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.
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How to Store Light – and to Understand the Laser Principle
Posted on 2015-11-28 as a part of the Photonics Spotlight (available as e-mail newsletter!)
Permanent link: https://www.rp-photonics.com/spotlight_2015_11_28.html
With this article, I want to show you a nice way to understand the basic operation principles of lasers – either for your own pleasure or when you try to explain it to beginners.
We begin by asking a seemingly unrelated question: How can we store light? Could we put some amount of light into some suitable kind of bucket, with which we could carry it around and use it later on?
An essential problem with storing light is that it moves away so fast. A relatively straightforward idea is to confine the light with some mirrors, which prevents it from escaping. In the simplest case, we would just use two highly reflecting mirrors in parallel, so that a light beam can be captured between those:
Such an optical arrangement is called an optical resonator. Ideally, the light would be perfectly reflected by the mirrors and circulate there forever.
One can easily imagine a number of problems with that approach, which however we will solve step by step.
The Divergence Problem
The first concern is that during many round trips the circulating light beam would diverge more and more, i.e., develop a larger and larger beam diameter, so that eventually it reaches the edges of the mirrors, and part of the light gets lost.
There is a simple solution to that: just make one or both mirrors slightly curved, so that the circulating light beam is constantly refocused:
With the proper amount of refocusing, the natural tendency of the beam to diverge can be fully compensated.
You might think that it is difficult to obtain exactly the right amount of refocusing. However, within some limits you can just choose some mirror curvatures, and there will always be a so-called resonator mode fitting to the setup. (Actually, there are normally many such resonator modes, having different intensity profiles.)
Isn't the Alignment Overly Critical?
One might think that perfect alignment of the mirrors is a prerequisite for storing the light over longer times. This is not the case, however: if you slightly tilt one mirror, for example, there is a correspondingly shifted version of our light beam which can still stay on that position for a long time. You may even slightly change the alignment while the beam is in the resonator, and the beam will be able to adjust to the new mirror positions as long as the movements are sufficiently slow – which is easy to guarantee, given that light is much faster than you can move any solid parts. Only if you misalign the resonator too much, the beam will reach the edges of the mirrors, and this results in strong power losses.
Doesn't the Light Fade Away?
This is the most serious concern: in each round-trip, the light will lose some of its energy, since the mirrors can never be perfectly reflecting, and there might be further power losses e.g. by scattering in the air. This problem becomes quite severe due to the very high velocity of light. For example, if the spacing of the mirrors is 1.5 m, the round-trip time will be only 10 ns, so that the light beam makes 100 million round trips per second. So even if you use so-called supermirrors with an excellent reflectivity of 99.999999%, within one second you will lose most of the circulating light energy. If you use ordinary laser mirrors with a reflectivities of 99.9%, it will only take the order of 100 round trips to lose most of the energy – these will be completed within only a microsecond. If you make the resonator shorter, that fading away of the energy happens even faster. Using a very long resonator would help in principle, but is not very practical.
This problem can be solved with the following trick: between the mirrors, put some medium which can not only transmit the light, but also amplify its power. For the moment, just imagine that you have some magic kind of crystal, which could amplify the light power by 10% in a single pass. That would be sufficient to compensate losses of 10% on each mirror, if no other losses occur (e.g. during propagation in air).
Of course, the balance of optical gain (amplification factor) and losses is then quite delicate:
- If the gain of your amplifier a slightly too low, there will still be some net losses per round trip, and the light energy will soon be lost.
- If the gain is slightly too high, there will be a positive net gain per round trip, and as a result the circulating optical power will rise exponentially. Given the very small round-trip time, the optical power might reach enormously high levels within a short time.
Actually, there is no risk that you will be killed by a disastrous power level arising from that setup, since there is no amplifier which can achieve a certain gain for arbitrarily high input powers. Any amplifier will exhibit some kind of gain saturation, i.e., its gain will drop under such conditions. If the circulating optical power rises and rises, the gain will eventually drop to the level which is needed to just keep the circulating power constant. It should not take long to reach that steady state, again because the light circulates so fast.
