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Abstract
Diamond films were deposited by chemical vapor deposition (CVD) on the tip of Fabry-Perot (FPI) and multi-mode (MMI) optical fiber interferometers. Diamond provides a robust interface capable of forming covalent bonds between atoms on its surface and receptor molecules, required for biosensing applications. The films were characterized by optical and scanning electron microscopy (SEM), optical profilometry and Raman spectroscopy. The diamond-coated interferometers were tested with different refractive index solutions. The sensors response was 40 ± 1 dB/RIU and −987 ± 70 pm/ RIU for the FPI and −11 ± 1 dB/RIU for the MMI.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical fiber (OF) based sensors have numerous advantages, such as biocompatibility, reduced size, capability to operate under hostile environments, immunity to electromagnetic interference, and multiplexing capability. These intrinsic properties make OFs very attractive for biosensing applications, allowing their use for the detection of proteins [1,2], antibodies, bacteria [3], DNA, and SARS-CoV-2 [4], among others.
OF sensors can be fabricated using different technologies. The most known types are fiber gratings (including fiber Bragg grating (FBG) [5] and long-period grating (LPG) [6]) and fiber interferometers (such as the Mach Zehnder interferometer (MZI) [7], the Michelson interferometer (MI) [8], the Sagnac interferometer (SI) [9], the Fabry-Perot interferometer (FPI) [10], and the multimode interferometer (MMI) [11]). The grating technology has been the most widely used due to its multiplexing capabilities, making these sensors adequate for multipoint sensing schemes. Despite that, the integration of those gratings into OFs requires expensive laser inscription techniques, the use of photosensitive fibers and, in some cases, laborious procedures. On the other hand, the fabrication of OF interferometers is simpler, since it only requires cleaving and splicing procedures. Furthermore, they provide higher sensitivities while keeping other interesting characteristics such as good precision and versatility [12].
The invention of the FPI was reported in 1897 by physicists Charles Fabry and Alfred Perot [13]. Since then, FPI sensors have been extensively studied due to their potential for signal amplification and filtering. Generally, FPI sensors can be fabricated with air-glass reflectors, in-fiber Bragg gratings, or through semi-reflective splices [12]. Since the sensing capability relies on the intrinsic properties of the fiber, these sensors can be used for high-temperature sensing, up to 1,000 °C [14]. Their compactness makes them attractive for measuring temperature in the human body [15]. FPIs can also detect small changes in the refractive index of the media [16] and, as such, they have been gaining momentum in research applications related to the detection of substances for chemistry and biomedicine [17–19]. Because of this, it is not surprising to find these OF sensors commercially available for markets ranging from biological sciences to medical applications [20].
The MMI was first reported by Mehta et al. [21]. The operating principle of this simple interferometer relies on the self-imaging phenomenon. The MMI is usually fabricated by fusion splicing a small section of a multimode fiber (MMF) between two single-mode fibers (SMFs), a procedure that can be considered low-cost [22]; in addition, MMIs have unique spectral features and high sensitivity. Due to these advantages, MMI sensors have been thoroughly studied in the last decade, and a variety of them have been reported [23], namely for applications regarding temperature, strain [24], humidity, refractive index [25] and liquid level [26] monitoring, biosensors [27] and biomedicine [28].
The use of OFs in biosensing applications has been a task difficult to attain, as the silica material that forms the fiber is a chemically inert material, making the functionalization process a challenging step [2]. When techniques such as sputtering, spin coating or dip coating are used, the adhesion between the deposited layer and the silica surface is compromised, hampering the sensor stability. If the functionalization involves the chemical modification of the silica surface, the stability and chemical resistance of the sensors are improved. Nevertheless, since the robustness of the detection method strongly relies on the functionalization step, more selective indicators and reproducible immobilization procedures are required to enable high sensitivity and long-term stability [2].
Diamond films have been studied extensively as a transducer material for the fabrication of biosensors [29]. Diamond can be deposited on different materials at temperatures typically between 600-800 °C by chemical vapor deposition (CVD) [30] in the form of poly, nano or ultrananocrystalline films, depending on the grain size. Diamond is inert in both acid and alkali environments and its biocompatibility is well-known [31,32]. Through proper functionalization, the diamond surface can be used to covalently attach larger molecules like DNA, proteins or antibodies [29]. The covalent bonds that form between the atoms on the diamond surface and the target receptor molecules result in a very robust interface with improved stability relative to other materials like gold, glassy carbon or silicon [33].
Due to the intrinsic properties of the diamond films, their integration with OFs could lead to the development of biosensors with improved stability, selectivity, and robustness. This can be achieved by depositing the diamond films directly on the surface of the silica fiber. Following this approach, in 1995 May and his co-workers coated SiC-based silica and ceramic fibers with diamond by hot filament chemical vapor deposition (HFCVD) [34]. Later, Rabeau et al. [35] coated bundles of fibers with nitrogen-doped films by microwave plasma chemical vapor deposition (MPCVD) for fluorescence waveguiding. In 2011 Neto et al. [36] coated an OF with an FBG inscribed on it, for the fabrication of a biological sensor. However, the FBG degraded during the HFCVD diamond growth. Later, the same group used a regenerated FBG [37], and, in another work, proposed the regeneration of the FBG during the diamond HFCVD process [38]. Using this latter approach, they were able to monitor the temperature in real-time during the diamond deposition process [39,40]. Another important work regarding diamond deposition was reported by Bogdanowicz et al. [41], who used MPCVD to deposit conductive boron-doped diamond films on SMFs containing LPGs for electrochemical and optical sensing. Later the group changed to a linear antenna MPCVD system, which allowed them to decrease the diamond deposition temperature [42] and to detect bovine serum albumin (BVA) with a concentration as low as 0.15 nM [43]. More recently, Hendrickson et al. [44] coated high-pressure CVD-fabricated optical fibers with diamond films by MPCVD.
The fabrication of diamond/OF-based has so far relied on the grating technology [37–41]. Despite the wide use of this technology, simpler and lower-cost OF sensors are more attractive. In addition, the grating technology can only safely work at temperatures below 400 °C, meaning that the fabrication of the sensors requires the use of gratings that have been previously regenerated [37], or that are regenerated during the CVD cycle [38]. In this work, we intend to make the leap to low-cost and simpler to fabricate OF technologies, namely FPIs and MMIs, and to compare the performance of each type of interferometer. Since these OF structures are all silica-based, the integrity of the OF sensors is expected to be maintained during the CVD process. The diamond films were initially deposited on SMFs for the optimization of the CVD conditions. Following this step, they were directly deposited on FPI and MMI OF structures. The deposited films were characterized by optical and scanning electron microscopy (SEM), optical profilometry, and Raman spectroscopy. The optical response of the diamond coated OF interferometers was measured by immersing them in solutions of isopropyl alcohol (IPA) and water, showing that the interferometers respond to the external refractive index. These results pave the way for the use of these structures in biosensing applications once the diamond surface has been functionalized for specific target molecules.
