1. Introduction

Ultrafast laser inscription (ULI) is an emerging advanced laser manufacturing technique that exploits focused ultrafast laser pulses of sub-bandgap laser radiation to induce localized structural changes inside dielectric materials [1]. Depending on the ULI parameters, the laser induced modification can manifest itself in a variety of ways, examples of which include variation to the refractive index and/or chemical etch rate [2–4]. Using these modifications, three-dimensional (3D) optical components, such as mode-multiplexer, integrated photonic lanterns and volume Bragg gratings (VBGs) can be fabricated [5–9].

One issue that is commonly encountered when performing ULI is that the maximum depth at which structures can be fabricated inside a substrate is limited by the effect of spherical aberration imparted on the ULI laser beam by the air-substrate interface [10] (we will refer to this aberration as the “substrate aberration”). The substrate aberration distorts the laser focus and resultant material modification. Since the amount of substrate aberration imparted on the laser beam increases as the depth of the focus inside the substrate increases, the laser modification itself becomes a function of depth, even if all other ULI parameters are held constant. This is particularly significant for high-numerical aperture (NA) focusing, where substrate aberration becomes severe even at shallow depths. High-NA inscription is desirable because the resolution of resolvable features increases with NA, according to the Sparrow criterion. Therefore, the substrate aberration limits the fidelity of structures fabricated at depths where aberrations become significant, and in the context of VBG fabrication, potentially limits the VBG thickness and depth at which high quality VBGs can be fabricated. The latter of these could be particularly important for fabricating advanced VBG structures, such as the stacked VBGs that have recently been used for astronomical spectrograph applications [11]. Previously, femtosecond laser written VBGs spanning a depth of 600 µm in fused silica has been demonstrated [12]. We note though that performance variation over the grating depth was not reported.

One solution to address the impact of the substrate aberration is to use a spatial-light-modulator (SLM) to shape the incident laser wavefront via the application of a “phase mask”. SLMs have been used previously to tune the periodicity when writing Bragg gratings with a traditional mask and cylindrical lens [13], and for correcting for aberrations when writing Bragg gratings in fibers [14]. Here we propose that with an appropriately designed phase mask, the writing beam wavefront can be shaped such that the substrate aberration effects are pre-compensated for [15–17] in order to write VGBs deep within a substrate. In this work, we investigated how the surface aberration affects the performance of VGBs fabricated in fused silica and demonstrate the use of a liquid crystal SLM for writing high quality VGBs at depths where substrate aberration would otherwise prevent this. We find that by using the SLM for aberration compensation, we can fabricate optimal gratings at a mean depth of 900 µm that exhibit a first-order relative diffraction efficiency of 42% for linearly polarized 633 nm light, close to the range of the 48% measured for optimal VBGs fabricated near the substrate surface without aberration correction.

2. Experimental methods

2.1 Ultrafast laser inscription system

Figure 1 is a schematic of the ULI system used in this work, which incorporates an SLM for surface aberration compensation. The fabrication laser used was a diode-pumped ytterbium-doped bulk laser system (Pharos, Light Conversion) with a 1030 nm central wavelength, allowing tuneable pulse duration and repetition rate. The components following the laser include a power control system directly at the output of the laser consisting of a half-wave plate (HWP) and polarizing beam splitter (PBS). The linearly polarized laser beam was expanded using lenses L1 (plano-concave, f = −25 mm, LC1054-B Thorlabs) and L2 (plano-convex, f = 75 mm, LA1608-B Thorlabs) to overfill the active area of the SLM, increasing the beam diameter from 4.5 mm to 13.2 mm (1/e²). The phase-only reflective liquid-crystal-on-silicon (LCOS) SLM (X13138, Hamamatsu) had an active area consisting of 1272 × 1024 pixels with a pixel pitch of 12.5 µm, each providing a 0 - 2π phase modulation at 1030 nm by applying an 8-bit value from 0 - 150, giving a pixel phase resolution of ∼0.042 radians. To enable shaping of the laser beams amplitude profile, a blazed grating was applied to the SLM to direct ∼80% of the incident power into the positive first diffraction order. A 4f imaging system was used to image the SLM onto the back aperture of the objective lens (OBJ1) which then focused the laser beam into the substrate. The first Fourier transform lens (F_T1) had a focal length of 1000 mm (bi-convex, LB1859-B Thorlabs) whereas the second (F_T2) had a focal length of 400 mm (bi-convex, LB1391-B Thorlabs). An iris (LCP50S, Thorlabs) placed at the focus of F_T1 was used to block all but the positive first diffraction order. The polarization of the laser reaching the substrate was controlled using a quarter-wave plate (QWP) and second HWP placed before OBJ1. The choice of writing objective (OBJ1) has a significant effect on the available dimensions of the modified volume and depth achievable within the selected sample. The selected objective lens had an effective focal length of 4 mm, an NA of 0.67, and a 10 mm working distance (PAL-50-NIR-HR-LC00, OptoSigma). For this work, we underfilled the objective to achieve an effective writing NA of 0.6, producing a focal volume with theoretical diffraction limited dimensions of 1.0 µm in the transverse plane and 8.3 µm in the axial plane. The substrate was mounted on computer controlled 3-axis air-bearing translation stages (ABL1000, Aerotech) that allowed the sample to be translated through the ULI laser focus with sub-micron precision and with a maximum travel of 100 mm by 100 mm by 25 mm along the x-, y-, and z-axis respectively. Two imaging systems, labeled C1 and C2 (both DCC2545M-GL, Thorlabs), were used for on-axis imaging of the substrate and side-view imaging of the free-electron plasma respectively.

 

Fig. 1. Schematic diagram of the ULI system. An ultrafast laser system (Pharos, Light Conversion) delivered pulses with a 1030 nm wavelength, 200 kHz pulse repetition frequency and 185 fs pulse duration. The laser power reaching the substrate was controlled using a half-waveplate (HWP) and polarizing beam splitter (PBS) placed directly after the laser aperture. Lenses L1 and L2 form a telescope that expands the laser beam to fill the active area of the SLM. The SLM, pictured with an example Zernike polynomial phase mask (inset next to the SLM), was followed by a 4f spatial filtering image relay system, constructed from F_T1, F_T2, and an iris to block all but one of the orders. The polarization of the laser beam on the substrate was controlled by a second HWP and a quarter-wave plate (QWP) placed before the final writing objective (OBJ1, ×50, 0.67 NA, OptoSigma). The substrate was mounted on a 3-axis air bearing translation stage (Aerotech). C1 and C2 are digital cameras used to monitor the positioning of the sample (C1) and to image the emission from the free electron plasma (C2). The inset below F_T2 shows the substrate mounted in front of OBJ1, with a two-dimensional array of VBGs inscribed.

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2.2 VBG characterization system

VGBs are periodic refractive index structures which reflect or diffract light with a highly wavelength and angle dependent efficiency. The behavior of VBGs can be described by coupled wave theory as set out in Refs. [18] and [7]. The performance of our laser fabricated gratings was characterized using the characterization system presented in Fig. 2(a). The diffraction efficiency of the VBG under test was determined using both a linearly polarized 633 nm HeNe laser (1125P, Uniphase), and across a broader range of wavelengths using an NKT Photonics SuperK supercontinuum (SC) broadband light source. In combination with a set of bandpass filters (10 nm bandwidth at the full-width half-maximum), the SC was used to study central wavelengths from 500 to 1100 nm in steps of 100 nm. A HWP was used to control the HeNe polarization, while the SC polarization was adjusted using a linear polarizer. The substrates containing the VBGs were mounted on a linear translation stage which enabled transitioning the VBGs between the HeNe (red arrows) and SC (white arrows) beams, Fig. 2(a). The VBGs were also held in a rotation mount that allowed the gratings to be orientated through a range of incident angles (α in Fig. 2(b)) to find the maximum diffraction efficiency of each grating for a given wavelength - in effect applying a blaze to the VBG. This is because the efficiency for a given wavelength is highly angle dependent [19]. The average optical power contained within the positive first-order was measured using an integrating sphere (S142C, Thorlabs), which reduced the possibility of an alignment error on the detector end. Once the diffraction power was maximized by varying the angle, the transmission through pristine (unmodified) material was measured for the same angle as a “zero-diffraction reference”. For our purposes, the diffraction efficiency of any VBG was defined as the optical power measured in the positive first-order relative to the zero-diffraction reference, referred to herein as the “relative diffraction efficiency”. The diffraction efficiencies were measured for two linear polarization states: perpendicular to the modified tracks of the grating, designated p-polarization, and parallel to the modified grating lines, designated s-polarization, as depicted in Fig. 2(b). These designations were chosen to adhere to convention, where s- and p-polarization are defined relative to the plane of incidence; which in our case, lay orthogonally to the grating lines.

 

Fig. 2. (a) Annotated digital photograph of the set-up used for characterizing the VGBs, showing the HeNe beam path with the red arrows, and the SC beam path with the white arrows. A half-wave plate (HWP) and polarizer (Pol) were used to control the linear polarization orientation of the HeNe and SC respectively, and a set of bandpass filters (BPF) (FKB-VIS-10, Thorlabs) within a rotating wheel mount was used to filter the SC wavelength. (b) Schematic of the grating showing the grating rotation axis, the positive first and the zero^th orders and the position of the power meter used to measure the positive first-order. Also detailed are the two polarization orientations relative to the sample, labelled P (p-polarization) and S (s-polarization). This is pictured with a scaled photo of a VGB array in the mount. (c) Digital photograph of the mounted sample in the foreground, and the integrating sphere with a 633 nm diffraction pattern in the background. The grating under test was written with a pulse energy of 225 nJ at a depth of 200 µm with the Z(0) phase mask on the SLM. We note the cloudiness of the VBG suggests some degree of glass modification beyond Type I [20].

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3. Results

3.1 Developing efficient shallow-depth VBGs

The starting point for the depth correction study was to find ULI parameters that produced an efficient VBG at a mean depth of 200 µm in the substrate, a depth where substrate aberrations are not expected to be signifcant. While highly efficient VBGs have been produce using ULI, it is important highlight that this was not the primary aim of this work [7]. Here, we required a grating with sufficiently high relative diffraction efficiency to investigate the evolution of the laser writing capabilities as a function of depth. For all ULI fabrication, the laser pulse repetition rate was set to 200 kHz, the pulse duration to 185 fs, the polarisation was circular, and the substrate translation speed was 4 mm·s^-1. The substrate used for this study was 1 mm thick fused silica (7980 0F grade, Corning). Each VBG layer was fabricated by translating the substrate through the ULI laser focus to inscribe a series of parallel lines of index modification separated by 6 µm. Each line was written along the same direction to ensure consistent modification of the material. The thickness of the VBG was determined by stacking multiple layers spaced by 2.26 µm. It was previously demonstrated that VBGs with a thickness of around 100 µm exhibit high absolute diffraction efficiency for 633 nm light [12]. Therefore, this was chosen as the target thickness, composed of 45 individual layers of index modification. The transverse dimensions of the VBG were 3 mm by 3.5 mm, chosen such that the interrogation source underfilled the grating area.

VBGs were fabricated using a range of pulse energies from 150 nJ to 250 nJ in steps of 25 nJ. Figure 3(a) depicts the diffraction efficiencies measured for the 45-layer VBGs as a function of the writing pulse energy. The VBG fabricated using 225 nJ pulses exhibited the optimum diffraction efficiency of 48% for p-polarized, and 44% for the s-polarized 633 nm light. Figure 3(b) presents the diffraction efficiency of this VBG as a function of wavelength, indicating that efficiencies of > 40% across the 600 nm to 900 nm spectral band were obtained. This set of ULI parameters, (225 nJ pulses and 45 layers) written at a mean depth of 200 µm below the sample surface, produced a grating with sufficiently high diffraction efficiency to serve as a “reference”. The reference was used to assess the success of the aberration compensation for gratings written deeper within the substrates.

 

Fig. 3. Measured diffraction efficiencies for p- (square markers, blue line) and s- (circle markers, red line) polarized light. (a) First-order diffraction efficiencies for VBGs fabricated using a range of pulse energies. It is observed that diffraction efficiencies >40% are realized using a pulse energy of 225 nJ. Here, the diffraction efficiency was measured using a HeNe laser at 633 nm. (b) Measured diffraction efficiency vs wavelength for the VBG fabricated with 225 nJ pulses, showing that diffraction efficiencies above 40% relative diffraction efficiency could be obtained for wavelengths between ∼600 nm and ∼1000 nm.

