The positional alignment of femtosecond laser written Bragg grating waveguides within standard and coreless optical fiber has been exploited to vary symmetry and open strong optical coupling to a high density of asymmetric cladding modes. This coupling was further intensified with tight focusing of the laser pulses through an oil-immersion lens to control mode size against an asymmetric refractive index profile. By extending this Bragg grating waveguide writing into bulk fused silica glass, strong coupling to a continuum of radiation-like modes facilitated a significant broadening to over hundreds of nanometers bandwidth that blended into the narrow Bragg resonance to form into a strongly isolating (43 dB) optical edge filter. This Bragg resonance defined exceptionally steep edge slopes of 136 dB/nm and 185 dB/nm for unpolarized and linearly polarized light, respectively, that were tunable through the 1450 nm to 1550 nm telecommunication band.
© 2013 Optical Society of America
Laser writing of finely pitched gratings within single mode optical waveguides such as in optical fibers and planar optical circuits have offered substantial opportunity of creating spectral filters for diverse application in optical communications, fiber lasers, and sensing [1–3]. Fiber Bragg gratings (FBG) are typically defined by a weak periodic modulation in the effective refractive index along the length of the pre-existing fiber core, which can be fabricated through phase masks or point-by-point direct writing by exposure with either UV [4, 5] or femtosecond [6–8] laser light. For the most part, a uniform transverse refractive index modification is desirable in the majority of these applications that strictly limits coupling to only between forward and backward propagating modes at the Bragg resonance. However, differing photosensitivity responses in the fiber core and cladding can break this symmetry to permit grating coupling of the fundamental LP01 core mode to backward-propagating LP0n cladding modes that manifest in an unwanted series of sharp resonance loss lines that appear blue-shifted from the Bragg resonance in the transmission spectrum .
While cladding modes are generally undesirable, coupling to such modes offer opportunities for extending the tuning range available for spectral shaping as well as new types of sensing such as at the outer cladding surface . Many groups have therefore endeavored to enhance the asymmetry of the refractive index profile and expand the Bragg coupling to odd symmetric LP1n modes in the cladding, for example, through tilting of the grating planes [11, 12], type II laser writing of gratings at the core-cladding interface [13, 14], and transversely offsetting the refractive index modification by focusing outside the axial center of the waveguide in point-by-point writing . In this way, tilted FBGs have been used for wideband gain flattening of an erbium fiber amplifier , refractometry of liquids outside of the cladding , temperature-insensitive gauging of non-uniform axial strain  and acceleration sensing .
Tilted chirped FBG have also been tuned to serve as in-fiber edge filters [19, 20]. While these fiber edge filters have the advantage of integration into compact optical fibers, their spectral isolation has been less favorable than that of traditional larger bulk devices such as dielectric thin-film stacks, doped glasses, and dyes where high optical density (OD > 5), low loss (< 5%) and moderate edge steepness (10 dB/nm) are readily available. FBG-based edge filters have generally provided only weak contrast with shallow edge slopes and narrow wavelength range, and tilted-grating edge filters have not been exploited for on-chip integration.
In recent years there has been significant progress in applying femtosecond lasers to directly write buried optical waveguides and other optical devices in bulk glasses for flexible integration into three-dimensional (3D) photonic circuits . This facile approach offers flexible manipulation of the refractive index profile to manipulate waveguide loss, mode size and birefringence that with strongly focused oil-immersion lenses can drive strong refractive index contrast (Δn = 0.022) and confine waveguiding to mode field diameters (MFDs) as small as 7.1 μm . Axial modulating during femtosecond laser waveguide writing with point-by-point single pulses [23, 24] or burst-trains of pulses  have further opened new directions for spectral filtering and sensing with 3D optical circuits in bulk glass without the requirement for a pre-existing guiding core. This flexible direct-write positioning of laser modification tracks was only recently exploited by Thomas et al. [15, 26] to asymmetrically shift the Bragg grating structure within the pre-existing guiding core of standard optical fiber and facilitate strongly enhanced coupling to higher azimuthal order cladding modes.