It has not yet been explained how such a magic amplifying crystal could be obtained. I will discuss that in detail in the next posting of the Photonics Spotlight. For now, I just tell you that some amount of power is required to operate such an amplifier; after all, it constantly adds energy to the optical field. If it is a transparent crystal, which is not electrically conducting, the only reasonable way way to supply such power is to shine light on it – for example, from the side. You should then have something in the crystal which can absorb that pump light and utilize it to provide the required gain.
How to Get the Light In?
There is only one problem remaining: how can we initially get the light in? It is of course not realistic to think that you could take off one of the mirrors, shine some light in and then quickly enough put the mirror on again. Also, you cannot put an ordinary light source into the resonator without blocking the circulating light.
Fortunately, you actually don't need to do anything to solve that problem, because you already have a light source in the resonator! Just turn on your optical amplifier, and it will produce a tiny amount of light even when there is nothing yet to be amplified; that phenomenon is called fluorescence. Beginning with that very small amount of light, the amplifier will now quickly increase the power until the above explained steady state is reached.
How to Make This Device Useful?
We have now managed to find a way for storing light over long times – even though we constantly need to supply energy in order to compensate for the permanent losses. In this sense, it is like a not perfectly insulated storage tank for hot water, which you permanently need to heat in order to keep it hot.
In the current form, however, the device is not particularly useful: there is some light captured between the mirrors, but you cannot do much with it. For example, you cannot put some absorbing workpiece into your resonator in order to irradiate it, since that would simply switch off the device. The thing becomes much more useful with a small modification: instead of highly reflecting mirrors, use at least one which transmits a certain percentage of the circulating power – for example, 10% of it. If the other mirror is highly reflecting, you will have about 10% power loss for the circulating light per round trip – which can be compensated if the amplifier can provide that amount of gain. Through that partially reflecting mirror, you now obtain an output light beam which you can use.
The device which we have got has (unfortunately) been invented and named already by others: it is called a laser! In the following, we will discuss some of its basic properties.
Threshold and Slope Efficiency
In order to obtain a substantial output power, you want to use an output coupling mirror having a substantial transmission. Only, you should not overdo that, because the more transmission you have, the lower will be the reflectivity and the higher the round-trip loss of the resonator will be; if you couple out too much, the available amplifier gain will no longer be sufficient, and the device will not work.
If you work with a fixed mirror set and vary the amount of pump power supplied to the amplifier, you will get the following:
- Below a certain amount of pump power, which is called the laser threshold power, the gain is too low to compensate the losses. You will then obtain nearly no output at all – only a very weak amount of fluorescence light, much of which is emitted in all sorts of directions.
- Above the laser threshold, most of the emitted light is contained in the mentioned output beam, although a little power is still emitted in all directions. For higher pump powers, the output power often rises about linearly. The slope of that line is called the slope efficiency.
High Beam Quality
In many cases, it is possible to obtain laser emission in a single spatial mode of the laser resonator. This results in a high spatial coherence and a very high beam quality of the output beam: particularly if the beam radius at the laser output is not too small, its beam divergence is very small, so that the beam radius rises only slowly. However, not all lasers can be made to admit with a high beam quality; examples for that are high-power laser diodes and lamp-pumped high-power solid-state lasers.
Small Emission Bandwidth
In many cases, the emission bandwidth of a laser is very small, and the temporal coherence correspondingly high. This is because there is some wavelength dependence of the amplifier gain, and the laser will then operate only in a narrow range of wavelengths where the gain is highest. Lasing at other wavelengths is suppressed, even if these have an only slightly lower gain: the laser light saturates the gain so much that the net round-trip gain is exactly zero for the optimum wavelengths. Any other wavelengths will see a negative round-trip gain, so that such light would be quickly fading away.
By using quite sophisticated means, one can optimize lasers for obtaining even a much reduced commission bandwidth. In some cases bandwidth values below 1 Hz are achieved – which is very remarkable considering the mean emission frequency of hundreds of terahertz. Such high precision lasers are used in optical frequency metrology, e.g. for making the most precise laser clocks.
