1. Introduction

Structural modifications on the surface and within the bulk of transparent materials can be induced by femtosecond pulsed lasers with high repetition rates which produce localized heating via nonlinear absorption [1–3]. Under the right conditions, these modifications can include the nucleation and growth of crystals [4–14]. Such a technique enables the creation of 3D integrated optical circuits within glass. To fully realize the potential of such an application, however, these crystals must act not only as passive elements such as waveguides [4, 5] and splitters [4], but also as active elements such as modulators, nonlinear sources, or lasers. Lasers, of course, require that the crystals are doped with appropriate ions.

For the present work LaBGeO₅ was chosen as model system because it crystallizes congruently and therefore avoids complications such as elemental diffusion. Furthermore, femtosecond laser-induced-crystallization in undoped LaBGeO₅ is already well studied [4]. Finally, any rare earth dopant should easily substitute for lanthanum, minimizing defects and fluorescence quenching due to clustering. Indeed, rare earth doping of LaBGeO₅ in both the glassy and crystalline phases has been a topic of interest for the past three decades, particularly in the pursuit of efficient and novel gain media for self-frequency-doubled lasers [15,16]. The optical properties of crystalline Nd³⁺- and Pr³⁺-doped LaBGeO₅ have been studied extensively [17], and CW laser radiation was achieved in bulk single crystal LaBGeO₅:Nd³⁺ by Capmany et al. [18]. However, little information exists related to the fluorescence properties of crystalline Er:LaBGeO₅. Rulmont and Tarte studied the synthesis and structural properties of various LnBGeO₅ borogermanates, including ErBGeO₅, determining that the crystal structure changes from hexagonal to monoclinic as the ionic size of the lanthanide decreases [19]. Malashkevich et al. have also investigated the characteristics of Er:LaBGeO₅ luminescence; however their study was limited to the glassy phase only, many of which were co-doped with Yb³⁺ [20]. Nevertheless, erbium is an important dopant ion due to its potential applications arising from its emission around 1.54 µm, which is conveniently within the transmission window of silica fibers. Therefore, this work endeavors to expand knowledge on the following two fronts with the ultimate goal of creating a new type of lasing medium for use in photonic integrated circuits: 1) erbium-doped LaBGeO₅ crystal versus glass as a material system, and 2) spatially-selective growth of crystals inside of an Er:LaBGeO₅ glass using a pulsed laser. Additionally, as an added benefit toward studying the laser-induced crystallization process, erbium fluorescence may be used as an excellent probe of the local structure when measured in combination with Raman spectroscopy.

For eventual applications in lasers for all-optical integrated circuits to be realized in crystals-in-glass, the properties of the erbium ions in both the glass and crystal phases must be understood. This work presents a quantitative analysis of the fluorescence properties of Er:LaBGeO₅, as well as comparisons between conventional glass-ceramics and laser-induced crystals of varying erbium concentrations.

2. Experimental setup and procedure

Neodymium-, praseodymium-, and erbium-doped lanthanum borogermanate glasses were prepared via the normal melt-quenching method using high purity La₂O₃ (99.99%), H₃BO₃ (99.99%), GeO₂ (99.999%), Nd₂O₃ (99.99%), Pr₂O₃ (99.9%), and Er₂O₃ (99.999%). The batch powder weights were determined for the desired composition while also compensating for the 1.9 wt% B₂O₃ loss reported by Sigaev et al. [21]. The mixture was melted in a platinum crucible at 1250 °C for one hour and the melt was subsequently quenched between two steel plates pre-heated to 500 °C. The cast was annealed for two hours at 650 °C. The resulting glasses were then cut and polished to optical quality.