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3.2 Developing efficient VBGs deep in fused silica

With appropriate laser writing parameters established to fabricate efficient VBGs at a depth of 200 µm, the capacity to write efficient VBGs at significantly larger depths in fused silica was investigated. The predominant substrate aberration is expected to be spherical aberration, originating from the air-glass interface as the laser is focused into the sample. A commonly used model for representing optical aberrations is the Zernike polynomials – a set of orthogonal polynomials which can describe any surface deviation on a unit disk [21]. Zernike polynomial, $ZP_4^0$, specifically represents primary spherical aberration, and was therefore used to compensate for surface aberration in this work. This phase mask was modulated by the Zernike expansion coefficient, or aberration coefficient, X, which is equal to the peak wavefront error in radians [22]. In the following, we represent an SLM phase profile that consists of a $ZP_4^0$ polynomial with an aberration coefficient, X, as Z(X). A phase profile denoted Z(0) therefore represents no spherical aberration compensation, and the challenge is to find the value of Z(X) for a given depth which compensates for the effect of the substrate aberration on the laser focus.

VBGs were fabricated using the ULI parameters identified in Section 3.1, at a mean depth of 900 µm. Each grating was written with a different aberration coefficient applied to the phase mask displayed on the SLM, with the magnitude ranging from Z(-3) to Z(-5) in steps of 0.5, and also with a mask of magnitude Z(0) representing a non-aberration compensated grating. The negative sign of the Zernike aberration coefficients simply derives from the phase delay introduced to the beam by the SLM when applying positive mask values. The relative diffraction efficiencies were measured with 633 nm light for both s and p polarization states. The relative diffraction efficiencies gave an indication of the extent of aberration compensation provided by the phase mask. The mask which produced a grating with an efficiency close to the reference seen in Fig. 3(a) was presumed to fully compensate for spherical aberration at the associated depth. Figure 4(a) presents VBG diffraction efficiency as a function of the magnitude of Z(X).

 

Fig. 4. (a) Relative diffraction efficiency versus aberration coefficient for a set of VBGs written at mean depth of 900 µm for a range of SLM profiles ranging from Z(0) to Z(-5), measured with both p- (square markers, blue line) and s- (circle markers, red line) interrogation beam polarizations. A blue dashed arrow highlights the best performance improvement when using the Z(-4.5) aberration coefficient mask. (b) Relative diffraction efficiency versus wavelength for a VBG written at a mean depth of 900 µm, for corrected (solid curves) and uncorrected (dashed dot curves), for both p- (square blue) and s- (circle red) polarizations. Inset: the Zernike polynomial component of the mask projected onto the SLM, for Z(-4.5) in grey scale from 0 to 2π.

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This peak efficiency is represented by the dashed blue arrow at Z(-4.5), highlighting an improvement from 6% to 42%, and 8% to 36% for p-polarized and s-polarized 633 nm light respectively. We note that the diffraction efficiency for the Z(-3.5) phase mask deviated from the expected efficiency trend, as affirmed by a repeated fabrication run. Although peculiar, this anomaly was not deemed significant to warrant further exploration within the scope of this work. Figure 4(b) presents first order diffraction efficiency results obtained as a function of wavelength for the best performing grating in Fig. 4(a). The diffraction efficiency for the Z(0) grating is represented by the dash-dot curve, while the Z(-4.5) grating is represented by the solid curve and the light polarizations are colored as before. The aberration correction resulted in a higher relative diffraction efficiency across all wavelengths tested, however they are found to be below the efficiencies detailed in Fig. 3(b). It is clear though that the diffraction efficiency at 633 nm is significantly improved from 6% to 42% by implementing the SLM-based aberration compensation. The inset in Fig. 4(b) shows the Zernike polynomial component of mask Z(-4.5) which was applied to the SLM.

The bandwidth of VBGs, for a given angle of incidence, is predicted by coupled wave theory [18]. To compare the performance of the laser inscribed VBGs to that predicted by theory, the bandwidths of two VBGs were measured: the reference grating at 200 µm and the best performing grating written at 900 µm, written with the -4.5 Zernike coefficient. The gratings were interrogated with the SC broadband source and colored filters, at a fixed angle (the optimum found for 633 nm light).

