Easier Self-Starting Passive Mode Locking for Short Lasers

Posted on 2008-05-13. Permanent link: http://www.rp-photonics.com/spotlight_2008_05_13.html

Ref.: encyclopedia articles on self-starting mode locking, mode-locked lasers

When a passively mode-locked laser is turned on, it can take a while – hundreds or even many thousands of resonator round trips – until an ultrashort pulse is formed. In some cases, the initial pulse formation even requires some external intervention – the laser is not self-starting. An interesting question is how the length of the laser resonator should influence the ease of self-starting.

In a discussion with me, a well-known expert in the field once expressed the following thoughts. The longer the laser resonator, the larger will the ratio of peak power to average power during ultrashort pulse operation be, assuming that the pulse duration achieved is not strongly dependent on the resonator length. Therefore, a passively mode-locked laser with a long resonator has a stronger "incentive" for being in the mode-locked state, and should thus exhibit easier self-starting than a short laser.

However, practical experience tells us the opposite. For example, Kerr lens mode-locked titanium-sapphire lasers usually have a resonator length of the order of 1 m or more, and often are not reliably self-starting, while some miniature Ti:sapphire lasers, also Kerr lens mode-locked, start quite easily. Also, in the very few cases where I saw a SESAM mode-locked laser with non-reliable self-starting, this always was a rather long one. Why is this?

The issue can be understood by considering the degree of saturation of the saturable absorber. The laser design must be made so that a reasonable degree of saturation is achieved during normal mode-locked operation. For a long-resonator laser, however, this means that the absorber saturation in the start-up phase is very weak, just because the peak power is still so far below the final peak power. Therefore, the absorber does very little to start the mode locking, and the tiniest disturbing effect (e.g. resulting from weak parasitic reflections) may prevent the pulse build-up. If one would design a laser so that it has any significant absorber saturation in the start-up phase, the absorber would be totally over-saturated during normal operation, and thus not work well: it could e.g. exhibit instabilities related to multiple circulating pulses, or at least produce longer pulses than necessary.

Finally, concerning "incentives": a laser is not cute enough to anticipate that it could have lower resonator losses if it would produce shorter pulses. Therefore, such an incentive cannot work.

Length of a Photon

Posted on 2008-05-05. Permanent link: http://www.rp-photonics.com/spotlight_2008_05_05.html

Ref.: encyclopedia article on photons

A question which is frequently brought up by lay persons, but sometimes also by journalists reporting about some scientific experiments, concerns the length (and possibly also the transverse extent) of a photon.

The trouble with that question is essentially that the photon is a theoretical construction which does not have any straightforward connection either with an entity of physical reality or with anything simple which we can imagine. Some people are so much disturbed by this problem that they even consider the notion of photons and the corresponding scientific theories as totally flawed. Others adhere to more or less mechanistic models of photons and feel free to equip those with some details which actually do not occur in any of the common scientific theories. The latter approach can lead to questions such as the one concerning the length of a photon. If a photon were known to be something like a hard particle, or alternatively perhaps a wavepacket, some kind of length could easily be defined. According to quantum theory, however, a photon is neither simply a particle nor simply a wave; instead, it has properties both of particles and waves, or more precisely, the phenomenon of light exhibits both features of particles and waves.

In this situation, it doesn't even make sense to ask about the length of a photon. If answers are given anyway, confusion is the natural consequence. Some people argue that a photon cannot be larger than the area which is filled by light, and this limits e.g. the transverse extent of photons in laser beams. Others consider the transfer of one photon energy to an atom, and conclude that this energy must be much more concentrated. Another approach is setting a lower limit to the extent, essentially by considering the minimum pulse duration of light with a certain optical bandwidth, and multiplying this with the velocity of light in order to convert it into a length.

Obviously, all these thoughts are based on particular physical models of reality, not on observations. The manifold of mutually contradicting results just reflects the manifold of more or less suitable physical models and more or less appropriate interpretations of those. In other words, there is no comprehensive model of a photon of a kind which makes that question sensible. At most, it can make sense to ask about the length in one particular sense, but not about the length of a photon.

By the way, the encountered problem is not specific to photons. The same occurs e.g. with electrons. In some sense, an electron can be considered as a point-like particle, but we also know about the electron's wave properties and in fact use wave functions which can be as extended as a whole atom or even a whole crystal. This leads to another hint for those denying the existence of photons (or more precisely, the validity of any photon concept) based on such problems: if you decide for that path, then you should do the same with electrons, protons, neutrons, etc.

Different Kinds of Polarization

Posted on 2008-04-28. Permanent link: http://www.rp-photonics.com/spotlight_2008_04_28.html

Ref.: encyclopedia articles on polarization of laser emission, polarization waves, nonlinear polarization

Did you know that the term "polarization", as used in photonics, can have entirely different meanings?

The more common meaning refers to the spatial direction in which the electric field e.g. of a laser beam is oriented. Laser beams are often linearly polarized, i.e., there is one direction perpendicular to the beam axis in which the electric field oscillates, while the magnetic field oscillates in a direction which is perpendicular to both the beam axis and the electric field.