The laser irradiation process was performed using a regeneratively amplified Ti:Sapphire pulsed laser with a wavelength of 800 nm, a pulse repetition rate of 250 kHz, and a pulse width around 60 fs. A 50x/0.55NA microscope objective focused the beam into the sample, which was mounted inside a heating chamber held at 500 °C in order to help relieve thermal stress and prevent cracking. The heating stage was mounted to an XYZ translational stage. Because the incident laser must travel through both the heating chamber window and the sample material above the desired focal point, it experiences significant spherical aberration which produces a long, narrow focal profile that results in elongated crystal cross-sections (e.g. Fig. 7, top). To correct for this effect, a liquid crystal on silicon spatial light modulator (LCOS-SLM) was used as described by Stone et al. [22]. After compensating for spherical aberration, the laser intensity is focused to a tighter volume rather than being spread out along the propagation axis, and the crystal cross-sections become shorter and wider relative to the uncorrected case (e.g. Fig. 7, bottom). In each new sample, a seed crystal was created by continuously irradiating a single spot until nucleation occurred. Once a seed crystal formed, a seed line from which all other lines were grown was produced. Crystalline lines were grown from these seed lines while systematically varying the laser power, focal depth, and sample translation (writing) speed for both aberration-uncorrected and aberration-corrected conditions. Once the laser crystallization process had been performed such that crystal lines were grown through the samples, the samples were cut perpendicular to the line growth direction so as to expose the crystalline cross-sections and then polished again to optical quality.

In order to compare the laser crystallization process to more conventional bulk crystallization techniques, small pieces of each glass composition produced were heated to 670 °C for two hours in order to stimulate crystal nucleation. The temperature was then ramped to 850 °C for seven hours to allow the nucleated crystals to grow throughout the entire sample, yielding bulk polycrystalline ceramics.

Laser-induced crystals and polycrystalline ceramics were characterized primarily using Raman and fluorescence spectroscopy. Simultaneous scanning confocal Raman and fluorescence microscopy was performed at room temperature using a homebuilt microscope with a 488 nm argon ion laser as the excitation source. The simultaneity of these techniques is enabled due to the strong fluorescence of erbium in the range of 530 nm, which is far enough from the laser wavelength that it does not overwhelm the Raman emission, but near enough to be recorded in the same spectrum on a CCD while still maintaining reasonable spectral resolution. The goal being the observation of any correlation between the two. Combined Excitation Emission Spectroscopy (CEES), a low-temperature fluorescence technique, was also performed using a homebuilt microscope and a liquid helium cryostat capable of cooling the sample to about 10 K. Tunable diode lasers in the range of 800 nm and 980 nm were used as excitation sources for the CEES technique, which produces 2D maps of excitation and emission spectra. This allows the site(s), or incorporation environment(s), of the emitting ions of interest to be distinguished. Finally, fluorescence lifetimes were measured using the CEES microscope where the excitation source was fixed to an optimal wavelength (which produced a strong emission) and mechanically chopped while the emission was sent to an InGaAs detector. The reference signal from the chopper and the emission collected by the InGaAs detector were then fed to a lock-in amplifier. The method for determining the lifetimes using this technique is described by Edmondson et al. [23]. This method was chosen over the standard pulsed-laser technique because of its sensitivity to small signals and the possibility for mapping the lifetime throughout the crystal cross-section with high spatial resolution.

3. Results and discussion

3.1. Low temperature fluorescence

As a first step toward understanding the properties of the erbium ion in LaBGeO₅, CEES maps were collected from both Er_.01La_.99BGeO₅ glass and glass-ceramic samples. Figure 1 presents CEES maps of the ${ }^4{I}_{\frac{15}{2}}\to { }^4{I}_{\frac{11}{2}}$ and ${ }^4{I}_{\frac{13}{2}}\to { }^4{I}_{\frac{15}{2}}$ transitions in excitation and emission, respectively, for the glass (left) and a glass-ceramic (center). As expected, the amorphous structure of the glass results in a CEES map which shows only broad excitation and emission peaks. In contrast to the glass, the crystal is anisotropic and possesses long range fields which break the degeneracy of the Stark levels within the spin-orbit multiplets. For LaBGeO₅, the local symmetry of every lattice site, including the lanthanum site which erbium is expected to occupy, is C₁ [17]. Because C₁ is a very low symmetry point group, all of the degeneracy is lifted and each multiplet splits into the full $J+\frac{1}{2}$ levels. This should yield 8, 7, 6, and 5 Stark sublevels for the four ⁴I terms, respectively. The CEES map for the glass-ceramic demonstrates that the material is indeed anisotropic and crystalline due to the splitting of the original broad excitation and emission peak into many discrete, sharp peaks. The emission exhibits predominantly one excitation profile and one emission profile, each of which is repeated at the different emission and excitation energies, respectively, suggesting a single incorporation environment/site which all erbium ions in the crystal experience. However, upon very close inspection, at least one other set of unique excitation and emission profiles is observed. A few of the emission peaks associated with this site are indicated by black arrows in Fig. 1. They indicate that the erbium ions occupy multiple different incorporation environments (sites). Due to the dominant nature of the spectra associated with the first site, the fact that they fit the expected symmetry, and the literature concerning other lanthanide dopants [17], we conclude that these spectra are characteristic of an erbium ion at the nominal lanthanum site. The nature of the additional site(s) is unknown, but could potentially be related to an erbium ion at or near a remaining boron vacancy related to the loss reported by Sigaev et al. [21], or some other defect. Because the CEES signal from this secondary site is very weak, the focus of this work is the primary site.