This manuscript is organized as follows: the state of the art is presented at the beginning and is followed by the description of the sensors operating principle The material and methods section follows, describing the fabrication of the OF sensors and the optimization of the diamond film CVD procedure. In the results section, the coating of the interferometers is presented and their response when immersed in solutions with different refractive index is characterized. The conclusions are given at the end of the manuscript.
2. Operating principle
2.1 FPI
Figure 1(a)) shows a classic example of an OF-FPI based on an air cavity between two SMFs.
Fig. 1. Schematic of OF-FPIs based on: a) one and b) two cavities. In a), the FPI is composed by an air cavity (between A and B), while in b), additionally to an air cavity, an OF cavity is formed between B and C. The “CT” acronym stands for capillary tube.
A light beam injected in the core of the SMF shown at the left-hand side of Fig. 1(a)) will be partially reflected at each of the two OF interfaces A and B. This occurs due to the refractive index mismatch between the media. Considering normal incidence, the Fresnel reflection coefficient between two media can be calculated as:
where n1 and n2 are the refractive indices of the 1st and 2nd media, respectively. Since the OF core refractive index is 1.45, and that of air is 1.00, the estimated reflectivity at each interface is ≈ 3.4%, and thus, the light interactions occurring in the FPI cavity can be mathematically described by a two-beam interference model. The reflections occurring at A and B will be recombined in the core of the left SMF, producing an interference reflection spectrum with a sinusoidal shape, containing maxima and minima, corresponding to constructive and destructive interference. Considering the intensities of the reflected beams obtained at interfaces A and B as I1 and I2, respectively, the output intensity resultant from the interference can be expressed as [12]: where Δϕ defines the phase difference between I1 and I2, and is given by Δϕ = (2π/λ)*OPL, being λ the free space wavelength, and OPL = (2nL + λ/2) the optical path length, where n and L are the refractive index and length of the medium filling the cavity, respectively. For such interferometer, the fringe contrast ratio can be described by: being R defined as R = I2/I1. OF-based FPIs are intrinsically immune to the external environment since light is confined within the core region. However, if the OF shown on the right side of Fig. 1(a) is cleaved orthogonally to its length at some distance from B, a new Fresnel reflection will occur at the interface between the SMF and the external environment (i.e. interface C), as shown in Fig. 1(b). This configuration corresponds to a three-beam interference. Thus, the resultant spectrum will be described by the superposition of the spectrum of each FPI cavity within the optical path of the light beam. The interest in this OF configuration relies on the fact that the fringe contrast of the resultant optical spectrum now depends on the refractive index of the external environment, since the Fresnel reflection at the interface between the SMF on the right-hand side of Fig. 1(b) and the external environment can change. This opens the possibility to use an FPI as a refractive index sensor while allowing it to work with low-cost intensity detection schemes.2.2 MMI
The principle of operation of the MMI can be explained by the self-imaging phenomenon. This occurs when the light field of a SMF is injected into a MMF, allowing the excitation of higher-order modes along the MMF. Interference between these modes will accumulate, giving rise to the formation of replicas in both amplitude and phase of the leading SMF, occurring at periodic intervals along the longitudinal axis of the MMF. The length at which the self-images are formed can be calculated from the restricted symmetric interference condition, given by [45]:
being nMMF and DMMF the effective refractive index and diameter of the MMF, respectively, λ the free space wavelength and p the self-image number. By cleaving the MMF at a distance where one of the self-images is being formed, a well-defined peak will occur at λ. The conventional way to produce these interferometers is through the fusion splicing of the MMF between two SMFs, being its characterization performed in the transmission mode. However, from a practical viewpoint, single-end-access configurations are preferable, due to their compact nature, offering easier access and low disturbance. Furthermore, since MMIs are sensitive to curvature, the single-ended-access allows easily keeping the fiber straight, which avoids issues related to the bending-sensitive nature of the interferometer. MMIs with single-ended-access have already been reported to measure displacements [21] and temperature [46]. The simplicity of MMIs led the scientific community to use them in biosensing applications. The use of unclad fibers in these sensors to allow the interaction of the evanescent field of light with the external environment is a common practice [25]. The employment of the commonly available step-index OFs in combination with the single-ended-access is simple and offers an attractive solution for biosensing applications, namely by using the Fresnel reflection principle (see Eq. (1)). A schematic of this MMF interferometer is shown in Fig. 2.Fig. 2. Schematic of a single-ended-access MMI sensor composed of an SMF fusion spliced to a step-index MMF. The self-imaging phenomenon is shown at the core region of the MMF.
In the MMI shown Fig. 2, the far end of the MMF acts as a low reflectivity mirror, and the light field is back-reflected to the SMF. The power observed at the output reflection spectrum is therefore dependent on the Fresnel reflection occurring at the far cleaved end of the MMF, and thus, any change in the refractive index of the external medium modifies the reflected optical power of the MMI spectrum. This property allows the use of the MMI as a refractive index sensor, similarly to what was explained in the previous subsection for the FPI.
3. Materials and methods
3.1 FPI & MMI sensor fabrication
The OF interferometers implemented in this work operated in reflection mode (the optical signal is sent and received through the same OF). The fabricated OF structures were consequently compact (a few microns or millimeters, for the FPI and MMI, respectively) and are, therefore, attractive for use in biosensing applications.
For the construction of the OF interferometers, ≈ 2 cm of the acrylate protective coating of a pigtail SMF (reference ITU G.652, distributed by Cabelte SA) were removed, and the OF was fixed into a fiber clamp solidary to the mobile part of a 0.1 µm resolution motorized linear stage (UTS150PP from Newport). An OF cleaver (model CT-30 from Fujikura) was located in front of it. The longitudinal axis of the fiber, the positioner travelling axis and the fiber cleaver v-groove axis were all concentrically aligned.
