Lattice-Like Waveguides With Integrated Bragg Gratings in Planar Cyclic Olefin Copolymers

This contribution demonstrates femtosecond laser direct writing of lattice-like waveguides in planar cyclic olefin copolymer substrates. Based on numerical simulation and experimental near-field analysis, stable single-mode waveguiding around wavelengths of 1550 nm is demonstrated. The waveguiding mechanism is based on a hexagonal array of laser-induced, positive refractive index modification lines. Thus, the lateral extension of the guided mode can be adapted by varying the fabrication parameters and, in consequence, the resulting cross-sectional arrangement of the refractive index perturbations. With an optical attenuation of 2.2 dB·cm-1 around 1550 nm, the fabricated waveguides are well-suited for on-chip integrated photonic devices. Moreover, the waveguides can also be equipped with Bragg gratings to enable the application of the photonic platform as a sensing device. Depending on their length, the Bragg grating structures exhibit reflectivities of up to 99% and spectral widths down to 0.3 nm. The flexibility of the fabrication process and the sensing capabilities of the lattice-like waveguides with integrated Bragg gratings are underlined by an exemplary application study demonstrating a relative pressure sensor. For that, a photonic platform is micromilled to generate a 300 μm thick diaphragm and a reference pressure chamber. The strain introduced to the diaphragm by external pressure changes can then be quantified by the integrated photonic structures. This way, absolute pressure sensitivities of up to 38 pm·kPa-1 can be achieved in a relative pressure range from −60 to 100 kPa. The newly-developed lattice-like waveguides with integrated Bragg gratings are therefore well-suited for the realization of novel and adaptable photonic devices and sensors.