 

Fig. 1 CEES maps of 980 nm excitation and 1550 nm emission in Er_.01La_.99BGeO₅ glass (left), glass-ceramic (center), and laser-induced crystal (right).

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Within each CEES map repeated energy differences between excitation and emission peaks and their relative positions can be used to quantify the energies of each possible Stark sublevel. Table 1 lists the expected Stark sublevels of the ⁴I multiplets and their respective energies as determined by this technique. Due to the symmetry of the site and experimental geometry, transitions between all possible states are allowed. However, due to the low probability of some transitions, as well as insufficient thermal energy when the samples are at 10 K to populate certain levels, not all transitions were observed.

Table 1. Observed energies (in eV) for erbium in Er_.01La_.99BGeO₅. Levels without energy values and marked with “x” are predicted but were not observed.

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The right panel of Fig. 1 is the CEES map of a laser-induced crystal in Er_.01La_.99BGeO₅ glass. This particular crystal was grown using an aberration-corrected focal profile at a depth of 600 µm below the sample surface, a laser power of 400 mW and a writing speed of 15 µm/s. The overall CEES map is generally representative of all laser-induced crystals in this glass, regardless of growth parameters. Despite having less intensity and showing significant broadening, the map is comparable to that of the glass-ceramic of the same composition. This demonstrates that the extreme conditions at the laser focus in which the crystal is grown do not appear to alter the dominant incorporation environment, the ratio of the primary and secondary erbium incorporation sites, or produce additional sites.

CEES maps collected for LaBGeO₅ glass-ceramics with erbium concentrations corresponding to 4%, 10%, and 20% molar replacement of lanthanum reveal that as the erbium concentration increases, the same energy level structure of the primary site is maintained, indicating that erbium continues to incorporate, and to do so at predominantly one site. However, the overall fluorescence intensity does not increase in proportion to the erbium concentration and all peaks are broadened as the concentration increases. Emission and excitation spectra for glass-ceramics and laser-induced crystals in 1% and 4% erbium-doped LaBGeO₅ glasses are shown in Fig. 2. As described earlier, all of the samples were ceramized at 850 °C. The broadening may be attributable to the possibility that as the erbium concentration is increased, the crystal nucleation and growth temperatures are increased, leading to incomplete crystallization of the higher-doped compositions. Nevertheless, though this may seem to be a reasonable conclusion, Differential Scanning Calorimetry confirmed that these temperatures are not significantly impacted by the erbium concentration and it is not supported by their respective Raman spectra, which show that the samples are fully crystalline. A more likely explanation for the broadening is that as the erbium concentration increases, each erbium ion has another erbium ion nearby and the disorder within the La/Er sublattice increases. In this case the local symmetry of each erbium incorporation site remains the same, the number of possible perturbations increases substantially due to interactions between different numbers of erbium ions. This results in the broadening of the energy levels involved in both excitation and emission processes, which in turn reduces the amount of light absorbed and thereby the fluorescence emitted. Similar behavior is, of course, observed in other crystalline materials as well. The CEES maps of Fig. 1 also show that fluorescence line narrowing, which arises due to the accumulated strain resulting from increasing amounts of smaller erbium ions replacing larger lanthanum ions, further magnifies this reduction of fluorescence.