The resultant bandwidths are presented in Fig. 5. This study showed that for both VBGs, the efficiency peaks at 633 nm wavelength, in agreement with theory. The spectral profile of the individual gratings differ slightly. The model predicts grating performance for an ideal sinusoidal index profile. In practice, the index profile induced by laser writing is more step like. Further, we expect the index morphology to vary over each grating thickness, such that the effective period of the grating is less well-defined. We also expect scattering to affect the performance of each grating with a wavelength and angle dependence. It is possible that the specific modification at shallow and deep depths in the material, even with aberration correction, would differ, resulting in variability in the scattering behavior. Considering these limitations, it is still possible to estimate the induced refractive index change from the theoretical model. Doing so, we estimate an index contrast of 1.25×10⁻³ and 1.15×10⁻³ for the shallow and deep gratings respectively.

 

Fig. 5. Plot of relative diffraction efficiency versus wavelength for the reference grating (dashed line, light blue), and corrected VBG written at a mean depth of 900 µm (Solid line, dark blue). The theoretical efficiency predicted by coupled wave theory [18] is also included (black line).

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3.3 Free-electron plasma imaging

To provide further insight into the effect that aberration compensation has on the laser fabrication, we performed free-electron plasma emission imaging experiments, with the aim of correlating the plasma emission properties with VBG diffraction efficiency trends depicted in Fig. 4(a). As proposed by Jesacher et al., the emission of the free electron plasma can provide a useful metric to determine the optimum SLM profile for aberration compensation [16]. As shown in Fig. 1, a camera (DCC2545M-GL, Thorlabs) with a 6.5× magnification zoom lens (MV6X12Z, Thorlabs) and a 0.67× extension lens (MVL067A, Thorlabs) (C2, Fig. 1) was used to record images of the emission from the free electron plasma. A shortpass filter with a cut-off wavelength at 1 µm (FESH1000, Thorlabs) was used to block the 1030 nm laser light scattered from the focus, ensuring only light originating from the broadband plasma was measured. The laser parameters were consistent with the VBG writing experiment excluding the pulse energy which was increased from 225 nJ to 300 nJ to improve the signal to noise ratio on recorded plasma images.

The study was performed at depths of 200 and 900 µm, corresponding to the inscription depths of the VBGs. As before, plasma emission at a depth of 200 µm without aberration compensation was used as a reference to compare to writing at depth with compensation. Since the 100 µm thick gratings spanned a depth of 850 to 950 µm, plasma emission was investigated at 850 µm, 900 µm, and 950 µm, corresponding to the top, middle, and bottom positions of the grating respectively. The phase masks applied for each of the three depths included Z(0), and the range from Z(-3) to Z(-7) in steps of 1 coefficient magnitude. We observed that the plasma intensity diminished over time when the laser was focused into static material, which we assume is related to the laser induced material modification. Therefore, images were taken immediately upon laser exposure in a pristine region of material to capture the plasma intensity consistently. A 0.5 OD neutral density filter (NE05A, Thorlabs) was used to avoid camera pixel saturation for the brightest plasma generation, namely at 200 µm and at 900 µm, with Z(-3) to Z(-6) applied. Five plasma images were recorded for each mask and depth. The five peak pixel values from each plasma image were averaged, and then the average value normalized to the average peak pixel intensity of the reference value measured at 200 µm. Figure 6 is a plot of the normalized average peak pixel intensity observed for the range of phase masks, measured when writing at 850–950 µm depths (green lines). The measured plasma emission observed at 200 µm without aberration compensation is included for comparison (black datapoint). The error bars represent the minimum and maximum recorded values from the five repeat measurements. The p-polarized diffraction efficiencies (blue square) measured in Fig. 4(a) are also represented for comparison.

 

Fig. 6. The normalized average peak pixel intensity recorded when imaging plasma produced with a range of aberration coefficients at shallow and deep depths, namely: 200 µm (shallow reference, black point), 850 µm (dark-green upward triangle), 900 µm (green diamond), and 950 µm (light-green downward triangle). Each point is the normalized average of five measurements and the error bars represent the minimum and maximum measured values. The blue line represents the relative diffraction efficiency of a VBG written at 900 µm (interrogated with horizontally polarized 633 nm light).