such as their inherent photosensitivity and a significantly reduced Young's modulus, which yields devices with increased mechanical flexibility.Furthermore, a variety of polymer classes, such as thermosets, thermoplastics or photopolymers, is nowadays easily accessible and thus, the right substrate material can be straightforwardly chosen and tailored towards specific photonic applications [1], [2], [3].With this in mind, a multitude of polymer-based photonic devices, including waveguides, interferometric structures, Bragg gratings, couplers as well as biomedical platforms, have been realized using various optical polymers [4], [5], [6].Furthermore, significant potential on the journey towards novel quantum technologies is attributed to polymer-based integrated photonics [7].However, conventional polymer substrates, such as poly(methyl methacrylate) (PMMA) or polycarbonate (PC), also come with significant drawbacks, mainly related to their limited temperature resistance and their pronounced water absorption [8].
This can be overcome by employing cyclic olefin copolymers (COC), since this novel, high-grade optical polymer features a vastly reduced water absorption below 0.01% as well as glass transition temperatures of up to 250 °C [9].COCs are thus especially well-suited to serve as a substrate for photonic sensing devices.While there is successful research towards COC-based fiber sensors with integrated Bragg gratings (BG) [10], a lot of effort is currently invested in the development of integrated photonics in injection-molded, planar COC substrates.Over the past decade, several novel photonic devices based on planar COC substrates have been demonstrated.Some examples are temperature sensors, capable of quantifying elevated temperatures of up to 160 °C, hydrogen detectors and refractive index sensors [11], [12], [13].The concept also enables fabrication of temperature-referenced devices by multiplexing multiple BGs within one single photonic platform [14].Furthermore, the impact of relative humidity changes on the Bragg reflection signal of these devices is negligible due to the COCs water absorption properties [15].Besides the fact that, in comparison with polymer optical fibers, planar substrates enable utilization of COC grades with higher temperature stability, handling and post-processing of planar devices is straightforward, while injection-molded substrates are also reasonably priced if they are manufactured in large quantities.Furthermore, the inherent robustness of COC substrates enables the harsh-environment application of these devices and also their subsequent electrification via femtosecond laser-based sintering processes [16], [17].Additionally, COC is hemocompatible and the feasibility of merging integrated photonics with microfluidics on a single COC platform is already proven, thus paving the way towards COC-based lab-on-a-chip devices [18], [19].
Most COC-based polymer planar Bragg gratings (PPBG) are fabricated using a specialized approach denoted as singlewriting-step (SWS) procedure, a methodology based on the utilization of amplitude and phase masks [20], [21].Alternatively, it is possible to employ femtosecond (fs) lasers to realize direct-writing approaches.In general, fs direct writing offers several advantages in comparison to the SWS method, such as an increased flexibility and the possibility to manufacture three-dimensional and complex photonic networks on a single platform [22].Recently, fs laser-based generation of so-called Type-I waveguides, a structure where the radiation is confined within a single positive refractive index modification, with integrated BGs was successfully demonstrated within COCs [23].Alternative waveguiding concepts are also realizable with fs laser-based direct writing.Besides Type-II waveguides, where light propagates within the stress field in-between two or more parallel damage tracks, it is also possible to enable waveguiding by lowering the effective volume refractive index around a pristine substrate section.The latter is also often denoted as Type-III, depressed cladding or lattice-like waveguide (LLWG), whereas LLWG specifically refers to waveguides consisting of multiple refractive index modification lines with periodical arrangement.Normally, the modification lines are arranged in a circular or hexagonal manor, surrounding a pristine material section denoted as core [24], [25].The waveguide cross-section thus consists of pristine material with defined lattice defects, or perturbations, as outlined in Fig. 1.
In comparison to the other waveguide types, LLWGs offer even greater flexibility, since the cross-section of the guided mode can be altered by adapting the cross-sectional arrangement of the modification lines.This is achieved by adapting the modification line distance in x-direction d x .Thus, also the outer circumcircle D x and incircle D y of the hexagonal modification line arrangement are changed, as being defined as and respectively.Besides altering the guided mode's diameter, LL-WGs also enable mode-shape transformation and photonic splitters.Furthermore, mainly but not solely for sensing purposes, the LLWG core can also be equipped with Bragg grating (BG) structures [26], [27].This contribution demonstrates the fabrication of LLWGs in planar COC substrates.Furthermore, a sophisticated near-field analysis of the waveguiding properties is conducted and the optical attenuation of the photonic structures is determined.Moreover, LLWGs with integrated BGs are demonstrated and an in-depth discussion of the BG properties is provided.Additionally, in order to underline the flexibility of the fabrication process and to demonstrate the practical applicability of the concept, an optical pressure sensor is realized and its performance is analyzed.Finally, the experimental findings are validated by a numerical simulation study based on the beam propagation method.

II. SIMULATION STUDY
Most LLWGs demonstrated so far are based on negative refractive index perturbations, which lead to confinement of the electromagnetic radiation in the waveguide's pristine core [24], [28], [29], [30].However, recently, Wang et al. demonstrated the first LLWG based on positive refractive index modifications fabricated in silica glass, where light is instead guided in-between the modification lines [31].In order to provide a better insight into the material modification and the resulting light-guiding mechanisms, a sophisticated numerical simulation study, based on the beam propagation method (BPM, RSoft Photonic Device Tools, Synopsis), is conducted.For the study, a propagation wavelength of 1550 nm and an elliptic modification line crosssection, with a minor and major axis of 1.2 μm and 2.4 μm, respectively, are assumed.Please note that these values are based on experimental observations (see Section III).Furthermore, the refractive index modification of the perturbations is assumed to be constant throughout their whole cross-section, with a step transition to the adjacent, pristine COC substrate.The refractive index of the unmodified material is defined as 1.52, based on previously reported data [12], [32].Exemplarily chosen results of the study, i.e., a comparison of the mode-field distributions of LLWGs with negative and positive refractive index perturbations as well as the light propagation within a 15 mm long LLWG, are shown in Fig. 2.
According to Fig. 2(a), negative refractive index modifications result in strong modal confinement within the pristine waveguide core, while positive refractive index perturbations (see Fig. 2(b)) result in light propagation in the core as well as in and in-between the modification lines.For a sufficiently small modification line distance d x , which is set to 3 μm for all results presented in Fig. 2, a significant amount of light is still guided within the pristine core of the photonic structure and can therefore interact with a Bragg grating located therein.It is also found that the refractive index perturbation magnitude Δn, to obtain stable waveguiding, is significantly smaller for positive refractive index modifications (Δn ≥ 1.3•10 -3 ) than in the case of negative refractive index modifications (Δn ≤ −5•10 -3 ).Furthermore, the iterative mode solver does not yield any results for higher order modes in the investigated parameter regime 1.3•10 -3 ≤ Δn ≤ 3•10 -3 and 2 μm ≤ d x ≤ 4 μm, even if the LLWG structure is excited with a Gaussian launch field, which is asymmetrically offset from the LLWG propagation axis [33].Finally, Fig. 2(c) depicts the simulated light propagation within the xz-plane of a COC-LLWG, fabricated with a refractive index modification of 2•10 -3 .The data underlines that light is well confined in the photonic structure and stable waveguiding is achieved in the examined range.