 

Fig. 2 Emission (left) and excitation (right) spectra extracted from CEES maps of Er_.01La_.99BGeO₅ (top) and Er_.04La_.996BGeO₅ (bottom) polycrystalline glass-ceramics (solid) and laser-induced crystals in glass (dashed). The emission spectra arise due to excitation at 1.266 eV. The excitation spectra correspond to emission at 0.808 eV. Laser-induced crystal spectra have been multiplied by a factor of 10 to allow for easier comparison.

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The overall emission is also reduced due to the relatively long lifetime of the excited state making energy transfer to non-radiative decay pathways, which may be more abundant in higher-doped crystals, more likely. For example, the energy levels involved with the erbium emission at 1.54 µm are susceptible to non-radiative decay via excitation energy exchange into antisymmetric stretching vibrations of boron tetrahedra and/or vibrations of impurity OH-groups [20]. In samples with higher erbium concentrations, clustering makes it easier for one erbium ion to transfer its energy to a different erbium ion and so on, and thus the lifetime decreases. Additionally, clustering broadens the absorption lines which in turn leads to a lower excitation cross-section. Both of these effects lead to less radiative emission and effectively remove the proportionality between the fluorescence intensity and the erbium concentration.

Figure 3 shows excitation spectra extracted from CEES maps collected from six different laser-induced crystals grown in Er_.01La_.99BGeO₅ glass under various laser power, writing speed, and focal depth conditions. All of the crystals exhibit the same characteristic spectrum, indicating that the growth conditions do not significantly influence the erbium incorporation site. However, it is interesting to note that depending on the growth conditions, particularly for crystals grown using an aberration-corrected focal profile, the spectra exhibit different ratios of certain transitions. Specifically, the transition at 1.2934 eV exhibits the biggest difference. According to the level assignment presented earlier, this represents the ${ }^4{I}_{\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\to { }^4{I}_{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ transition and is labeled as A Fig. 3. The strength of this transition relative to the ${ }^4{I}_{\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$13$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\to { }^4{I}_{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ transition at 1.29075 eV, labeled as B in Fig. 3, may be used as a proxy for measuring the temperature of the crystal, since the ${ }^4{I}_{\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ state would be less thermally populated in a warmer crystal and therefore less able to be excited. All of the crystals to which the spectra in Fig. 3 correspond are in the same piece of glass. The CEES measurements of these crystals were performed sequentially without removing the glass from the cryostat or changing its temperature. Therefore, theoretically, all of the crystals should have been at the exact same temperature, and the ratios of various transitions should be the same for every crystal. However, this is clearly not the case, and it appears that certain crystals are at a lower temperature than others. Specifically, the colder crystals are those which were grown with more “ideal” laser irradiation conditions (i.e. more homogeneous temperature profile during growth through the use of aberration correction). Since each CEES map was collected under identical conditions, the fact that the crystals themselves are at different temperatures implies that their structures vary slightly in such a way as to influence their thermal conductivities and that these differences may be controlled via the irradiation conditions. For example, by optimizing the irradiation conditions to create an environment which is more ideal for crystal growth, strain throughout the crystal may be minimized. This, in turn, reduces the number of small-angle grain boundaries which may act as phonon scattering centers. The end result is a crystal which has a better thermal conductivity and is better able to conduct heat caused by the probe laser away from the collection volume.

 

Fig. 3 Fluorescence excitation spectra from CEES maps collected from laser-induced crystals in Er_.01La_.99BGeO₅ glass grown under different conditions. The legend indicates the parameter values: writing speed (µm/s), laser power (mW), focal depth (µm), and aberration correction (yes/no). The transitions labeled A and B correspond to the ${ }^4{I}_{\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\to { }^4{I}_{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ and ${ }^4{I}_{\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$13$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\to { }^4{I}_{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, $m_J=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ transitions, respectively.

