Non-linear optical techniques have been exploited to develop a new generation of optical microscopes with unprecedented capabilities. These new capabilities include the ability to use near-infrared (IR) light to induce absorption, and hence fluorescence, from fluorophores that absorb in the ultraviolet wavelength region. Other capabilities of non-linear microscopes include improved spatial and temporal resolution without the use of pinholes or slits for spatial filtering, improved signal strength, deeper penetration into thick, highly scattering tissues, and confinement of photobleaching to the focal volume [1]. Two-photon excitation offers major advantages when working in the thick tissue, such as brain slices or developing embryos, due to the dramatically reduced effects of light scattering. This is partly because the longer red and near-IR wavelengths used for two photon illumination penetrate deeper into biological tissue with less absorption and scattering. However, the main advantage comes from the non-linear excitation. The requirement for two coincident (or near coincident) photons to achieve excitation of the fluorophore means that only focused light reaches the required intensities and that scattered light does not cause excitation of the fluorophore.

The introduction of two-photon excitation [1] to life sciences has opened novel experimental territories [2]. Two-Photon Laser Scanning Microscopy is a fluorescence imaging technique that allows imaging living tissue up to depth of one millimeter. It is a special variant of the multiphoton fluorescence microscopy. Two-Photon excitation may in some cases be a viable alternative to confocal microscopy due to its deeper tissue pentration and reduced phototoxicity [1]. It is employs a concept first described by Maria Goppert-Mayer (b. 1906) in her 1931 doctoral dissertation [3].

The use of infrared light to excite fluorophores in light-scattering tissue has added benefits [4]. Longer wavelengths are scattered to a lesser degree than shorter ones, which is a benefit to high-resolution imaging. In addition, these lower-energy photons are less likely to cause damage outside of the focal volume.

Ultrashort pulse systems have a unique set of characteristics caused by the high peak powers and temporal conditions, which must be considered in their design. The envelope of an ultrashort pulse contains a large number of frequencies; hence, such pulses have very large bandwidths. This bandwidth sets the limit for the shortest pulse duration with the relationship

Δ*τ*_{
p
}Δ*ν* = *X*

where Δ*τ*_{
p
}is the temporal full-width half-maximum of the pulse and Δ*ν* is the spectral bandwidth. The value *X* will be a minimum when the pulse is said to be fourier-transform-limited, at which point the spectral bandwidth is unable to support shorter pulse durations. In optical materials, the refractive index is frequency dependent. This dependence can be calculated for a given material using a Sellmeier equation, typically of the form:

{n}^{2}\left(\lambda \right)=1+\frac{{B}_{1}{\lambda}^{2}}{{\lambda}^{2}-{C}_{1}}+\frac{{B}_{2}{\lambda}^{2}}{{\lambda}^{2}-{C}_{2}}+\frac{{B}_{3}{\lambda}^{2}}{{\lambda}^{2}-{C}_{3}}

(2)

where *B*_{1,2,3} and *C*_{1,2,3} are the Sellmeier constants derived from experimental data. Equation 2 is valid over a range of wavelengths dependent on the material it describes. Hence, dispersion arises from the fact that light of different wavelengths travels through the material at different speeds. In a normally dispersive material blue light travels more slowly and is refracted more than red light.

Frequency components within a pulse will travel with a unique phase velocity of *ν*_{
φ
}= *c*/*n*(*λ*) through a dispersive medium. Pulse broadening occurs when the faster components extend the leading edge of the pulse envelope, while the slower components retard the trailing edge. The instantaneous velocity of this pulse envelope is called the group velocity, *v*_{
g
}. Group velocity dispersion (GVD) is often responsible for producing linear phase changes or chirp across the pulse.

The majority of pulse broadening in ultrashort pulse lasers is caused by the positive group-velocity dispersion of the gain medium. Other intracavity elements such as prisms will also contribute positive dispersion. To obtain the shortest possible pulses from the laser cavity the overall GVD has to be near zero. A practical method for doing this is to introduce pairs of prisms into the cavity, as described by Fork et al. in 1984 [5]. This is known as dispersion compensation. The prism material will itself contribute positive dispersion, but it is possible to configure the prism pairs so that the overall contribution is negative (see Fig. 1). Kang et al. [6] generate negative group velocity dispersion by a single prism and wedge mirror in femtosecond lasers. They discuss that both theoretical analyses and the experimental results show that the GVD is directly proportional to the distance between the prism and the Ti:sapphire crystal. Also they prove that the amount of GVD generated by this method approach that generated by a pair of prisms. Andreas et al. [7] used dielectric mirrors for group-delay dispersion control of s laser cavity free from the problems of cubic dispersion, asymmetric spectra and increased sensitivity of pulse width to cavity and prism alignment. By use of Kerr-lens mode locked Ti:sapphire laser without any intracavity prisms for generating highly stable optical pulses as short as 11 fs. Recently Zeng et al. [8, 9] introduce a single prism before the two dimensional acousto-optical deflector (AOD) to allows simultaneous compensation of spatial and temporal dispersion for two-dimensional scanning.

A prism sequence that provides a way of introducing GVD that is low loss and is adjustable through both positive and negative values. The prisms are cut and orientated so that the rays are incident at minimum deviation and Brewster's angle, to minimize losses. The total dispersion of the prism sequence is calculated as

D=\left[\frac{\lambda}{cL}\right]\frac{{d}^{2}P}{d{\lambda}^{2}}

(3)

where *L* is the physical length of the light path, P is the optical path length. The derivative d^{2}*P*/d*λ*^{2} is a function of the angular divergence *α*, the refractive index of the prism material and the apex separation, *l*, of the prisms. It can be shown that for sufficiently large values of *l* the overall dispersion becomes negative. Therefore, by changing the prism positions it is possible to vary the total dispersion of the cavity from positive to negative. The geometric configuration of the prism pairs can only shorten Ti:sapphire laser pulses to the sub-100 fs regime before which third order dispersion becomes a limiting factor. In order to achieve shorter pulse durations it is necessary to choose a prism glass that has a combined geometric and material contribution which compensates the third order dispersion of the gain medium [10].

Another way of controlling group velocity dispersion, without the need of introducing intracavity glass, is by using chirped dielectric mirrors as the source of broadband negative GVD [7, 11]. Such mirrors have facilitated the generation of sub-5 fs laser pulses [12]. The general formula of group delay dispersion (GDD) as obtained for a general arrangement of the prisms can be written as [13];

GDD=\frac{{\lambda}^{3}}{2{\pi}^{2}{c}^{2}}\frac{{d}^{2}P}{d{\lambda}^{2}}

(4)