III. FABRICATION
A frequency-doubled femtosecond laser (Pharos-10-600, Light Conversion), emitting radiation at a wavelength of 514 nm, is employed for the fabrication of LLWGs with integrated BGs.Its raw beam is extended to a diameter of 10 mm by means of a beam expansion telescope (BET) before it is guided onto a spatial light modulator (SLM, Pluto VIS 21, Holoeye).The SLM, which exhibits an array of 1920 x 1080 pixels with a pixel size of 8 μm, serves multiple tasks in the laser setup.First, it is programmed to act as a blazed diffraction grating in order to redirect the laser beam.Second, it is used for adaptive beam shaping purposes, enabling manipulation of the focal intensity cross-section while possible wavefront aberrations can be compensated as well.Thus, the programmable focal voxel shape is independent of the writing depth [34], [35].The SLM is then imaged onto the focusing objective (EC Epiplan-Neofluar, Carl Zeiss Microscopy) by a 4f telescope with a focal length of 300 mm.Additionally, an iris is placed in the telescope's focal plane to remove any unwanted extraneous radiation from the beam path.With an objective magnification of 20, and a numerical aperture (NA) of 0.5, which is fully exploited by the expanded beam, focal cross-section diameters down to 1.2 μm

TABLE I PROCESS PARAMETERS FOR THE fs LASER-BASED FABRICATION OF COC-BASED LLWGS WITH INTEGRATED BGS
(1/e 2 ) can be realized.A schematic of the employed fs laser setup is depicted in Fig. 3.
In contrast to the LLWG modification lines, BGs are fabricated with an elliptical focal cross-section in order to increase the cross-sectional area of the resulting refractive index modification and, thus, the interaction of BG structure and guided light.An overview of the employed process parameters, for the LLWG modification lines as well as the integrated BG structures, is given in Table I.
Please note that the LLWGs are fabricated with a parameter combination that yields a pulse overlap of 50% while, for BGs, repetition rate and translation speed result in a pulse separation of 2.08 μm.This defines the Bragg grating period Λ and, in combination with the effective refractive index n eff , the BG's wavelength of main reflection, or Bragg wavelength λ B , according to Here, the factor m represents the Bragg grating order.To omit unwanted thermal effects due to insufficient pulse separation, all BGs fabricated in this study are fourth-order gratings.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
The injection-molded COC samples (TOPAS 6017S-04, Topas Advanced Polymers) are cut to appropriate size by means of a desktop micro mill (CNC Mini-Mill/4, Minitech Machinery).An insight into the employed milling process and its parameters is provided in [36].All COC substrates have a rectangular footprint with a thickness of 1.5 mm and edge lengths between 15 mm and 40 mm, in dependance of the conducted experiment.During fs laser processing, the COC samples are positioned by means of a high-precision translation stage (ANT130-XY, Aerotech), which provides a positioning accuracy of 250 nm and a repeatability of 75 nm.This way, the 120 LWG modification lines and the integrated BG are fabricated successively, in a bottom-to-top fashion.
Multiple devices with different modification line distances d x are manufactured, whereas modification line arrangement as well as distances are based on the simulation study results (see Section II).The center of all the resulting hexagonal modification arrays is thereby located in a depth of 300 μm below the substrate surface (y-direction).Subsequently, the resulting refractive index modifications are analyzed qualitatively via bright-field microscopy.Top-view images of multiple LLWGs with varying modification line distances, as well as a crosssectional view of an LLWG with a modification line distance of 3 μm, are depicted in Fig. 4.
The LLWG modification lines are barely perceivable as bright perturbations of the substrate in parallel to the z-axis.The BG modifications, which are also depicted in Fig. 4(a), are instead clearly discernible as black structures.From a cross-sectional perspective, as shown in Fig. 4(b), the LLWG modifications are also perceptible.The lines exhibit an elliptic cross-section with a minor axis of approximately 1.2 μm and noticeable ellipticity.

