4. Application of Čerenkov harmonic generation to 3D imaging of ferroelectric domain patterns

High-quality visualization of ferroelectric domain structures plays a key role in understanding material property and better control of domain inversion process. However, due to the equality of antiparallel 180� ferroelectric domains in linear optical properties, the common imaging techniques do not apply to the detection of these domains. Currently the selective chemical etching [30] based on the different etching rates of antiparallel domains in hydrofluoric acid is still the most common method used for this purpose. Not only this is a destructive technique, but moreover, it is ineffective in revealing the internal domain structures hidden deep inside the crystals. To overcome some of these drawbacks, a large number of alternative approaches have been adapted to imaging ferroelectric domains, such as advanced electron microscopy [31] and piezo-forced microscopy [32]. However, most of these methods also fail in visualization of deep internal domain structures, which can be diverse and more complex than those on the surface [33]. For example, the inverted domains undergo sidewise expansion with depth [34], transform to preferred shapes depending on the crystallographic symmetry [35, 36], and sometimes merge to form a bigger structures [37]. The details about these domain formation processes such as when, where, and how they occur are very little known due to the lack of reliable techniques for three-dimensional visualization of domain patterns.

It has been shown in Section 2 that when a femtosecond laser beam is tightly focused to produce a focus that is narrow enough to cover a single ferroelectric domain wall, a pair of Čerenkov second harmonic beams will be generated. The Čerenkov signal disappears if the laser beam is moved away from the domain wall. In this way, by recording the second harmonic strengths at different positions inside the crystal, one can obtain a three-dimensional image reflecting the spatial distribution of ferroelectric domain walls (and subsequently domains) inside the crystal. This is a nondestructive imaging method and can offer submicrometer resolution because of its nonlinear optical mechanism [18]. This is a 3D optical method as it also enables one to reveal the details of inverted domains beneath the surface.

Figure 9 displays a schematic illustration of the nonlinear Čerenkov second harmonic imaging system. The fundamental femtosecond laser beam is provided here by a titanium-sapphire laser (Mai Tai, Spectra Physics, 80 MHz repetition rate and up to 12 nJ pulse energy). It is known that in the regime of a tightly focused fundamental beam, the Čerenkov process is insensitive to the wavelength of the fundamental wave. Therefore, this imaging system can operate at a wide range of wavelength limited only by the absorption edge of second harmonic and the total reflection condition. The latter condition means the Čerenkov harmonic emission angle has to be smaller than its total reflection angle so that the Čerenkov signals can get out from the sample for detection. For traditional nonlinear optical ferroelectric materials, such as LiNbO3 and LiTaO3 crystals, the Čerenkov angle becomes larger at shorter wavelength, so the fundamental wavelength used for the visualization cannot be shorter than the critical wavelength.

The main part of this imaging system is a commercial laser scanning confocal microscope (Zeiss, LSM 510 + Axiovert 200). The femtosecond laser beam is coupled into the confocal microscope and then illuminates the sample after being tightly focused by an objective lens (Plan Apochromat, NA = 1.46). A pair of galvanometric mirrors is used to adjust the focus position in the X-Y plane, and a motorized stage is used to move the objective lens in the Z direction. To collect and detect the emitted second harmonic signal, a condenser lens and a

4. Application of Čerenkov harmonic generation to 3D imaging of

Figure 8. Multi-order nonlinear Raman-Nath SHG as a function of crystal thickness (or interaction distance) [29].

reliable techniques for three-dimensional visualization of domain patterns.

High-quality visualization of ferroelectric domain structures plays a key role in understanding material property and better control of domain inversion process. However, due to the equality of antiparallel 180� ferroelectric domains in linear optical properties, the common imaging techniques do not apply to the detection of these domains. Currently the selective chemical etching [30] based on the different etching rates of antiparallel domains in hydrofluoric acid is still the most common method used for this purpose. Not only this is a destructive technique, but moreover, it is ineffective in revealing the internal domain structures hidden deep inside the crystals. To overcome some of these drawbacks, a large number of alternative approaches have been adapted to imaging ferroelectric domains, such as advanced electron microscopy [31] and piezo-forced microscopy [32]. However, most of these methods also fail in visualization of deep internal domain structures, which can be diverse and more complex than those on the surface [33]. For example, the inverted domains undergo sidewise expansion with depth [34], transform to preferred shapes depending on the crystallographic symmetry [35, 36], and sometimes merge to form a bigger structures [37]. The details about these domain formation processes such as when, where, and how they occur are very little known due to the lack of

It has been shown in Section 2 that when a femtosecond laser beam is tightly focused to produce a focus that is narrow enough to cover a single ferroelectric domain wall, a pair of Čerenkov second harmonic beams will be generated. The Čerenkov signal disappears if the laser beam is moved away from the domain wall. In this way, by recording the second harmonic strengths at different positions inside the crystal, one can obtain a three-dimensional

ferroelectric domain patterns

30 Ferroelectrics and Their Applications

Figure 9. Schematic of the Čerenkov harmonic imaging system for visualization of ferroelectric domain patterns in a nonlinear photonic crystal (NPC) [18].

photomultiplier are employed, respectively. Short-pass filters are used to prevent the transmitted fundamental beam from entering the detectors.

The advantages of this nonlinear Čerenkov imaging system include:
