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The sensitivity of bimodal waveguides for integrated optical biosensors is compared to single mode waveguides and grating-assisted bimodal interferometers are proposed as improved sensor concept. Grating-assisted bimodal interferometers are an elegant and compact sensor concept, which features easy fabrication and overcomes typical weaknesses of classical Mach-Zehnder interferometers. Long period gratings for mode conversion in the proposed sensor concept have been simulated employing the FDTD method. Such gratings give full control over the power distribution in the waveguides modes, which is not possible with other methods. Designs for three typical material systems are given and fabrication tolerances were investigated.
© 2014 Optical Society of America
1. Introduction
Currently, most clinical diagnostic tests are laborious, require sophisticated equipment operated by specially trained staff, and are, therefore, expensive. These tests often involve time consuming labeling techniques that attach fluorescent or chemiluminescent markers on the analytes to be measured.
Integrated optical biosensors, in particular those based on the evanescent wave principle, in combination with microfluidic systems, represent a promising way to overcome these disadvantages and allow affordable point-of-care diagnostic systems. They promise rapid and label-free detection of biomolecules, high sensitivity and online measurement capability as well as a small device footprint, which facilitates high levels of integration and parallel measurements with large numbers of sensors on a single chip.
Therefore, evanescent sensing devices for biosensing have been in the focus of scientific interest for many years and have been proposed and demonstrated in various configurations, e.g. as grating sensors in titanium dioxide [1], as MZIs in silicon oxynitride [2] or as ring resonators in silicon on insulator (SOI) [3–5]. Many devices have been realized in inorganic material systems, e.g [6,7]. employing standard semiconductor technology, which represents a powerful and reliable fabrication platform. Polymer based devices have also been investigated [8–10] as polymer technologies provide efficient means of low cost mass production.
Among the various optical sensor concepts, interferometric sensors have always been among the most sensitive devices demonstrated [11,12]. In particular, the Mach-Zehnder interferometer (MZI) concept [13,14] was intensively investigated as it combines high sensitivity, internal referencing and an easy readout system. Such MZI biosensors have been realized for example with silicon nitride (SiN) rib waveguides [15,16] or with SOI wire waveguides [17].
Recently, a new variant of interferometric devices was proposed and demonstrated by the group of Prof. Lechuga, the so called bimodal interferometer [18]. In MZIs, light from two spatially separated single mode waveguides interferes in order to modulate the output power of the interferometer as function of the phase difference between both paths. In a bimodal interferometer, the fundamental mode and the vertically first higher mode in the same waveguide are brought to interference. Due to the different mode profiles the effective indices of these modes are influenced differently when biomolecules bind to the sensor surface. In the concept proposed in [19,20], light is coupled into a vertically single mode input waveguide. Then, by an abrupt rise in the waveguide thickness, the fundamental mode and the first higher mode of the now thicker sensing waveguide are excited with certain efficiency. At the end interface of the waveguide, both waveguide modes interfere and, in analogy to the Young interferometer, a farfield interference pattern is created, which in this particular case is recorded by a two-segment photodiode. Although the bimodal interferometer configuration, in principle offers several advantages over standard single mode waveguide MZIs, the single step mode converter has some intrinsic short comings. As we will show later, the rapid change in the waveguide cross section at the point of mode conversion cannot excite both modes with the same power. Moreover, scattering losses occur at the mode conversion interface.
In this work, we propose novel structures of grating-assisted bimodal interferometers, as shown in Fig. 1. In grating-assisted interferometers, long period gratings (LPGs) are responsible for two tasks. Before the sensing region, the first LPG distributes half of the incoupled optical power guided in the fundamental mode into the higher order mode. The period, the coupling strength and the length of the grating, i.e., the number of grating periods, have to be chosen accordingly. The use of a grating instead of a step in the waveguide height gives precise control over the power distribution in the desired modes. After the sensing region, the second LPG intermixes both modes and transforms the phase difference between both modes into a modulation of the power in each individual mode. A balanced mode power is of essence to guarantee perfect intermixing of the modes, resulting in a signal with large modulation. Both modes can travel further along the waveguide until they are outcoupled by a grating coupler. Since both waveguide modes have different effective indices, they are outcoupled under different angles. Two photodiodes can then be used to determine the outcoupled power for each mode.
In the first part of this study, we optimize the waveguide cross section and analyze the theoretical sensitivity of bimodal waveguides. This allows setting the bimodal sensor in context with sensors based on single mode waveguides. In the second part, we focus on the designs of LPGs as the essential components of grating-assisted bimodal sensors and give concrete designs for LPGs for common sensing platforms. All simulations were carried out for TE-polarized light.