A. Near-Field Analysis
All near-field data shown in this study is acquired with the self-built near-field imaging setup depicted in Fig. 5(a).A pigtailed semiconductor laser diode (LU1550M150-1A06F30H, Lumics) is used to generate radiation at a wavelength of 1550 nm.The light is coupled into the integrated photonic structure by means of butt coupling a single-mode fiber (SMF) pigtail to the LLWG.Alternatively, a telescope setup can be used to excite the waveguide via free-space coupling.The telescope's collimating lens L1 is designed to generate a collimated beam that fully exploits the clear aperture of the focusing lens L2.This results in an effective numerical aperture of 0.46 and thus guarantees satisfaction of the overfilling condition in the freespace coupling situation [37].The waveguide output is imaged onto an infrared camera (1460−1600 nm Near-Infrared Camera, Edmund Optics) through a microscope setup consisting of a 50x objective (M Plan Apo NIR HR 50X, Mitutoyo) and a tube lens (TTL200-S8, Thorlabs).Each evaluated image is actually the average of 50 individual frames.Prior to evaluation, the raw images are optimized by means of dark-frame correction and sensor linearization algorithms.Afterwards a two-dimensional Gaussian fit [38] is performed in order to locate the centroid of the near-field image for subsequent evaluation of the 1/e 2 mode-field diameter (MFD).
Multiple COC-LLWGs, with modification line distances d x (see Fig. 1) ranging from 2 μm to 4 μm, are fabricated and their 1/e 2 mode-field diameter is examined.The photonic structures exhibit a length of 15 mm and are buried in a depth of 300 μm underneath the substrate surface.The waveguides are also equipped with a Bragg grating.This enables straightforward butt coupling of the pigtailed single-mode fibers to the respective waveguides by observing and optimizing the BG reflection signal during the coupling process with the interrogation setup outlined in Section IV.C.However, with a main wavelength of reflection around 1580 nm, the BG does not interfere with the 1550 nm radiation employed throughout this experiment.Exemplary near-field data of LLWGs, fabricated with a modification line distanced of 2 μm and 4 μm, is depicted in Fig. 5(b) and (c), respectively.The near-field intensity distribution of both photonic structures can be correlated to the hexagonal arrangement of the LLWG modification lines.Moreover, since light is guided within the region of the refractive index perturbations, a waveguiding mechanism based on positive refractive index modifications is inferred.Furthermore, the observed MFD unambiguously increases with larger modification line distances.Note that in practice, material degradation due to thermal accumulation prevents the fabrication of LLWGs with modification line distances below 2 μm.Additionally, no waveguiding is observed if d x exceeds 4 μm.In this case, the proximity of neighboring modification lines is insufficient.Since butt coupling with an SMF does not necessarily guarantee overfilling of the LLWG, and can thus result in the distinct excitation of specific waveguide modes, the experimental results are verified with the free-space coupling configuration.It is found that the resulting near-field images of both coupling situations do not differ significantly.
Fig. 6 summarizes the determined MFDs for all examined configurations.It furthermore depicts the theoretical outer diameters of the LLWG and the corresponding MFDs obtained via numerical simulation (Δn = 2•10 -3 , see Section II).The study shows that the MFD is noticeably astigmatic and directly proportional to the LLWG's modification line distance in x-as well as in y-direction.On the x-axis, the MFD is between 26 μm and 55 μm, while it is ranging from 23 μm to 47 μm on the y-axis, for modification line distances between 2 μm and 4 μm.Additionally, the determined MFDs exceed their respective outer diameters of the hexagonal modification line arrangement by approximately 13%.It is worthwhile to note, however, that the theoretical approximation of the outer circumcircle and the incircle neglects the lateral extension of Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the modifications themselves.The determined MFD asymmetry is attributed to the inherent direction-dependent diameter of the LLWG's cross-section and is possibly amplified by the ellipticity of the individual modification lines.The asymmetry of the MFDs obtained via numerical simulation, however, is significantly less pronounced.Possible reasons for this are deviations of the assumed refractive index modification lines from reality, i.e., cross-section, lateral extension as well as intrinsic and evanescent refractive index profile.Especially the latter is presumably governed by the intensity distribution within the femtosecond laser focus and thus more complex than the assumed constant and homogeneous refractive index modification [39].Although there is a deviation between the MFDs acquired via butt coupling and free-space coupling, the difference is less than 3 μm and therefore attributed to measurement uncertainties.The comparable waveguiding behavior in both coupling configurations underlines the BPM simulation-based hypothesis that the demonstrated COC-LLWGs are single-mode waveguides at wavelengths around 1550 nm.

