Record-high positive refractive index change in bismuth germanate crystals through ultrafast laser enhanced polarizability

Unlike other crystals, the counter intuitive response of bismuth germanate crystals (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {Bi}}_4{\text {Ge}}_3{\text {O}}_{12}$$\end{document}Bi4Ge3O12, BGO) to form localized high refractive index contrast waveguides upon ultrafast laser irradiation is explained for the first time. While the waveguide formation is a result of a stoichiometric reorganization of germanium and oxygen, the origin of positive index stems from the formation of highly polarisable non-bridging oxygen complexes. Micro-reflectivity measurements revealed a record-high positive refractive index contrast of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4.25\times 10^{-2}$$\end{document}4.25×10-2. The currently accepted view that index changes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>1\times 10^{-2}$$\end{document}>1×10-2 could be brought about only by engaging heavy metal elements is strongly challenged by this report. The combination of a nearly perfect step-index profile, record-high refractive index contrast, easily tunable waveguide dimensions, and the intrinsic high optical non-linearity, electro-optic activity and optical transparency up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5.5\,\upmu {\text {m}}$$\end{document}5.5μm of BGO make these waveguides a highly attractive platform for compact 3D integrated optics.


Results and discussion
Differential interference contrast (DIC) microscope images of the inscribed waveguides are shown in Fig. 1. Terminologies of "shell" which is the highly distinguishable peripheral halo and "core", which is the region at the center will be used throughout the manuscript. The processing windows for type-I waveguides with smooth positive refractive index that are crack-free were found to be, 50-80 nJ for 2,000-4,000 mm/min and 50-130 nJ for 1,000 mm/min. Waveguides written with energies ≥ 90 nJ with 2,000-4,000 mm/min also exhibited a smooth positive refractive index change, but due to BGO's high thermal expansion coefficient 18 of 7 × 10 −6 / • C , cracks formed along the boundaries between modified and unmodified material and were running down the waveguiding structures. The inverted tear drop structure of the waveguides can be attributed to a combination of spherical aberrations, Kerr-nonlinearity and an extended confocal parameter due to the high linear and nonlinear refractive index of BGO. For feed rates slower than 1,000 mm/min, an additional optically dense vertical filament-like structure became apparent within the core ( Fig. 1f-h) . These filament structures likely resemble the shape of the laser induced plasma profile, as observed in phosphate glass 19 . This is supported by the observation of identical outer shell width irrespective of feed rates (Fig. 1c,f). Figure 1a-d shows waveguides written at 1,000 mm/ min with energies ranging between 60 and 130 nJ. Figure 1e illustrates the crack formation at high feed rates (4,000 mm/min). All waveguides shown in Fig. 1e-g were written with 90 nJ energy. With decreasing feed rate the index contrast gradually vanishes due to slow quenching and self-annealing. The waveguides in Fig. 1c,f formed by identical pulse energy (90 nJ) but at feed rates of 1,000 and 500 mm/min, respectively, exhibit significant differences. Quench times of 30 and 60 ms were calculated 20 from the time it takes to translate the sample by the average structure width of 5 um. Hence a 60 ms re-solidification window is too long to either produce a modification or provides enough time for the melt to re-attain its long range order.This suggests that in BGO the interplay between rapid thermal quenching and heat diffusion is critical for the formation of optical waveguides. Micro-reflectivity ( µ-PL) was used to measure the two-dimensional refractive index profiles (Fig. 2) at 833 nm with a spatial resolution of ∼ 0.25 µm (Olympus Plan N oil immersion microscope objective, 100× , 1.25 NA). The obtained 2-dimensional reflectance profile was converted into a refractive index profile using the Fresnel formula. The back surface was polished at ∼ 45 • to avoid retro reflections that affects the measurement. A record refractive index change value of 4.25 × 10 −2 is observed for the waveguide inscribed at 1,000 mm/min. A value of 1.7 × 10 −2 being the previous best was reported very recently using femtosecond-laser-induced electronic band-gap shift (FLIBGS) technique 21 . But the same was limited to a particular operating wavelength in visible. Also, unlike other previously reported peak index values in amorphous media, the index change in the current report is highly uniform throughout the core area and resemble a perfect step-index. Additionally, there is an absence of negative index zones, which are typically found for high-index waveguides in vitreous media 19,22 .