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In addition to the determination of the erbium transition energies, the radiative lifetimes of the ${ }^4{I}_{\raisebox{1ex}{$13$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\to { }^4{I}_{\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ transition in Er_xLa_1−xBGeO₅ glass, glass-ceramics, and laser-induced crystals (LIC) were also measured. The data and fit to Eqs. 13 and 14 in [23] are shown in Fig. 4 and the lifetimes are listed in Table 2. Two general trends are apparent. First, regardless of material phase, the lifetime decreases with increasing erbium concentration. As discussed earlier, any perturbation introduced by the presence of additional erbium ions will reduce the lifetime. Second, as the level of structural disorder increases (ceramic → LIC → glass) and introduces more perturbations to the erbium environment, the lifetime decreases. Glass, being the most disordered, has the shortest lifetimes. LIC and glass-ceramics, inherently more ordered than glass, have longer lifetimes. Ideally, the LIC and glass-ceramics would have the same lifetimes. However, as Table 2 indicates, they do not. This discrepancy may arise due to the fact that the glass-ceramics were created under isothermal conditions while the LIC inherently experiences some thermal gradient, even with aberration correction. Due to various experimental limitations, there is some uncertainty concerning the precise location of the excitation beam within the crystal cross-section during the lifetime measurement process. As will be discussed later in more detail, depending on this position, the LIC may experience more or less strain. Regardless, even after averaging a number of measurements on different locations of different crystals, the lifetimes for the LIC are shorter than those of the glass-ceramics. To what extent the reduced lifetimes for the LIC relative to the glass-ceramics are influenced by nonradiative decay due to defects as opposed to the effect of strain on the radiative rates is unclear. Notably, the fit equation of [23] assume only one unique lifetime. Since the measured data is fit well by this equation, the notion of a single incorporation site is reinforced.

 

Fig. 4 Fluorescence intensity (red dots) as a function of chopping frequency for various crystals and the fit to Eqs. 13 and 14 in [23] (blue).

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Table 2. Observed lifetimes, in milliseconds, of the ${ }^4{I}_{\raisebox{1ex}{$13$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\to { }^4{I}_{\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ transition in Er_xLa_1−xBGeO₅.

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3.2. Simultaneous room temperature Raman and fluorescence

The nature of the laser-irradiation technique necessarily results in a thermal gradient, which may be very steep or fairly flat depending on the specific irradiation conditions, surrounding the laser focus. Additionally, the coefficient of thermal expansion for undoped LaBGeO₅ glass is α_g = 7.6 × 10⁻⁶ K⁻¹ while it is, on average, α_c = 6.5 × 10⁻⁶ K⁻¹ for the corresponding crystal [21]. Therefore, not only will different points within the radial heat distribution expand by different amounts due to the thermal gradient, but following crystallization the crystalline region will contract by a different amount compared to the surrounding glass. This creates a potentially complicated spatial behavior for the structural and fluorescence properties of the crystal. These properties were explored via spatially resolved simultaneous Raman and fluorescence spectroscopy.

Crystal lines grown in both undoped and erbium-doped LaBGeO₅ glasses were diced so that their cross-sections were exposed. These cross-sections were scanned, and two-dimensional maps were created in which a single spectral feature of interest is presented in color-space. The spectral features are, unless otherwise noted, the peak position and full width at half maximum (FWHM) of the −803 cm⁻¹ and −207 cm⁻¹ Raman vibrational modes. These modes will hereafter be referred to as A(LO)₁₈ and E(TO)₆, respectively. These modes correspond to symmetric Ge-O stretching and La displacement, respectively [24]. The E(TO)₆ mode was chosen due to the involvement of lanthanum, and therefore its potential sensitivity to the presence of erbium. The A(LO)₁₈ mode was chosen for examination due to its strength and the ease with which it is fitted. Finally, for doped samples, the total integrated erbium fluorescence intensity (EFI) from 515 nm – 572 nm, which corresponds to emission from both the ${ }^4{S}_{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ and ${ }^4{H}_{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ multiplets to the ${ }^4{I}_{\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ multiplet, was also mapped.