In this paper, we build on our prior demonstration  of oil-immersion lens focusing to write Bragg grating waveguides (BGWs) flexibly positioned within either the core or cladding of standard optical fiber and thereby enhance the core-to-cladding mode coupling. A strong broadening to a near-continuum loss spectrum is reported as the laser modification track moves from inside the doped fiber core to the all-silica cladding, revealing a favorable merging of the cladding mode spectrum with the sharp Bragg resonance. With further engineering to manipulate the mode size relative to the formation of a highly asymmetric refractive index profile, a dramatically amplified coupling was demonstrated. In extending the BGW writing from standard to coreless optical fiber, and then to bulk glass, this asymmetry gave way to a dense continuum of radiation-like modes, defining a uniquely strong and broadband edge filter with a steep edge that was shaped by the narrow Bragg grating response. In this way, direct femtosecond laser writing of grating waveguides promises new filtering devices for in-fiber or bulk glass optical circuits.
2. Waveguide fabrication and characterization
A femtosecond fiber laser (IMRA America; μJewel D-400-VR) of 420 fs pulse duration and 500 kHz pulse repetition rate was frequency-doubled to 522 nm and directed into an acousto-optic modulator (AOM; NEOS 23080-3-1.06-LTD) controlled by a 500 Hz, 60% duty cycle, square-wave to create burst trains of 600 laser pulses as previously reported . As shown in Fig. 1, the laser burst trains were focused 50 μm below the surface of a fused silica substrate (Corning 7980; 50.8 mm × 25.4 mm × 1 mm with all faces optically polished) with a 100×, 1.25 NA oil-immersion objective lens to form a segmented waveguide consisting of an array of partially overlapping refractive index voxels, resulting in a first order BGW. The Bragg wavelength is governed by the Bragg relation: λB = 2neffΛ, where neff is the effective index (1.445) of the waveguide mode and Λ is the grating period, which was controlled by the ratio of the scan speed to the AOM modulation frequency. For optical fiber, the oil-immersion focusing avoided the otherwise strong astigmatic optical aberration of an air-cladding interface and enabled precise positioning of the BGW anywhere in the core or cladding of Corning SMF-28 fibers as previously demonstrated . BGWs were written in coreless fused silica (Suprasil F100) fiber with 125 μm diameter to reduce refractive effects from the Δn = 0.36% index contrast between the fiber core and cladding. Optical fibers were stripped of their polymer buffer and held taught with ±1 μm accuracy to the laser scanning direction over a distance of 10 cm. Motion control stages (Aerotech ABL1000 with 2.5 nm resolution and 50 nm repeatability) translated the sample with respect to the laser beam, which was linearly polarized parallel to the direction of motion, at a speed of 0.268 mm/s to form BGWs of ∼25 mm length. AOM modulation frequencies from 534.4 Hz to 500 Hz served to tune the Bragg resonance wavelength from 1450 nm to 1550 nm. Pulse energies over the range from 80 nJ to 140 nJ were explored to manipulate the refractive index profile and MFD.
The transmission and reflection spectra of the BGWs were recorded by coupling unpolarized light from broadband infrared light sources (Thorlabs; ASE-FL7002, 1520 nm to 1610 nm or Agilent 83437A, 1200 nm to 1700 nm) through single mode fibers (SMF) and an optical fiber circulator and end-coupled to the BGW devices. Index matching oil was applied at all glass-fiber interfaces to reduce the Fresnel reflections and Fabry-Perot effects. All spectra were normalized relative to direct fiber-to-fiber transmission and recorded with an optical spectrum analyzer (OSA; Ando AQ6317B, with 0.01 nm resolution). To probe the birefringence of the BGWs, the infrared light source was coupled to free space and passed through a broadband polarizer (Thorlabs LPNIR) and a 10× (0.16 NA) lens to excite either horizontally or vertically polarized eigenmodes with electric fields aligned with the y- or z-axis (Fig. 1), respectively. The intensity profiles of the BGW modes were captured by launching tunable laser light (Photonetics Tunics-BT, 1 pm resolution) into the BGW and imaging the end facet onto a phosphor coated CCD camera (Spiricon SP-1550M) with a 60× (0.65 NA) lens.