B. Waveguide Attenuation
A cut-back approach is used to estimate the optical attenuation of COC-based LLWGs.Therefore, both ends of a waveguide, manufactured with a d x of 3 μm, and a length of 40 mm, are butt-coupled to fiber-optic pigtails by means of a UVcurable Adhesive (NOA78, Norland Optical Adhesives).The photonic structure is then excited with radiation generated by the swept laser diode of a commercial-grade interrogation device (HYPERION si155, LUNA).The evaluation unit is also employed to record the transmission spectrum, as depicted in Fig. 7(a).The COC substrate is then mounted on the axis of the micro mill, to incrementally reduce its length in 1 mm steps with high precision and surface quality [36].Subsequent to each length reduction step, a new physical connection between waveguide output and the respective pigtail is reestablished, before the transmission spectrum is recorded.Averaging the transmitted power over a wavelength regime from 1545 nm to 1555 nm results in the transmitted power around 1550 nm as a function of the waveguide length.By means of linear regression, the optical attenuation of the LLWG is determined.Exemplary transmission spectra as well as the transmitted power as a function of the waveguide length are shown in Fig. 7(b) and (c), respectively.With overall optical losses of 2.2 dB•cm -1 , this value is about twice the attenuation of COC-based waveguides fabricated via direct laser writing or by employing the SWS procedure [20], [23].The increased optical losses are attributed to the light propagating in waveguide areas where modifications lines are present.These regions are more likely to comprise scattering centers that interact with the guided photons due to material impurities, micro fissures or cracks introduced by thermal effects or local modification line inconsistencies caused by pulse instabilities.However, keeping in mind that propagation distances on planar photonic platforms are in the order of a few centimeters, this magnitude of optical loss is acceptable.

