For over 100 years fluorescence microscopy has been utilized in biological sciences as a means for identifying the spatial distribution of molecules of interest in complex heterogeneous samples. The first fluorescence microscopes invented by Otto Heimstaedt and Heinrich Lehmann relied on ultraviolet light to induce autofluorescence . Shortly after, in 1914 Stanislav Von Prowazek showed that fluorescent dyes could be bound to living cells  allowing the excitation and emission wavelengths to be engineered independently of the samples native properties.
These fluorescent tags, as they later became known, quickly became standard practice in fluorescence microscopy for many years because they allowed the excitation energy required to induce fluorescence to be greatly reduced. This, in turn, reduced photochemical degradation of the sample by moving from ultra-violet to visible excitation wavelengths, which was extremely advantageous for biological studies allowing for sample integrity to maintained especially for live samples. As a result, fluorescence microscopy has become one of the most widely utilized techniques in biological sciences.
For many years the advantages of fluorescence tags outweighed the disadvantages of the sample preparation requirements, but with the emergence of two-photon fluorescence microscopy in the 1990s , many of these same advantages can now be achieved without any sample pretreatment. As a result, two-photon microscopy, also referred to as multiphoton microscopy, has once again revolutionized the field of biological imaging allowing for the creation of high-resolution images of living cells. Even today, new uses are constantly being discovered.
In this article, we will explore how two-photon microscopy has evolved over the years and the integral role that the mode-locked laser has played in its evolution.
The first prediction of multiphoton excitation was presented in Nobel laureate Maria Göppert-Mayer’s dissertation in 1931, and then experimentally verified 30 years later by multiple research groups including Franken et al. and Kaiser & Garret. Even though the first mode-locked laser was demonstrated around the same time by Logan E. Hargrove, Richard L. Fork, and M.A. Pollack, it took another 30 years before Winfried Denk and his colleagues at Cornell University used one to build the first two-photon microscope. 
In order to fully understand the early technological challenges with this technique, and the important role the mode-locked laser has played in overcoming them, it is important to first have a fundamental understanding of the underlying nonlinear process at hand. As shown in Figure 1 above, two-photon fluoresce utilizes sum frequency generation inside of the sample in order to induce a fluoresces excitation equivalent of a photon with twice the excitation energy.
The simplest way of understanding this nonlinear optical effect is by looking at the relationship between the polarization density (P), the materials susceptibility tensor (X) which is related to the index of refraction of the marital, and the electric field of the incident laser (E). Sum frequency generation, also referred to as second harmonic generation, is what is known as a second-order nonlinear effect and obeys the following relationship,
From Equation 1, it is clear that the effect is highly dependent on the magnitude of the electric field. Since the electric field density is dependent upon both the laser’s spot size and the pulse duration, a tighter focus and a shorter pulse width will result in more efficient two-photon absorption.
In a diffraction limited microscope, the spot size at the sampl