3. Bragg grating waveguide spectra and discussion
BGWs were fabricated in the center of single mode and coreless optical fibers to explore the symmetric coupling to cladding modes from a pre-existing germanium-doped and a femtosecond laser formed core, respectively. BGWs were also positioned off-center in the cladding of SMF to enhance the coupling to higher azimuthal order cladding modes and in bulk glass where coupling to a broad continuum of radiation-like modes was explored.
3.1. Cladding and radiation mode coupling
The transmission spectra of BGWs written with nearly identical exposures (120 nJ to 130 nJ) are shown in Figs. 2(a) – 2(d) for the respective cases of positioning the BGW near-center in the pre-existing core of SMF, the center of a coreless optical fiber, off-center (Δr = 30 μm) in the cladding of a SMF and 50 μm deep in bulk fused silica glass. The inset images of waveguide end-facets and their magnified views reveal similar attributes of a dual modification zone of positive increase in refractive index of a larger diameter (3.6 μm) white zone under a smaller diameter zone (2.1 μm) of negative refractive index change. The spectra are similar in providing a narrow Bragg resonance (Δλ = 0.3 nm) near λB = 1550 nm, but differ significantly in terms of the spectral density and the strength of coupling to the permitted cladding modes or the radiation-like modes in the bulk glass.
For BGWs centered in both the core of the SMF (Fig. 2(a)) and the coreless fiber (Fig. 2(b)), a very open spectrum is dominated by strong coupling to the discrete LP0n cladding modes that are seen to match well with the stick spectra as shown in the SMF case (Fig. 2(a)), calculated according to :
Here, the spacing between adjacent cladding modes (δλS) is related to the wavelength offset (λS) of the cladding mode from the first cladding mode (λL at LP01), the cladding refractive index (ncl) and the cladding radius (acl). This well matched stick spectra was calculated with the measured values of λL = 1549.49 nm and the refractive index of fused silica at 1550 nm (ncl = 1.44402) while adjusting the cladding radius to acl = 64.25 μm, which slightly exceeded the expected fiber radius of 62.5 ± 0.3 μm.
In the case of a BGW fabricated in the core of an SMF (Fig. 2(a)), the strong coupling observed to the symmetric LP0n cladding modes can be anticipated from the large asymmetrical mismatch in the size of the guiding structure (5.2 μm × 2.16 μm) and the mode profile (7.4 μm × 6.9 μm MFD). A moderately strong coupling is also observed to a higher order azimuthal cladding mode (LP1n) that may arise from imperfect centering of the BGW in the fibers as reported by [15, 26], as well as from an asymmetric refractive index profile as seen in the higher resolution images inset in Fig. 2. Coupling to an increasing density of azimuthal cladding modes was observed as the BGW position was increasingly offset from the center axis, leading to a broadened but weakened coupling that in the case of Fig. 2(c) shows a coarse continuum of 7.3 dB loss when the BGW was offset by 30 μm from the fiber center. Similar broadening of the cladding modes is expected for a BGW positioned in the cladding of coreless optical fiber. Extending further to position the BGW inside the much larger glass plate (Fig. 2(d)) was significant in opening the coupling to a much higher density of radiation-like modes, producing a smooth continuous rejection-band that is 9.4 dB deeper than for wavelengths longer than the Bragg wavelength.
The strong refractive index contrast (ncore − ncl = 0.0052) of the doped core over the fiber cladding therefore predicts a large λoff = 2.78 nm, which aligns well with the λoff = 1.88 nm offset seen in Fig. 2(a). On the other hand, the small refractive index contrast expected between the waveguide (neff = 1.44499 measured from the Bragg relationship) written in the fused silica and the background glass (ncl) predicts a small λoff = 0.52 nm offset, which then leads to a favorable closing of the cladding-mode and Bragg gap for the cases of BGWs written in the SMF cladding (Fig. 2(c)), the coreless fiber (Fig. 2(b)) and the bulk glass (Fig. 2(d)). Hence, Fig. 2 demonstrates how the positioning of BGWs in the core and cladding of optical fibers and in bulk glass further expands the control over cladding and radiation mode coupling to open into a broad continuum that can blend into the Bragg resonance and open an opportunity to create a strong and broad rejection-band optical filter within the waveguide.