To reveal the structural dynamics of waveguide formation, micro-Raman spectroscopy was carried out using 633 nm excitation wavelength on a Renishaw inVia Raman microscope in confocal mode using a 100× objective (spatial resolution ∼ 0.5 µm ). Figure 3 depicts the Raman spectrum of unmodified BGO exhibiting peaks between 65 and 820 cm −1 . The key features of BGO's crystalline structure are (1) a distorted octahedral environment of oxygen around the Bi 3+ ions, (2) influence of heavier Bi-O atoms on the low Raman frequencies and   23,24 . The Raman spectrum of BGO is generally divided into two regions. The first region between 60−300 cm −1 , referred to as external vibrations, are the lattice vibrations corresponding to the motion of whole GeO 4 tetrahedral groups against the Bi 3+ ion sub-lattice. The second region between 360−820 cm −1 corresponds to isolated GeO 4 tetrahera and is typically referred to as internal vibrations 23,24 . Since the vibrations are originating from a crystal, they are assigned to possible transverse optic (TO) or longitudinal optic (LO) phonons. The bulk crystal featured two additional Raman peaks at 1, 210 cm −1 and 1, 627.5 cm −1 (inset of Fig. 3), which have not been reported previously. Their high frequencies suggest that they are likely a combination mode from low frequency vibrations or vibrations of H 2 O that are trapped within the matrix. The elevated baseline at higher wavenumbers ( > 2, 000 cm −1 ) is due to the luminescence tail caused by defects which will be discussed in detail later on. For Raman mapping a waveguide free of cracks, written at 90 nJ and with 1,000 mm/min, was chosen ( Fig. 4). Figure 4a shows the spatial map of the peak at 201.5 cm −1 , which arises from lattice vibrations. While the peak frequency shift for lattice vibration ( 60−300 cm −1 ) was fairly low, the 201.5 cm −1 band shows a distinct increase in frequency ( +0.3 cm −1 ) in the shell (red pixels) and decrease in the core (dark blue pixels) relative to the pristine bulk. For the internal vibration, assigned to wavenumbers > 360 cm −1 , none of the peaks exhibit a peak   (Fig. 4b). This band is assigned to the degenerate bending vibration of the isolated GeO 4 tetrahedron. Unlike for lattice vibrations, both core and shell regions exhibit a decrease in frequency shift, with the decrease more pronounced in the shell. The 361.5 cm −1 band shows an increase in frequency at the bottom tip of the modification due to the mechanical stress typical for laser inscribed modifications in crystalline materials 7 . Additionally, the 361.5 cm −1 band shows an increase in frequency at the bottom tip of the modification. This could be a result of mechanical stress, which is typical for laser inscribed modifications in crystalline materials 7 . Also, the lattice vibration at 123.8 cm −1 exhibits a similar feature (Fig. 4c). The peaks at 361 cm −1 and 123.8 cm −1 arise from transverse optical phonons which have an additional magnetic field component in comparison to the longitudinal optical phonon vibration at 201.5 cm −1 . A detailed polarized Raman spectroscopy could reveal further information on the origin of this stress field. By comparing the spatial morphology of the frequency shift of the 201.5 cm −1 (lattice, low frequency vibrations) and 361.5 cm −1 (internal, high frequency vibrations) peak, a pattern of inversion is evident. This is indicative of the migration of elements between the core and shell, since bismuth based vibrational units occupy the low frequency region ( < 360 cm −1 ) and germanium associated bands occupy the higher frequency regions ( > 360 cm −1 ). Mapping the distribution of FWHM (Fig. 4d-f) reveals an overall broadening of the vibrational bands in the laser modified regions with respect to the pristine bulk material. This indicates amorphisation within the structures. The lattice vibrations at 201.5 cm −1 and 123.8 cm −1 exhibit the strongest broadening in the core region. In contrast, the internal vibration at 361.5 cm −1 only features a marginal bandwidth increase in both core and shell. Changes in bandwidths are more pronounced in comparison to peak shifts, which indicates that amorphisation is one of the key initiator for waveguide formation.
The field-emission backscattered electron (BSE) image, which gives contrast based on atomic number (Z-contrast) of the same 1,000 mm/min, 90 nJ waveguide reveals strong elemental variation across the waveguide's cross-section (Fig. 5). The shell region (bright boundary) shows an increase in heavy elements, whereas relatively lighter elements are accumulated in the core (dark area). The BSE image rules out the possibility of refractive index increase through stress-induced localized density variation due to the rapid quench at high feed rates. If that was the case then the core would generate more backscattered electrons and a higher Z-contrast(psuedo) due to incident electron beam interacting with more nuclei (protons) of stress accumulated constituent atoms compared to the unirradiated zones 20 .The compositional maps (insets of Fig. 5) acquired using electron probe micro-analysis (EPMA) by utilising wavelength dispersive X-ray spectroscopy (WDS) clearly confirm elemental migration. A migration of the heavy bismuth (at. no. 83) to the shell and migration of the lighter germanium (at. no. 32) and oxygen (at. no. 8) to the core. The secondary electron image showed an entirely flat and featureless surface morphology except for a sub-micron void structure found at the focal point (black spot in Fig. 5 BSE  image).
