Nonlinear contrast mechanisms

Nonlinear light-matter interactions have been successfully applied to create new visualization contrast mechanisms for optical microscopy. Nonlinear optical microscopy employs femtosecond and picosecond lasers to achieve a high photon flux density by focusing the beam onto a sample with a high numerical aperture (NA) microscope... 

This chapter introduces principles of three nonlinear contrast mechanisms— MPF, SHG, and THG—for microscopic imaging. The instrumentation of nonlinear multicontrast microscopy is described, and the methods of multicontrast image analysis are presented. The later parts of the chapter focus on several examples of multicontrast nonlinear microscopy applications in biological imaging. 

Two-photon excitation fluorescence is currently the most widely nsed nonlinear contrast mechanism for microscopic investigations. The first experimental demonstration of two-photon excitation fluorescence was provided in 1961 (Kaiser and Garrett 1961), even though the first theoretical description of two-photon excitation flnorescence stems back to 1931 (Goppert-Mayer 1931). Three-photon absorption was demonstrated a few years later by Singh and Bradley (1964). Two-photon absorption is a third-order nonlinear effect, whereas three-photon absorption is a fifth-order nonlinear effect. The transition rate for two-photon absorption, R, depends on the square of the intensity, /, as follows (see Boyd 1992) ... 

In regard to Equation (5.4), we have to note that without the above mentioned assumptions the nonlinearities will contain weighting factors that are proportional to the corresponding wave-vector mismatch and inversely proportional to refractive index, thus suggesting that the THG signal is sensitive to the refractive index interface(s) as well. In order to differentiate between contrast mechanisms in THG imaging of soft tissue materials it would be important to know the relationships of the corresponding linear and nonlinear optical parameters. A nonlinear optical... 

In this chapter we explore several aspects of interferometric nonlinear microscopy. Our discussion is limited to methods that employ narrowband laser excitation i.e., interferences in the spectral domain are beyond the scope of this chapter. Phase-controlled spectral interferometry has been used extensively in broadband CARS microspectroscopy (Cui et al. 2006 Dudovich et al. 2002 Kee et al. 2006 Lim et al. 2005 Marks and Boppart 2004 Oron et al. 2003 Vacano et al. 2006), in addition to several applications in SHG (Tang et al. 2006) and two-photon excited fluorescence microscopy (Ando et al. 2002 Chuntonov et al. 2008 Dudovich et al. 2001 Tang et al. 2006). Here, we focus on interferences in the temporal and spatial domains for the purpose of generating new contrast mechanisms in the nonlinear imaging microscope. Special emphasis is given to the CARS technique, because it is sensitive to the phase response of the sample caused by the presence of spectroscopic resonances. 

One of the most common trends in the recent development of nonlinear optical spectroscopies for biological imaging is the multimodal approach, which incorporates several spectroscopic techniques in one instrument. This approach allows the employment of several contrast mechanisms, such as fluorescence, second harmonic, and third harmonic (Cisek et al., Chapter 4), significantly increasing the informational content of microscopic imaging. 

The complex quantity, y6br = e (y(3)r) + i Im (x r), represents the nuclear response of the molecules. The induced polarization is resonantly enhanced when the Raman shift wp — ws matches the frequency Qr of a Raman-active molecular vibration (Fig. 6.1A). Therefore, y(3)r provides the intrinsic vibrational contrast mechanism in CRS-based microscopies. The nonresonant term y6bnr represents the electronic response of both the one-photon and the two-photon electronic transitions [30]. Typically, near-infrared laser pulses are used to prevent the effect of two-photon electronic resonances. With input laser pulse frequencies away from electronic resonances, y(3)nr is independent of frequency and is a real quantity. It is important to realize that the nonresonant contribution to the total nonlinear polarization is simply a source for an unspecific background signal, which provides no chemical contrast in some of the CRS microscopies. While CARS detection can be significantly effected by the nonresonant contribution y6bnr [30], SRS detection is inherently insensitive to it [27, 29]. As will be discussed in detail in Sects. 6.3 and 6.4, this has major consequences for the image contrast mechanism of CARS and SRS microscopy, respectively. 

For the understanding of CARS contrast mechanisms, it is essential to discuss in more detail the proportionality of the CARS intensity to the modulus square of the total nonlinear susceptibility in (6.9). Substituting (6.4) into (6.9) yields... 

The chemical specificity of CARS microscopy is readily combined with other nonlinear optical image contrast mechanisms, such as two-photon fluorescence (TPF), SHG, and THG, resulting in a multimodal CARS microscopy [88, 118, 117, 43]. In multimodal nonlinear optical imaging, TPF, SHG, and THG signals all benefit from the use of femtosecond laser pulses of high peak intensities, whereas the contrast and chemical selectivity of CARS benefits from the use of picosecond (narrow-bandwidth) pulses (see discussion in Sect. 6.2.3). As demonstrated by Pegoraro et al. [43], this apparent... 

To date, a number of chemically selective near-field imaging methods have been demonstrated. Near-field contrast mechanisms that rely on electronic spectroscopy (UV-visible absorption and fluorescence),204 vibrational spectroscopy (IR absorption and Raman spectroscopies), dielectric spectroscopy (microwave dispersion), and nonlinear spectroscopy (second harmonic generation) have all been demonstrated at length scales well below the diffraction limit of light. 

In contrast, the nonlinearities in bulk materials are due to the response of electrons not associated with individual sites, as it occurs in metals or semiconductors. In these materials, the nonlinear response is caused by effects of band structure or other mechanisms that are determined by the electronic response of the bulk medium. The first nonlinear materials that were applied successfully in the fabrication of passive and active photonic devices were in fact ferroelectric inorganic crystals, such as the potassium dihydrogen phosphate (KDP) crystal or the lithium niobate (LiNbO,) [20-22]. In the present, potassium dihydrogen phosphate crystal is broadly used as a laser frequency doubler, while the lithium niobate is the main material for optical electrooptic modulators that operate in the near-infrared spectral range. Another ferroelectric inorganic crystal, barium titanate (BaTiOj), is currently used in phase-conjugation applications [23]. 

Oscillations have been observed in chemical as well as electrochemical systems [Frl, Fi3, Wol]. Such oscillatory phenomena usually originate from a multivariable system with extremely nonlinear kinetic relationships and complicated coupling mechanisms [Fr4], Current oscillations at silicon electrodes under potentio-static conditions in HF were already reported in one of the first electrochemical studies of silicon electrodes [Tul] and ascribed to the presence of a thin anodic silicon oxide film. In contrast to the case of anodic oxidation in HF-free electrolytes where the oscillations become damped after a few periods, the oscillations in aqueous HF can be stable over hours. Several groups have studied this phenomenon since this early work, and a common understanding of its basic origin has emerged, but details of the oscillation process are still controversial. 

Note that the applicahon of representation theory to quantum mechanics depends heavily on the linear nature of quantum mechanics, that is. on the fact that we can successfully model states of quantum systems by vector spaces. (By contrast, note that the states of many classical systems cannot be modeled with a linear space consider for example a pendulum, whose motion is limited to a sphere on which one cannot dehne a natural addition.) The linearity of quantum mechanics is miraculous enough to beg the ques-hon is quantum mechanics truly linear There has been some inveshgation of nonlinear quantum mechanical models but by and large the success of linear models has been enormous and long-lived. 

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