Mode-locking

Although 0-switching produces shortened pulses, typically 10-200 ns long, if we require pulses in the picosecond (10 s) or femtosecond (10 s) range the technique of mode locking may be used. This technique is applicable only to multimode operation of a laser and involves exciting many axial cavity modes but with the correct amplitude and phase relationship. The amplitudes and phases of the various modes are normally quite random. 

Each axial mode has its own characteristic pahem of nodal planes and the frequency separation Av between modes is given by Equation (9.4). If the radiation in the cavity can be modulated at a frequency of cjld then the modes of the cavity are locked both in amplitude and phase since t, the time for the radiation to make one round-trip of the cavity (a distance 2d), is given by 

One method of mode locking a visible laser is by placing an acoustic modulator in the cavity and driving it at a frequency of c/2d. 

An important consequence of shortening a laser pulse is that the line width is increased as a result of the uncertainty principle as stated in Equation (1.16). When the width of the pulse is very small there is difficulty in measuring the energy precisely because of the rather small number of wavelengths in the pulse. For example, for a pulse width of 40 ps there is a frequency spread of the laser, given approximately by (2 iAt), of about 4.0 GFIz (0.13 cm ). 

Pulse lengths of 100 fs (1 femtosecond = 10 s) have been achieved by mode locking. 

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In the previous section we discussed light and matter at equilibrium in a two-level quantum system. For the remainder of this section we will be interested in light and matter which are not at equilibrium. In particular, laser light is completely different from the thennal radiation described at the end of the previous section. In the first place, only one, or a small number of states of the field are occupied, in contrast with the Planck distribution of occupation numbers in thennal radiation. Second, the field state can have a precise phase-, in thennal radiation this phase is assumed to be random. If multiple field states are occupied in a laser they can have a precise phase relationship, something which is achieved in lasers by a teclmique called mode-locking Multiple frequencies with a precise phase relation give rise to laser pulses in time. Nanosecond experiments... 

Kneipp K, Kneipp H and Seifert F 1994 Near-infrared excitation profile study of surface-enhanced hyper-Raman scattering and surface-enhanced Raman scattering by means of tunable mode-locked... 

In order to achieve a reasonable signal strength from the nonlinear response of approximately one atomic monolayer at an interface, a laser source with high peak power is generally required. Conuuon sources include Q-switched ( 10 ns pulsewidth) and mode-locked ( 100 ps) Nd YAG lasers, and mode-locked ( 10 fs-1 ps) Ti sapphire lasers. Broadly tunable sources have traditionally been based on dye lasers. More recently, optical parametric oscillator/amplifier (OPO/OPA) systems are coming into widespread use for tunable sources of both visible and infrared radiation. 

The development of ultrafast spectroscopy has paralleled progress in the teclmical aspects of pulse fomiation [Uj. Because mode-locked laser sources are tunable only with diflSculty, until recently the most heavily studied physical and chemical systems were those that had strong electronic absorption spectra in the neighbourhood of conveniently produced wavelengths. 

As one important example, the introduction of the prism-controlled, colliding-pulse, mode-locked (CPM) dye laser [12,13] led almost innnediately to developments in measurement teclmique with pulses of less than 100... 

These limitations have recently been eliminated using solid-state sources of femtosecond pulses. Most of the femtosecond dye laser teclmology that was in wide use in the late 1980s [11] has been rendered obsolete by tliree teclmical developments the self-mode-locked Ti-sapphire oscillator [23, 24, 25, 26 and 27], the chirped-pulse, solid-state amplifier (CPA) [28, 29, 30 and 31], and the non-collinearly pumped optical parametric amplifier (OPA) [32, 33 and 34]- Moreover, although a number of investigators still construct home-built systems with narrowly chosen capabilities, it is now possible to obtain versatile, nearly state-of-the-art apparatus of the type described below Ifom commercial sources. Just as home-built NMR spectrometers capable of multidimensional or solid-state spectroscopies were still being home built in the late 1970s and now are almost exclusively based on commercially prepared apparatus, it is reasonable to expect that ultrafast spectroscopy in the next decade will be conducted almost exclusively with apparatus ifom conmiercial sources based around entirely solid-state systems. 

