Modelocking
Encyclopedia
Mode-locking is a technique in optics
by which a laser
can be made to produce pulses of light
of extremely short duration, on the order of picoseconds (10−12 s) or femtoseconds (10−15 s).
The basis of the technique is to induce a fixed phase
relationship between the mode
s of the laser's resonant cavity. The laser is then said to be phase-locked or mode-locked. Interference between these modes causes the laser light to be produced as a train of pulses. Depending on the properties of the laser, these pulses may be of extremely brief duration, as short as a few femtoseconds.
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
that the laser is constructed from, and the range of frequencies that a laser may operate over is known as the gain bandwidth. For example, a typical helium
-neon
(HeNe
) gas laser has a gain bandwidth of approximately 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 centred around 800 nm).
The second factor that determines a laser's emission frequencies is the optical cavity or resonant cavity of the laser. In the simplest case, this consists of two plane (flat) mirror
s facing each other, surrounding the gain medium of the laser (this arrangement is known as a Fabry–Pérot cavity). Since light is a wave
, when bouncing between the mirrors of the cavity the light will constructively and destructively interfere with itself, leading to the formation of standing wave
s or modes
between the mirrors.
These standing waves form a discrete set of frequencies, known as the longitudinal mode
s of the cavity. These modes are the only frequencies of light which are self-regenerating and allowed to oscillate by the resonant cavity; all other frequencies of light are suppressed by destructive interference. For a simple plane-mirror cavity, the allowed modes are those for which the separation distance of the mirrors L is an exact multiple of half the wavelength of the light λ, such that , where q is an integer known as the mode order.
In practice, the separation distance of the mirrors L is usually much greater than the wavelength of light 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−1).
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 itself some bandwidth or narrow range of frequencies over which it operates, but typically this bandwidth, determined by the Q factor (see Inductor
) of the cavity (see Fabry–Pérot interferometer), is much smaller than the inter-mode frequency separation.
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 random fluctuations in intensity; in lasers with many thousands of modes, these interference effects tend to average to a near-constant output intensity, and the laser operation is known as a c.w. or continuous wave.
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 , 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, .
The duration of each pulse of light is determined by the number of modes which are oscillating in phase (in a real laser, it is not necessarily true that all of the laser's modes will be 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 time-bandwidth product of the pulse, and varies depending on the pulse shape. For ultrashort pulse lasers, a hyperbolic-secant
-squared (sech2) pulse shape is often assumed, giving a time-bandwidth product of 0.315.
Using this equation, we can calculate the minimum pulse duration consistent with the measured laser spectral width. For the HeNe laser with a 1.5 GHz spectral width, 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 be only 3.4 femtoseconds. These values represent the shortest possible Gaussian pulses consistent with the laser's linewidth; 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.
It should be noted that subsequent modulation could in principle shorten the pulse width of such a laser further, however the measured spectral width would then be correspondingly increased.
of the intra-cavity 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.
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 sideband
s at optical frequencies and . 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 and 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 frequency modulation
(FM) mode-locking, which uses a modulator device based on the electro-optic effect
. This device, when placed in a laser cavity and driven with an electrical signal, induces a small, sinusoidally varying frequency shift in the light passing through it. If the frequency of modulation is matched to the round-trip time of the cavity, then some light in the cavity sees repeated up-shifts in frequency, and some repeated down-shifts. After many repetitions, the up-shifted and down-shifted light is swept out of the gain bandwidth of the laser. The only light which is unaffected is that which passes through the modulator when the induced frequency shift is zero, which forms a narrow pulse of light.
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.
A saturable absorber is an optical device that exhibits an intensity-dependent transmission. What this means is that the device behaves differently depending on the intensity of the light passing through it. For passive mode-locking, ideally a saturable absorber will selectively absorb low-intensity light, and transmit light which is of sufficiently high intensity.
When placed in a laser cavity, a saturable absorber will attenuate 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 will be 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 sideband
s at optical frequencies and 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 organic
dyes, but they can also be made from doped crystal
s and semiconductors. Semiconductor absorbers tend to exhibit very fast response times (~100 fs), which is one of the factors that determines the final duration of the pulses in a passively mode-locked laser. In a colliding-pulse mode-locked laser the absorber steepens the leading edge while the lasing medium steepens the trailing edge of the pulse.
In particular, graphene
can be saturated over the visible to near-infrared region and it has a smaller non-saturable loss and higher damage threshold, compared with SWCNTs.
