minimum pulse duration. (In such lasers, the pulse duration varies substantially in each resonator round-trip.) There is no evidence for any excess noise, resulting from the strong pulse breathing. At least, this holds for the investigated cases. It is not excluded that excess noise arises when one optimizes such lasers for highest pulse energies, penetrating an operating regime which is no longer described with the simple pulse breathing model.
• Wavebreaking-free fiber lasers can exhibit substantial excess noise, apparently arising from the strong nonlinear interaction. This has already been found in a recent experiment, see O. Prochnow et al., Opt. Express 17 (18), 15525 (2009). Again, there may well be configurations where such excess noise is avoided, but at least we know for sure that strong excess noise (well above 10 dB) is possible. This also effects the noise of the carrier–envelope offset and thus the performance of frequency comb sources for optical metrology. Note that this excess noise is not resulting from technical noise sources. It rather arises from quantum noise only, which however has stronger effects in such lasers than one would expect from simplified models.
• An interesting anomaly has been discovered. In 2008, Schibli et al. reported in Nature Photon. 2, 355 (2008) a wavebreaking-free laser with surprisingly low noise of the carrier–envelope offset phase. This noise level is substantially lower than expected from theory, even considering only the timing jitter arising from the direct effect of quantum noise from the laser gain. So far, a discussion with the authors did not resolve this issue. There is no evidence that the measurements are wrong, but from the theoretical standpoint it is also hardly conceivable that the random timing errors which are inevitably introduced by the gain medium could be compensated by any other effect in the laser. (Note that such a correction would require some external timing reference, which for example all sorts of nonlinear effects cannot have.) It also appears unlikely that some parameters assumed for that laser are totally wrong. I suspect that we have some additional (yet unknown) effect at work in that laser, and hope that this will be found out soon.

A main conclusion from this work is that in order to improve the noise performance of mode-locked fiber lasers, it is not sufficient to raise the pulse energy with any means available. One also has to be careful to avoid regimes where substantial excess noise is introduced. Besides, there is a chance that we discover something interesting and useful by further investigating the discovered anomaly.

Those interested in such topics are advised also to look at the following earlier papers of mine:

• R. Paschotta, “Noise of mode-locked lasers. Part I: numerical model”, Appl. Phys. B 79, 153 (2004)
• R. Paschotta, “Noise of mode-locked lasers. Part II: timing jitter and other fluctuations”, Appl. Phys. B 79, 163 (2004)
• R. Paschotta et al., “Relative timing jitter measurements with an indirect phase comparison method”, Appl. Phys. B 80 (2), 185 (2005)
• R. Paschotta et al., “Optical phase noise and carrier–envelope offset noise of mode-locked lasers”, Appl. Phys. B 82 (2), 265 (2006)

Scientific Conferences and Publications: Emphasize Device Performance or Insight?

Posted on 2010-02-06, revised on 2010-02-11. Permanent link: http://www.rp-photonics.com/spotlight_2010_02_06.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

When attending the conferences Photonics West in San Francisco and Advanced Solid-State Photonics (ASSP) in San Diego, I learned a lot, but also thought about some deficits which are typical for such conferences as well as for scientific journals. The selection process for the submitted papers often favors strongly such papers which report advances in laser performance, even though many of these papers do not generate any significant new insight. In many cases, good performance results from more or less systematically applying the already available knowledge, or even from details which people are not willing to disclose. I then often think that such presentations help me mostly to see that certain persons, research groups of companies can do certain things, but not really to learn much about the scientific technical subject – which would be more useful, of course.

Different Types of Papers

There are other types of papers which transfer really interesting and valuable information but nevertheless are more difficult to get accepted for presentation or publication. For example, there are papers presenting a theoretical analysis of certain technical aspects which are crucial for further progress in the field. Instead of appreciating such contributions, some committee members tend to derate them on the ground that an improved laser devices has not been demonstrated yet.

Admittedly, if someone wanted to build a better laser, didn't succeed for some reason and wants to present only the idea as such, this can rightly be considered less valuable than the completed experiment. Sooner or later, ideas need to be tested in our discipline. However, there can be very valuable information extracted from a theoretical analysis only. Even when the core result is a negative one, saying for example that a certain strategy to overcome some common problem does not work in certain situations, or does not work as expected, this can be very useful to know. As an example, I would definitely appreciate a paper which explains clearly why the common understanding of stimulated Brillouin scattering in optical fibers is not accurate, and what that means for strategies (based on new fiber designs, for example) for raising the Brillouin threshold. (Some people have strong views on such issues, but I found interesting information on those only in discussions with colleagues, but nothing new in the conference programs.) On the other hand, I may well live without being told that some research group tweaked a little more power out of a laser using a well-known technique with slightly improved components. So why are we then getting so much stuff of that kind?

Criteria for Scoring Papers

I think it is important to think carefully about the right criteria for scoring (and finally accepting or rejecting) papers. The final criterion should always be to what extent the community will presumably profit from a certain paper being presented or published. Various typically considered aspects are not always very relevant for this:

• Is the achieved device performance really convincing? This is rightly asked when a paper emphasizes performance itself, but even then one should also ask other questions: Did they just use better components, or do we learn about any new ideas, concepts, problems, etc.? Will the paper help others to get better, or is it more about raising the prestige of a certain research group or company?
• Have they got experimental results, or only theory? This question can be annoying when it means that we are interested only in devices and not in thoughts, analysis, concepts, etc. If you like, science is all about constructing mental models of reality, not primarily about building things. Therefore, to be contemptuous of theory (a system of mental models) is hardly compatible with being a scientist. The point is whether any experiment or any theoretical treatment is valuable, i.e., helpful, convincing, original, etc. We should pick the neat experiments as well as the helpful theory, while filtering out the poor stuff of any kind.
• Is the presented material well described? This can apply to experimental circumstances, to the characterization of devices, or to the assumptions underlying a theoretical model. We like to get informed clearly, and do not appreciate to get only preliminary results. However, we shouldn't insist on completeness where it is not relevant for the actual question of interest.
• Is it all correct? Obviously, I would have difficulties supporting a paper which I am sure is based on wrong reasoning. However, there is a risk that we let all non-controversial (but often boring) stuff pass while losing some of the important materials which may be somewhat more controversial. Particularly at conferences, it may not be a problem to have something presented which turns out to be questionable: even more people may have the opportunity to get some views corrected if such views are presented but then criticized.
• Are the authors already known to be good in their area? If yes, this may increase the confidence that something useful will be presented. However, for obvious reasons it is highly problematic to score more highly the well-known guys.

Inviting Useful Contributions

Having realized what kind of papers we need to advance our science and technology, we may not only score papers more diligently, but also encourage the submission of useful papers. Calls for papers usually define the subject areas which are considered suitable for some conference or some special issue of a journal. This is obviously needed, but it may help also to name specifically what types of presentations are welcome: not just reports of advances in performance, but also anything which improves our understanding, corrects problematic views and points out new perspectives.

Committee members regularly have to think about possible invited speakers. I would warmly recommend to think not only about which research groups or companies are leading in terms of impressive performance advances. We should also think about who should be able to give us new insight and perspectives by explaining and discussing clearly certain relevant aspects. It can also be a good starting point to ask what open questions we would like to be addressed. For example, these could be questions about some physical mechanisms or about the suitability of certain measures, techniques and technologies.

I am quite sure that our conferences and journals will become even more useful if we think more carefully about such things. We could have more of the stimulating ideas – including some controversial ones –, more precise reasoning and judgment, and less of the boring routine stuff which does not really bring forward our discipline.