1. Introduction

Second harmonic generation (SHG) is a non-linear parametric optical process that involves the creation of a photon of frequency 2ω in a single quantum-mechanical process simultaneously with the destruction of two photons of frequency ω [1]. It takes place in non-centrosymmetric materials, with non-vanishing second-order susceptibility χ⁽²⁾, such as anisotropic crystals [2], or biological tissues with fibrillar micro-structures (e.g., collagen [3]). Second harmonic (SH) can also be generated and detected in the interfaces between centrosymmetric materials provided that, at the boundaries, the symmetry is broken [4]. The quadratic dependence of the generated second harmonic field (2ω) with the incident fundamental one (ω) implies that the efficiency of the process increases with laser power, and, for that reason, ultrashort laser pulses are the most suitable sources to generate measurable 2ω signals. Besides the possibility of accessing new spectral regions from a given laser wavelength, SHG has become very important due to its complex dependence on the microscopic structure of matter, through the second-order susceptibility tensor, that is exploited in second harmonic microscopy (SHM) [5–7]. SHM is based on scanning the sample (organic or inorganic) with a strongly focused ultrashort laser, measuring the SH signal that is generated at each scanned position of the sample. The SHM technique can reveal rich morphological and structural information in the micro-scale [8], nonlinear properties and/or different chemical composition of the sample [9]. In addition, due to the quadratic dependence of the generated SH signal with the ω intensity, the main non-linear laser-matter-interaction is strongly restricted to the focal volume, thus allowing intrinsic confocal measurements and therefore allowing for precise 3D sectioning of the sample.

Concerning materials science, SHM has shown exceptionally good performance for analyzing different features of non-linear crystals [5,10], and it is particularly useful for 3D imaging of non-linear photonic devices. On the one hand, the boundaries between ferroelectric domains can be detected [11], thus allowing the mapping of complex non-linear structures [12] in materials such as in LiNbO₃ or LiTaO₃. On the other hand, SHM can be used to analyze the modification of the non-linear coefficient in waveguides or other photonic elements fabricated by femtosecond laser irradiation in non-linear crystals [13]. It has been successfully applied to the analysis of depressed-cladding waveguides in BaB₂O₄, BiB₃O₆ and Nd:GdCa₄O(BO₃)₃, showing the preservation of the non-linear susceptibility in the core region and the modification in the irradiated areas [14,15].

In this work we analyze with SHM the damage tracks created by femtosecond laser irradiation in a Nd:YAG single crystal sample. Nd:YAG is a cubic (centrosymmetric) crystal, being one of the most widely used gain media for solid-state lasers due to its outstanding fluorescence yield, thermal and mechanical properties. It has also attracted great attention for the possibility to fabricate embedded compact photonic devices by femtosecond laser irradiation, such as waveguide lasers [16,17], active beam shapers [18], photonic nanostructures [19], or active biosensors [20]. Here, we demonstrate, for the first time to our knowledge, that femtosecond laser damage tracks created inside a cubic crystal such as Nd:YAG may lead to a measurable generation of SH signal, thus producing a localized non-vanishing second-order non-linear coefficient. The effect of the irradiation conditions on the generated SH signal is analyzed in detail and the main mechanisms responsible for this emission are discussed, opening the door to new strategies for the design and fabrication of new non-linear photonic devices working under this SHG scheme. These results showcase as well, the convenience of applying SHM to obtain 3D maps from photonic devices inscribed by femtosecond laser irradiation in Nd:YAG.

2. Experiments in detail

2.1 Nd:YAG sample

The Nd:YAG single crystal sample used in this work was cut with a cuboid shape of dimensions (x × y × z) 10 × 10 × 2 mm³ (see Fig. 1). The two largest faces of the sample and two additional opposing faces were polished to optical grade.

 

Fig. 1. Scheme of the Nd:YAG sample irradiation. Red arrows indicate the propagation direction of the femtosecond laser beam used to inscribe the microstructures. The images in the insets correspond to examples of the structures inscribed in the sample.