There are also passive mode-locking schemes that do not rely on materials that directly display an intensity dependent absorption. In these methods, nonlinear optical
effects in intracavity components are used to provide a method of selectively amplifying high-intensity light in the cavity, and attenuation of low-intensity light. One of the most successful schemes is called Kerr-lens mode-locking (KLM), also sometimes called "self mode-locking". This uses a nonlinear optical process, the optical Kerr effect
, which results in high-intensity light being focussed differently than low-intensity light. By careful arrangement of an aperture in the laser cavity, this effect can be exploited to produce the equivalent of an ultra-fast response time saturable absorber.
of the laser's optical resonator, which can be controlled with a prism compressor
or some dispersive mirrors placed in the cavity, and optical nonlinearities. For excessive net group delay dispersion (GDD) of the laser cavity, the phase
of the cavity modes can not be locked over a large bandwidth, and it will be difficult to obtain very short pulses. For a suitable combination of negative (anomalous) net GDD with the Kerr nonlinearity
, soliton
-like interactions may stabilize the mode-locking and help to generate shorter pulses. The shortest possible pulse duration is usually accomplished either for zero dispersion (without nonlinearities) or for some slightly negative (anomalous) dispersion (exploiting the soliton mechanism).
The shortest directly produced optical pulses are generally produced by Kerr-lens mode-locked Ti-sapphire lasers, and are around 5 femtoseconds long. Alternatively, amplified pulses of a similar duration are created through the compression of longer (e.g. 30 fs) pulses via self-phase modulation
in a hollow core fibre or during filamentation. However, the minimum pulse duration is limited by the period of the carrier frequency (which is about 2.7 fs for Ti:S systems), therefore shorter pulses require moving to shorter wavelengths. Some advanced techniques (involving high harmonic generation with amplified femtosecond laser pulses) can be used to produce optical features with durations as short as 100 attoseconds in the extreme ultraviolet spectral region (i.e. <30 nm). Other achievements, important particularly for laser applications
, concern the development of mode-locked lasers which can be pumped with laser diodes, can generate very high average output powers (tens of watts) in sub-picosecond pulses, or generate pulse trains with extremely high repetition rates of many GHz.
Pulse durations less than approximately 100 fs are too short to be directly measured using optoelectronic techniques (i.e. photodiode
s), and so indirect methods such as autocorrelation
, Frequency-resolved optical gating
, Spectral phase interferometry for direct electric-field reconstruction
or Multi-photon Intrapulse Interference Phase Scan are used.
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
by which a laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
can be made to produce pulses of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
of extremely short duration, on the order of picoseconds (10−12 s) or femtoseconds (10−15 s).
The basis of the technique is to induce a fixed phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
relationship between the mode
Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies...
s of the laser's resonant cavity. The laser is then said to be phase-locked or mode-locked. Interference between these modes causes the laser light to be produced as a train of pulses. Depending on the properties of the laser, these pulses may be of extremely brief duration, as short as a few femtoseconds.
Laser cavity modes
Although laser light is perhaps the purest form of light, it is not of a single, pure frequencyFrequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
or wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
. 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
Laser construction
A laser is constructed from three principal parts:*An energy source ,*A gain medium or laser medium, and*Two or more mirrors that form an optical resonator.-Pump source:...
that the laser is constructed from, and the range of frequencies that a laser may operate over is known as the gain bandwidth. For example, a typical helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
-neon
Neon
Neon is the chemical element that has the symbol Ne and an atomic number of 10. Although a very common element in the universe, it is rare on Earth. A colorless, inert noble gas under standard conditions, neon gives a distinct reddish-orange glow when used in either low-voltage neon glow lamps or...
(HeNe
Helium-neon laser
A helium–neon laser or HeNe laser, is a type of gas laser whose gain medium consists of a mixture of helium and neon inside of a small bore capillary tube, usually excited by a DC electrical discharge.- History of HeNe laser development:...
) gas laser has a gain bandwidth of approximately 1.5 GHz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
(a wavelength range of about 0.002 nm
Nanometre
A nanometre is a unit of length in the metric system, equal to one billionth of a metre. The name combines the SI prefix nano- with the parent unit name metre .The nanometre is often used to express dimensions on the atomic scale: the diameter...
at a central wavelength of 633 nm), whereas a titanium-doped sapphire (Ti:Sapphire
Ti-sapphire laser
Ti:sapphire lasers are tunable lasers which emit red and near-infrared light in the range from 650 to 1100 nanometers. These lasers are mainly used in scientific research because of their tunability and their ability to generate ultrashort pulses...
) solid-state laser has a bandwidth of about 128 THz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
(a 300 nm wavelength range centred around 800 nm).
