**1.3. Modelocked lasers**

In laser technology, modelocking refers to a technique by which a laser can be made to generate pulses of extremely short duration, of the order of picoseconds (10−<sup>12</sup> s) or femtoseconds (10−<sup>15</sup> s). This is achieved by establishing a fixed-phase relationship between the longitudinal modes of the laser's resonant cavity. The laser is then referred as phaselocked or modelocked. Interference between these modes causes the laser light to be produced as a train of pulses. In a simple laser, different modes oscillate independently, without a fixed relationship between each other, like a set of independent lasers all emitting light at slightly different frequencies. In lasers with few oscillating modes, interference between the modes produces beats in the laser output, leading to fluctuations in intensity; whereas in lasers with many thousands of modes, interference between modes tend to average to a near-constant output intensity. **Figure 6** shows the electric fields of five modes with random phase and the power of the total signal distributed in a random fashion.

On the other hand, if each mode operates with a fixed phase relationship between it and the other modes, all modes of the laser will periodically constructively interfere with one another, generating an intense burst or pulse of light instead of random or constant output intensity as shown in **Figure 7**. Such a laser is termed as modelocked or phaselocked laser. These pulses are separated in time by τ = 2 L/c, where τ is the time taken for the light to make exactly one round trip of the laser cavity, L is the length of laser cavity, and c is the speed of light. The frequency is exactly equal to the mode spacing of the laser, Δν = 1/τ. The duration of each pulse is determined by the number of modes which are oscillating in phase. Suppose there are N modes locked with a frequency separation Δν, the overall modelocked bandwidth is NΔν, and the wider the bandwidth, the shorter the pulse duration of the laser [5].

The actual pulse duration is determined by the shape of each pulse, which is measured by the amplitude and phase relationship of each longitudinal mode. As an example, a laser producing pulses with a Gaussian temporal shape, the minimum possible pulse duration Δt is given by the equation

$$
\Delta t = \frac{0.441}{\text{N} \Delta \text{v}} \tag{1}
$$

The value 0.441 is known as the "time-bandwidth product" of the pulse and varies depending on the pulse shape. Generally for ultra-short pulse lasers, a hyperbolic-secant-squared (sech2

**Figure 7.** Plots of (a) electrical field amplitudes of five in-phase individual modes and (b) the total power of a periodic

**Figure 6.** Plots of (a) electric field amplitudes of five individual modes of randomly distributed phases and (b) power of

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the total signal of a multi-longitudinal mode laser [13].

pulse train [13].

pulse shape is considered, giving a time-bandwidth product of 0.315. Using this equation,

)

to absorb pumped energy. As soon as the energy is depleted in the resonator, the absorber recovers to its high loss state before the gain recovers, so that the next pulse is delayed until the energy in the gain medium is fully replenished. In this way, it works as an on-off optical switch to generate pulses. The pulse repetition rate can only be controlled indirectly by varying the laser's pump power and the amount of saturable absorber in the cavity. For direct

Passive Q switching is simpler and cost effective as compared to the active one. It eliminates the modulator and its electronics. Moreover, it is suitable for very high pulse repetition rates, but with lower pulse energies. External triggering of the pulses is not possible (except with an optical pulse from another source), and also pulse energy and duration are often more or less independent of the pump power, which only determines the pulse repetition rate [11, 12].

In laser technology, modelocking refers to a technique by which a laser can be made to generate pulses of extremely short duration, of the order of picoseconds (10−<sup>12</sup> s) or femtoseconds (10−<sup>15</sup> s). This is achieved by establishing a fixed-phase relationship between the longitudinal modes of the laser's resonant cavity. The laser is then referred as phaselocked or modelocked. Interference between these modes causes the laser light to be produced as a train of pulses. In a simple laser, different modes oscillate independently, without a fixed relationship between each other, like a set of independent lasers all emitting light at slightly different frequencies. In lasers with few oscillating modes, interference between the modes produces beats in the laser output, leading to fluctuations in intensity; whereas in lasers with many thousands of modes, interference between modes tend to average to a near-constant output intensity. **Figure 6** shows the electric fields of five modes with random phase and the power of the total

