Mode locking
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Mode locking is a technique in
Laser cavity modes
Although laser light is perhaps the purest form of light, it is not of a single, pure frequency or wavelength. All lasers produce light over some natural bandwidth or range of frequencies. A laser's bandwidth of operation is determined primarily by the gain medium from which the laser is constructed, and the range of frequencies over which a laser may operate is known as the gain bandwidth. For example, a typical helium–neon laser has a gain bandwidth of about 1.5 GHz (a wavelength range of about 0.002 nm at a central wavelength of 633 nm), whereas a titanium-doped sapphire (Ti:sapphire) solid-state laser has a bandwidth of about 128 THz (a 300 nm wavelength range centered at 800 nm).
The second factor to determine a laser's emission frequencies is the
In practice, L is usually much greater than λ, so the relevant values of q are large (around 105 to 106). Of more interest is the frequency separation between any two adjacent modes q and q + 1; this is given (for an empty linear resonator of length L) by Δν:
where c is the speed of light (≈ 3×108 m/s).
Using the above equation, a small laser with a mirror separation of 30 cm has a frequency separation between longitudinal modes of 0.5 GHz. Thus for the two lasers referenced above, with a 30 cm cavity, the 1.5 GHz bandwidth of the HeNe laser would support up to 3 longitudinal modes, whereas the 128 THz bandwidth of the Ti:sapphire laser could support approximately 250,000 modes. When more than one longitudinal mode is excited, the laser is said to be in "multi-mode" operation. When only one longitudinal mode is excited, the laser is said to be in "single-mode" operation.
Each individual longitudinal mode has some bandwidth or narrow range of frequencies over which it operates, but typically this bandwidth, determined by the Q factor of the cavity (see Fabry–Pérot interferometer), is much smaller than the intermode frequency separation.
Mode-locking theory
In a simple laser, each of these modes oscillates independently, with no fixed relationship between each other, in essence like a set of independent lasers, all emitting light at slightly different frequencies. The individual phase of the light waves in each mode is not fixed and may vary randomly due to such things as thermal changes in materials of the laser. In lasers with only a few oscillating modes, interference between the modes can cause beating effects in the laser output, leading to fluctuations in intensity; in lasers with many thousands of modes, these interference effects tend to average to a near-constant output intensity.
If instead of oscillating independently, each mode operates with a fixed phase between it and the other modes, the laser output behaves quite differently. Instead of a random or constant output intensity, the modes of the laser will periodically all constructively interfere with one another, producing an intense burst or pulse of light. Such a laser is said to be "mode-locked" or "phase-locked". These pulses occur separated in time by τ = 2L/c, where τ is the time taken for the light to make exactly one round trip of the laser cavity. This time corresponds to a frequency exactly equal to the mode spacing of the laser, Δν = 1/τ.
The duration of each pulse of light is determined by the number of modes oscillating in phase (in a real laser, it is not necessarily true that all of the laser's modes are phase-locked). If there are N modes locked with a frequency separation Δν, the overall mode-locked bandwidth is NΔν, and the wider this bandwidth, the shorter the pulse duration from the laser. In practice, the actual pulse duration is determined by the shape of each pulse, which is in turn determined by the exact amplitude and phase relationship of each longitudinal mode. For example, for a laser producing pulses with a Gaussian temporal shape, the minimum possible pulse duration Δt is given by
The value 0.441 is known as the "
Using this equation, the minimum pulse duration can be calculated consistent with the measured laser spectral width. For the HeNe laser with a 1.5 GHz bandwidth, the shortest Gaussian pulse consistent with this spectral width would be around 300 picoseconds; for the 128 THz bandwidth Ti:sapphire laser, this spectral width would correspond to a pulse of only 3.4 femtoseconds duration. These values represent the shortest possible Gaussian pulses consistent with the laser's bandwidth; in a real mode-locked laser, the actual pulse duration depends on many other factors, such as the actual pulse shape and the overall dispersion of the cavity.
Subsequent modulation could, in principle, shorten the pulse width of such a laser further; however, the measured spectral width would then be correspondingly increased.
Principle of phase and mode locking.
There are many ways to lock frequency but the basic principle is the same which is based on the feedback loop of the laser system. The starting point of the feedback loop is the quantity that must be stabilized (frequency or phase). To check whether frequency changes with time or not, a reference is needed. A common way to measure laser frequency is to link it with the geometrical property of an optical cavity. The
∆νC=∆νFSR/ℱ
Where ∆νFSR=C/2L is frequency difference between adjacent resonances (i.e., the free spectral range) and ℱ is finesse, ℱ = πR½/(1-R). R is the reflectivity of mirrors. As it’s clear from the equation, to obtain a small cavity line width, mirrors must have higher reflectivity. Therefore to reduce the line width of the laser to the lowest extent, a high finesse cavity is required.