The OPA should not be confiised with an optical parametric oscillator (OPO), a resonant-cavity parametric device that is syncln-onously pumped by a femtosecond, mode-locked oscillator. 14 fs pulses, tunable over much of the visible regime, have been obtained by Hache and co-workers [49, with a BBO OPO pumped by a self-mode-locked Ti-sapphire oscillator. 

Figure B2.1.3 Output of a self-mode-locked titanium-sapphire oscillator (a) non-collinear intensity autocorrelation signal, obtained with a 100 pm p-barium borate nonlinear crystal (b) intensity spectrum.

Spence D E, Kean P N and Sibbett W 1991 60 fs pulse generation from a self-mode-locked Ti sapphire laser Qpt. Lett. 16 42—4... 

Asaki M T, Huang C-P, Garvey D, Zhou J, Kapteyn H C and Murnane M M 1993 Generation of 11 fs pulses from a self-mode-locked Tfsapphire laser Opt. Lett. 977 977-9... 

Bade P, Bourvier M and Coe J S 1987 Nd YLF mode-locked oscillator and regenerative amplifier Opt. Lett. 12 319-21... 

The importance of laser light, in brief, is tliat its base characteristics, coherence, spectral and polarization purity, and high brilliance allow us to manipulate its properties. Gain switching [i, 10] and mode locking [16] are prime examples of our ability to very specifically control tire laser output. It is easy to see why lasers are tire ideal sources for optoelectronic applications. 

The result is that, for the case of a cavity operated with, say, seven modes, the output is like that in Figure 9.5 when the cavity is mode locked. Only the modes which have a node at one end of the cavity are output from the laser and all others are suppressed. 

Figure 9.5 Suppression of five out of seven axial cavity modes by mode locking...

In 1991 a remarkable discovery was made, accidentally, with a Tp -sapphire laser pumped with an Ar+ laser. Whereas we would expect this to result in CW laser action, when a sharp jolt was given to the table supporting the laser, mode locking (Section 9.1.5) occurred. This is known as self-locking of modes, and we shall not discuss further the reasons for this and how it can be controlled. One very important property of the resulting pulses is that they are very short. Pulse widths of a few tens of femtoseconds can be produced routinely and with high pulse-to-pulse stability. Further modification to the laser can... 

Modacrylic Modacrylic fibers Modacrylics Modane Modeling Modeling systems Mode-locked lasers Model rocket engines Models... 

Fig. 4. Temporal pulse characteristics of lasers (a) millisecond laser pulse (b) relaxation oscillations (c) Q-switched pulse (d) mode-locked train of pulses, where Fis the distance between mirrors and i is the velocity of light for L = 37.5 cm, 2L j c = 2.5 ns (e) ultrafast (femtosecond or picosecond) pulse.

It is also possible to switch a single picosecond pulse out of the train of mode-locked pulses using an electrooptic switch. It is possible to obtain a single pulse having duration in the picosecond regime or even less. Pulses with durations in the regime of a few hundred femtoseconds (10 s) are also available (Fig. 4e). 

Another variation is the mode-locked dye laser, often referred to as an ultrafast laser. Such lasers offer pulses having durations as short as a few hundred femtoseconds (10 s). These have been used to study the dynamics of chemical reactions with very high temporal resolution (see Kinetic LffiASURELffiNTS). 

Nonlinear refraction phenomena, involving high iatensity femtosecond pulses of light traveling in a rod of Tfsapphire, represent one of the most important commercial exploitations of third-order optical nonlinearity. This is the realization of mode-locking ia femtosecond Tfsapphire lasers (qv). High intensity femtosecond pulses are focused on an output port by the third-order Kerr effect while the lower intensity continuous wave (CW) beam remains unfocused and thus is not effectively coupled out of the laser. 

The requited characteristics of dyes used as passive mode-locking agents and as active laser media differ in essential ways. For passive mode-locking dyes, short excited-state relaxation times ate needed dyes of this kind ate characterized by low fluorescence quantum efficiencies caused by the highly probable nonradiant processes. On the other hand, the polymethines to be appHed as active laser media ate supposed to have much higher quantum efficiencies, approximating a value of one (91). 

Also, using dyes as laser media or passive mode-locked compounds requires numerous special parameters, the most important of which ate the band position and bandwidth of absorption and fluorescence, the luminiscence quantum efficiency, the Stokes shift, the possibiHty of photoisomerization, chemical stabiHty, and photostabiHty. AppHcations of PMDs in other technical or scientific areas have additional special requirements. 

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