Some other lasers are optimized for broadband emission. For example, this often happens in the context of mode-locked femtosecond lasers; see our article on mode-locked lasers. Sometimes, one further broadens the emission bandwidth with external means; see the article on supercontinuum generation.
If the laser gain medium is pumped continuously, the laser output will also usually be continuous. However, one can apply additional tricks for obtaining short or even ultrashort laser pulses. For example, one can employ the method of Q switching: one suppresses lasing for some time by somehow causing a strong additional resonator loss and then suddenly switches that loss to a much lower level. Laser action will then begin and lead to an output pulse which often has a pulse duration of only a couple of nanoseconds, a substantial amount of pulse energy and a correspondingly high peak power – sometimes many gigawatts.
Another method is mode locking, where one has an ultrashort circulating pulse in the laser resonator and obtains one output pulse for every resonator round trip – for example once every 10 nanoseconds. The pulse duration can then easily be a few picoseconds or under best conditions down to roughly five femtoseconds – an enormously short time.
Explaining the Amplifier
I hope you have enjoyed these explanations and will make others aware of them. In the next Spotlight article, I will explain how the optical amplifier works, which is needed for any laser.
The Linewidth of Single-frequency Lasers
Posted on 2015-10-17 as a part of the Photonics Spotlight (available as e-mail newsletter!)
Permanent link: https://www.rp-photonics.com/spotlight_2015_10_17.html
Single-frequency lasers are lasers operating on a single resonator mode. This does not mean that the electric field oscillates according to a perfect sinusoidal wave with absolutely constant instantaneous frequency; there is always some phase noise which leads to a finite optical linewidth.
In this article, I discuss some facts in this context which are important but often misunderstood.
What Phenomenon Determines the Laser Linewidth?
If a laser would not be subject to any technical noise – i.e., to noise sources which could in principle be eliminated –, that would still be some level of phase noise resulting from quantum noise. That leads to a quantum-limited linewidth, which I discuss further below. That linewidth can be extremely small – for solid-state lasers easily far below 1 Hz. However, it is often very difficult to push technical noise sources so far down that the quantum-limited linewidth can be observed. In particular, one is often dealing with acoustical and thermal vibrations.
Semiconductor lasers (mostly laser diodes) usually have a very compact and robust setup, which is not very sensitive to technical noise influences. However, they tend to have a fairly high quantum-limited noise. This is partially due to their substantial round-trip losses in combination with a very short resonator (see below), and the noise level is substantially increased further by a coupling of amplitude to phase noise due to the dependence of the refractive index on the carrier density in the semiconductor. That coupling is quantified with the so-called linewidth enhancement factor α.
Of course, when minimizing the linewidth of a laser one should know which effects are really the limiting ones, so that one can concentrate on those measures which have a chance to improve the situation.
The Quantum Limit
The quantum-limited linewidth is given by the famous Schawlow-Townes equation. From that, one can learn a couple of interesting relations:
- If we assume for simplicity that the round-trip loss of the resonator is caused only by the output coupler transmission, the linewidth is proportional to the square of the optical power loss per resonator round trip. This is essentially because both the optical losses and the laser gain required for compensating these losses introduce quantum noise, which affects the optical phase of the circulating electromagnetic wave.
- Also, the linewidth is inversely proportional to the square of the round-trip time of the resonator. The shorter the resonator, the more often per second the mentioned quantum noise can contaminate the circulating wave. Therefore, one may try to make the laser resonator as long as possible. That, however, leads to a setup which is tentatively more subject to technical noise. Also, it can be more difficult to obtain stable single-frequency operation.
- The linewidth is also inversely proportional to the optical power; a strong circulating field is less strongly affected (in terms of phase changes) than a week field.
Effect of Subsequent Amplification
Many believe that the linewidth must be increased if one amplifies the output of a single-frequency laser in some kind of optical amplifier, e.g. a fiber amplifier. After all, such an amplifier usually exhibits much more gain than used in the laser, so that one may expect to get much more quantum noise introduced there. This is wrong, however; in fact, the optical linewidth is usually not at all increased in an optical amplifier.