2. Sensitivity of bimodal waveguides
The figure of merit for evanescent waveguides is the induced phase shift during a biological measurement. A biosensing experiment, where biomolecules bind to their counterparts immobilized on the sensor surface, is commonly modeled as a thin biosensitive film on top of the waveguide that changes either its height or its refractive index during such a measurement. As the change in the effective index of a guided mode is proportional to the induced phaseshift in the waveguide, the sensitivity parameter of a waveguide structure can be defined as change in the refractive index per change in the sensing layer. The sensitivity parameter defined by Tiefenthaler et al. [21] for single mode waveguides can be generalized for higher order modes in waveguides as
where Si is the sensitivity of the i-th order mode in the waveguide (i = 0 for the fundamental mode), neff,i is the effective index of the i-th order mode and tsl is the thickness of the sensing layer. In the two-dimensional model used for this calculation as given in Fig. 2(a), Si depends on the thickness and the refractive index of the waveguide as well as on the wavelength. Figure 2(b) presents calculated sensitivities for the fundamental and first higher mode for a silicon waveguide system as function of the waveguide thickness (λ = 1310 nm, TE-polarization).
Fig. 2 (a) Schematic of the slab waveguide system used for calculations of waveguide sensitivities. (b) Sensitivities Si for different modes in a silicon waveguide (nwg = 3.48, λ = 1310 nm, TE-polarization) as function of waveguide thickness twg. The arrows in (b) indicate the maximum sensitivities S0,max for single mode waveguides as well as S1-0,max for bimodal waveguides, which is defined in Eq. (2) as difference of the sensitivities of the fundamental and the higher order mode.
In bimodal waveguides, two different modes travel in the same waveguide and both modes are influenced by changes in the sensing layer. Due to the larger thickness of bimodal waveguides compared to single mode waveguides, the fundamental mode is stronger confined and less influenced than higher order modes. As a result, only the difference in the respective phase shifts can be measured. Therefore, in analogy to Tiefenthaler's sensitivity parameter, we define the sensitivity parameter for bimodal waveguides as
where neff,i is the effective index of the fundamental (i = 0) and first (i = 1) higher mode.The sensitivity parameters for single mode and bimodal waveguides were compared as function of the refractive index of the waveguide layer at a wavelength of 1310 nm. The sensitivity parameters were analyzed by calculating the effective indices of the waveguides modes using the matrix method as outlined in [22] for slightly different thicknesses of the sensing layer. For each value of the waveguide refractive index, the waveguide thickness wasoptimized. The maximum sensitivity Smax as well as the corresponding optimum waveguide layer thickness topt are given in Fig. 3(a) and 3(b), respectively. The results of the calculations reveal that bimodal waveguides are only about half as sensitive as single mode waveguides. This can be attributed to two facts. Firstly, the higher order mode has, even in optimized bimodal waveguides, a more extended mode profile than the fundamental mode in an optimized single mode waveguide. Therefore, less optical intensity can be concentrated in the thin sensing layer by higher order modes than by a fundamental mode in an optimized waveguide, thus leading to a smaller change in the effective index for higher order modes. Secondly, although the fundamental mode is much stronger confined than the higher order mode in bimodal waveguides, it is still affected by changes in the sensing layer, which further reduces the overall sensitivity S1-0.
Fig. 3 (a) Comparison of maximum sensitivity for λ = 1310 nm of single mode and bimodal waveguides as function of the refractive index of the waveguide. For each system the optimum waveguide layer thickness as given in (b) was used.
Although bimodal waveguides have a lower theoretical sensitivity than single mode waveguides, interferometers built from these waveguides have proven to be sensitive biosensors [19,20,22,23]. Additionally, the proposed concept overcomes certain weaknesses of the classical MZI improving the characteristics of real sensor devices. Firstly, at the end of the interferometer, the power in both modes is accessible, thus, the total power at the end of interferometer can be measured. This allows compensating for fluctuations in the input laser power or the coupling mechanism as well as for dynamic loss phenomena during measurements, e.g. absorption in the sample fluid. Secondly, both modes travel in the same waveguide structure. Drawing an analogy to the MZI, which relies on referencing the light in the measurement arm with the light in a spatially separated reference arm, here the “reference mode”, i.e., the fundamental mode and the “measurement mode”, i.e., the higher order mode, propagate in the same waveguide, which can improve the quality of the referencing. Moreover, while integrated MZI concepts necessitate vertically and laterally single mode waveguides, the waveguides in grating-assisted bimodal interferometers can be laterally multi mode, or even slab waveguides, reducing or eliminating losses stemming from rough and uneven side walls. For the grating couplers for incoupling and outcoupling, the beam diameter of the incident beam must be matched to the coupling strength of the grating, adjusted by the modulation depth, in order to achieve high coupling efficiency. Relieved from the need for laterally single mode waveguides, the beam diameter and, thus, the modulation depth of the gratings can be chosen in accordance to the modulation depth of the LPGs. Then, the whole grating-assisted bimodal sensor can be fabricated in a single etch step.