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2.2 Sample irradiation

An amplified Ti:Sapphire femtosecond laser system (Spitfire ACE, Spectra Physics) was used to irradiate the sample in order to produce the micro-modifications inside the crystal bulk. In the following we refer to this laser beam as “writing laser” to differentiate it from the laser beam used for SHM measurements (described in section 2.3). The writing laser delivers 60 fs pulses at a central wavelength of 800 nm and at a repetition rate of 5 kHz. Pulse energy and polarization were controlled with a variable attenuator (half-wave plate and linear polarizer), and a calibrated neutral density filter. The beam was focused inside the sample using a 40× microscope objective (NA 0.65), leading to a beam radius at the focal plane of ∼ 0.55 µm (approximated by calculating the beam radius at 1/e² for a Gaussian beam propagating in vacuum). The sample was placed on a computer-controlled three-axes motorized stage with 0.25 µm resolution.

Different sets of irradiations were carried out in the Nd:YAG sample (see Fig. 1). Each set was carried out by irradiating the sample through one of the 10 × 10 mm² faces (pulse propagation along z-axis) and focusing the beam 75 µm below this surface. These sets of irradiations consisted of parallel lines along the x-axis with a length of 250 µm, lateral separation of 15 µm, and increasing pulse energies starting from a value slightly above the damage threshold (42 nJ, 56 nJ, 112 nJ and 224 nJ). The same sequence of energy values was repeated at different scanning velocities (50, 200 and 500 µm/s) and the laser polarization was kept along y-axis (perpendicular to scanning direction). For the selected scanning velocities, the estimated number of pulses reaching each point of the sample were ∼110, 27 and 11, respectively. In addition, different photonic elements were inscribed in the sample. A set of optical waveguides (depressed-index cladding waveguides [16] with hexagonal lattice structure [18]) were fabricated along the z axis, by using a pulse energy of 56 nJ and scanning velocity of 250 µm/s. Finally, some 1D and 2D 60 × 60 µm² microgratings were inscribed at a depth of 25 µm under the sample surface by using a pulse energy of 56 nJ and scanning velocity of 200 µm/s.

2.3 SH microscope

A homemade microscopy set-up, able to operate as a conventional optical microscope and as a nonlinear microscope, was used for the SHM measurements. In the nonlinear mode of operation, the sample is illuminated with 120 fs laser pulses with a central wavelength of 795 nm delivered by a Ti:Sapphire oscillator (Tsunami, Spectra Physics) at a repetition rate of 80 MHz. In the following we refer to this laser beam as “measuring laser”. To ensure the spatial mode quality, the beam was spatially filtered by using a 1:1 telescope composed of two convergent lenses (f = 100 mm) and a 30 m diameter pinhole. A continuous neutral filter wheel allows for gradual regulation of the laser power, reaching a maximum value of ∼ 1 nJ per pulse at the microscope input.

A general sketch of the microscope can be seen in Fig. 2(a). The main components of the system are described in the following. For operation as conventional optical microscope, the sample is illuminated with a white light source (H) from the bottom of the set up. With the help of a tube lens (L) and a polarizing cube (A), the image of the sample is formed on a CMOS camera (K). For the SHM measurements, the measuring laser polarization was controlled by a $\mathrm{\lambda }$/2 plate (B). In the following, we denote as ω₀ and ω₉₀ the horizontal (x-axis) and vertical (y-axis) polarization directions of the fundamental field of the measuring laser, respectively. The measuring laser beam was focused inside the sample using a 50× microscope objective (C) with NA 0.55. Under these conditions, the beam radius at 1/e² is estimated around 0.5 µm. The generated 2ω signal was collected in the forward direction (transmission) with the help of a collector lens (F), followed by a dichroic mirror (G), which reflects wavelengths below 420 nm towards the detection system (J). To further isolate the second harmonic signal at 400 nm from the fundamental beam, a set of two spectral filters, a 335-610 nm band pass filter, and a short-pass filter with 750 nm cut-off, was used in conjunction with the dichroic mirror in order to ensure that no fundamental radiation reaches the detection system. Detection can be performed either by a Photomultiplier Tube (PMT), a CMOS camera or a spectrograph equipped with an intensified CCD camera. Samples (D) were placed between the objective and the collector lens on a piezoelectric positioner (P-545 F, PI-Micos) coupled to a digital piezo controller (E-727, PI-Micos). This positioner (E) has a precise movement control of <1 nm and a maximum travel range of up to 200 µm in the xyz axes. The PMT signal was amplified with the lock-in technique and the intensified signal was sent to the digital piezo controller, while being also simultaneously monitored by a digital oscilloscope. In this way, sample motion and signal acquisition are synchronized. All SHM images shown are background corrected without any further signal processing.