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Figure 6 shows that optimally selected Zernike expansion coefficients had a considerable effect on the plasma intensity at a specific depth. For the three depths centered at 900 µm (green shades), the Z(-4) phase mask produced similar and consistent plasma emission, all within the range of the reference point at 200 µm (black point) with an average value of ∼0.9. We observed a high peak intensity for Z(-3) for top layers (0.98 at 850 µm) but a significant drop in intensity for the deepest grating layer (0.73 at 950 µm). The global trend of the plasma imaging corroborates the previous results with peaks of plasma intensity and relative efficiency between Z(-4) and Z(-4.5). With a long manufacturing time of ∼12 hours for each 3 mm by 3.5 mm by 100 µm VBG presented in this work, obtaining aberration compensation parameters by trial and error is impractical. The plasma imaging study is therefore very useful, as it allows approximately optimal aberration correction parameters to be obtained immediately at any depth.

The plasma imaging results provide further insight into depth dependent surface aberration. For gratings spanning greater than 100 µm thickness, it may be beneficial to tune the aberration coefficient dynamically to correct for aberration precisely over the range of depths. The significant writing time per grating attracts system stability issues arising from, for example, fluctuations in the environmental temperature. Fortunately, methods of reducing fabrication times have been reported, including using beam shaping, which are compatible with the aberration correction approach described here [23]. It may also be possible to combine traditional VBG fabrication techniques, such as using physical phase-masks, with SLM controlled aberration correction, or indeed, generate the intensity modulation via the SLM directly. It has been predicted that depth dependent spherical aberration can be compensated for up to a depth of ∼6 mm for a 0.6 NA in fused silica using an SLM [17]. These results show that by shaping the wavefront across the beam using an SLM, the quality of the laser spot and plasma intensity at 900 µm depth, and hence the fidelity of laser written VGBs, can be restored close to that seen at a mean depth of 200 µm.

4. Conclusions

The range of substrate depths that ULI can be applied to is conventionally limited by the spherical aberration imparted on the laser beam by the substrate surface – the substrate aberration. This aberration degrades the focal spot as the depth of the focus increases and also limits the resolution of the manufacturing process. To overcome this, an SLM can be used to pre-compensate the phase profile across the laser beam before it enters the lens used to focus the laser light inside the substrate [15–17]. In this work, a preliminary investigation was performed to acquire optimal ULI parameters to produce a “reference” VBG at a depth of 200 µm without aberration correction. This reference grating exhibited a relative diffraction efficiency of 48% for p-polarization at 633 nm. A set of VBGs were then fabricated at a depth of 900 µm using SLM profiles with different Zernike expansion coefficients. The relative diffraction efficiencies of VBGs fabricated at a mean depth of 900 µm were found to increase from 6% and 8% for p- and s- polarizations respectively when no aberration compensation is used, to 42% and 36% for p- and s- polarizations respectively when a Z(-4.5) Zernike expansion coefficient was used. These values are close to the diffraction efficiencies measured for the reference grating written at 200 µm without aberration compensation, strongly indicating that the SLM has successfully compensated for the majority of the substrate aberration. A further VBG characterization study using light across a wide spectral region showed that although the aberration corrected VBG maintained the diffraction efficiency at the designed working wavelength of 633 nm, the diffraction efficiency at other wavelengths did not match the values exhibited by the reference grating. This clearly indicates that the VBG fabricated at a depth of 900 µm with optimized aberration compensation does not fully replicate the optical properties of the reference grating, and further studies are required to ascertain why this is the case. A plasma imaging study was also performed that revealed that the intensity of the emission from the free electron plasma at a depth of 900 µm was maximized using an SLM phase profile similar to the phase profile that resulted in optimal VBGs. This suggests that the emission intensity from the free-electron plasma can potentially be used to optimize the VBG fabrication process in other materials, without the requirement for time-consuming parameter scans based on VBG characterization. In summary, this work has demonstrated that with suitable optimization, ULI has the potential to enable the manufacture of complex, high efficiency and extremely robust glass VBGs in dielectric materials for applications ranging from astronomical instrumentation to ultrafast optics.