The fabrication of the FPI started with the cleavage of the SMF terminal (Fig. 3(a)). Next, the OF tip was relocated to a fusion splicer machine (model FSM-60S, from Fujikura). This splicer already contained a 3 cm-long fused silica capillary tube (CT) (reference TSP050150 from CM Scientific). The inner and outer diameters of the CT were 50 and 125 µm, respectively, and its polyamide coating was mechanically stripped using a razor blade, followed by the cleavage of its terminal with the fiber cleaver. The SMF and CT were fusion spliced (Fig. 3(b)) with an arc discharge of STD – 20 bit and an arc time of 700 ms. These splice parameters were determined to prevent the collapse CT, and at the same time, to guarantee a robust OF connection. Next, the fused section was laid down onto the v-groove of the cleaver and the linear stage was translated 50 µm backwards. A new cleavage was performed (Fig. 3(c)), leaving an SMF pigtail with a 50 µm-long CT on its tip. This newly formed structure was moved again to the fusion splicer, which now contained the ≈ 3 cm-long cleaved SMF section in the other fiber clamp. Those were fused again, with the parameters described before (Fig. 3(d)). The OF structure was moved once again to the cleaver and the linear stage was set to travel 50 µm backwards one last time. Finally, the OF was cleaved (Fig. 3(e)), concluding the FPI fabrication process. The newly formed structure was based on two cavities, a 50 µm air cavity formed between the two sections of the SMFs, and a second cavity, formed by the last segment of the SMF. This allowed to create an OF structure similar to the one shown in Fig. 3(f). The step-by-step fabrication process of the FPI structure is shown in Fig. 3(a)-(d).
Fig. 3. Step-by-step fabrication of the FPI: a) SMF cleavage; b) fusion splicing between the SMF and the CT; c) cleavage of the CT with a length of 50 µm; d) fusion splicing of the CT to an SMF; d) cleavage of the SMF tip with a length of 50 µm; f) inset of the fabricated OF structure.
The MMI was fabricated following the same procedure used for the fabrication of the FPI, namely the steps described in Fig. 3(a)-(c). However, a step-index MMF (AFS50/125Y, from Fiberguide Industries, Inc.) was used instead of the CT. This 125 µm-diameter OF is composed of silica with a refractive index of 1.444 at 1.55 µm. A 10 µm-thick fluorine-doped trench surrounds a 50 µm-diameter inner core region. The lower refractive index fluorine-doped region allows the guidance of light in the fiber core. The MMI interferometer was fabricated by fusion splicing the SMF to the MMF. The MMF length calculated using Eq. (4) was about 9.32 mm. This calculation was made to guarantee a spectral peak power centered at 1550 nm, considering the 8th self-image (i.e. 4 self-images in the forward direction and 4 self-images in the backward direction (after reflection at the cleaved MMF end face).
3.2 Deposition and characterization of the diamond film
Before coating the FPI and the MMI, the diamond deposition procedure was optimized using standard SMFs. Those were initially prepared by striping their coating and cleaving their terminals; the OFs were later ultrasonically cleaned in IPA followed by ethanol. The diamond coating process followed a three-step procedure, similar to the one reported in [47]: (i) pre-treatment (PT), (ii) seeding and (iii) growth. The PT and growth cycles were performed in a custom-made HFCVD system with two 0.5 mm-thick rhenium filaments, and at a pressure of 50 mbar. The filament temperature was measured with an optical pyrometer and was kept between 1940 and 2060 °C; a thermocouple was placed at the same distance from the filaments as the OF tip, thus allowing the estimation of the OF tip temperature (TT). The PT was performed for 1 hour with constant H2/CH4 flows of 100/1 sccm and an OF tip temperature of ≈ 700 °C.
Three different seeding procedures were used: ultrasonic seeding (US) during 1 hour in two different diamond suspensions (6.0-10.0 µm grit in ethanol or 0.5-1.0 µm grit in distilled water (DW)) and dip-coating (DC) in a solution with 4-5 nm detonation nanodiamond (DND) particles dispersed in dimethyl sulfoxide (DMSO) diluted in ethanol (1:3 ratio). Following the seeding step, the OFs were ultrasonically cleaned in DW followed by ethanol for 5 minutes.
The growth cycle was optimized by varying the fiber tip temperature, the CH4/H2 flows and the duration of the growth cycle. The experimental parameters are compiled in Table 1. In the first round, the OFs were kept in the vertical position by inserting one of their terminals in the holes of a graphite cylinder placed on the bottom of the HFCVD chamber (Fig. 4(a)); the three OFs were coated together in the same growth cycle (Fig. 4(b)). Since the diameter of the holes in the cylinder was much larger than the diameter of the OFs (400 µm against 125 µm, respectively), the OFs tilted slightly during the deposition, which prevented the accurate control of the position of their terminals relatively to the filaments. To overcome this issue, in the following rounds the graphite holder was replaced by a copper holder with v-grooves as shown in Fig. 4(c). This allowed attaching the OFs and more accurately controlling the relative position and distance between their tip and the filaments. To control the OFs tip temperature only one fiber was coated during each growth cycle. The MMI and the PFI were coated with diamond following the optimization of the seeding and deposition parameters using the conditions listed in Table 1.
Fig. 4. OFs on a) graphite cylinder, b) inside the HFCVD chamber, and c) attached to a copper holder. Blue dashed lines mark the position of the OFs for clarity.
Table 1. Seeding and growth conditions
After the diamond deposition process, the coated OFs were observed in a Leica DM750 optical microscope and in a Hitachi SU70 SEM. The surface roughness was measured using a 3D optical profiler from Sensofar (S neox), in confocal mode. To measure the thickness of the deposited film, the OF was broken close to the tip and the cross-section of the broken OF was observed in the SEM. Furthermore, micro Raman measurements were performed at room temperature with a Jobin-Yvon LabRaman HR800 spectrometer, equipped with a grating of 600 grooves/mm and a multi-channel air-cooled (−70 °C) CCD detector in backscattering geometry, using the 442 nm (2.805 eV) and 532 nm (2.330 eV) lines of a He–Cd laser. The excitation laser was focused with a 50× objective onto the sample surface and the spectra were acquired with an experimental error of ± 2 cm−1.