In order to understand this, one should recall that a finite linewidth is related to an unbounded random walk of the optical phase: as more and more time passes, phase errors in a laser resonator can grow without any limit. (In simple cases, the standard deviation of the phase error grows in proportion to the square root of the passed time.) An optical amplifier will now contribute phase errors, but the added phase error will stay within certain limits: the optical field passes the amplifier only once (or some limited number of times), the temperature of the device always stays within certain limits, etc. Therefore, the long-term drift of the optical phase is not increased by the amplifier. The optical spectrum consists of a narrow line sitting on some noise background; usually, the amplifier somewhat raises that noise background while leaving the full width at half maximum (measured at a much higher level) more or less unchanged.
It is instructive to consider the amplification of the signal with zero linewidth. That is not a purely theoretical imagination; the linewidth of an oscillator can be exactly zero if it is locked to some frequency reference and the phase noise is understood to be relative to that reference. (See also the Spotlight article of 2008-07-26.) The optical spectrum is then a delta peak (see the Dirac delta function) sitting on some noise background. The effect of a noisy amplifier is then to raise the level of the mentioned noise background, but the Delta peak is preserved, i.e., the width of that peak remains exactly zero.
Q-switched Lasers: Nd:YVO4 better suited than Nd:YAG for High Pulse Repetition Rates
Posted on 2015-09-24 as a part of the Photonics Spotlight (available as e-mail newsletter!)
Permanent link: https://www.rp-photonics.com/spotlight_2015_09_24.html
It is quite well known than when building a Q-switched laser for operation with a high pulse repetition rate (e.g. 100 kHz), an Nd:YVO4 laser crystal is better suited than a Nd:YAG crystal. What is not so well known, however, is the reason for that.
Many believe that the shorter upper-state lifetime of Nd:YVO4 is the reason. This is wrong, however. The perhaps most compelling proof of that statement is obtained by considering a hypothetical laser crystal which has the same properties as Nd:YAG except that its upper-state lifetime is strongly reduced (e.g. by some quenching process); one could demonstrate with a numerical model, for example, that this would not work better (even worse!) than Nd:YAG.
On the other hand, a hypothetical laser crystal with the properties of Nd:YVO4, except for a long upper-state lifetime as for Nd:YAG, would work well – only that such a combination is physically not possible, since the upper-state lifetime cannot be longer than the radiative lifetime: the lifetime is limited by the population decay through spontaneous emission.
The real problem with Nd:YAG for operation at high pulse repetition rates is totally different and not related to the upper-state lifetime. In this regime, there is only very limited time for pumping between the emission of two pulses. Therefore, one can deposit only a quite limited amount of energy in the laser crystal, and consequently one obtains a rather small laser gain. This leads to a slow rise of optical power after opening the Q switch. The resulting pulse than exhibits a rather long pulse duration and correspondingly low peak power; it can even happen that the available time is not sufficient for generating the pulse, so that only e.g. every second pulse is emitted: the laser operates with a lower pulse repetition rate than desired. One may also obtain an unstable regime.
The described problem is much reduced when using Nd:YVO4, because that gain medium has a much higher gain efficiency: it delivers more decibels of gain per millijoule of stored energy. The high gain efficiency results from a very high emission cross section (roughly 4 times higher than for Nd:YVO4).
The above-described misconception may be related to the following aspects:
- It is true that a short upper-state lifetime can be a problem for operation with low repetition rates (limited energy storage). This does not imply, however, that a long upper-state lifetime is bad for high repetition rates.
- Gain media with high emission cross sections tend to have short upper-state lifetimes. However, the short upper-state lifetime is then just another consequence, rather than the reason for the better laser performance.
One could also increase the gain efficiency by working with a reduced mode area in the laser crystal. However, there are limits to this approach, set e.g. by the limited pump beam quality (particularly for high-power lasers) or by thermal effects.