From the BSE image, the positive index in the shell can be explained by densification due to the migration of relatively heavy Bi (bright zones due to the at. no. contrast) but the positive index in the core could not be explained as it shows as a rarefied zone (darker zones) 20 . The increase of refractive index in the core due to the migration of elements that exhibit a higher electronic polarizabiliy ( α e ), as for instance observed in the case of chalcogenide glass 25 , can be ruled out since the discrepancy of polarizability between Ge ( 0.137 × 10 −24 cm 3 ) and Bi(1.508 × 10 −24 cm 3 ) is more than one order of magnitude 26 . This indicates the possible formation of a large number of non-bridged oxygen in the core. Non-bridging oxygen possesses a significantly higher polarizability To investigate the presence and identify the type of non-bridged oxygen, confocal micro-photoluminescence ( µPL ) was carried out using excitation lasers between 442 and 1,064 nm. Due to the wealth of publications based on Si compared to relatively few on Ge, the discussion here is based on Si as it is isochemical to Ge. No PL relating to interstitial O 2 , O 3 29 , oxygen deficiency related centers (ODC) 30 or Ge based non-bridging oxygen ( ≡ Ge−O − ) 31 was detected. The excess availability of oxygen in the core due to migration can induce the formation of nonbridging oxygen hole centers (NBOHCs) and/or interstitial molecular oxygen, which are generally found and reported in oxygen excess silica. From the experimental observation, no Raman vibrations or PL of interstitial O 2 ( O + O → O 2 , ex = 1,064 nm , em = 1,275 nm , FWHM =∼ 12 nm ) molecules were found and the luminescence of O 3 are usually in the UV region ( O 2 + O → O 3 , em = 258 nm), which is below the UV absorption edge of BGO crystals 29 . It is possible that O 2 and O 3 are formed, but their existence might be a transient phase before they are converted to other defects. PL due to oxygen deficiency related centers (ODC) 30 was absent or could not be observed with any of the excitation wavelengths. Since the core is enriched by the influx of oxygen, PL from the oxygen excess defects 30 is expected, such as Ge based non-bridging oxygen ( ≡ Ge-O − , ex = 590−656 nm , em = 666 nm, FWHM =∼ 58 nm) 31 and/or peroxy linkage or peroxy radical center based defects.
Of all the excitation wavelengths, only 785 and 830 nm laser wavelength gave a PL spectra centered between 890 and 900 nm for different waveguides, as shown in Fig. 6a. The PL was observed only from the core of the waveguide for feed rates between 1,000 and 4,000 mm/min. The bulk crystal did not show any PL (plotted in red in Fig. 6a). From the broad peak it can be understood that the PL arises from amorphous sites and no crystalline stark splitting is observed. The previous reports tentatively attributed the broad PL band centered at 867 nm (1.43 eV) to the presence of a higher energy lying (326 nm/3.8 eV for silica) absorption band 32 . This UV absorption band was in turn attributed to the presence of peroxy radicals or otherwise known as superoxide   Figure 6b shows the spatial map of PL intensity for the 90 nJ and 1,000 mm/min waveguide. It indicates a higher density of peroxy linkages at the top of the core overlapping with the location of the vertical filament-like structure observed in Fig. 1f for waveguides written at lower feed rates. This suggests that the formation and distribution of such defects tend to follow a thermal gradient profile which is effectively the in-situ plasma profile as reported in phosphate glass waveguides (figures 4 & 8 in 19 ). Hence shaping the plasma profile within the matrix should provide a direct tunability on the waveguide morphology, a key factor in waveguide design. Using the same excitation wavelengths (785 and 830 nm), the peroxy radical PL was absent for feed rates slower than 500 mm/min. This is also reflected in the absence of a positive index zone at the core (Fig. 1d).