 

Fig. 2. (a) Schematic representation of the SHM set-up: A, Polarizer cube; B, λ/2 plate; C, objective; D, sample; E, piezoelectric positioner; F, collecting lens; G, dichroic mirror and filters; H, white light illumination source; J, detection system (photomultiplier tube, CMOS camera or spectrograph); K, CMOS camera; L collecting lens. (b) SH signal beam projected onto a CMOS camera in J. The inset shows a conventional microscope image of the analysed damage track and corresponding scanned position (yellow circle). (c) Typical SH spectrum obtained from the scanned position.

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2.4 Micro-Raman spectroscopy

The nature of the modifications induced by the writing laser was studied by analyzing the damage tracks by micro-Raman spectroscopy. For that purpose, a confocal Raman microscope (Renishaw inVia Reflex) was used. For excitation, a laser centered at 514 nm was used to target the T2g ∼378 cm^-1 phonon mode, since it is characteristic of the YAG lattice. The laser beam, focused through a 100× objective (1.4 NA), was linearly polarized along the x-axis. The step size of the measurements was set to 0.8 µm. The backscattered signal was collected through the microscope and linearly filtered also along the y-axis before reaching a high-resolution spectrometer. Raw data were processed with the help of Renishaw WIRE 3.2 software.

3. Results and discussion

In a first experiment, the measuring laser beam was focused on the center of one of the inscribed damage tracks, detecting the generated signal with the CMOS camera of the microscope in the transmission configuration. The obtained image is shown in Fig. 2(b), displaying the SH beam generated at the focusing point. As it can be seen, the signal exhibits an elongated shape in the perpendicular direction with respect to the track orientation (see Fig. 2(b) inset). Moving the focusing point along the track results in a slight variation of the signal shape and intensity. The SH beam shape could be explained by the spatial confinement of the modified region (∼1 µm) in the transverse direction. Then, we checked the spectral features of the SH signal replacing the camera by the tip of a spectral fiber coupled to the spectrograph. As it can be seen in Fig. 2(c) we obtained a very clean spectrum with large signal-to-noise ratio. The peak of the SH signal is centered at 397.2 nm, in good agreement with the peak of the fundamental pulse (∼795 nm), and it has a spectral width (FWHM) of 6.5 nm, fitting well with the 16 nm spectral width of the fundamental pulse.

Once we confirmed the generation of SH signal localized at the damage tracks, we analyzed in detail the features of the SH emission in terms of the irradiation parameters of the inscribed damage tracks. For that purpose, we used the PMT coupled to the microscope for detection, obtaining several SH maps by scanning the sample with the focus of the measuring laser in the XY plane. The depth at which the measuring beam was focused was stablished by searching for the maximum intensity of the SH signal at the tracks. Then, 2D maps with dimensions of 20 × 54 µm² were obtained adjusting a step size of 0.3 µm in the nanopositioning system. As example, we show in Fig. 3 the recorded maps of parallel damage tracks inscribed at 50 µm/s, for the two polarizations of the measuring laser. As can be seen, the emitted SH signal is clearly localized at the damage tracks, and it exhibits a clear dependence with the inscription pulse energy as well as with the polarization of the measuring laser.

 

Fig. 3. (a) Conventional optical microcopy image (white light illumination) of the damage tracks produced at a scanning velocity of 50 µm/s for different pulse energies, as indicated. (b) and (c) Corresponding SHM maps obtained from the tracks using different polarizations of the measuring laser (black arrow indicates the polarization direction, ω₀ for horizontal and ω₉₀ for vertical polarization). SHM maps were acquired with a step size of 0.3 µm. Note that (b) and (c) SHM maps have different intensity scale bars, thus background noise appears higher in the map in (b).