The second factor that determines a laser's emission frequencies is the optical cavity or resonant cavity of the laser. In the simplest case, this consists of two plane (flat) mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...
s facing each other, surrounding the gain medium of the laser (this arrangement is known as a Fabry–Pérot cavity). Since light is a wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
, when bouncing between the mirrors of the cavity the light will constructively and destructively interfere with itself, leading to the formation of standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...
s or modes
Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies...
between the mirrors.
Longitudinal mode
For the longitudinal mode of conduction of electric currents, see Common modeA longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive...
s of the cavity. These modes are the only frequencies of light which are self-regenerating and allowed to oscillate by the resonant cavity; all other frequencies of light are suppressed by destructive interference. For a simple plane-mirror cavity, the allowed modes are those for which the separation distance of the mirrors L is an exact multiple of half the wavelength of the light λ, such that , where q is an integer known as the mode order.
In practice, the separation distance of the mirrors L is usually much greater than the wavelength of light 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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
(≈3×108 m·s−1).
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 itself some bandwidth or narrow range of frequencies over which it operates, but typically this bandwidth, determined by the Q factor (see Inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
) of the cavity (see Fabry–Pérot interferometer), is much smaller than the inter-mode frequency separation.
Mode-locking theory
In a simple laser, each of these modes will oscillate 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 phasePhase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
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
Beat (acoustics)
In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies....
effects in the laser output, leading to random fluctuations in intensity; in lasers with many thousands of modes, these interference effects tend to average to a near-constant output intensity, and the laser operation is known as a c.w. or continuous wave.
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 , 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, .
The duration of each pulse of light is determined by the number of modes which are oscillating in phase (in a real laser, it is not necessarily true that all of the laser's modes will be 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
Pulse duration
In signal processing and telecommunication, the term pulse duration has the following meanings:#In a pulse waveform, the interval between the time, during the first transition, that the pulse amplitude reaches a specified fraction of its final amplitude, and the time the pulse amplitude drops,...
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 time-bandwidth product of the pulse, and varies depending on the pulse shape. For ultrashort pulse lasers, a hyperbolic-secant
Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" , and the hyperbolic cosine "cosh" , from which are derived the hyperbolic tangent "tanh" and so on.Just as the points form a...
-squared (sech2) pulse shape is often assumed, giving a time-bandwidth product of 0.315.
Using this equation, we can calculate the minimum pulse duration consistent with the measured laser spectral width. For the HeNe laser with a 1.5 GHz spectral width, 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 be only 3.4 femtoseconds. These values represent the shortest possible Gaussian pulses consistent with the laser's linewidth; 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
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
of the cavity.
It should be noted that subsequent modulation could in principle shorten the pulse width of such a laser further, however the measured spectral width would then be correspondingly increased.
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 modulationModulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted...
of the intra-cavity 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 acousto-opticmodulator into the laser cavity. When driven with an electrical signal, this produces a sinusoidal amplitude modulation
Amplitude modulation
Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent...
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 sideband
Sideband
In radio communications, a sideband is a band of frequencies higher than or lower than the carrier frequency, containing power as a result of the modulation process. The sidebands consist of all the Fourier components of the modulated signal except the carrier...
s at optical frequencies and . 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 and 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
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
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 frequency modulation
Frequency modulation
In telecommunications and signal processing, frequency modulation conveys information over a carrier wave by varying its instantaneous frequency. This contrasts with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant...
(FM) mode-locking, which uses a modulator device based on the electro-optic effect
Electro-optic effect
An electro-optic effect is a change in the optical properties of a material in response to an electric field that varies slowly compared with the frequency of light...
. This device, when placed in a laser cavity and driven with an electrical signal, induces a small, sinusoidally varying frequency shift in the light passing through it. If the frequency of modulation is matched to the round-trip time of the cavity, then some light in the cavity sees repeated up-shifts in frequency, and some repeated down-shifts. After many repetitions, the up-shifted and down-shifted light is swept out of the gain bandwidth of the laser. The only light which is unaffected is that which passes through the modulator when the induced frequency shift is zero, which forms a narrow pulse of light.
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 saturable absorber.A saturable absorber is an optical device that exhibits an intensity-dependent transmission. What this means is that the device behaves differently depending on the intensity of the light passing through it. For passive mode-locking, ideally a saturable absorber will selectively absorb low-intensity light, and transmit light which is of sufficiently high intensity.
When placed in a laser cavity, a saturable absorber will attenuate 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 will be 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 sideband
Sideband
In radio communications, a sideband is a band of frequencies higher than or lower than the carrier frequency, containing power as a result of the modulation process. The sidebands consist of all the Fourier components of the modulated signal except the carrier...
s at optical frequencies and 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 organic
Organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, composition, reactions, and preparation of carbon-based compounds, hydrocarbons, and their derivatives...
dyes, but they can also be made from doped crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
s and semiconductors. Semiconductor absorbers tend to exhibit very fast response times (~100 fs), which is one of the factors that determines the final duration of the pulses in a passively mode-locked laser. In a colliding-pulse mode-locked laser the absorber steepens the leading edge while the lasing medium steepens the trailing edge of the pulse.