3.3 Evaluation of the sensors response
Different solutions of water and IPA were prepared for the sensor characterization. The refractive index of the resulting water + IPA solutions ranged between the one of water (nD = 1.3330) and the one of IPA (nD = 1.3769). The refractive index of the solutions was measured at the sodium D-line at 22 °C, using an Abbemat refractometer from Anton Paar GmbH. The tip of the OF sensors (≈ 10 mm) was immersed in each of the calibrated solutions and the corresponding reflection spectrum was taken using a fiber optic interrogator (Hyperion Si155 from Luna Innovations Inc.). Between each measurement the tip of the fiber sensors was washed in pure IPA and allowed to dry at ambient temperature for a few seconds.
4. Results and discussion
4.1 Optimization of HFCVD parameters
All the OFs belonging to the first round were fully coated with diamond. The tip of SMF B is shown in Fig. 5(a); the film was fully closed and covered the tip and body of the OF conformally. SMF A and SMF C (not shown) were also fully covered with diamond. Despite having been deposited during the same run, the thickness (d) of the films on the three OFs was different (see Table 1). This was probably related with the fact that the tips of the OFs were not at the same distance from the filaments, causing the tip temperature of the three OFs to be different. Since higher deposition temperatures lead to higher growth rates [30] this may explain the difference in the film thickness. The films had cracks – one of them is clearly visible in Fig. 5(a) – that formed during the cooling down of the OFs from deposition temperature (740-800 °C) to room temperature. This occurred as a consequence of the difference in the coefficients of thermal expansion of SMF and diamond (0.55 × 10−6 °C−1 against 0.80 × 10−6 °C−1, respectively), which causes the building up of thermal stress at the OF/film interface and, consequently, fracture of the films.
Fig. 5. a) SEM image and b) Raman spectrum of SMF B coated in the first round and seeded with 0.5-1.0 µm diamond grit.
The quality of the deposited films was evaluated with Raman spectroscopy; Fig. 5(b) shows the Raman spectrum obtained with sample SMF B. To distinguish the contribution of the Raman signal originating from the underlying fused silica, the spectrum of a virgin OF is displayed in red; it can be seen that no significant signal coming from the OF overlaps with the bands typically observed in CVD diamond in the 1150-1700 cm−1 spectral range. The first-order diamond-related peak is observed at 1333 ± 2 cm−1 [48], with FWHM of ≈ 10 cm−1. Other features usually observed in CVD carbon structures are also present. Under visible excitation, the π states resonate with the excitation energy, thus the D (1360-1380 cm−1) and G (1500-1600 cm−1) bands due to sp2 sites may dominate the Raman spectra. The signature of trans-polyacetylene is revealed by the presence of the peak close to 1150 cm−1 (υ1) together with the shoulder at ≈ 1480 cm−1 (υ3) close to the G band [49]. The same bands were found in the spectra of samples SMF A and SMF C (not shown), with the exception of the D band that was missing in the spectrum of sample SMF A. As D band is related with the breathing modes of sp2-bonded carbon atoms in rings, the absence of this band may suggest that sample SMF A has fewer sp2 carbon rings [50] than the others.
In order to alleviate the thermal stress that develops at the OF/diamond interface – and thus prevent the formation of cracks – in the subsequent runs the deposition time (and hence the thickness of the diamond film) was decreased. SMFs D, E, F, G, were ultrasonically seeded with the 6.0-10.0 µm diamond suspension and the CH4 flow and tip temperature were varied (see Table 1 for details). However, the films deposited on these samples were not closed; different factors may have contributed to this, namely the lower deposition temperature, the shorter growth cycle, and the inefficiency of seeding procedure
Following these results, the next set of OFs was US seeded with smaller diamond grit (0.5-1.0 µm); the diamond was deposited during 2 hours with 1 sccm (SMF H) and 2 sccm (SMF I) of CH4 diluted in 100 sccm of H2. The SEM images of the tip of SMFs H and I are shown in Fig. 6(a) and (b), respectively. As can be seen, the diamond film totally covers the tips of both OFs conformally. The difference in the CH4/H2 ratio and deposition temperature lead to different film morphologies: the 2-3 µm sized diamond crystals in SMF H show sharp facets whereas the film deposited on SMF I has a much smaller crystal size (≈ 200 nm) and, correspondingly, a higher density of grain boundaries (composed of non-sp3 carbon).
4.2 Diamond coating of the OF interferometers
The choice of the deposition parameters for coating the FPI and MMI described in section 3.2 was made based on the results obtained from the previous section: US seeding with 0.5-1.0 µm diamond grit in DW, 2 hours deposition, 1% CH4 diluted in H2 (since a lower density of grain boundaries means a film with improved quality and hence higher transparency) and 600 °C tip temperature (that leads to a lower thermal stress in comparison to higher deposition temperatures). Figure 7 shows the optical microscope images of the coated interferometers under different magnifications. As can be seen in the left (FPI) and right (MMI) images, the surface of the OFs is totally covered with a closed diamond film with ≈ 200 nm average crystal size and 0.06 µm average surface roughness on the top and lateral regions of the OFs. However, both films have a few cracks, which were more dominant at the circumference of the OFs and more predominant for the MMF that composes the MMI, compared to the SMF of the FPI. The crack formation can be associated with the different thermal expansion coefficients of the OFs and diamond as explained earlier. Since both the CT and SMF (excluding the ≈ 8 µm-diameter germanium-doped core region) are composed of undoped silica, while most of the MMF (except the 50 µm-diameter undoped silica core) is fluorine-doped silica, their expansion coefficients are also different. This difference in the thermal expansion coefficients of the materials of both interferometers will impact the thermal stress at the OF/diamond interface, which may in turn result in the formation of a different number of cracks at each of the diamond films [51]. Nevertheless, the appearance of cracks is not considered an issue, since the operating principle of the interferometers relies on the Fresnel reflection at the tip of the OFs, and as observed in Fig. 7(d) and (e), the film deposited on the inner regions of the tip of the OFs does not have any cracks.
Fig. 7. Optical microscope images of the OF tips corresponding to the a)-d) FPI and e)-h) MMI. a), b), e) and f) transversal view; c), d), g) and h) top view.
The Raman spectra of the diamond film deposited on the FPI and MMI are shown in Fig. 8(a) and (b), respectively. The diamond-related peak is located at 1332 ± 2 cm−1 and the major features identified before are also present. As the Raman analysis was done using lower excitation energy the dispersive Raman bands are located at different frequencies. This is the case of υ1 and υ3 [49] detected in sample FPI, that shifted to lower frequencies, as expected. The discussion about the dispersive behavior of the D [52] or even G bands (only in higher disorder carbons) is hampered by their enlargement and the superposition with υ3 band. Nevertheless, by comparing the spectra of both samples it can be seen that the G band in the MMI is located at lower frequencies when compared to the one of the FPI. This shifting of the G band suggests that the remaining sp2 bonds are weaker in the MMI, softening the corresponding vibrational mode.