Mode-locking methods
Methods for producing mode locking in a laser may be classified as either "active" or "passive". Active methods typically involve using an external signal to induce a modulation of the intracavity light. Passive methods do not use an external signal, but rely on placing some element into the laser cavity which causes self-modulation of the light.
Active mode locking
The most common active mode-locking technique places a standing wave electro-optic modulator into the laser cavity. When driven with an electrical signal, this produces a sinusoidal amplitude modulation of the light in the cavity. Considering this in the frequency domain, if a mode has optical frequency ν and is amplitude-modulated at a frequency f, the resulting signal has sidebands at optical frequencies ν − f and ν + f. If the modulator is driven at the same frequency as the cavity mode spacing Δν, then these sidebands correspond to the two cavity modes adjacent to the original mode. Since the sidebands are driven in-phase, the central mode and the adjacent modes will be phase-locked together. Further operation of the modulator on the sidebands produces phase locking of the ν − 2f and ν + 2f modes, and so on until all modes in the gain bandwidth are locked. As said above, typical lasers are multi-mode and not seeded by a root mode. So multiple modes need to work out which phase to use. In a passive cavity with this locking applied, there is no way to dump the entropy given by the original independent phases. This locking is better described as a coupling, leading to a complicated behavior and not clean pulses. The coupling is only dissipative because of the dissipative nature of the amplitude modulation. Otherwise, the phase modulation would not work.
This process can also be considered in the time domain. The amplitude modulator acts as a weak "shutter" to the light bouncing between the mirrors of the cavity, attenuating the light when it is "closed" and letting it through when it is "open". If the modulation rate f is synchronised to the cavity round-trip time τ, then a single pulse of light will bounce back and forth in the cavity. The actual strength of the modulation does not have to be large; a modulator that attenuates 1% of the light when "closed" will mode-lock a laser, since the same part of the light is repeatedly attenuated as it traverses the cavity.
Related to this amplitude modulation (AM), active mode locking is
The third method of active mode locking is synchronous mode locking, or synchronous pumping. In this, the pump source (energy source) for the laser is itself modulated, effectively turning the laser on and off to produce pulses. Typically, the pump source is itself another mode-locked laser. This technique requires accurately matching the cavity lengths of the pump laser and the driven laser.
Passive mode locking
Passive mode-locking techniques are those that do not require a signal external to the laser (such as the driving signal of a modulator) to produce pulses. Rather, they use the light in the cavity to cause a change in some intracavity element, which will then itself produce a change in the intracavity light. A commonly used device to achieve this is a
A saturable absorber is an optical device that exhibits an intensity-dependent transmission, meaning that the device behaves differently depending on the intensity of the light passing through it. For passive mode locking, ideally a saturable absorber selectively absorbs low-intensity light, but transmits light of sufficiently high intensity. When placed in a laser cavity, a saturable absorber attenuates low-intensity constant-wave light (pulse wings). However, because of the somewhat random intensity fluctuations experienced by an un-mode-locked laser, any random, intense spike is transmitted preferentially by the saturable absorber. As the light in the cavity oscillates, this process repeats, leading to the selective amplification of the high-intensity spikes and the absorption of the low-intensity light. After many round trips, this leads to a train of pulses and mode locking of the laser.
Considering this in the frequency domain, if a mode has optical frequency ν and is amplitude-modulated at a frequency nf, the resulting signal has sidebands at optical frequencies ν − nf and ν + nf and enables much stronger mode locking for shorter pulses and more stability than active mode locking, but has startup problems.
Saturable absorbers are commonly liquid
There are also passive mode-locking schemes that do not rely on materials that directly display an intensity-dependent absorption. In these methods,
Hybrid modelocking
In some semiconductor lasers a combination of the two above techniques can be used. Using a laser with a saturable absorber and modulating the electrical injection at the same frequency the laser is locked at, the laser can be stabilized by the electrical injection. This has the advantage of stabilizing the phase noise of the laser and can reduce the timing jitter of the pulses from the laser.
Mode locking by residual cavity fields
Coherent phase-information transfer between subsequent laser pulses has also been observed from
Fourier-domain mode locking
Fourier-domain mode locking (FDML) is a laser mode-locking technique that creates a continuous-wave, wavelength-swept light output.[2] A main application for FDML lasers is optical coherence tomography.