Influence of variations in the waveguide thickness on the sensitivity were calculated for three material systems for which the LPG designs will be presented later, namely silicon on insulator, silicon nitride, and polyimide. Those curves are shown in Fig. 4. Single modewaveguides are more tolerant and variations in the thickness of ± 10% reduce the sensitivity by only about 2%. For bimodal waveguides, the waveguide thickness has a narrower, however, achievable tolerance. Variations in the waveguide thickness of ± 5% do not reduce the sensitivity by more than 5%. In our experience, this lies well within the tolerances of semiconductor deposition processes. On this relative scale, the three material systems show very similar behavior.
Fig. 4 Influence of variations in the waveguide thickness on the sensitivity parameters for single mode waveguides (solid lines) and bimodal waveguides (dashed lines) normalized to the maximum sensitivity. Curves for the SOI (blue, λ = 1310 nm), SiN (red, λ = 633 nm) and PI (green, λ = 1310 nm) material system are shown.
3. Design of long period grating couplers
Excitation of higher order modes employing a LPG is a method well known in fiber optics. If the period of the grating Λ is chosen in a way that the grating bridges the gap between the wavevectors of the fundamental and the higher order mode, i.e.,
where λ is the free space wavelength, the grating introduces coupling between these two modes. The coupling strength is described by the coupling coefficient κ, which depends on the geometrical properties of the grating, particularly on the modulation depth e. Mathematically, the coupling of theses mode can be described in a similar way as the codirectional coupler in coupled mode theory, as outlined e.g. in [24]. If, at the beginning of a grating with the correct period, all the incident power is concentrated in a single mode, the grating starts to couple power into the other mode. Within the length π/(4κ) half of the power will be coupled into the other mode. In the proposed sensor concept, this behavior is exploited before the sensing window. The input grating coupler couples light from a free space beam selectively into the fundamental waveguide mode, which then incidents the first LPG. The period, the modulation depth e, and the length of the LPG are chosen such that the grating couples 50% of the power from the fundamental into the higher order mode. Both modes then propagate independently in the sensing region. We define the modulation depth e as the height of the surface corrugation of the LPGs.After the sensing region, a second, identical LPG is used for intermixing both modes. Now two modes with the same power are incident on the LPG. The direction of the power coupling in the LPG, i.e., from the fundamental into the higher mode or vice versa, is determined by the phase relation between both modes. If both incident modes have the same power Pin and if the grating has the correct period and a length of π/(4κ), the power in the fundamental mode P0 and the power in the higher order mode P1 after the LPG are described by
with Δφ being the phase difference between the two incident modes. Therefore, such a LPG transforms a phase difference between both modes into a modulation of the power in both modes with nearly no losses. At the end of the device, a waveguide grating coupler deflects both modes under different angles and the power in both modes can be detected using two photodiodes.If both incident modes do not carry the same power, the modulation of the power signal will suffer and it will be more difficult to detect the phase shift precisely. In the original bimodal waveguide biosensor concept, as given in reference [19], a sudden raise in the silicon nitride (SiN) waveguide thickness is responsible for exciting both modes. By calculating the overlap integral of the fundamental mode in the thin input waveguide and the two modes in the 350 nm thick sensing waveguide, we modeled the modal power conversion that can be achieved with this system as function of the input waveguide thickness for a wavelength of 633 nm. The visualization of these data in Fig. 5(a) reveals that in the best case the higher mode can be excited with only less than 25% instead of the 50% required for perfect interference, emphasizing the need for an alternative power transfer scheme between the modes.
Fig. 5 (a) Fraction of power in fundamental and higher mode that can be excited employing a step in the waveguide thickness for a SiN bimodal waveguide system as given in reference [19]. The inset compares calculated mode profiles of the fundamental mode in a 150 nm thick input waveguide with the higher mode in the 350 nm thick bimodal waveguide (λ = 633 nm). (b) Total power and power in both waveguide modes as function of the LPG length for a bimodal SiN (nwg = 2, λ = 632.8 nm) waveguide system, when launching only the fundamental mode into the LPG (LPG parameters given in Table 1).