4.3 Characterization of the interferometers response
The spectral responses of the FPI and MMI OF sensors obtained after their fabrication and after being coated with diamond are shown in Fig. 9(a) and (b), respectively. Due to the difference between the refractive indices of diamond and silica (2.40 and 1.45, respectively) and according to Eq. (1) the Fresnel reflectivity at the tip/external medium interface will increase after the deposition of diamond on the terminal of each OF interferometer. However, in the case of the FPIs, it can be seen that this increase in the Fresnel reflectivity does not translate in an increase of the optical power. During the fabrication of the FPI shown at the bottom of Fig. 9(a) (namely during the procedures presented in Fig. 3(d)) and e)), the reflection spectrum changed from a two-beam interference (CT and SMF cavities) to a three-beam interference, or in other words, the reflection spectrum now results from the superposition of the spectrum of each of the three cavities formed by the CT, the SMF in front of the CT and the diamond film. The spectrum from the CT and SMF cavities shows a beat signal with peaks and dips with different amplitudes that repeat at every ≈ 25 nm wavelength, as shown by the dashed blue line in Fig. 9(a). A 3rd cavity is formed after the diamond deposition. The final reflection spectrum shown in the same figure by a continuous black line displays again an interferometric fringe pattern due to the multiple phase changes reached along the serialized cavities. Thus, it is composed by multiple interference fringes associated to the constructive and destructive interference. However, due to the span range of the interrogator, we can’t visualize one full period of the beat signal. Despite that, it is possible to observe that the reflected optical power is increasing along the wavelength span under study, reaching reflectivity values slightly above the ones reached for the interferometer without the diamond coating, namely for wavelengths above 1600 nm.
Fig. 9. Reflection spectra of the a) FPI and b) MMI OF sensors, before and after diamond deposition. The insets show the OF cross-section and top-view microscope images of the interferometers tip.
Regarding the MMI results, the spectrum obtained right after its fabrication is shown by the dashed blue line in Fig. 9(b)). The maximum peak power was reached in the 1550 nm region, as predicted by Eq. (4). In this case, after diamond deposition the spectrum reflectivity increases as a consequence of the reflectivity enhancement provided by the Fresnel reflection at the diamond-air interface at the far tip of the sensor. For this interferometer, the output spectrum is easier to predict since the spectral signature is maintained, compared to the case without diamond.
To better understand the response of the sensors after the diamond deposition, the spectral response of a 125 µm-diameter OF tip with an 8.2 µm-diameter core with 1.45 refractive index and covered with a diamond film with 2.40 refractive index and thickness ranging from 600–900 nm was simulated using Comsol Multiphysics. The results revealed that the spectrum of the diamond-coated OF has an interferometric fringe pattern as shown in Fig. 10. It can be seen that, that in the span range under study (1460 – 1620 nm), the reflectivity is highly dependent on the film thickness. Experimentally it was observed that, while the reflectivity of the FPI decreased after the diamond deposition, in the case of the MMI the effect was opposite. This is probably related with the fact that the thicknesses of the diamond films deposited on the MMI and on the FPI were not the same. In fact, due to the manual mounting of the interferometers in the CVD chamber, it is not possible to guarantee that the distance between the filament and the interferometer tip is exactly the same. A difference in a few tens of milimeters will impact the tip temperature – and hence the growth rate and the final thickness of the diamond film.
Fig. 10. Spectra obtained by numerical simulations, considering a silica fiber with a diamond film on top of it, with thickness ranging from 600 – 900 nm. The external medium was considered as air. The inset shows the response obtained for the wavelength range studied in this work.
To evaluate the impact of the surface roughness, the spectrum of the diamond film was also obtained for different roughness values. It was observed that the surface roughness of the film has a negligible impact on the reflectivity of the fiber tip.
4.4 Response of diamond-coated OF interferometers to refractive index
The spectral response of the interferometers obtained when the tip was immersed in solutions with different refractive indices is shown in Fig. 11. The spectral response showed small changes when the refractive index of the solution was varied. Figure 11(a) shows a magnified region of one of the spectral dips of the FPI, found at ≈ 1544.4 nm, while Fig. 11(b) shows a magnified region of the MMI spectra for the minimum located at ≈ 1493 nm.
Fig. 11. Spectral response of the OF interferometers as a function of the external refractive index. a) Response of the FPI spectral dip that appears at 1544.4 nm in Fig. 9(a)); b) response of the MMI spectral dip that appears at 1493 nm in Fig. 9(b)). The marker points represent the minimum dip power wavelength.
Figure 11(a) and (b) show that the optical power changes linearly with the refractive index of the surrounding medium, increasing (for the FPI) and decreasing (for the MMI) as the refractive index increases. The response of the sensors depends on the Fresnel reflection occuring at the interface between the far end of the fiber and the external environment and, thus, on the refractive index of the material that composes the fiber tip interface, which is n1 ≈ 1.45 or n1 ≈ 2.40, for the fiber tip uncoated or coated with diamond, respectively. The dependency of the theoretical Fresnel reflectivity with the external refractive index was calculated with Eq. (1) and is shown in Fig. 12.
Fig. 12. Left side - Theoretical Fresnel reflectivity calculated using Eq. (1), as a function of external refractive index, n2, considering the fiber sensor tip without (black line) and with (blue line), diamond coating. Right side - Corresponding sensitivity response as a function of n2.
According to the data presented in Fig. 12, the Fresnel reflectivity of the diamond-coated fiber tip is higher than that of the raw fiber tip. Also, the Fresnel reflectivity for both coated and uncoated fibers decreases with the increase of the external refractive index. The sensitivity of the response can be obtained by performing the derivative of the curves, as shown in the right-hand side of the graph. It can be seen that, even though the sensitivity decreases with n2, the sensitivity of the diamond coated fiber tip sensor is higher than that of the raw fiber tip, for the whole refractive index under study. This shows that in addition to the advantages regarding the easiness of functionalization, the diamond coating also plays an important role in enhancing the sensitivity of the sensors. Nevertheless, one should keep in mind that in the case of the FPI the optical response is the result of the superposition of the response of the 3 different cavities and, as such, this simple analysis does not explain the dependency of its optical response on the refractive index of the external media.