C. Bragg Grating Performance
In theory, the reflectivity ρ of a BG, in dependance of its length L, is given by Here, κ ac represents the coupling constant, a factor accounting for the interaction of the guided modes with the Bragg grating structure [40].Furthermore, according to the approximation the BG length impacts the reflection peaks spectral full width at half maximum FWHM as well, since the number of grating planes N is directly proportional to L. Here, the factor S is a measure for the grating strength while Δn BG represents the amplitude of the grating's reflective index modulation [41].
Multiple COC-LLWGs with a d x of 3 μm, comprising integrated BGs with lengths between 1 mm and 10 mm, are fabricated in order to examine the reflection and transmission properties of the BGs.For this purpose, the interrogation unit is additionally connected to an external optical circulator so that reflection and transmission spectra can be recorded simultaneously on different channels of the same device.A schematic of the setup is depicted in Fig. 8(a), while Fig. 8(b) shows exemplary reflection and transmission spectra of a COC-LLWG equipped with a 5 mm long BG.The reflection signal exhibits a pronounced Bragg peak with a Bragg wavelength of 1582.26 nm and a FWHM of 0.3 nm, respectively.With a refractive index of 1.52, around wavelengths of 1580 nm [12], the resulting Bragg wavelength correlates well with theoretical calculations based on (3).Furthermore, the BG peak's narrow spectral width is another indication for single-mode operation of the photonic platform [41], [42], while the absence of peak splitting or multi peaks proves that the photonic structures exhibit no or negligible birefringence [43].In the transmission spectrum, a pronounced dip at the Bragg wavelength position is observed.According to the reflectivity ρ of a BG can be quantified by measuring the depth of the reflection dip T d [40].Based on the determined T d value of −19.45 dB, the 5 mm long BG exhibits a reflectivity of 99%.Fig. 8(c) correlates reflectivity and FWHM with the length of the respective BG.It is found that reflectivity as well as spectral width change drastically for BG lengths between 1 mm and 4 mm.While the reflectivity increases from 20% to 98%, the peak's FWHM decreases from 0.54 nm to 0.33 nm.BGs with lengths between 5 mm and 10 mm, however, exhibit a constant reflectivity around 99% and spectral widths down to 0.3 nm.In both cases, the experimental results correlate well with the respective theory provided by ( 5) and ( 6), as underlined by the respective least-square fit curves also shown in Fig. 8(c).Overall, the Bragg grating performance is similar to that of COC-based planar Bragg grating devices manufactured via the SWS method [20].However, the determined reflectivity values of a 5 mm long BG within a COC-LLWG are superior to comparable BGs integrated into Type-I waveguides, also fabricated via femtosecond laser-based direct writing.There, maximum reflectivities of up to 95% were demonstrated [23].

