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We report a novel micro-fiber Bragg grating (µFBG) sensor that takes advantage of the degeneracy of stop-band and rapid emergence of spectral modes when an effective phase shift occurs. The phase shift can be enabled by a range of perturbations in a central segment of the grating, including monolayer immobilization of bio-molecules or change in refractive index in the surrounding, thereby constituting the possibility of a highly sensitive sensor with the merit of scalable performance. The use of µFBG ensures strong evanescent field coupling to the surrounding in order to maximize signal transduction. Simulation results indicate very favorable sensor signal characteristics such as large wavelength shift and sharp reflection dips. A general relation between the peak position within the stop-band and the amount of effective phase shift is also provided, and may generally serve as helpful guideline for FBG sensor design. A typical µFBG sensor device may detect surface protein/DNA adsorption with limit-of-detection (LOD) as low as 3.3 pg.mm −2 for surface mass density and 51.8 fg for total mass. For refractive index (RI) sensing, the LOD is 2.5*10−6 refractive index unit (RIU).
©2011 Optical Society of America
1. Introduction
Fiber Bragg grating (FBG) sensors have been intensively studied and deployed for temperature, strain, pressure sensing, due to many of their advantages, such as efficient input/output delivery, wavelength multiplexing and high sensitivity [1,2]. Evanescent wave based FBG sensors require interaction between the evanescent wave and the surrounding. Various approaches have been reported to enhance the evanescent field, including D-shaped FBG [3], thinned fiber FBG [4,5], and microfiber [6,7] or un-cladded fiber FBG [8]. Microfiber is a promising structure with large evanescent field, as a result of its sub-wavelength dimension [9,10]. On the other hand, in order to enhance the wavelength selectivity, phase shift in FBG has been introduced to degenerate the FBG stop-band and offers a sharp peak inside. Phase shifted FBGs are widely used in optical fiber communications and optical fiber sensors, such as wavelength multiplexer [11], strain sensor [12]. Typical fabrication steps of phase shifted structures require the use of a special phase mask or post processing (thermal, CO2, UV) [13–15]. While post processing typically has quite limited range for parameter adjustment, phase shifted masks are generally expensive. Nonetheless thermal effects have been shown to be useful for fine-tuning of refractive index in a small volume of material, and consequently introducing phase-shifting in FBGs [13,16]. Indeed this technique may be used in distributed feedback lasers [17]. In chemical sensing and biosensing applications, a question thus arises naturally: can we combine the best features of strong evanescent field and enhanced wavelength selectivity by having a phase shifted FBG in the micro-fiber Bragg grating (µFBG) sensor? In this work, we report a novel and simple scheme to introduce significant modification of the FBG transmission stop-band by means of a sensor-induced effective phase shift. Phase shift is achieved by bio-molecules immobilization (protein, DNA) [18] or immersing the central segment into an analyte surrounding. Simulation results show that a spectral peak (which will also be described as spectral dip in the reflection spectrum hereafter) in the transmission stop-band will begin to emerge as a consequence. In distributed feedback lasers, phase shift has been used for tuning the spectral peak in the stop-band. Instead, we do the inverse of tuning. That is, the movement of the spectral peak is used for monitoring the amount of phase shift, which readily leads to the capability of sensing changes in the surrounding. From the dispersion relation of FBG, a general relation between the peak position within the stop-band and the amount of effective phase shift is provided, and may generally serve as helpful guideline for FBG sensor design. Furthermore, the position of the peak is very sensitive to the amount of phase shift and its narrow bandwidth permits measurement with high degree of accuracy. The spectral peak shift can be used for registering the surface mass density, total mass adsorption of bio-molecules or RI change of the surrounding medium. Increased wavelength shift for sensing very small perturbations is also achievable by length scaling of the sensing grating segment with longer interaction length.
2. Theoretical modeling and analysis
The µFBG may be fabricated by several methods [4,6–8]. We shall adopt two models for the aforementioned sensing applications, i.e. detecting the thickness (surface density) of bio-molecule adsorption and sensing of refractive index (RI) change in the surrounding medium. In both cases, the net effect is a phase shift in the µFBG, which will then introduce peak shifts in the stop-band. The physical model of the first case is shown in Fig. 1 , where D is the microfiber diameter; Λ is the pitch; δndc and δnac are the original DC and AC components of the FBG effective index change.
Fig. 1 Schematic model (a) and index profile (b) of adsorption induced phase shifted µFBG with selected area immobilization of bio-molecules. The coating with thickness d is located only at the middle segment with length L2, and it will introduce an increase of effective index.