An entirely different thing is the polarization of a transparent medium through which light propagates. The electric field of a light beam generates an electric polarization, and the magnetic field a magnetic polarization. The latter is usually very weak, since transparent media are normally either paramagnetic or diamagnetic, not ferromagnetic. In an isotropic medium, the electric polarization has the same direction as the electric field of the propagating light; in anisotropic media, these directions can differ. In any case, the propagating electric wave is then accompanied by a polarization wave in the medium, traveling with the same phase velocity.

Particularly in the context of nonlinear frequency conversion, both types of polarization come together. The polarization of the input beam(s) determine the direction of the nonlinear polarization. The resulting nonlinear polarization wave(s) then radiate light at new optical frequencies. Of course, the polarization state of that light is determined by the direction of the nonlinear polarization of the medium.

Abused Photonics Terms: Coherence

Posted on 2008-04-22. Permanent link: http://www.rp-photonics.com/spotlight_2008_04_22.html

Ref.: encyclopedia articles on coherence, coherence length and coherence time; spotlight articles of 2008-02-22 (Launching Light from a Bulb into a Single-Mode Fiber), 2007-06-24 (The Plague of a Narrow Emission Linewidth), 2006-09-22 (Coherence Length of Ultrashort Pulses)

The concept of coherence is sufficiently complex to allow for significant confusion, at least when the corresponding terms are used in a vague way. A very common problem is the distinction between temporal coherence and spatial coherence. It happens quite frequently that authors celebrate the notable feature of laser beams (or other light beams) to be coherent, without telling which kind of coherence they mean. Obviously, this doesn't convey a lot of information. After all, there are optical sources with high spatial coherence, but low temporal coherence (see e.g. the articles on supercontinuum generation or white light sources), and other sources where the opposite holds.

In the context of trains of ultrashort pulses, the temporal coherence cannot be called either high or low. As discussed in the Spotlight article of 2006-09-22, the coherence function exhibits a fast decay but also "revivals" for rather long delay times. This shows that coherence cannot be quantified just with one number.

The (ab)use of the term "coherence length" in the context of nonlinear parametric interactions is particularly problematic. Here, a deterministic rather than random mismatch of the optical phases of two beams is interpreted like a loss of coherence. If we would apply that idea to a quasi-monochromatic laser beam, two points on the beam axis with a distance of only half a wavelength would be considered to see mutually incoherent light – which is of course nonsense. It would be clearly better to diagnose coherence whenever two oscillating fields exhibit a predictable phase relationship. Therefore, the mentioned use of the term "coherence length" should actually be called an abuse. I think the only argument against this is that it is frequently done.

Abused Photonics Terms: Modes

Posted on 2008-04-15. Permanent link: http://www.rp-photonics.com/spotlight_2008_04_15.html

Ref.: encyclopedia articles on modes, mode cleaners, frequency combs

One of the most often abused terms in photonics is that of modes. Sentences such as the two following ones are sometimes heard:

• "The mode coming out of this laser looks somewhat distorted, doesn't it?"
• "Let's try to fix this with a mode cleaner."

Precisely, however, a mode will never come out of a laser, and it also cannot be cleaned. After all, a mode is a concept of thinking, not a physical entity. What is meant in the above sentences is actually a laser beam, the intensity and/or phase profile of which has been distorted, and may be "cleaned up".

Perhaps more importantly, we can clean up our use of language. Some people find this pedantic, but who would seriously claim that the meaning of words is not important in science?

In fact, the trouble with such abuse of scientific terms is often that the actual meaning gets lost – in our concrete case, the concept of modes. Essentially, modes are self-consistent field configurations. In the case of resonator modes, these are self-consistent in the sense that they reproduce themselves after a full resonator round trip, disregarding some possible change of total optical power. In the case of free space (or some other optically homogeneous medium), modes preserve their change during propagation; in that case, some widening or contraction of the intensity distribution is allowed, if it is only a rescaling.

Another popular way to abuse the term:

• "The output of a mode-locked laser consists of exactly equidistant modes."

Again, the output is a beam, not one or several modes. A partly improved version would be:

• "The optical spectrum of the output of a mode-locked laser consists of exactly equidistant modes."

This is better, but still incorrect and misleading. The spectral properties of the laser output are strongly influenced, but not fully determined by the properties of the modes of the laser resonator. The optical spectrum of the laser output does contain exactly equidistant lines, while the optical frequencies of the resonator modes are not exactly equidistant due to chromatic dispersion. This shows very clearly that confusing the lines in the spectrum with the modes is not just sloppy language, but rather misrepresents what is physically happening: There is some kind of mode locker (→ mode locking) which forces the laser to emit on frequencies which somewhat deviate from the mode frequencies. This doesn't work well if these deviations are strong. In that case, the optical bandwidth and thus the number of lines in the spectrum is relatively small.

P.S. Readers are welcome to suggest the discussion of other abused terms in photonics.