3.2. Optical edge filter waveguide
To manipulate the waveguide mode confinement and further optimize the coupling to the radiation modes, BGWs were fabricated over a range of pulse energies from 80 nJ to 140 nJ at a depth of 50 μm below the surface of bulk fused silica glass. Scan directions were also reversed (±x) along directions that were perpendicular to the grating compressor axis of the laser in order to minimize the effect of pulse front tilt on non-reciprocal writing (i.e. “quill” effect) . The transmission spectra of unpolarized light guided through BGWs having Bragg resonances at 1550 nm are shown in Figs. 3(a) and 3(b) for the −x and +x scanning direction, respectively. At a maximum available pulse energy of 140 nJ (entering the glass), a strong grating strength of 39.5 dB, a 3 dB bandwidth of 0.2 nm, a 5 dB radiation mode loss, and a 5 dB total insertion loss (1.9 dB/cm) are reported for −x scanning direction (Fig. 3(a)), confirming that femtosecond laser writing of strong, first-order BGW can be extended from low NA writing  to high NA oil-immersion writing . However, as the pulse energy was decreased from 140 nJ to 80 nJ, the radiation mode loss increased dramatically to 36 dB and opened into the Bragg resonance (λoff ≈ 0), resulting in the formation of an optical edge filter waveguide.
BGW response for +x scanning direction (Fig. 3(b)) yielded a similar BGW strength device but with broader 3 dB bandwidth (0.4 nm) and stronger (21 dB) radiation mode loss. The trend to lower pulse energy generated substantially stronger radiation mode loss (43 dB) compared with the BGWs fabricated in the −x direction, reinforcing a non-reciprocal writing effect in the unexpected direction orthogonal to the pulse front tilt as reported by . Such large coupling to the radiation-like modes, which was not seen in BGWs previously written with a weaker 0.55 NA lens , is due to the smaller refractive index structure (4 μm × 10 μm) formed with the 1.25 NA oil-immersion writing process relative to the guided mode sizes. This is visualized in Fig. 4 where the top row shows optical micrographs of the BGW end-facets and the bottom row shows the guided mode profiles at 1560 nm, for the BGWs of Fig. 3(b). The measured MFD values defined the ellipses (dotted lines) that were superimposed over the optical micrographs to indicate the size and approximate position of the mode relative to the positive (white) and negative (black) refractive index zones of the BGW end-facets. As the pulse energy was decreased from 140 nJ to 80 nJ, the MFD increased from 10.5 μm × 10 μm to 16.4 μm × 13.9 μm, extending the mode partially into the negative index region. This lower energy exposure therefore defines a highly asymmetric grating index profile that breaks the symmetry to permit strong coupling to the continuum of available radiation modes that is especially strongest (43 dB) for the 100 nJ case in Fig. 3(b) and diminishes for the case of 80 nJ when the asymmetric negative zone is fully encapsulated by the larger mode profile.
The strong coupling of light into the continuum of radiation modes in bulk glass reveals an opportunity for very sharp and potentially broadband edge filters. The transmission and reflection spectra for the BGW written in the +x direction with a pulse energy of 100 nJ (Fig. 5(a)) show a strong and narrow Bragg response seen only in reflection while the strong cladding mode coupling is seen only in transmission. The 3 dB bandwidth of 0.56 nm as seen in reflection is 2.8× larger than that reported for BGWs fabricated with a 0.55 NA lens [25, 30]. This broadening may be due to an increased grating strength with higher resolution focusing, but waveguide birefringence is also a contributing factor. The inset in Fig. 5(a) reveals a 114 ± 3 pm shift in the edge wavelengths when the BGW was probed with vertical and horizontal polarization, leading to an inferred waveguide birefringence of (1.06±0.03)×10−4. This birefringence is 2-fold larger in comparison to waveguides written with weaker focusing of 0.55 NA in air at the same pulse energy  and may arise from increased asymmetric stress [32, 33] for focusing with the 1.25 NA oil immersion lens.