Using the above evidence the waveguide formation can be explained as follows: As soon as the excitation/heat source is spatially displaced (at feed rates > 500 mm/min) and thus initiating fast quenching, oxygen migrates to the core, forming large numbers of superoxide radicals. This must occur within the re-solidification window. As a crystal with long range order (Fig. 7a), the bond breakage and formation of non-bridging oxygens can preferentially attract divalent cations to fulfill a cross link between two entirely different chains terminated with NBO. Germanium, as the divalent cation among the two glass formers, therefore undertakes paired migration towards the core with oxygen (Fig. 7b). However from the PL results it is clear that Ge migration is insufficient for a complete cross linking of NBOs ( · · ·O − ↔ Ge 2+ ↔O − · · · ). The magnitude of polarizability induced by the non-bridging oxygen depends on the linking cation field strength. The linked cation Germanium possesses a small ionic radius and a strong field strength, causing strong electron cloud asymmetry (Fig. 7c) that induces a high polarizability on the terminal NBOs which are present within its chain. Bismuth on the other hand suffers from a bulk steric effect due to its larger ionic radius and thus can only induce weak polarizability on terminal NBOs (Fig. 7d) 33 . This explains how the paired migration of Germanium and oxygen result in an increase of refractive index to such unprecedented high levels.
Utilizing polarizability of oxygen in glass making is a well known technique to obtain high refraction without engaging heavy elements. Also, a possibility of producing positive index waveguides in diamond by tuning its polarizability through ion beam damage was proposed recently 34 . But this report is the first instance where such a technique is fully exploited to produce and tune type-I waveguides, thereby demonstrating its superiority over other techniques 22 . Hitherto it was generally accepted that tunable index changes of 10 −2 could be brought about only by engaging heavy metal elements within waveguiding structure 22 . While all other factors leading to density decrease (outflow of Bi 3+ and phase change from cyrstalline to amorphous) and molar refraction (outflow of Bi 3+ ) effectively work to lower the index, the observed increase in refractive index of 4.25 × 10 −2 ( ≈ 6.4% increase from its base crystal refractive index) proves the importance of polarizability linked to anions. These observations provide more insights towards the future design of super-high refractive index waveguides in dielectric media induced by ultrafast lasers.  To conclude, type-I waveguide formation by femtosecond laser direct-writing in a BGO is explained for the first time. Raman spectra demonstrated inverted behaviour of peak shift between external and internal vibrations, indicating migration of elements between the core and cladding of the inscribed structure. The large peak bandwidth increase for all the Raman bands indicated significant amorphisation within the structure. BSE and WDS confirmed the migration of bismuth to the peripheral shell and germanium and oxygen to the core. This revealed that the positive index core, with a record value of 4.25 × 10 −2 , is not formed due to densification or change in molar volume. A µPL spectroscopy from the waveguiding region confirmed the formation of large numbers of non-bridging oxygen associated to the peroxy radical. Non-bridged oxygen has a high polarizability compared to bridged oxygen causing the significant increase in refractive index.

Methods
The waveguides were fabricated in commercially acquired BGO crystals ( n D = 2.109 18 ) using an extended cavity Ti:Sapphire chirped pulse oscillator (CPO), operating at a 5.1 MHz repetition rate, emitting sub-50 fs laser pulses at a center wavelength of 800 nm (FEMTOSOURCE scientific XL 500, Femtolasers GmbH). The circularly polarized laser beam was focused to a depth of 170 µm below the sample surface by a 100 × 1.25NA oil immersion objective (refractive of the immersion oil used was n D = 1.518 ). To fabricate the waveguides, pulse energy was varied between 50 and 250 nJ and the feed rates between 10-4,000 mm/min. The micro-reflectivity technique was used to quantitatively measure the refractive index profile of the waveguides. For this purpose, the back surface of the BGO sample was polished at a 45 • angle to avoid back reflections from the waveguide end. The light from a single-mode fibre-coupled superluminescent diode ( = 833 nm , FWHM = 20 nm) was focused by an Olympus 100× oil immersion microscope objective (Plan N, NA 1.25) to achieve a spatial resolution/spot size of ≈ 0.3 µm . The recorded 2-dimensional reflectance profile was converted into a refractive index profile using the Fresnel formula. Micro-Raman spectroscopy was carried out using 633 nm excitation wavelength on a Renishaw inVia Raman microscope in confocal mode using a 100× objective (spatial resolution ∼ 0.5 µm ). The obtained spectra were deconvolved by pseudo-Voigt curve fitting to identify the Raman bands. A mapping of 30 × 40 µm area with waveguide as the center was done to understand the material response to ultrafast laser pulses. Micro-photoluminescence measurements were also conducted in confocal mode to maximize the resolution and restrict the light excitation and luminescence collection exclusively from the area of interest. A 100× objective with a spatial resolution of ∼ 0.5 µm was used. To reveal the elemental migration an electron probe micro analysis (EPMA) based on wavelength dispersive spectroscopy (WDS) was used. Scanning electron microscope imaging and X-ray intensity mapping of constituent elements were carried out on a JEOL JXA-8500F field-emission EPMA.

Data availability
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.