D. Photonic Pressure Sensor
As an application example, a photonic pressure sensor is realized with help of the newly-developed photonic structures.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Therefore, two LLWGs are fabricated within a COC substrate that exhibits a quadratic footprint with an edge length of 15 mm and a thickness of 1.5 mm.Note, as shown in Fig. 9(a), that the photonic structures are generated in different depths.At a depth of 60 μm, one of the LLWGs is positioned close to the substrate surface, while the other waveguide is generated at a depth of 240 μm.Afterwards, a cavity with a radius of 5 mm and a depth of of 1.2 mm is fabricated underneath the photonic structures by means of a micromilling process.This process yields a diaphragm with a thickness of 300 μm, which comprises the LLWGs.Please note that, since the photonic structures are integrated directly within the diaphragm, this approach differs significantly from most other BG-based pressure sensors, where fiber Bragg gratings are bonded to diaphragms machined from various materials [44], [45].The resulting cavity is then sealed by bonding the sensor substrate to another micromachined COC workpiece with a UV-curable adhesive.This way, a reference gas pocket is created, hence, external pressure changes will lead to the deformation of the diaphragm.This, in turn, leads to position-dependent stress or strain within the diaphragm [46].More information on the working principle of suchlike platforms and their fabrication is provided in [47].
The LLWGs are also equipped with 1 mm long BGs, their ends aligned with the respective diaphragm edge on each substrate side.Please note that the BG length is deliberately set to a small value in order to achieve the best possible strain distribution homogeneity along the BG axis, while still obtaining a sufficient signal to noise ratio for sensing purposes.A schematic of the photonic pressure sensing platform as well as an image of the device are shown in Fig. 9(a).
The absolute strain along the diaphragm's surface is the superposition of radial strain ε r and tangential ε t strain, at the radial position r, according to and Here, d is the diaphragm thickness while ν and E are Poisson's ratio and Young's modulus of the COC, respectively.P 2 represents external pressure changes whereas P 1 is the reference pressure within the sealed air pocket.For radial positions approaching the diaphragm radius R, the local tangential strain can be neglected and the overall strain at the diaphragm edge is governed by ε r [48].Thus, the pressure-dependent strain ε, experienced by the BGs in the proposed configuration, can be derived from (7) as The correction factor C accounts for the absolute positioning of the integrated BGs with respect to the diaphragm's center line, i.e., its neutral axis, and its thickness.Consequently, in this configuration (see Fig. 9(a)), C is determined as −0.6 for BG1 and 0.6 for BG2, respectively.Based on these considerations, the impact of pressure changes on the resulting Bragg wavelength shift Δλ B of each BG can be estimated by ) where p e represents the photoelastic coefficient of the COC diaphragm.
After aligning the fiber-optic pigtails to both waveguides, the photonic sensor is placed in a pressure chamber.By connecting the chamber either to an external compressed air supply or a vacuum pump, the relative pressure within the chamber can be altered.The experimental setup, which is also equipped with a pressure and temperature referencing device (CPG1500, WIKA), enables the application of relative external pressures between -60 kPa and 100 kPa to the photonic platform.Fig. 9(b) depicts the resulting Bragg wavelength shift in dependance of the applied relative pressure changes.
The experimental data shows that both integrated BGs exhibit a distinct response towards external pressure variations.While the reflection peak of BG1 shifts towards longer wavelengths with increasing relative pressures, the Bragg reflection of BG2 experiences a spectral blue shift.Furthermore, BG1 provides an evaluable reflection signal up to pressures of 100 kPa, while the reflection amplitude of BG2 is no longer quantifiable for pressures beyond 60 kPa.In general, the signal reduction experienced while exceeding certain pressure values, are correlated to waveguide bending losses induced by the diaphragm deflection.Nevertheless, from a principal point of view as well as in magnitude, the observed Bragg wavelength shifts of both BGs correlate well to the theoretical approach outlined in (10).While BG2 exhibits a linear response, which yields a pressure sensitivity of −38 pm•kPa -1 , the Bragg wavelength shift of BG1 shows a certain degree of nonlinearity.Still, the response is comparable to that of BG2 and can be well fitted with a second order polynomial, as also shown in Fig. 9(b).The deviation of both BGs, in terms of maximum pressure values as well as linearity, is attributed to positioning inaccuracies mainly induced by the necessity to reposition the photonic platform in-between laserbased material modification and the subsequent micromilling process.Please note that neither the fabrication parameters of the photonic structures nor the diaphragm parameters have been optimized towards maximum sensor performance yet.However, this exemplifying application study underlines the flexibility of the femtosecond laser-based fabrication of LLWGs, since it is possible to generate photonic structures at different depths within a polymer substrate.Furthermore, the applicability of LLWGs with integrated BGs as photonic sensing devices is proven.Finally, with absolute pressure sensitivities of up to 38 pm•kPa -1 in a pressure range of 120 kPa, the performance of the newly-developed concept surpasses most diaphragm-based fiber Bragg grating pressure sensors [44], [45] and silica-based diaphragms with integrated photonic structures [49], [50].