The extinction ratio between the passband and rejection-band in Fig. 5(a) was measured to be 43 dB, with an edge steepness of 136 dB/nm when probed with unpolarized light from 3 dB to the bottom of the rejection-band (43 dB). When probing with linearly polarized light (Fig. 5(a) inset) this edge steepness increases to 185 dB/nm, which is approximately two orders of magnitude higher than the 0.7 dB/nm to 13 dB/nm values reported in FBG-based edge filters [19, 20]. A broader spectral examination of two edge filter waveguides (Fig. 5(b)) shows the edge filter response to extend from the Bragg wavelengths (1450 nm and 1550 nm) to the limit of our source (1250 nm). The 1550 nm edge filter waveguide maintains an extinction ratio of 43 dB until 1520 nm, diminishing to 18 dB at 1370 nm before increasing again to 30 dB at 1250 nm. These edge filters waveguides are therefore 15 times broader than the 2 nm to 20 nm bandwidths reported for tilted FBG  and further represent the highest attenuating and steepest edge filter responses reported to date for a single mode waveguide.
Figure 5(b) shows the transmission spectra for an edge filter waveguide with an edge wavelength of 1450 nm that was tuned by changing the AOM modulation frequency. In this way, the Bragg wavelength and hence the edge filter wavelength can be tuned for applications requiring filtering across the 1200 nm to 1700 nm spectrum tested here. The weaker extinction ratio for this shorter wavelength edge filter can be recovered by increasing the laser pulse energy to compensate for the smaller mode size expected at this wavelength.
The 7 dB insertion loss for the edge filter in Fig. 5(a) mostly consists of waveguide propagation loss, found here to be 2.2 dB/cm, since only a small 0.13 dB modal mismatch is expected at 1560 nm for coupling between SMF (MFD = 10.4 μm) and BGW mode (13.3 μm × 10.8 μm) shown in Fig. 4(c). This propagation loss is comparable to the lowest loss (2.27 dB/cm) for the waveguide with the sharp Bragg resonance in Fig. 3(a), but is 3.6 times higher than the lowest losses reported for BGW fabrication with weaker 0.55 NA air lens focusing . Edge filter devices with lengths shorter than the 25 mm presented here may be considered to reduce the total insertion loss, with a trade off of weaker extinction ratio.
Despite the moderate propagation loss, the reported edge filter waveguide devices offered very steep slopes (185 dB/nm) for linearly polarized light, a large attenuation (OD 4) over a 30 nm wavelength range, and approximately OD 2 attenuation over 300 nm bandwidth. These devices are attractive for inserting into 3D bulk optical circuits or planar waveguide circuits which cannot be achieved with the traditional, lower loss, bulk optical edge filters. A major advantage of the femtosecond laser written edge filter waveguides is the steep edge cut off that is defined by the sharp resonance of the Bragg grating edge together with the strong coupling light to the continuum of radiation modes in bulk glass. A similarly dense range of cladding modes could also be made available for BGWs written asymmetrically in optical fiber by adopting an index-matched coating around the fiber  and thus broaden the spectrum reported in Fig. 2(a). However, writing in the fiber cladding or in coreless fiber is preferred to close the λoff gap and merge the cladding mode spectrum with the sharp Bragg resonance. Further exploration of laser beam shaping and focusing techniques would be attractive to generate more asymmetric refractive index profiles and couple even more strongly to higher order cladding modes to broadened the spectral control of Bragg grating and edge filter waveguide devices in bulk and fiber glasses.
Strong coupling to a high density of asymmetric cladding and radiation modes was explored by controlling the position of BGWs written into standard and coreless optical fiber and in bulk glass with a femtosecond laser. Strong focusing with an oil-immersion lens further offered strongly asymmetric refractive index profiles that together with manipulation of the MFD could control the modal overlap for strong coupling to a continuum of radiation modes in bulk glass. In this way, the first demonstration of strongly isolating (43 dB) optical edge filter waveguides with exceptionally steep edge slope of 185 dB/nm was reported for linearly polarized light. These edge-filter waveguides extend the spectral filtering functions available in optical fiber and 3D integrated optical circuits that are attractive for facile monolithic integration with other optical and optofluidic devices for broad based applications in telecommunications, fiber lasers, and micro-total analysis systems, optical sensing, and spectroscopy.
This work was supported by the National Science and Engineering Research Council of Canada, the Canadian Institute for Photonic Innovation and the Portuguese Fundação para a Ciência e Tecnologia.
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