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For the sake of clarity, we have integrated the SH intensity emitted at each sampled position along the damage tracks, plotting the result in a single 2D graph. In this way, we reduce the signal fluctuations that arise from possible variations in the sample response coming from sample inhomogeneities or caused by fluctuations in the irradiation conditions. In Fig. 4 we show the results obtained for the two polarizations of the measuring laser. From the results, some general trends can be extracted. The first one is that the SH signal increases with increasing the inscription pulse energy, although the slope does not remain constant and tends to decrease for pulse energies above 112 nJ. The second one concerns the scanning velocity, with the overall trend showing an increase in the SH signal as the scanning velocity is reduced (increased pulse overlap). Finally, it can be seen that irradiation with the measurement laser polarization along the y-axis (ω₉₀) generates a more intense SH signal than with the polarization set along the x-axis (ω₀).

 

Fig. 4. Integrated SH signal intensity as a function of the energy of the writing laser pulses used for the inscription of the damage tracks in the Nd:YAG at the indicated writing velocities and polarizations of the measuring laser.

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The origin of the SH signal generated at the damage tracks must be explained in terms of the micro-modifications induced in the YAG structure by the laser irradiation. Different studies have revealed a very complex phenomenology that takes place at the microscopic scale, depending on the irradiation conditions: pulse energy, pulse duration, repetition rate, pulse overlap or polarization direction. A first kind of modification is described as a locally modified crystalline state characterized by different inter-atomic distances as well as by the presence of lattice defects [21]. This modification has been also reported in [22] and explained in terms of a plastic deformation in the crystal (dislocations) that may also present different modes depending on the pulse overlap. This mechanism can be found both in the thermal [21] and non-thermal irradiation regimes [22] and can also be linked to the presence of an amorphized region [23,24] in the core of the damage tracks. Another modification type is the formation of periodic structures or nanogratings in the amorphized region [24]. Finally, phase transformation can also be found at the tracks [24,25]. Both the nanograting formation and the phase transformation require, in general, irradiation in the thermal regime.

Our experiments have been performed in the non-thermal regime (low repetition rate), and with pulse energies ranging from the modification threshold (∼ 40 nJ) up to 5 times that value, and then, in such a wide range of pulse energies, different modification mechanisms are expected to take part. For pulse energies near the damage threshold, we expect the pre-damage state and dislocation mechanism to be present [21,22], and a severe damage with the appearance of an amorphized region [23,24] could be found as the pulse energy increases. Both, dislocations and the presence of an amorphized region, can be responsible for the generation of SH. In the case of the dislocations, the SH signal may appear due to the change in the inter-atomic distances in the dislocation surfaces. The presence of a large density of dislocations could lead to a rather uniform SH signal along the damage track. In the case of the appearance of an amorphized region, the boundary between the crystal and the amorphous region breaks the inversion symmetry and a second-order non-linear response will appear at the interface. In this case, the laser polarization for a more efficient SH signal is the one perpendicular to the interface [26], provided it is the field orientation that probes the damage-induced anisotropy. Our hypothesis is that the larger SH signal measured for the polarization perpendicular to the tracks comes mainly from the boundaries of a severe damage region where a core of amorphous material would be present. The SH signal generated for the parallel polarization, most probably comes from the dislocations and from the inhomogeneities of the amorphized region boundaries. Reducing the scanning velocity or rising the pulse energy could both increase the density of defects or enlarge the extension of the damaged area, effects that can contribute to an increase in the SH signal.

To gain more insight into the damage mechanisms underlying the non-linear response, we carried out micro-Raman measurements for different damage tracks, as well as detailed SH maps in the transverse plane to the track direction. In Fig. 5(a-c) we show the measurements corresponding to a writing laser pulse energy of 56 nJ and a scanning velocity of 200 µm/s and polarization along y-axis (perpendicular to the writing direction). As it can be seen in Fig. 5(b), the SH is generated in a well-defined central region of the track extended along a width around 0.5 µm (in the limit of our resolution). In Fig. 5(c) we show the micro-Raman spectra of the points marked in Fig. 5(a) with yellow circles. Those points correspond to the central core of the damage track and to a non-irradiated region. At the track, the spectrum structure is well preserved with respect to the non-irradiated bulk, but a slight decrease in the peak intensities appear, revealing the presence of defects in the irradiated region. The same study was performed for a damage track inscribed with a higher pulse energy of 224 nJ (Fig. 5(d)-(f)). In this case, the SH map in Fig. 5(e) reveals a larger damage region with a more complex structure. The most intense emission is produced in the central part, denoting probably the presence of amorphous material, and it is surrounded by an area with less intense SH emission that extends for 12 × 1.5 mm². The corresponding micro-Raman spectra (Fig. 5(f)) shows again that the peak structure is preserved (dismissing the presence of phase transformation) but a drastic decrease in the intensity appears. Although it is not evident in the plot, a careful analysis of the spectra also reveals a peak widening. Such behavior is in agreement with the induction of a strong damage, disorder, and the possible presence of an amorphous core [23].