For designing such lasers, one should definitely have a good qualitative and quantitative understanding of the laser dynamics, because this is essential for finding appropriate parameter values (e.g. concerning the chosen laser crystal, the mode size in the crystal, the resonator length, etc.). For Q-switched bulk lasers (not for fiber lasers), it is often sufficient (at least for rough estimates) to use some relatively simple equations, which might even be solved on a pocket calculator. More sophisticated numerical models are required if certain additional effects are of interest, such as gain guiding (which might strongly affect the obtained beam diameter) or a limited speed of the Q-switch.
2015-08-08: Gain Saturation with Pulses
2015-02-05: Attenuating Laser Beams – not That Easy
2014-10-03: Fiber Optics Tutorials
2014-07-28: How to Define the Mode Radius of a Fiber?
2014-05-16: 10-Year Anniversary of RP Photonics
2014-01-17: Mediation in Disputes on Laser Technology
2013-12-13: Avoiding Trouble with Laser Specifications
2013-11-12: Beam Quality Limit for Multimode Fibers
2013-08-26: Frequency Doubling and the Reverse Process
2013-06-13: Two New Photonics Newsletters
2012-08-06: The New RP Photonics Buyer's Guide
2012-03-12: New Raman Lasers
2012-03-03: Conflicting Definitions of s and p Polarization
2011-12-23: Kerr-lens Mode-locked Thin-disk Laser
2011-06-10: Are Compact Resonators More Stable?
2010-07-12: Laser Development: Get an Expert Early on!
2010-06-09: Poor Man's Isolator
2010-04-26: Resolution and Accuracy of Measurements
2010-04-08: Creating a Top-hat Laser Beam Focus
2010-03-22: All-in-one Concepts versus Modular Concepts
2010-03-09: Nonlinearities in Fiber Amplifier Modeling
2010-01-29: Far From Maturity: The Photonics Industry
2010-01-22: Pumping Fiber Lasers with Fiber Lasers
2010-01-11: Beams of Laser Pointers: Visible in Air?
2009-12-31: Tilt Tuning of Etalons
2009-12-13: Johnson–Nyquist Noise in Photodiode Circuits
2009-11-18: Articles and a Quiz on Photonics Issues
2009-11-13: Photodetection: Optical and Electrical Powers
2009-11-03: Coherent Light from a Bulb?
2009-10-03: Peak Intensity of Gaussian Beam
2009-09-27: Lasers with Short Upper-state Lifetime
2009-09-19: Are Laser Resonators Power Scalable?
2009-09-01: Fresnel Reflections from Double Interfaces
2009-08-14: Progress on Green Laser Diodes
2009-08-12: What is an Optical Transistor?
2009-07-29: No Beat Note for Orthogonal Modes
2009-07-21: Signal-to-Noise Ratio and Measurement Bandwidth
2009-07-09: Gain-guiding Index-antiguiding Fibers
2009-06-29: Doing Things Properly: It's the Economy, Stupid!
2009-06-23: Coherence – a Black-or-White Issue?
2009-06-08: Prizes of the European Physical Society
2009-06-02: 5 Years of RP Photonics Consulting
2009-05-13: The Minimum Time–Bandwidth Product
2009-04-28: SPIE Field Guides
2009-04-05: Stability of Resonators – an Ambiguous Term
2009-03-02: User Interfaces for Simulation Software
2009-01-12: Chaotic Lasing Generates Random Numbers
2009-01-05: Extremely Long Mode-locked Fiber Laser
2008-12-16: Why Fiber Amplifiers, not Fiber Lasers?
2008-11-25: The Gouy Phase Shift Speeds up Light
2008-11-08: Validating Numerical Simulation Software
2008-09-24: Decoupling Pulse Duration and Pulse Energy
2008-09-10: Unpolarized Single-Frequency Output
2008-07-26: Beat Signals with Zero Linewidth
2008-07-02: Stronger Focusing Avoids SESAM Damage
2008-06-20: All-in-One Ultrafast Laser Systems
2008-06-06: Fiber Lasers Which Are No Fiber Lasers
2008-05-25: Einstein and the Laser
2008-05-05: Length of a Photon
2008-04-28: Different Kinds of Polarization
2008-04-22: Abused Photonics Terms: Coherence
2008-04-15: Abused Photonics Terms: Modes
2008-03-10: Automatic Phase Matching
2008-03-04: What is a “High” Laser Beam Quality?