Practical mode-locked lasers
In practice, a number of design considerations affect the performance of a mode-locked laser. The most important are the overall
The shortest directly produced optical pulses are generally produced by
Pulse durations less than approximately 100 fs are too short to be directly measured using
Applications
- Nuclear fusion (inertial confinement fusion).
- Nonlinear optics, such as parametric down-conversion, optical parametric oscillators, and generation of terahertz radiation.
- Optical data storage uses lasers, and the emerging technology of 3D optical data storage generally relies on nonlinear photochemistry. For this reason, many examples use mode-locked lasers, since they can offer a very high repetition rate of ultrashort pulses.
- Femtosecond laser nanomachining – the short pulses can be used to nanomachine in many types of materials.
- An example of pico- and femtosecond micromachining is drilling the silicon jet surface of inkjet printers.
- Two-photon microscopy.
- Corneal surgery (see refractive surgery). Femtosecond lasers can be used to create bubbles in the cornea. A line of bubbles can be used to create a cut in the cornea, replacing the microkeratome, e.g. for the creation of a flap in LASIK surgery (this is sometimes referred to as Intralasik or all-laser surgery). Bubbles can also be created in multiple layers so that a piece of corneal tissue between these layers can be removed (a procedure known as small incision lenticule extraction).
- A laser technique has been developed that renders the surface of metals deep black. A femtosecond laser pulse deforms the surface of the metal, forming
- Photonic sampling, using the high accuracy of lasers over electronic clocks to decrease the sampling error in electronic ADCs.
Locking mechanism of laser cavity
Error signal generation
The reason for generation to create error signals is to create an electronic signal which is proportional to the laser's deviation from a particular set frequency or phase which is called ‘Lock point’. If the laser frequency is large then the signal is positive, if frequency is very small then the signal is negative. The point where the signal is zero is called a lock point. Laser locking based on an error signal which is a function of frequency is called frequency locking and if the error signal is a function of phase deviation of laser then this locking is referred to as phase locking of laser. If the signal is created using an optical setup involving references like frequency references. Using the reference, the optical signal is directly converted in over frequencies which can be detected directly. The other way is to record the signal using a photodiode or camera and further change this signal electronically.
See also
- Disk laser
- Dissipative soliton
- Femtotechnology
- Fiber laser
- Frequency comb
- Laser construction
- Q-switching
- Saturable absorption
- Solid state laser
- Soliton
- Ultrafast optics
- Vector soliton
References
- ^ Mayer, B., et al. "Long-term mutual phase locking of picosecond pulse pairs generated by a semiconductor nanowire laser". Nature Communications 8 (2017): 15521.
- ^ R. Huber, M. Wojtkowski, J. G. Fujimoto, "Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography", Opt. Express 14, 3225–3237 (2006).
- ^ "Ultra-Intense Laser Blast Creates True 'Black Metal'". Retrieved 2007-11-21.
- .
Further reading
- Andrew M. Weiner (2009). Ultrafast Optics. Wiley. ISBN 978-0-471-41539-8.
- H. Zhang et al, “Induced solitons formed by cross polarization coupling in a birefringent cavity fiber laser”, Opt. Lett., 33, 2317–2319.(2008).
- D.Y. Tang et al, “Observation of high-order polarization-locked vector solitons in a fiber laser”, Physical Review Letters, 101, 153904 (2008).
- H. Zhang et al., "Coherent energy exchange between components of a vector soliton in fiber lasers", Optics Express, 16,12618–12623 (2008).
- H. Zhang et al, “Multi-wavelength dissipative soliton operation of an erbium-doped fiber laser”, Optics Express, Vol. 17, Issue 2, pp. 12692–12697
- L.M. Zhao et al, “Polarization rotation locking of vector solitons in a fiber ring laser”, Optics Express, 16,10053–10058 (2008).
- Qiaoliang Bao, Han Zhang, Yu Wang, Zhenhua Ni, Yongli Yan, Ze Xiang Shen, Kian Ping Loh, and Ding Yuan Tang, Advanced Functional Materials,"Atomic layer graphene as saturable absorber for ultrafast pulsed lasers "
- Zhang, H.; et al. (2010). "Graphene mode locked, wavelength-tunable, dissipative soliton fiber laser" (PDF). Applied Physics Letters. 96 (11): 111112. S2CID 119233725. Archived from the original(PDF) on July 16, 2011.