For a realistic silica µFBG, which can be achieved experimentally, the diameter could range from several hundred nanometers to several micrometers. For best sensing performance, in this simulation work, we select a diameter of around 1 µm. For larger diameter µFBGs, the performance would degrade in some degree, however the sensing principle will be the same. The wavelength is assumed to be around 1.55 µm, i.e. wavelength for common optical communication systems. Then the effective index neff is about 1.18, which is much smaller than that of normal single mode fiber. So due to the relation between resonance wavelength and effective index, the grating pitch, Λ, that we used is around 0.645 µm, which is larger than that of normal fiber FBG. For easy implementation, we also assume that other µFBG parameters are δndc = δnac = 10−4, L = 1.5 cm. A segment L 2 in the middle is covered by an adsorption layer of thickness d, which is directly related to surface density of bio-molecules adsorption as mentioned later in Part 3.
Due to the presence of the layer of adsorbed biomolecules, the microfiber’s mode effective index neff changes linearly with the adsorption thickness d, which is typically in the nm regime, as described in Eq. (1). A similar protein monolayer immobilization method was used for planar waveguide grating in [18]. For the second case of surrounding medium RI detection, the mode effective index change is also linearly proportional to the RI change of the analyte, Δna, as described in Eq. (2):
where np is the protein RI (1.35~1.38); na is the surrounding analyte RI and ns is the RI of the background medium, e.g. RI of air or an aqueous solution. The coefficient χ is the sensitivity of effective index change due to adsorption thickness change, while α is for change of surrounding medium index. Both can be identified by modeling using a finite element scheme or through analyzing the dispersion equation [19], as shown in Fig. 2 . For adsorption layer thickness sensing shown in Fig. 2(a), the sensitivity of effective index change in a gaseous medium background is much better than the aqueous case. The sensitivity varies with the microfiber’s diameter. Interestingly, the sensitivity of effective index change does not go to maximum at minimum microfiber diameter. In gas background case, χ reaches maximum when the microfiber diameter approaches 0.8 µm, while in aqueous medium background, χ has a maximum at D = 1.2µm. Beyond these maximum points, the sensitivity decreases with increasing microfiber diameter due to weakening of evanescent wave. For the case of RI sensing, when the sensor is placed in a medium with index na, as shown in Fig. 2(b), the sensitivity decreases with increasing fiber diameter. Furthermore, the achievable sensitivity is higher for aqueous based sensing as compared to the gaseous case because the higher index cladding results in a stronger evanescent field. With this analysis, one could find a balance between the system sensitivity and system robust requirement. The mode effective index change induced by a 1 nm protein immobilization in first model corresponds to a 7.5 × 10−4 RIU change in the surrounding medium in the second case. In an analysis described later, we will combine both models by using effective index change Δneff.Fig. 2 Sensitivity of microfiber effective index change as a function of diameter, (a) for sensing layer thickness (surface density) of bio-molecule adsorption and, (b) for sensing refractive index (RI) change in the surrounding medium.
If the adsorption of biomolecules or the change of surrounding index occurs only in a middle segment of the µFBG, the induced mode effective index variation in the middle part of µFBG will significantly change the stop-band characteristics and two effects will emerge. First, Δneff will increase the DC index component of middle segment from δndc to δndc + Δnneff, while the AC index part, δnac, will remain unchanged. Consequently, for the middle segment, the AC component κ, and DC component σ of the coupling coefficient will be described in Eq. (3) and (4) respectively.
σ 0 is DC component of the coupling coefficient of the original FBG. Then the middle segment will act as a separate FBG and generate a right-shifted stop-band with the Bragg wavelength shifted by 2Δneff Λ, which will partially overlap with the spectrum of original FBG. The spectrum of the middle segment is shown as dotted line in Fig. 3 . If the grating of the middle segment is too strong, i.e. large κL2, its stop-band will suppress new spectral modes generated by the adsoprtion coating. Consequently, one should choose an appropriate length for the middle segment so that κL2≤1. Second, Δneff in the middle segment will produce an additional phase shift between segment 1 and segment 3. Moreover, as shown later one also sees that the mode effective index change Δneff is near linearly related to the amount of phase shift. The complex amplitude of forward (F) and backward (B) propagating waves at the input and output of the middle segment are determined as Eq. (5) using a matrix method [1].where γ = (κ2-φ2)1/2 is imaginary for |φ|>κ; φ is a general detuning or phase matching parameter for the middle segment as shown in Eq. (6). φ0 is detuning of the original unperturbed µFBG. After describing these three segments using 3 matrices, similar to Eq. (5), the overall input and output relation can be calculated by Eq. (7).From (7), the reflection spectra for different protein coating thickness are plotted in Fig. 3. From this figure, by changing the protein layer thickness from 0 to 0.37nm, the dip position shifts from the left edge to the center of the stop-band. The overall calculated behavior is shown as circle dotted line in Fig. 4 . It is calculated directly by the multiplication of three matrices, with the middle one from Eq. (5) perturbed by the effective index change. There is no concept of phase shift and we label it as ‘numerical’ method.Fig. 3 Reflection spectra (Y axis on the left) and total round-trip phase change in entire µFBG (Y axis on the right) for different thicknesses of protein coating, with 1/3 of the total length in the middle is coated. Solid lines represent the spectrum and total round-trip phase change without coating, while dashed broken lines are for 0.2nm thick coating, and dashed lines are for a thickness of 0.37nm. The spectrum of the middle segment is shown as dotted line, where κL2 should be less than 1.