A further analysis to the experimental results presented in Fig. 11 shows an apparent spectral wavelength shift. By tracking the minimum dip power wavelength, it was possible to get the responses shown in Fig. 13.
Fig. 13. a), b) Dip power, and c), d) dip wavelength shift observed for the spectral dips found at 1544.4 nm and 1493 nm for the a), c) FPI and b), d) MMI, respectively.
From Fig. 13(a) and (b), it can be seen that the dip power increases and decreases with the refractive index of the solution, with slopes of 40 ± 1 dB/RIU and −11 ± 1 dB/RIU, for the FPI and MMI, respectively. The optical power changes are intrinsically related to the Fresnel reflection at each of the OF terminals that compose the interferometers. From Eq. (1), one can understand that when the external refractive index increases, the Fresnel reflection decreases and thus, the received reflected optical power should be reduced. This is exactly what was observed in the MMI response. This effect is independent of the length of the MMI, since the Fresnel reflectivity only depends on the external refractive index. On the other hand, the FPI shows an opposite response, presenting an increase in the optical power with the extrenal refractive index, and a sensitivity higher than the MMI. This happens because the spectral response of the FPI is modulated by the net response of the air cavity and the terminal SMF cavity and, thus, spectral superpositioning also plays a role in the response of the FPI. This superpositioning leads also to another interesting opportunity for the FPI, namely the capability to detect changes in the refractive index through the spectral wavelength shift with a sensitivity of −987 ± 70 pm/RIU as shown in Fig. 13(c). On the other hand, the response of the MMI wavelength shift as function of the refractive index shown in Fig. 13(d) presented a non-linear dependence with a maximum wavelength shift of ≈ 120 pm in the range under study. This low value is related with the absence of a clear relation between the refractive index and the wavelength, being the values presented here associated with the large bandwidth of the dip and the low resolution of the detection algorithm used to find the center of the dip, which together prevented the accurate determination of the central wavelength. Nevertheless, the absence of a wavelength response by the MMI sensor was not surprising since its response only relies on the reflection coefficient at the MMF.
As a conclusion, one can say that while the FPI sensor is able to detect the refractive index changes in both optical power and wavelength detection schemes, the MMI only shows a response in optical power and with lower sensitivity; nevertheless it is worth mentioning that the MMI sensor is much easier to fabricate than the FPI. Thus, a compromise between simplicity and sensitivity should be taken into account to select which of the sensors is more attractive for a specific target application.
5. Conclusions
This work presents preliminary results of the sensing properties of diamond-coated interferometers. The seeding and growth process were optimized to allow the deposition of uniform diamond films on the tip and body of OFs. Diamond films with 2-3 µm/≈ 200 nm crystal size were obtained with a pressure of 50 mbar, 1/2% CH4 diluted in H2 and a tip temperature around 720/600 °C, respectively. The FPI and MMI were coated with a pressure of 50 mbar, 1% CH4 diluted in H2 and a tip temperature around 600 °C. The reflected spectra were obtained before and after diamond deposition. The diamond-coated interferometers were immersed in solutions with different refractive indices and their spectral response was characterized. Since the response of the sensors relies on the reflectivity at the tip of the fiber sensors and, according to the Fresnel reflection, the higher the difference between the refractive index of the media (fiber tip terminal and environment), the higher the reflectivity, the diamond coating may contribute to enhance the sensors sensitivity, when compared to the raw-fiber configuration. This was observed in the case of the MMI. Results showed sensitivities of 40 ± 1 dB/RIU and −987 ± 70 pm/RIU for the FPI, and −11 ± 1 dB/RIU for the MMI. Despite the possibility of using both OF interferometers, the FPI offers more attractive characteristics when compared to the MMI, not only in terms of dip power sensitivity, but also because it shows a dual response in power and wavelength. This is particularly relevant for temperature compensation methods, were the dual response sensitivity allows the discrimination between refractive index and temperature.
This work showed that diamond can be used to coat OF-based interferometers, paving the way for an easier and more affordable way to use OF sensors in biosensing applications. Future work involves functionalizing the surface of the diamond films with specific biological molecules and testing the applicability of diamond coated FPIs and MMIs as biosensors.
Funding
Fundação para a Ciência e a Tecnologia (CEECIND2021.01066, LA/P/0006/2020, PTDC/EEI-TEL/1511/2020, UID/EEA/50008/2019, UIDB/50008/2020-UIDP/50008/2020, UIDB/50011/2020, UIDP/50011/2020).
Acknowledgments
This work is funded by national funds through FCT/MEC (PIDDAC) and where applicable co-funded by EU, under projects UIDB/50008/2020-UIDP/50008/2020, UID/EEA/50008/2019, UIDB/50011/2020, UIDP/50011/2020 and LA/P/0006/2020, X-0009-AV-20 BioPlus, FOPEComSens (PTDC/EEI-TEL/1511/2020) and CEECIND2021.01066, and contract program under the degree law Nr. 57/2016.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publically available at this time but may be obtained from the authors upon reasonable request.
References
1. A. George, M. S. Amrutha, P. Srivastava, S. Sunil, V. V. R. Sai, and R. Srinivasan, “Development of a U-bent plastic optical fiber biosensor with plasmonic labels for the detection of chikungunya non-structural protein 3,” Analyst 146(1), 244–252 (2021). [CrossRef]
2. M. Mehrvar, C. Bis, J. M. Scharer, M. Moo-Young, and J. H. Luong, “Fiber-optic biosensors - Trends and advances,” Anal. Sci. 16(7), 677–692 (2000). [CrossRef]
3. A. B. Bandara, Z. Zuo, K. McCutcheon, S. Ramachandran, T. Inzana, and J. R. Heflin, “Rapid Detection of Histophilus somni by a Nanomaterial Optical Fiber Biosensor Assay,” in Biophotonics Congress: Biomedical Optics 2020 (2020), p. TTh4B.7.