Because an isolated bulk single crystal was unavailable, Raman scans were performed on the exposed cross-sections of laser-induced crystals in undoped LaBGeO₅ glass as a baseline and standard by which to compare all of the laser-induced crystals in erbium-doped LaBGeO₅ glasses. The specific crystal used for this purpose exhibited both the most consistent cross-section profile along its length and the lowest power losses (2.64 dB/cm) in waveguiding measurements [4]. Figure 5 presents spectra taken from successive points beginning in the center of a crystal and moving outward into the glass. The Raman modes behave as follows: the A(LO)₁₈ mode shifts toward lower energies away from the center of the crystal and the E(TO)₆ mode shifts toward higher energies away from the center of the crystal. Both modes broaden toward the outer edge of the crystal. The spectral feature maps for this crystal show these effects more clearly and are presented in Fig. 6. Within the finer details shown by these maps, these shifts and broadenings behave differently throughout the crystals cross-section. These regions correlate well with the model of growth dynamics proposed in [25], which consists of two different transverse growth zones and explains the observed bean-like shape.

 

Fig. 5 Raman spectra from the crystal shown in Fig. 6. The spectra are taken from successive points in the horizontal direction along y=25 µm beginning in the center of the crystal and moving outward into the glass.

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Fig. 6 Peak position and full width at half maximum spatial maps of the −803 cm⁻¹ (left) and −207 cm⁻¹ (right) Raman modes for a laser-induced crystal in undoped LaBGeO₅ glass.

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Coussa et al. observed via in situ Raman spectroscopy that applying hydrostatic pressure using a diamond anvil to a LaBGeO₅ single crystal causes the A(LO)₁₈ Raman mode to shift to higher energy [26]. Considering this, and given the observed shifts within the laser-induced crystals, either the center of the crystal experiences compressive strain or the edges of the crystal experience tensile strain due to the surrounding glass. Given the confinement of the crystal within the glass, the fact that α_g > α_c, and the temperature distribution during crystallization, it is reasonable to assume the latter case. However, without a bulk single crystal for comparison, it is impossible to know for sure. Regardless, we can say with certainty that the density at the center of the crystal is higher than at the glass/crystal boundary and that this produces some form of strain throughout the crystal. The confocal scanning Raman technique allows this density gradient/strain to be determined with high spatial resolution and thereby quantified. Using this information, the properties and quality of the crystal may be tailored via adjustment of the initial glass composition or laser irradiation and growth conditions. For the crystal shown in Fig. 6, the magnitude of the shift of the A(LO)₁₈ mode from the center of the crystal to the edge is approximately 2.5 cm⁻¹. Based on the results presented by Coussa et al., this corresponds to a pressure of approximately 2.5 cm⁻¹/3.3 cm⁻¹GPa⁻¹=0.75 GPa over a length of 4.5 µm, which equates to a strain gradient of 0.168 GPa/µm in this direction. Such a gradient may be useful in that it would result in a variation of the refractive index across the crystal cross-section. Although it is a different root mechanism, the effect is the same in that it potentially enables a graded-index waveguide similar to that proposed by Veenhuizen et al. [5].

Figures 7 and 8 present the maps of the chosen spectral features for laser-induced crystal lines in Er_.01La_.99BGeO₅ and Er_.04La_.96BGeO₅. Each figure contains a spatial map of the normalized erbium fluorescence intensity in addition to the same set of maps concerning the A(LO)₁₈ and E(TO)₆ Raman modes for two different crystals. A number of interesting effects are immediately apparent.

 

Fig. 7 From left to right, spatially resolved maps of erbium fluorescence intensity, A(LO)₁₈ peak position, A(LO)₁₈ FWHM, E(TO)₆ peak position, and E(TO)₆ FWHM for two laser-induced crystals in Er_.01La_.99BGeO₅ glass. The top set of maps correspond to a crystal grown with the following conditions: writing speed=15 µm/s, laser power=750 mW, focal depth=300 µm, and no aberration correction. The bottom set of maps correspond to a crystal grown with the following conditions: writing speed=10 µm/s, laser power=400 mW, focal depth=600 µm, and aberration correction.

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Fig. 8 From left to right, spatially resolved maps of erbium fluorescence intensity, A(LO)₁₈ peak position, A(LO)₁₈ FWHM, E(TO)₆ peak position, and E(TO)₆ FWHM for two laser-induced crystals in Er_.04La_.96BGeO₅ glass. The top set of maps correspond to a crystal grown with the following conditions: writing speed=10 µm/s, laser power=750 mW, focal depth=600 µm, and no aberration correction. The bottom set of maps correspond to a crystal grown with the following conditions: writing speed=10 µm/s, laser power=400 mW, focal depth=600 µm, and aberration correction.