 

Fig. 5. (a) Conventional microscopy image of the transverse section of a laser induced damage track inscribed with a pulse energy of 56 nJ. The yellow circles indicate the sampled positions where the micro-Raman measurements were performed. (b) Corresponding SHM map obtained with a step of 0.3 µm. (c) Corresponding micro-Raman spectra. Panels (d), (e), and (f) show the equivalent optical image, SHM map and micro-Raman spectra for a damage track inscribed with a higher pulse energy of 224 nJ. The contrast of the optical images has not been artificially modified to emphasize the good performance of the SHM technique.

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A direct application of our results is the 3D imaging of photonic devices, such as optical waveguides or microgratings, inscribed by femtosecond laser irradiation in centrosymmetric crystals. We have tested such capability firstly, with depressed-index cladding waveguides fabricated with hexagonal lattice geometry and laser parameters chosen for optimum light confinement (see Section 2.2). In order to characterize the three-dimensional structure of the waveguide, a set of x-y maps performed at different depths of the sample, using ω₉₀ polarization (that is, perpendicular to the tracks orientation) were obtained. The 3D waveguide profile reconstruction based on the SHM maps is shown in Fig. 6(a). As it can be seen, we retrieve the perfectly defined 3D structure of the damage tracks forming the waveguide cladding. The areas between tracks, as well as the waveguide core, remain completely dark, as it is expected due to the absence of damage in those regions. Finally, we show the SHM maps obtained from 1D (Fig. 6(b)) and 2D (Fig. 6(c)) microgratings inscribed in Nd:YAG with periodicity of 3 µm and 2 µm, respectively. As it can be observed, the signal is strongly localized at the damage tracks, clearly revealing the grating structures. In the case of the 2D grating, the signal is enhanced at the crossings between two lines, most probably due to the damage overlap in these regions. The signal intensity drift towards the bottom of the structure is most probably caused by a small tilt of the sample during the measurements.

 

Fig. 6. (a) 3D reconstruction of the SH signal obtained from a section of a cladding waveguide with hexagonal profile fabricated by femtosecond laser irradiation in a Nd:YAG crystal. Top left: frontal view; top right: side view; bottom left and right: oblique views. Dotted green lines serve as a guidance for better 3D visualization. (b) SHM map of a 1D micrograting inscribed in Nd:YAG. (c) SHM map of a 2D micrograting inscribed in Nd:YAG.

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4. Conclusion

In summary, the micro-modifications induced by the irradiation of a centrosymmetric crystal (Nd:YAG) with femtosecond pulses, enable the creation of localized second-order non-linear response that can be revealed with the process of SH generation. A wide range of pulse energies above the modification threshold were explored, demonstrating SHG in all the cases, being the most efficient polarization of the measuring laser the one perpendicular to the damage tracks orientation. The origin of the laser-induced second-order non-linear response can be well explained in terms of the different damage mechanisms of Nd:YAG reported in literature, such as the creation of defects and dislocations, or the formation of an amorphous core. The observed non-linear behavior allows the use of SHM as a powerful technique for 3D imaging and diagnosis of photonic devices micro-structured by femtosecond lasers, not only in non-linear materials (where the technique had been extensively employed) but also in centrosymmetric crystals. Finally, the possibility to generate localized SH from the bulk of Nd:YAG opens the door to the design and fabrication of a novel family of non-linear photonic devices, whose efficiency could probably be enhanced by strategies similar to quasi-phase-matching. Our findings suggest that this strategy could be extended to other centrosymmetric crystals.