In particular, graphene
Graphene
Graphene is an allotrope of carbon, whose structure is one-atom-thick planar sheets of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. The term graphene was coined as a combination of graphite and the suffix -ene by Hanns-Peter Boehm, who described single-layer...
can be saturated over the visible to near-infrared region and it has a smaller non-saturable loss and higher damage threshold, compared with SWCNTs.
There are also passive mode-locking schemes that do not rely on materials that directly display an intensity dependent absorption. In these methods, nonlinear optical
Nonlinear optics
Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...
effects in intracavity components are used to provide a method of selectively amplifying high-intensity light in the cavity, and attenuation of low-intensity light. One of the most successful schemes is called Kerr-lens mode-locking (KLM), also sometimes called "self mode-locking". This uses a nonlinear optical process, the optical Kerr effect
Kerr effect
The Kerr effect, also called the quadratic electro-optic effect , is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric...
, which results in high-intensity light being focussed differently than low-intensity light. By careful arrangement of an aperture in the laser cavity, this effect can be exploited to produce the equivalent of an ultra-fast response time saturable absorber.
Hybrid Mode-locking
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.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 dispersionDispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
of the laser's optical resonator, which can be controlled with a prism compressor
Prism compressor
A prism compressor is an optical device used to shorten the duration of a positively chirped ultrashort laser pulse by giving different wavelength components a different time delay. It typically consists of two prisms and a mirror. Figure 1 shows the construction of such a compressor...
or some dispersive mirrors placed in the cavity, and optical nonlinearities. For excessive net group delay dispersion (GDD) of the laser cavity, the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
of the cavity modes can not be locked over a large bandwidth, and it will be difficult to obtain very short pulses. For a suitable combination of negative (anomalous) net GDD with the Kerr nonlinearity
Kerr effect
The Kerr effect, also called the quadratic electro-optic effect , is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric...
, soliton
Soliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...
-like interactions may stabilize the mode-locking and help to generate shorter pulses. The shortest possible pulse duration is usually accomplished either for zero dispersion (without nonlinearities) or for some slightly negative (anomalous) dispersion (exploiting the soliton mechanism).
The shortest directly produced optical pulses are generally produced by Kerr-lens mode-locked Ti-sapphire lasers, and are around 5 femtoseconds long. Alternatively, amplified pulses of a similar duration are created through the compression of longer (e.g. 30 fs) pulses via self-phase modulation
Self-phase modulation
Self-phase modulation is a nonlinear optical effect of light-matter interaction.An ultrashort pulse of light, when travelling in a medium, will induce a varying refractive index of the medium due to the optical Kerr effect...
in a hollow core fibre or during filamentation. However, the minimum pulse duration is limited by the period of the carrier frequency (which is about 2.7 fs for Ti:S systems), therefore shorter pulses require moving to shorter wavelengths. Some advanced techniques (involving high harmonic generation with amplified femtosecond laser pulses) can be used to produce optical features with durations as short as 100 attoseconds in the extreme ultraviolet spectral region (i.e. <30 nm). Other achievements, important particularly for laser applications
Laser applications
Many scientific, military, medical and commercial laser applications have been developed since the invention of the laser in the 1958. The coherency, high monochromaticity, and ability to reach extremely high powers are all properties which allow for these specialized applications.-Scientific:In...
, concern the development of mode-locked lasers which can be pumped with laser diodes, can generate very high average output powers (tens of watts) in sub-picosecond pulses, or generate pulse trains with extremely high repetition rates of many GHz.
Pulse durations less than approximately 100 fs are too short to be directly measured using optoelectronic techniques (i.e. photodiode
Photodiode
A photodiode is a type of photodetector capable of converting light into either current or voltage, depending upon the mode of operation.The common, traditional solar cell used to generateelectric solar power is a large area photodiode....
s), and so indirect methods such as autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
, Frequency-resolved optical gating
Frequency-resolved optical gating
In optics, frequency-resolved optical gating is a derivative of autocorrelation, but is far superior in its ability to measure ultrafast optical pulse shapes...
, Spectral phase interferometry for direct electric-field reconstruction
Spectral phase interferometry for direct electric-field reconstruction
In ultrafast optics, spectral phase interferometry for direct electric-field reconstruction is an ultrashort pulse measurement technique.-The basics:...
or Multi-photon Intrapulse Interference Phase Scan are used.