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First, all of the crystal cross-sections are fairly symmetric about their vertical axes (i.e. the axis of modifying laser incidence). This is a significant difference from the asymmetric crystals produced in undoped LaBGeO₅ discussed previously (see Fig. 6), as well as others observed by Stone et al. [4, 22]. The reason for this difference is unclear, but it is potentially an important improvement relative to possible applications. This difference could be related to the very different writing speeds used. Crystals in this work were grown at writing speeds of 10–15 µm/s, while those grown by Stone et al. in undoped LaBGeO₅ were grown at writing speeds of approximately 45 µm/s, despite similar laser power, focal depth, repetition rate, and ambient heating parameters. Thus, there is clearly a strong compositional effect on the crystal growth process. One possible cause for the significant difference is the fact that the modifying laser energy is very close to that of an erbium transition energy. This is inconsequential for undoped glasses, but could have significant consequences for the present work. Because of this overlap, some of the deposited laser energy is subsequently lost radiatively. Therefore, it necessarily takes either more incident laser power or a longer irradiation time for heat accumulation sufficient for crystal growth to occur, and thus the writing speed must be slower.

On the other hand, it should be noted that the writing speed is growth-limited, and therefore only a narrow range of speeds may be used to produce a continuous crystal line with a uniform cross-section in the first place. Stone observed a slightly wider range of possible writing speeds, but chose a value toward the higher end of that range in order to suppress the growth of competing nuclei and thereby achieve a single, homogeneous crystal waveguide [25]. For the crystals grown in Er:LaBGeO₅ glass the observed range was quite narrow, and moving the laser focus through the sample at speeds greater than 15 µm/s resulted in termination of crystal growth. It is also worth noting that similar ranges were observed for crystals grown in Pr:LaBGeO₅ (15–25 µm/s) and Nd:LaBGeO₅ (10–20 µm/s) glasses with equivalent dopant concentrations to the present Er:LaBGeO₅ glasses. Interestingly, the maximum writing speed decreases as the size disparity between the dopant and lanthanum increases. This may be a result of forcing the material to a hexagonal crystal structure (nominal LaBGeO₅, stillwellite) despite the dopants (especially Nd and Er) preferring a monoclinic structure (datolite) [19]. Regardless, the effect is the same. Moving the laser focus through the glass at a slower rate produces a more symmetric crystal cross-section. At the same time, the growth of competing nuclei are avoided since the composition is less favorable to nucleation in the first place.

A second effect apparent from Figs. 7 and 8 is that the Raman modes still generally shift in the same manner; the A(LO)₁₈ shifts to higher energy and the E(TO)₆ shifts to lower energy at the center of the crystal compared to the periphery of the crystal. Both modes continue to broaden toward the edge of the crystal. These effects are also evident from the individual spectra shown in Fig. 9. However, while Figs. 6 and 5 show these shifts very clearly, Figs. 7, 8, and 9 are much more subtle, with the crystals grown in Er_.04La_.96BGeO₅ being even more homogeneous than those in Er_.01La_.99BGeO₅. For example, at certain points within the crystals shown in Fig. 7, the A(LO)₁₈ mode shifts by about 1.5 cm⁻¹ over 5 µm from the center of the crystal to its edge. This corresponds to a strain of 0.091 GPa/µm, which is much lower than what the undoped crystal experiences. Furthermore, these results are examples of the most extreme cases, and the relative shifts throughout the entire crystal are smaller on average. Given that the fitting error for the peak position of this Raman mode is about 0.2 cm⁻¹, any difference of less than 0.4 cm⁻¹ cannot be considered a definitive effect.

 

Fig. 9 Raman (inset) and erbium fluorescence spectra from the crystal shown on the right in Fig. 7. The spectra are taken from successive points in the horizontal direction along y=4.5 µm (near top) beginning in the center of the crystal and moving outward into the glass.