4. N. Cennamo, G. D. Agostino, C. Perri, F. Arcadio, G. Chiaretti, E. M. Parisio, G. Camarlinghi, C. Vettori, F. Di Marzo, R. Cennamo, G. Porto, and L. Zeni, “Proof of Concept for a Quick and Highly Sensitive On-Site Detection of SARS-CoV-2 by Plasmonic Optical Fibers and Molecularly Imprinted Polymers,” Sensors 21(5), 1681 (2021). [CrossRef]
5. R. Oliveira, T. H. R. Marques, C. M. B. Cordeiro, and R. Nogueira, “Strain Sensitivity Enhancement of a Sensing Head Based on ZEONEX Polymer FBG in Series With Silica Fiber,” J. Lightwave Technol. 36(22), 5106–5112 (2018). [CrossRef]
6. R. Oliveira, R. Nogueira, and L. Bilro, “3D printed long period gratings and their applications as high sensitivity shear-strain and torsion sensors,” Opt. Express 29(12), 17795–17814 (2021). [CrossRef]
7. D. Wu, T. Zhu, M. Deng, D.-W. Duan, L.-L. Shi, J. Yao, and Y.-J. Rao, “Refractive index sensing based on Mach–Zehnder interferometer formed by three cascaded single-mode fiber tapers,” Appl. Opt. 50(11), 1548–1553 (2011). [CrossRef]
8. H. Meng, W. Shen, G. Zhang, X. Wu, W. Wang, C. Tan, and X. Huang, “Michelson interferometer-based fiber-optic sensing of liquid refractive index,” Sens. Actuators, B 160(1), 720–723 (2011). [CrossRef]
9. B. Culshaw, “The optical fibre Sagnac interferometer: An overview of its principles and applications,” Meas. Sci. Technol. 17(1), R1–R16 (2006). [CrossRef]
10. R. Oliveira, L. Bilro, and R. Nogueira, “Fabry-Pérot cavities based on photopolymerizable resins for sensing applications,” Opt. Mater. Express 8(8), 2208 (2018). [CrossRef]
11. R. Oliveira, L. Bilro, T. H. R. Marques, C. M. B. Cordeiro, and R. Nogueira, “Simultaneous detection of humidity and temperature through an adhesive based Fabry – Pérot cavity combined with polymer fiber Bragg grating,” Opt. Lasers Eng. 114, 37–43 (2019). [CrossRef]
12. Yun-Jiang Rao, Z.-L. Ran, and Y. Gong, Fibre-Optic Fabry-Perot Sensors: An Introduction (Taylor & Francis Group, 2017).
13. C. Fabry and A. Perot, “Sur les franges des lames minces argentées et leur application à la mesure de petites épaisseurs d’air,” Ann. Chim. Phys. 12, 459–501 (1897).
14. M. Rajibul Islam, M. Mahmood Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “Chronology of fabry-perot interferometer fiber-optic sensors and their applications: A review,” Sensors 14(4), 7451–7488 (2014). [CrossRef]
15. D. Tosi, E. G. Macchi, M. Gallati, G. Braschi, A. Cigada, S. Rossi, S. Poeggel, G. Leen, and E. Lewis, “Fiber-Optic EFPI/FBG Dual Sensor for Monitoring of Radiofrequency Thermal Ablation of Liver Tumors,” Opt. InfoBase Conf. Pap.AW1L, AW1L.4 (2014).
16. O. Frazao, J. M. Baptista, J. L. Santos, J. Kobelke, and K. Schuster, “Refractive index tip sensor based on Fabry-Perot cavities formed by a suspended core fibre,” J. Eur. Opt. Soc. Rapid Publ. 4, 09041 (2009). [CrossRef]
17. S. Poeggel, D. Tosi, F. Fusco, V. Mirone, S. Sannino, L. Lupoli, J. Ippolito, G. Leen, and E. Lewis, “Fiber optic extrinsic Fabry-Perot interferometry pressure sensors for in-vivo urodynamic analysis,” IEEE Sens. J. 14(7), 2335 (2014). [CrossRef]
18. D. Tosi, S. Poeggel, I. Iordachita, and E. Schena, Fiber Optic Sensors for Biomedical Applications (Elsevier Inc., 2018).
19. D. Inaudi and E. Pinet, “Large-volume Fabry-Pérot fiber-optic sensors production for medical devices and industrial applications,” in 26th International Conference on Optical Fiber Sensors, L. Thévenaz, ed. (OSA, 2018), p. TuE32.
20. FISO Technologies Inc., “http://www.fiso.com,”.
21. A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode Interference-Based Fiber-Optic Displacement Sensor,” IEEE Photonics Technol. Lett. 15(8), 1129–1131 (2003). [CrossRef]
22. K. Wang, X. Dong, M. H. Kohler, P. Kienle, Q. Bian, M. Jakobi, and A. W. Koch, “Advances in Optical Fiber Sensors Based on Multimode Interference (MMI): A Review,” IEEE Sens. J. 21(1), 132–142 (2021). [CrossRef]
23. J. R. Guzmán-Sepúlveda, R. Guzmán-Cabrera, and A. A. Castillo-Guzmán, “Optical sensing using fiber-optic multimode interference devices: A review of nonconventional sensing schemes,” Sensors 21(5), 1862 (2021). [CrossRef]
24. R. Oliveira, T. H. R. Marques, L. Bilro, R. Nogueira, and C. M. B. Cordeiro, “Multiparameter POF Sensing Based on Multimode Interference and Fiber Bragg Grating,” J. Lightwave Technol. 35(1), 3–9 (2017). [CrossRef]
25. R. Oliveira, J. H. Osório, S. Aristilde, L. Bilro, R. N. Nogueira, and C. M. B. Cordeiro, “Simultaneous measurement of strain, temperature and refractive index based on multimode interference, fiber tapering and fiber Bragg gratings,” Meas. Sci. Technol. 27(7), 075107 (2016). [CrossRef]
26. R. Oliveira, S. Aristilde, J. H. Osório, M. A. R. Franco, L. Bilro, R. N. Nogueira, and C. M. B. Cordeiro, “Intensity liquid level sensor based on multimode interference and fiber Bragg grating,” Meas. Sci. Technol. 27(12), 125104 (2016). [CrossRef]
27. A. B. Socorro, E. Santamaria, J. Fernandez-Irigoyen, I. Del Villar, J. M. Corres, F. J. Arregui, and I. R. Matias, “Fiber-Optic Immunosensor Based on an Etched SMS Structure,” IEEE J. Sel. Top. Quantum Electron. 23(2), 314–321 (2017). [CrossRef]