V. CONCLUSION
In conclusion, this article demonstrates and discusses the femtosecond laser-based fabrication of lattice-like waveguides in planar cyclic olefin copolymer substrates.The generated photonic structures are based on a hexagonal arrangement of positive refractive index modification lines.As confirmed by near-field analysis in combination with numerical simulations based on the beam propagation method, the refractive index change of a single modification line is estimated as 2•10 -3 .The photonic structures exhibit stable single-mode waveguiding around wavelengths of 1550 nm, for modification line distances between 2 μm and 4 μm.Thereby, the resulting mode-field diameter is proportional to the modification line distance and thus governed by the associated cross-sectional extension of the modification line array.In consequence, the asymmetric mode-field diameters and can be adapted from 26 μm to 55 μm in x-direction and from 23 μm to 47 μm in y-direction, respectively.This underlines the flexibility of the LLWG concept in comparison to other waveguide types and also paves the way towards application-related optimization of the integrated waveguides.Furthermore, the optical attenuation of the COC-LLWGs is determined as 2.2 dB•cm -1 for wavelengths around 1550 nm.
Additionally, the newly-developed photonic waveguide can be equipped with Bragg grating structures.Depending on the length of the integrated BG's, reflectivity values of up to 99% and spectral widths down to 0.3 nm are achieved.Thus, the photonic platform ins unambiguously well-suited to serve as a sensing device.This is underlined by an exemplary application study, wherein the demonstrated concept is employed to realize a photonic pressure sensor.Therefore, a micromilling process is used to fabricate a diaphragm with 300 μm thickness, which comprises the photonic structures.After encapsulation, and thus generation of an air-filled reference pocket, the diaphragm is deformed by external pressure changes which translate into Bragg wavelength shifts of the integrated BGs.The demonstrated device allows quantification of relative pressure changes in a range from −60 kPa to 100 kPa with absolute sensitivity values up to 38 pm•kPa -1 , in dependence of the BG's location.Thus, the concept of COC-based LLWGs with integrated BGs paves the way towards adaptable and robust devices and sensors based on integrated photonics.

Fig. 1 .
Fig. 1.Schematic (cross-sectional view as well as isometric view) of an LLWG with integrated BG.

Fig. 2 .
Fig. 2. Simulated mode fields of LLWGs (d x = 3 µm) based on (a) negative and (b) positive refractive index perturbations.(c) Simulated light propagation in the xz-plane of a 15 mm long COC-LLWG based on positive refractive index modification lines.

Fig. 3 .
Fig. 3. Schematic of the employed laser setup including the focal crosssections used for the fabrication of LLWG modification lines and Bragg grating structures.The inset shows the respective focal cross-sections employed for the fabrication of modification lines (circular) and BG structures (elliptic).

Fig. 4 .
Fig. 4. (a) Top-view bright-field microscopy images of LLWGs with integrated BGs.LLWGs with modification line distances of 2, 3 and 4 µm are depicted.(b) Cross-sectional view of an LLWG with a modification line distance of 3 µm.

Fig. 5 .
Fig. 5. (a) Schematic of the employed near-field evaluation setup.Near-field images and cross-sectional intensity distributions for an LLWG with a modification distance of (b) 2 µm and (c) 4 µm.The locations of the respective refractive index perturbations are also indicated.

Fig. 6 .
Fig. 6.Mode-field diameters of COC-LLWGs as function of the modification line distance d x .The determined values for both coupling situations (free-space and butt coupling) as well as the respective values for outer circumcircle D x and incircle D y are shown.Furthermore, the MFDs obtained via numerical simulation are depicted.

Fig. 7 .
Fig. 7. (a) Schematic of the experimental setup used for cut-back measurements.(b) Exemplary transmission spectra for different LLWG lengths.(c) Transmitted power around wavelengths of 1550 nm as a function of waveguide length.

Fig. 8 .
Fig. 8. (a) Schematic of the employed setup to determine the reflection and transmission properties of Bragg gratings.(b) Exemplary reflection and transmission spectra of a BG with a length of 5 mm, fabricated within a COC-LLWG.(c) Reflectivity and spectral width of BGs integrated in COC-LLWGs as a function of their length.

Fig. 9 .
Fig. 9. (a) Cross-sectional schematic and photography of the photonic pressure sensor based on COC-LLWGs with integrated BGs.(b) Respective response of the integrated BGs to relative pressure changes.