Applications
- Nuclear fusion. (inertial confinement fusionInertial confinement fusionInertial confinement fusion is a process where nuclear fusion reactions are initiated by heating and compressing a fuel target, typically in the form of a pellet that most often contains a mixture of deuterium and tritium....
). - Nonlinear optics, such as second-harmonic generation, parametric down-conversion, optical parametric oscillatorOptical parametric oscillatorAn optical parametric oscillator is a parametric oscillator which oscillates at optical frequencies. It converts an input laser wave into two output waves of lower frequency by means of second order nonlinear optical interaction. The sum of the output waves frequencies is equal to the input wave...
s, and generation of Terahertz radiationTerahertz radiationIn physics, terahertz radiation refers to electromagnetic waves propagating at frequencies in the terahertz range. It is synonymously termed submillimeter radiation, terahertz waves, terahertz light, T-rays, T-waves, T-light, T-lux, THz... - Optical Data Storage uses lasers, and the emerging technology of 3D optical data storage3D optical data storage3D optical data storage is the term given to any form of optical data storage in which information can be recorded and/or read with three dimensional resolution ....
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 micromachining – The short pulses can be used to micromachine in many types of materials. The Handbook of Femtosecond Micromachining (link following) gives additional information. http://www.cmxr.com/mmhandbook.html
- An example of pico- and femtosecond micromachining is drilling the silicon jet surface of ink jet printers
- Two-photon microscopy
- Corneal Surgery. Femtosecond lasers can create bubbles in the corneaCorneaThe cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Together with the lens, the cornea refracts light, with the cornea accounting for approximately two-thirds of the eye's total optical power. In humans, the refractive power of the cornea is...
, if multiple bubbles are created in a planar fashion parallel to the corneal surface then the tissue separates at this plane and a flap like the one in LASIKLASIKLASIK or Lasik , commonly referred to simply as laser eye surgery, is a type of refractive surgery for correcting myopia, hyperopia, and astigmatism...
is formed (Intralase: Intralasik or SBK (Sub Bowman Keratomileusis) if the flap thickness is equal or less than 100 micrometres). If done in multiple layers a piece of corneal tissue between these layers can be removed (Visumax: FLEX Femtosecond Lenticle 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 nanostructureNanostructureA nanostructure is an object of intermediate size between molecular and microscopic structures.In describing nanostructures it is necessary to differentiate between the number of dimensions on the nanoscale. Nanotextured surfaces have one dimension on the nanoscale, i.e., only the thickness of the...
s. The immensely increased surface area can absorb virtually all the light that falls on it thus rendering it deep black. This is one type of black gold - Photonic Sampling, using the high accuracy of lasers over electronic clocks to decrease the sampling error in electronic ADCs
Further reading
See also
- Fiber laserFiber laserA fiber laser or fibre laser is a laser in which the active gain medium is an optical fiber doped with rare-earth elements such as erbium, ytterbium, neodymium, dysprosium, praseodymium, and thulium. They are related to doped fiber amplifiers, which provide light amplification without lasing...
- Disk laserDisk laserA disk laser or active mirror is a type of solid-state laser characterized by a heat sink and laser output that are realized on opposite sides of a thin layer of active gain medium...
- Laser constructionLaser constructionA laser is constructed from three principal parts:*An energy source ,*A gain medium or laser medium, and*Two or more mirrors that form an optical resonator.-Pump source:...
- SolitonSolitonIn mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...
- Vector solitonVector solitonIn physical optics or wave optics, a vector soliton is a solitary wave with multiple components coupled together that maintains its shape during propagation. Ordinary solitons maintain their shape but have effectively only one polarization component, while vector solitons have two distinct...
- Dissipative solitonDissipative solitonDissipative solitons are stable solitary localizedstructures that arise in nonlinear spatially extendeddissipative systems due to mechanisms of self-organization.They can be considered as an extension of the classical...
- Saturable absorptionSaturable absorptionSaturable absorption is a property of materials where the absorption of light decreases with increasing light intensity. Most materials show some saturable absorption, but often only at very high optical intensities ....
- Solid state laser
- FemtotechnologyFemtotechnologyFemtotechnology is a hypothetical term used in reference to structuring of matter on a femtometer, which is 10-15 m. This is a smaller scale in comparison to nanotechnology and picotechnology which are 10-9 m and 10-12 m respectively...
Further References
- 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).
- http://www.batop.com/index.html
- 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).
- http://www.natureasia.com/asia-materials/highlight.php?id=594
- http://www.nanowerk.com/spotlight/spotid=30x.php
- 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 "