2008-02-14: How Laser Development Can Go Wrong
2008-02-03: Quantifying the Chirp of Ultrashort Pulses
2008-01-27: Beam Quality in Second-Harmonic Generation
2008-01-14: Frequency Doubling: Long Pulses Cause Trouble
2007-12-18: The Role of Laser Safety Goggles
2007-12-03: New Paper on Power Scaling of Lasers
2007-11-26: Solving Laser Problems Step by Step
2007-11-10: Retirement of Prof. David C. Hanna
2007-11-02: Ultrafast Laser Kills Viruses
2007-10-31: Thermal Equilibrium in Laser Crystals
2007-10-25: The Gain Bandwidth of Laser Crystals and Glasses
2007-10-17: Why the Second-Harmonic Beam is Smaller
2007-10-11: Understanding Fourier Spectra
2007-09-21: Optimum Crystal Length for Frequency Doubling
2007-09-07: Power Scaling in Downward Direction
2007-08-27: Distant Healing of Lasers
2007-08-23: An OPO Without Resonator Mirrors
2007-08-15: Light = Electromagnetic Waves?
2007-07-06: Promoting Dangerous Practices in Laser Labs
2007-07-01: Nonsensical Regulations Undermine Laser Safety
2007-06-24: The Plague of a Narrow Emission Linewidth
2007-06-11: Beam Quality Measurements Can Easily Go Wrong
2007-06-01: Characterize Your Pump Beam!
2007-05-19: Why Strong Birefringence in Fibers Helps
2007-04-16: Questions and Answers on Shot Noise
2007-03-23: Explaining the Nature of Photons to Lay Persons
2007-03-11: Divided-Pulse Amplification
2007-03-09: The Trouble with Crystal and Coating Damage
2007-02-26: No Laser, no Result?
2007-02-22: Lossy Laser Cavities
2007-02-16: The Science of Biophotons
2007-02-09: Papers Reporting Yet Another Laser Crystal
2007-02-04: Continuing Struggle for Larger Fiber Mode Areas
2007-01-27: Noise Figure of Amplifiers
2007-01-21: Operation Far Above Threshold
2007-01-15: Origins of Heating in Laser Crystals
2007-01-09: The Myth of Fiber-Optic Polar Bears
2006-12-31: Peak Position of an Optical Spectrum
2006-12-16: Dangerous Green Laser Pointers
2006-12-09: The Laser Industry - High Tech or Low Tech?
2006-12-03: Diffraction in Optical Fibers
2006-11-28: The Role of Diffraction in Optical Resonators
2006-11-21: The Resonator Mystery
2006-11-16: Laser Models - not Always Useful
2006-11-02: Reflection Spectrum of Tilted Dielectric Mirrors
2006-10-22: Lasers Attract Dust to Cavity Mirrors
2006-10-01: Stability Zones of Laser Resonators
2006-09-22: Coherence Length of Ultrashort Pulses
2006-09-16: Q-switched Lasers: YAG versus Vanadate
2006-09-01: Test Yourself with the Photonics Quiz
2006-08-20: Lower Noise from Longer Lasers
2006-08-12: Understanding Quasi-Three-Level Lasers
2006-08-10: Single-Mode Fibers with Large Mode Areas
2006-08-01: Lasers Disturbed by Vacuum?
2006-07-24: Beam Distortions in Laser Cavities
2006-07-23: Single-Atom Lasers
2006-07-22: No Magnetic Field on the Axis of a Coil?
2006-07-16: Spontaneous Emission and Amplifier Noise
2006-07-14: Lasers Like it Cool
2006-07-10: Strength of Thermal Lensing Effects
2006-07-01: Characterizing a Cavity with a Frequency Comb
2006-07-01: With Wavelength Combs to Picometer Resolution