Fig. 4 Dip positions in reflection spectrum with varying protein coating thickness for a sensing length of L2 = L/6. Circle dotted line represents numerical method from multiplication of three matrixes, while triangle-dotted line and cross-dotted line are obtained from modeling using strict phase shift and linear phase shift approximation, respectively. The curve of “original reflection spectrum” inserted is used to show the positions of band-edge visually.
An important aspect of this work is the establishment of a general relation between the peak position within the stop-band and mode effective index change in the middle segment. When the phase shift at the FBG center is π/2, the peak obviously occurs at the center of the stop-band. Generally, when the phase shift is not equal to π/2, the peak is located at the wavelength that corresponds to a total round-trip phase change of multiples of 2π for the entire FBG. The total phase change for one round-trip, Φ as Eq. (8) and shown as slanted lines in Fig. 3, is the summation of reflection phase shifts of both half-FBGs and 2 times of the additional phase shift at the center segment [20].
Θ is the phase shift associated with mode effective index variations in the middle segment and can be identified by calculating the phase difference between F(L1) and F(L1 + L2),(described as the strict phase shift method hereafter).By assuming that this phase shift only happens at the center point of the grating, we can treat it as a normal phase shifted grating. Therefore, the dip position predicted by Φ = 2π in Eq. (8), shown as zero-crossing points in Fig. 3, is agree well with the simulated dip position from Eq. (7). Based on strict phase calculations, the general relation of dip position and coating thickness is shown as triangle-dotted line in Fig. 4, which is labeled ‘strict phase’.
Under strict phase conditions, the wavelength shift sensitivity S due to the change of coating thickness is shown as Eq. (9).
In addition, another approximation approach for calculating the coating-induced phase shift is to assume that the phase shift is linearly proportional to index variation as Eq. (10):The dip positions obtained by strict phase shift, linear phase shift approximation as found from Eq. (10) and numerical methods directly from multiplication of three matrixes in Eq. (7) are compared in Fig. 4.Here we can see that the strict phase shift method offers better approximation for the dip positions compared to the linear phase shift approach. Meanwhile, the linear phase shift also provides a very good approximation. So, using the phase shifted modeling, we establish a general relation between the peak position within the stop-band and mode effective index change (namely, coating thickness and surface mass density changes) in the middle segment. From the figure, the peak position moves near linearly with the coating thickness. This general relation could be used as sensing mechanism.
From Eq. (10), one can see that Θ is proportional to the length of middle segment, implying that sensitivity is proportional to the length of middle segment. If index variation is small, a longer middle segment may be required to achieve better sensitivity performance, namely, the sensitivity is scalable for very thin coating. Beside the accuracy and scalable measurement for very thin coating, the device could have wide dynamic range sensing capability by cooperation with other low accuracy measurement. When the thickness increases, the first dip moves out of the stop-band and the second dip will move in. From Fig. 4, we can see that there could be two dips for some coating thickness, simultaneously. One is close to left edge, and the other is close to right edge. If we know the approximate range of thickness in advance, for example in the range of 0~1nm, 1~2nm or 3~4nm, our measurement could provide more significant digits. For example, our sensor can work in parallel with another µFBG sensor that does not have any pre-fabricated phase shift. The one without phase shift provides the approximate range by monitoring the Bragg wavelength shift, while the one containing a phase shift will provide high resolution measurements. From Eq. (10), we also notice that the sensitivity is a function of effective index change Δneff. Consequently, the overall sensitivity S also varies with the microfiber diameter, following a similar trend shown in Fig. 2. For the µFBG described earlier, with L2 = L/3, each nm of protein adsorption will lead to a shift of the peak/dip by a value of 0.3 nm. So the wavelength shift sensitivity S equals to 0.3. Typically, for a spectrometer with resolution of 1 pm, the thickness limit-of-detection (LOD) is therefore 3.3 pm. In term of surface mass density, the LOD is 3.3 pg.mm −2, which is a very attractive figure in comparison to most reported biosensors [21]. In term of gas sensing, the detection limit of index change is about 2.5 × 10−6 RIU. With a narrow peak having a full-width-half-maximum (FWHM) bandwidth of around 0.02 nm, the figure-of-merit, which is defined as the sensitivity divided by the FWHM of the spectra peak [22], has improved by 10 times when compared to typical µFBG sensors that do not incorporate any phase shifting effect, and their FWHM bandwidth is about 0.2 nm when all other structural parameters remain unchanged.