On the other hand, if each mode operates with a fixed phase relationship between it and the other modes, all modes of the laser will periodically constructively interfere with one another, generating an intense burst or pulse of light instead of random or constant output intensity as shown in **Figure 7**. Such a laser is termed as modelocked or phaselocked laser. These pulses are separated in time by τ = 2 L/c, where τ is the time taken for the light to make exactly one round trip of the laser cavity, L is the length of laser cavity, and c is the speed of light. The frequency is exactly equal to the mode spacing of the laser, Δν = 1/τ. The duration of each pulse is determined by the number of modes which are oscillating in phase. Suppose there are N modes locked with a frequency separation Δν, the overall modelocked bandwidth is NΔν,

The actual pulse duration is determined by the shape of each pulse, which is measured by the amplitude and phase relationship of each longitudinal mode. As an example, a laser producing pulses with a Gaussian temporal shape, the minimum possible pulse duration Δt is given

*<sup>N</sup>*∆ν (1)

and the wider the bandwidth, the shorter the pulse duration of the laser [5].

<sup>∆</sup>*<sup>t</sup>* <sup>=</sup> \_\_\_\_\_ 0.441

control of the repetition rate, a pulsed pump source is needed.

**1.3. Modelocked lasers**

28 Laser Technology and its Applications

signal distributed in a random fashion.

by the equation

**Figure 6.** Plots of (a) electric field amplitudes of five individual modes of randomly distributed phases and (b) power of the total signal of a multi-longitudinal mode laser [13].

**Figure 7.** Plots of (a) electrical field amplitudes of five in-phase individual modes and (b) the total power of a periodic pulse train [13].

The value 0.441 is known as the "time-bandwidth product" of the pulse and varies depending on the pulse shape. Generally for ultra-short pulse lasers, a hyperbolic-secant-squared (sech2 ) pulse shape is considered, giving a time-bandwidth product of 0.315. Using this equation, the minimum pulse duration can be calculated consistent with the measured laser spectral width [13].

Solitons have been discovered in many branches of physics. In the field of photonics, especially in fiber optics, solitons not only are of fundamental interest, but they have also found

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The pulse maintains the shape and width, along the entire length of the fiber, if the effects of SPM and GVD cancel out with each other. Such a pulse is called solitary wave pulse or soliton. The pulse that has the above property is the sech profile pulse, which is a solution of

**Figure 8** shows the spectrum of different types of modelocked fiber lasers. The conventional soliton and stretched pulse are obtained in anomalous dispersion fiber laser setup, where the pulse shaping is mainly due to the natural balance between the anomalous dispersion and the fiber nonlinearity. On the other hand, dissipative solitons (DSs) are obtained in the normal dispersion region as a result of the combined effects among the fiber nonlinearity, cavity dispersion, gain and loss, and spectral filtering [13]. Moreover, the soliton shaping is strongly dependent on the dissipative effects. Consequently, dissipative solitons have a wider pulse duration and lower peak power, compared to conventional solitons and stretched

practical applications in the field of fiber-optic communications [16].

the nonlinear Schrodinger equation NLSE [13].

solitons [17].

**Figure 8.** Different types of solitons [17].

Modelocked fiber lasers are capable of producing pulses with widths from close to 30 fs to 1 ns at repetition rates, ranging from less than 1 MHz to 100 GHz. This broad range along with a compact size of optical fiber lasers is quite unique in laser technology, making them feasible for a large range of applications. As modelocked fiber laser technology was developed and these lasers became commercially available, they have been used in various fields, such as laser radar, all-optical scanning delay lines, THz generation, injection-seeding, twophoton microscopes, optical telecommunications, and nonlinear frequency conversion, just to mention the most widely publicized areas [12]. Surely, modelocked fiber lasers are a premier source of short optical pulses sharing an equal position with semiconductor and solid-state lasers [14].