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Although the general trends remain the same, it is interesting to note the effect that the irradiation conditions within the erbium-doped samples have on the absolute values of the Raman mode energies and widths for individual crystals. Specifically, the use of aberration correction produces the biggest differences beyond just affecting the the shape of the crystal cross-section. As shown in Figs. 7 and 8, when aberration correction is used, both the A(LO)₁₈ and E(TO)₆ modes shift to higher energies over the entire cross-section and become much narrower. So not only does aberration correction produce a better cross-sectional shape, in doing so it directly affects the structure of the crystal by creating a more densely-packed lattice.

The erbium fluorescence intensity (EFI) within the crystalline region is less than that of the surrounding glass. In the glass, the absorption is broad, but all ions have the same probability of absorbing the incident light. When the glass is crystallized, the dopant ions incorporate at a single site, and the single absorption peak of the glass narrows due to the presence of the crystal field. Since the excitation at 488 nm is non-resonant, this results in less absorption and therefore less fluorescence.

Despite the relative homogeneity exhibited by the Raman maps, the EFI within the crystalline region is inhomogeneously distributed in some crystals. In some extreme cases, such as the crystals shown in Fig. 7, the fluctuation of the EFI can be correlated to the frequency shift of the Raman modes, as shown in Fig. 10. A reasonable explanation for this phenomenon is that as the structure changes ever so slightly, the narrow absorption peaks of the erbium ions are shifted either nearer or further from the energy of the excitation source, and thereby more or less absorption and subsequent fluorescence occurs. This makes erbium fluorescence potentially useful as a probe of the strain experienced by the crystal.

 

Fig. 10 Horizontal line profiles of the erbium fluorescence intensity and peak position of the A(LO)₁₈ Raman mode from the cross-sections of the crystals shown in Fig. 7 showing the correlation of the EFI to the shift of the Raman modes due to strain. The line profiles on the left show the spectral feature behavior at y=25 µm of the crystal shown on the top of Fig. 7. The line profiles on the right show the spectral feature behavior at y=11.7 µm of the crystal shown on the bottom of Fig. 7.

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Finally, many of the EFI maps show a narrow band surrounding the crystalline region with enhanced fluorescence relative to both the glass and crystal. This may indicate that erbium ions may diffuse outward and into the surrounding glass during the crystallization process. This possibility is further explored in Fig. 11, in which a typical spectrum from the region of enhanced EFI is compared to spectra from the glass and crystal regions. While the boundary spectrum is predominantly glassy in nature, some weak crystalline features are also present. The shape of the crystalline contribution to the fluorescence in this region matches the nominal crystal spectrum, and therefore the total EFI would be expected to be somewhat diminished relative to the nominal glass spectrum. That the intensity is greater suggests an accumulation of extra erbium ions.

 

Fig. 11 Raman (inset) and erbium fluorescence spectra from the crystal shown on the top in Fig. 7. The spectra are taken from various points in the horizontal direction along y=23.1µm corresponding to the center of the crystal (red) and the glass (blue) as well as from the boundary (green). Specifically, the boundary spectrum is taken from the bright white region surrounding the crystal where the EFI is greatest.

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4. Conclusion

Laser induced crystallization of glass is a spatially selective technique for growing optically active crystals inside of a bulk glass which are promising for the creation of photonic integrated circuits. Toward this goal, erbium was found to incorporate in LaBGeO₅ at primarily one site, and the energy levels of this site were quantified. The radiative lifetimes of this site in various erbium concentrations and morphologies were measured and found to be consistent with those measured in similar bulk crystals and sufficient for laser applications. The radiative lifetimes were also found to be significantly reduced as the erbium concentration increased. LIC exhibited slightly shorter lifetimes than the corresponding glass-ceramics. Raman and fluorescence mapping showed that crystals grown in Er:LaBGeO₅ exhibit significantly more symmetric cross-sectional profiles than previous work in undoped LaBGeO₅, suggesting that, in combination with the resonant wavelength of the femtosecond pulsed laser, erbium helps to create a more homogeneous temperature profile surrounding the laser focus. This, in turn, reduces strain within the crystal, though even small amounts of strain strongly affect the erbium fluorescence observed under non-resonant excitation. Finally, an anomalous band of enhanced erbium fluorescence at the crystal-glass interface suggests an accumulation of erbium ions in this region.