Another application of phase shifted µFBG is for total mass detection. From Eq. (1) and (10), the phase shift Θ as a function of total mass M is expressed as Eq. (11),
where ns is equal to 1 in air, and ρ is the coating material density, which is roughly proportional to refractive index minus one with coefficient η, ρ = η(np-1) [23]. So the mass measurement is independent of refractive index value, density or length of the coating. The peak position is related only to the total mass of materials deposited on the middle segment. In term of total mass measurement, the calculated LOD is 51.8 fg.The position of the middle segment also should be carefully controlled. Sensing performance will degrade if the position of middle segment has a large bias from the center of L. With a bias of Δl, total phase change for one round-trip, Φ as Eq. (8), will slightly change. The last item in Eq. (8) will split into two items, one half with (L/2 + Δl) and the other half with (L/2-Δl). However, Φ is a continuous function in a small region, if Δl is relatively small comparing with L/2 (less than 5%), the bias will not change the spectrum severely.
3. Modeling of biosensor application
For the case described in Eq. (1), which is for coating thickness sensing, we specifically analyze the biosensing performance of our µFBG. The coating thickness in the middle segment will be contributed by proteins adsorption. Since the spacing between proteins is much smaller than the incident wavelength, we can assume an effective thickness with certain surface mass density for the protein adsorption layer. From conservation of mass, we can draw a link between effective thickness and surface mass density as Eq. (12)
P is surface mass density; n0 is the index of the effective film with thickness of deff. For the easy implementation, we also can transfer the coating layer to a silica film.To detect specific bio-molecules through coating on the microfiber, first we need to immobilize bio-molecules around silica microfiber surface. Antibodies cannot be attached directly to a glass surface. Furthermore, localized selective binding is needed and antibodies should only immobilize at the middle segment. Here, two methods for selected surface functionalization are introduced. Bhatia et al. immobilized antibodies onto glass slides by using silane and crosslinked layers [24], and Ruan et al. used this method for silica microstructured fiber [25]. For our µFBG, first one can put the µFBG at the top of a silane solution droplet, with the middle segment immersed into the solution as shown in Fig. 5(a) . Then it is not difficult to control the coating length within a segment of 0.5cm. After silanization, a so-called crosslinker is used to connect silane with antibodies. Apart from the silane method, photo-immobilizable polymer monolayer [26] can also be used as a bridge for linking silica surface with antibodies [26]. The photo-immobilization of polymer monolayer on µFBG is shown in Fig. 5(b). Then, the antibodies are attached to the crosslinker or the polymer monolayer, as shown in Fig. 5(c). Finally, the antibody-antigen binding process as shown in Fig. 5(d), can be monitored by the phase shift measurement, where the density of bio-molecules is equivalent to film coating with effective thickness of deff. Before the bonding process, the silane layer, the polymer monolayer and antibody layer may already have contributed an initial phase shift. Consequently, the peak in the stop-band may not start from the band edge.
Fig. 5 Bio-molecules immobilized onto the silica surface of middle segment of µFBG. Two methods for localized surface functionalization are proposed, (a), by immersing the middle segment in a silane solution, or (b), by photo-immobilization of polymer monolayer onto middle segment. With functionalization taking place only in the middle segment, the bonding of antibody molecules (c) and antigens (d) are shown schematically.
4. Conclusions
In conclusion, we have investigated a novel microfiber Bragg grating sensor that utilizes stop-band mode changes associated with the phase shift in a central grating segment. Such a phase shift can be introduced through localized immobilization of bio-molecules or RI change of the surrounding medium. Beside the simulation for sensing application, a general relation between the peak position within the stop-band and the amount of effective phase shift is provided, and may generally serve as helpful guideline for FBG sensor design. To demonstrate its realizability, we proposed a novel biosensing application for the measurement of surface density of protein molecules. This kind of sensors can provide very favorable sensing resolution and figure-of-merit. For a realistic 1.5 cm µFBG with 1/3 of its length coated with protein, the LOD of surface mass density is 3.3 pg.mm −2, and the LOD of total mass is 51.8 fg, which compares very favorably with most of the reported protein sensors. For RI sensing, the LOD is about 2.5 × 10−6 RIU. In term of figure-of-merit, it offers 10 times improvement compared to non-phase-shifted µFBG sensors.
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