28. X. Li, D. Liu, R. Kumar, W. P. Ng, Y. Q. Fu, J. Yuan, C. Yu, Y. Wu, G. Zhou, G. Farrell, Y. Semenova, and Q. Wu, “A simple optical fiber interferometer based breathing sensor,” Meas. Sci. Technol. 28(3), 035105 (2017). [CrossRef]
29. N. E. Santos, F. Figueira, M. Neto, F. A. A. Paz, S. S. Braga, and J. C. Mendes, “Diamonds for Life: Developments in Sensors for Biomolecules,” Appl. Sci. 12(6), 3000 (2022). [CrossRef]
30. J. J. Gracio, Q. H. Fan, and J. C. Madaleno, “Diamond growth by chemical vapour deposition,” J. Phys. D: Appl. Phys. 43(37), 374017 (2010). [CrossRef]
31. L. Tang, C. Tsai, W. W. Gerberich, L. Kruckeberg, and D. R. Kania, “Biocompatibility of chemical-vapour-deposited diamond,” Biomaterials 16(6), 483–488 (1995). [CrossRef]
32. N. E. Santos, J. C. Mendes, and S. S. Braga, “The Gemstone Cyborg: How Diamond Films Are Creating New Platforms for Cell Regeneration and Biointerfacing,” Molecules 28(4), 1626 (2023). [CrossRef]
33. J. Raymakers, K. Haenen, and W. Maes, “Diamond surface functionalization: from gemstone to photoelectrochemical applications,” J. Mater. Chem. C 7(33), 10134–10165 (2019). [CrossRef]
34. P. W. May, C. A. Rego, M. N. R. Ashfold, K. N. Rosser, G. Lu, T. D. Walsh, L. Holt, N. M. Everitt, and P. G. Partridge, “CVD diamond-coated fibres,” Diamond Relat. Mater. 4(5-6), 794–797 (1995). [CrossRef]
35. J. R. Rabeau, S. T. Huntington, A. D. Greentree, and S. Prawer, “Diamond chemical-vapor deposition on optical fibers for fluorescence waveguiding,” Appl. Phys. Lett. 86(13), 1–3 (2005). [CrossRef]
36. V. F. Neto, J. A. Santos, N. J. Alberto, J. L. Pinto, R. N. Nogueira, and J. Grácio, “Evaluation of diamond coatings on optical fibre sensors for biological use,” J. Nanosci. Nanotechnol. 11(6), 5408–5412 (2011). [CrossRef]
37. N. J. Alberto, J. A. Santos, C. A. F. Marques, V. F. S. Neto, and R. N. Nogueira, “Nanodiamond coated Bragg gratings for sensing applications,” OFS2012 22nd Int. Conf. Opt. Fiber Sensors 8421, 842120 (2012). [CrossRef]
38. N. J. Alberto, H. J. Kalinowski, V. F. Neto, and R. N. Nogueira, “Regeneration of FBGs during the HFCVD diamond-fiber coating process,” Second Int. Conf. Appl. Opt. Photonics 9286, 928643 (2014). [CrossRef]
39. N. J. Alberto, H. J. Kalinowski, V. F. Neto, and R. N. Nogueira, “Simultaneous regeneration of seed FBGs during the HFCVD diamond-grating coating process and its thermal monitoring,” 24th Int. Conf. Opt. Fibre Sensors 9634, 96343U (2015). [CrossRef]
40. N. Alberto, H. José Kalinowski, V. Neto, and R. Nogueira, “Diamond-coated fiber Bragg grating through the hot filament chemical vapor process for chemical durability improvement,” Appl. Opt. 56(6), 1603–1609 (2017). [CrossRef]
41. R. Bogdanowicz, M. Sobaszek, M. Ficek, M. Gnyba, J. Ryl, K. Siuzdak, and M. Śmietana, “Nanocrystalline diamond microelectrode on fused silica optical fibers for electrochemical and optical sensing,” Fifth Asia-Pacific Opt. Sensors Conf. 9655, 965519 (2015). [CrossRef]
42. M. Ficek, S. Drijkoningen, J. Karczewski, R. Bogdanowicz, and K. Haenen, “Low temperature growth of diamond films on optical fibers using Linear Antenna CVD system,” IOP Conf. Ser.: Mater. Sci. Eng. 104, 012025 (2016). [CrossRef]
43. M. Ficek, P. Niedziałkowski, M. Śmietana, M. Koba, S. Drijkoningen, R. Bogdanowicz, W. J. Bock, and K. Haenen, “Linear antenna microwave chemical vapour deposition of diamond films on long-period fiber gratings for bio-sensing applications,” Opt. Mater. Express 7(11), 3952–3962 (2017). [CrossRef]
44. A. T. Hendrickson, K. W. Hemawan, M. G. Coco, S. C. Aro, S. A. Mcdaniel, P. J. Sazio, G. Cook, J. V. Badding, and R. J. Hemley, “Diamond encapsulated silicon optical fibers synthesized by chemical vapor deposition,” AIP Adv. 10(9), 1–5 (2020). [CrossRef]
45. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]
46. E. Li, X. Wang, and C. Zhang, “Fiber-optic temperature sensor based on interference of selective higher-order modes,” Appl. Phys. Lett. 89(9), 091119 (2006). [CrossRef]
47. D. Mukherjee, F. Oliveira, S. C. Trippe, S. Rotter, M. Neto, R. Silva, A. K. Mallik, K. Haenen, C.-M. Zetterling, and J. C. Mendes, “Deposition of diamond films on single crystalline silicon carbide substrates,” Diamond Relat. Mater. 101, 107625 (2020). [CrossRef]
48. S. Prawer and R. J. Nemanich, “Raman spectroscopy of diamond and doped diamond,” Philos. Trans. R. Soc., A 362(1824), 2537–2565 (2004). [CrossRef]
49. C. Castiglioni, M. Tommasini, and G. Zerbi, “Raman spectroscopy of polyconjugated molecules and materials: confinement effect in one and two dimensions,” Philos. Trans. R. Soc., A 362(1824), 2425–2459 (2004). [CrossRef]
50. A. C. Ferrari and J. Robertson, “Raman spectroscopy of amorphous, nanostructured, diamond-like carbon, and nanodiamond,” Philos. Trans. R. Soc., A 362(1824), 2477–2512 (2004). [CrossRef]
51. P. K. Bachmann, D. U. Wiechert, and T. P. M. Meeuwsen, “Thermal expansion coefficients of doped and undoped silica prepared by means of PCVD,” J. Mater. Sci. 23(7), 2584–2588 (1988). [CrossRef]
52. C. Thomsen and S. Reich, “Double Resonant Raman Scattering in Graphite,” Phys. Rev. Lett. 85(24), 5214–5217 (2000). [CrossRef]
