Mode Locking is a technique to generate ultra-short pulses in the order of picoseconds (10^-12) or femtoseconds (10^-15). Lasers that generate a train of periodic ultra-short pulses are called mode-locked lasers. Laser light does not have a single, unmixed frequency or wavelength. All lasers emit light over a natural frequency spectrum or bandwidth.

Figure 1: Mode-locked pulses by superposition of sinusoidal oscillations

In a laser cavity, when two light waves of the same frequency and amplitude move in the opposite direction create a standing wave. These standing waves form a discrete set of frequencies called longitudinal modes of the cavity. These multiple longitudinal modes of oscillation with frequencies are separated by intermodal spacing 

where c is the speed of light and L is the resonator length. These longitudinal modes will interfere with each other. If their phases are not having a definite relationship, they will interfere destructively causing a fluctuation in the laser intensity irregularly with time. But if there is a fixed phase (in-phase) relationship, they interfere constructively which causes the generation of a series of ultrashort pulses as the laser output and it is mode-locking. The mode-locked pulses are separated in time 

which is the round-trip time T_R for a laser light beam. This time corresponds to a frequency equal to the laser’s mode spacing given by 

The number of modes that are oscillating in phase determines the length of each light pulse. If there are N number of modes separated by a frequency ∆ν, then the overall mode-locked bandwidth is N∆ν.

The laser pulse duration decreases as this bandwidth widens.

An optical modulator or a saturable absorber is used for mode-locking in lasers. If there is no mode locking, the laser performs a continuous wave mode operation.  Mode locking is all about creating a phase relation between the modes and maintaining it. Figure 1 shows the mode-locked pulses.

Types of mode locking

There are mainly two types of mode-locking in lasers: 

• Active mode locking 
• Passive mode locking

Active mode locking

Active mode locking is mainly performed on continuous wave lasers like Nd:YAG laser, Nd:YVO₄ laser, DPSS lasers, etc. They generate equal pulses with a repetition rate in the range of 80-250 MHz having nanojoules pulse energy range. Figure 2 shows active mode locking in a laser. The resonant cavity of the laser contains a gain medium and an optical loss modulator which changes the resonant cavity loss with time. When an external signal is applied to the optical modulator, amplitude or phase modulation takes place inside the cavity which causes the mode-locking of the laser. An acousto-optic (AO) or electro-optic (EO) effect is used to introduce a periodic modulation of the loss in the laser cavity. The optical modulator blocks the passage except when the pulse is about to pass. It will be open only during the pulse durations thus creating a giant narrow pulse.

Figure 2: Active mode-locking

Acousto-Optic Modulation

Acousto-optic devices are used to control the laser beams. They work on the principle of photo-elastic effect or interaction of sound waves with the light on a crystal material. A transducer that creates ultrasonic waves or acoustic waves is used as an acousto-optic modulator. When a sound wave is applied to this modulator, a sinusoidally varying frequency shift is created to the light signal that passes through it. The amplitude modulator act as a shutter to the light bouncing inside the cavity mirrors causing the attenuation of light when closed and allowing them to pass when opened. 

Electro-Optic Modulation 

An electro-optic modulator is a device used to control the power, phase, or polarization of a laser beam with the application of an electric signal. When a voltage is applied, the refractive index of a nonlinear crystal is modified and causes birefringence. A plane-polarized light beam splitting into two orthogonal beam vectors is called birefringence. When an electric signal is applied to this modulator, a sinusoidally varying frequency shift is induced to the light passing through it. If the modulation frequency and cavity round-trip time are matched, some light in the cavity experiences repeated frequency upshifts while some light experiences repeated frequency downshifts. The up-shifted and down-shifted light is swept out of the gain bandwidth of the laser after many repetitions. The only light that is unaffected is the small pulse of light that emerges from the modulator when the induced frequency shift is zero. A pockels cell is an example of an electro-optic modulator.

There is one more active mode-locking method called synchronous mode-locking.  This technique effectively turns on and off the laser to create pulses by modulating the laser's pump source. The pump source itself is typically another mode-locked laser. The cavity lengths of the driving laser and the pump laser must be precisely matched for this approach.

Passive mode locking

Passive mode locking is a method of generating ultra-short pulses in a laser using non-electronic means. This is achieved with a saturable absorber. A saturable absorber is an optical component whose absorption coefficient decreases with an increase in the intensity of incident light. It absorbs weak pulses while transmitting strong ones with comparatively little absorption. A saturable absorber is made from organic dyes that have the ability to absorb light at the specific wavelength of the laser. Liquid organic dyes are commonly used for saturable absorbers. At higher pulse intensities, the ground state of the dye gets depleted, which decreases resonator losses. The saturable absorber is kept inside the optical resonator cavity next to the gain medium. They do not require an external signal for this type of mode-locking. The laser light within the cavity itself will make changes in the intracavity elements.

Figure 3: Passive mode-locking

At the steady state, a short pulse circulates inside the laser cavity and hits the saturable absorber. The absorption is saturated every time the pulse hits the saturable absorber thereby reducing the losses inside the cavity. The laser gain will then reach a saturation state at which it compensates for the cavity losses. But if a low intense pulse hits the absorber, it cannot saturate the light. So, the cavity loss will be greater than the gain. The pulse width is narrower for the passive mode-locking pulses than for active mode-locking pulses. Figure 3 shows passive mode locking in a laser.

Typically used passive techniques are Kerr lens mode-locking (KLM), Colliding pulse mode-locking (CPM), and Additive pulse mode-locking (APML).

Kerr Lens Mode-Locking (KLM)

An intracavity saturable technique in passive mode-locking with kerr effect is called Kerr lens mode-locking. Kerr lens mode-locking is based on the optical Kerr effect. The principle behind the kerr effect is the intensity-dependent refractive index. This effect leads to self-focusing and filamentation of high-intensity laser beams. It is similar to that of the electro-optic effect. In kerr lens mode-locking, the strong self-focusing effect of the intense light beam is combined with a hard or soft gain aperture that causes self-amplitude modulation like the working of a saturable absorber. It is an extremely fast mode-locking method allowing a continuous train of mode-locked pulses from a continuous wave-pumped laser.

Kerr Effect

A change in the refractive index of a crystal is caused by the application of an external electric field. In kerr effect, the refractive index is modified proportionally to the magnitude of the applied field. The variation of the refractive index is proportional to the square of the electric field applied. All centrosymmetric crystals exhibit kerr effect. 

The Kerr effect is also known as a quadratic electro-optic effect. It is of two types: Kerr electro-optic effect and the optical kerr effect (also called as AC kerr effect). 

In kerr electro-optic effect, a varying DC field is applied. By applying a varying DC electric field, refractive index perturbations occur and the material acts as a waveplate that polarizes the light in the desired direction.  

In AC kerr effect, there is no externally applied electric field, instead, the light source itself will act as an AC source. The AC kerr effect is a self-induced effect in which the refractive index of the high-intensity beam is modified according to 

where n₂ is the nonlinear refractive index and I is the intensity of the light beam and is proportional to the modulus square of the electric field. The optical kerr effect is stronger in liquids. When an electric field is applied, the liquid molecules align themselves with the electric field causing a change in the refractive index of the medium making it birefringent. Thus, the light incident is modulated.

Colliding Pulse Mode-Locking (CPM)

Colliding pulse mode locking is a method of mode locking a laser to produce ultra-short pulses. In CPM, two or more passive mode-locked laser pulses are combined using an optical element, such as a beamsplitter, to produce a single, shorter pulse. The collision of the pulses results in a nonlinear interaction that leads to the formation of a mode-locked pulse with a well-defined temporal profile.

This is produced by the interaction of two counter-propagating pulses in a thin saturable absorber installed within a ring laser cavity, as shown in Figure 4. When the two counter-propagating pulses meet within the saturable absorber, they produce an increased intensity that begins to bleach out or reduce the absorption or transmission of light in the medium. This type of mode-locking, which involves two pulses within the saturable absorber, has two advantages:

• It avoids the fabrication problems associated with having the saturable absorber in optical contact with one of the mirrors;
• It provides a synchronizing function that yields shorter and more stable pulses. Stable pulses of duration less than 100 fs have been produced with this technique.

Figure 4: Ring laser arrangement for colliding pulse mode-locking (CPM)

Additive Pulse Mode-Locking (APML)

Additive pulse mode locking is a technique for mode-locking laser systems. It involves the combination of multiple short laser pulses, each with its own phase and amplitude, to produce a single, longer pulse with a well-defined temporal profile.

A mode-locked laser can be designed such that part of its output is sent through an optical fiber, as shown in Figure 5. If a mirror is placed at the fiber end to return the beam to the cavity, then the portion of the laser pulse that travels through the fiber is re-injected into the cavity. The laser essentially has two connected cavities, an arrangement that is referred to as a coupled cavity.

Figure 5: Arrangement for additive pulse mode-locking (APM)

There is one more type of mode locking called hybrid mode-locking which is a combination of both active and passive mode-locking. This method is used for mode locking in semiconductor lasers.

Applications 

Mode-locked lasers are used for corneal eye surgery. Tiny gas bubbles are created in the cornea using femtosecond lasers and a line of such bubbles will create a cut in the cornea and replaces the microkeratome. Bubbles can be created also in multiple layers to remove a piece of corneal tissue between these layers.

Another application is femtosecond laser micromachining. They are used to drill the silicon jet surface of inkjet printers. In the nano machining of different types of materials, mode-locked femtosecond lasers are used. Since mode-locked lasers produce ultra-short pulses with a high repetition rate, they are used in optical computers, optical data storage, and for the emerging 3D optical data storage technology that often uses nonlinear photochemistry.

The high accuracy of mode-locked lasers is used for the photonic sampling to reduce the sampling error in electronic analog to digital converters (ADCs). These lasers are used in nonlinear optical processes like harmonic generation, parametric down-conversion, optical parametric oscillation, generation of terahertz radiation, etc. Mode-locked lasers also have applications in nuclear fusion, optical communication, two-photon microscopy, etc.