In this work, we present designs for LPGs for the three most common waveguide material systems for biosensing applications. SOI waveguides operated at near infrared wavelengths are currently intensively investigated as they feature high sensitivity due to the high refractive index of silicon and CMOS compatibility. The second material system is silicon nitride at a wavelength of 633 nm. Due to the use of a shorter wavelength, it offers the highest theoretical sensor response for a given waveguide length of all waveguide material systems. Also, the original bimodal waveguide biosensing concept was realized in this material system. Further, we present a design for a high index-contrast polymer material system, namely polyimide (PI) at a wavelength of 1310 nm. Although of lower theoretical sensitivity than the other investigated systems, sensitive biosensors have been realized [10]. This material system is interesting as polymer technology is very powerful in term of mass production and would allow the cost efficient fabrication of biosensor chips e.g. for screening applications.
The LPG designs were elaborated using 2D finite-difference time-domain (FDTD) simulations, i.e., in the approximation of wide or even slab waveguides, and TE-polarization. The same concept can be applied to laterally single mode waveguide as well. In such cases, the grating parameters would need to be found using 3D FDTD simulations, for which the parameters given here would give a good starting point. The thicknesses of the waveguideswere chosen to be of high sensitivity as calculated in the previous section. Then, the modulation depth, the period, and the length of the LPGs, given in number of periods, were optimized to achieve the above described behavior and a high transmission. Table 1 summarizes the simulation parameters and the optimized results for the LPG. It additionally gives the angle separation between the modes outcoupled by the output grating coupler. The substrate was silicon dioxide with a refractive index of 1.46 in all cases.
Table 1. Summary of the simulation parameters and the simulation results for the long period gratings for all three material systems. Silicon dioxide (n = 1.46) was used as substrate in all cases. Additionally, the angle separation Δα of the two modes at the output grating coupler is given, assuming a 45° output angle for the fundamental mode.
Figure 5(b) shows the power in the fundamental and the first higher order mode for a bimodal SiN waveguide system as function of the length of the LPG. Only the fundamental waveguide mode was launched into this LPG. The graph shows the sinusoidal power coupling characteristic of the LPG. The optimum LPG length for 50% power coupling, i.e., where both modes carry the same amount of output power, is 18 periods (38.5 µm). Figure 6 compares the spectral characteristics of the investigated LPGs. In all material systems the mode power ratio is very insensitive to the wavelength. For the SOI LPG, the spectrally broadest LPG, the mode powers do not deviate by more than 5% from the ideal 50% for a 150 nm wide wavelength window.
Fig. 6 Spectral characteristics of optimized LPGs for (a) bimodal SOI (nwg = 3.48), (b) bimodal SiN (nwg = 2), and (c) bimodal PI (nwg = 1.65) sensor systems (parameters given in Table 1). The fundamental mode is launched into the LPG. After the LPG, both waveguide modes, i.e., fundamental and first higher carry the same power at the design wavelength.
The modulation depth e of the LPGs has been chosen around 5% of the waveguide thickness. Since LPGs are no sub-wavelength structures, every period of this binary grating, comprising two steps in the waveguide thickness, will induce a certain amount of scattering. To minimize scattering and optimize transmission, a small modulation depth was chosen, resulting in transmissions of >95% for a 50% coupling LPG. With different grating profiles, e.g. a sinusoidal profile, scattering losses and LPG length could be further decreased, however at the cost of a more complex fabrication. The period of the LPGs varies strongly with the material system. In the polymer system, with only small differences in the effective indices ofthe waveguide modes, the LPG period is 15 µm, with LPG lengths of a few hundreds of micrometers. In SOI on the other hand, the LPGs have periods in the sub-micrometer regime and the total LPG length in SOI is shorter than a single period of a polymer LPG. In particular for high contrast material systems, the LPGs have a very small device footprint contributing to an overall compact sensor concept.
The influence of deviations in fabrication on the performance of LPGs was investigated. The graphs in Fig. 7 display the mode power ratio P0/(P0 + P1) after the LPG, which should be 50% in the optimum case, as function of variation of the two most important parameters: the waveguide thickness twg and the modulation depth e. The period of the LPG, defined by lithography, is not assumed to be subject to major variations. In general, it can be said that variations in the modulation depth are less critical. A 10% deviation in the modulation depth changes the mode power ratio typically by less than 10%. The performance of the LPG is more sensitive to changes in the waveguide thickness. Here, variations of ± 2% can already induce a significant change ( ± 10%) in the mode power ratio. Depending on the deposition technique for the waveguide layer, keeping these tolerances might be challenging. However, in our experience, the requested accuracies lay within the limits of standard semiconductor deposition processes such as PECVD or LPCVD.
Fig. 7 Influence of fabrication errors in (a) waveguide thickness twg and (b) modulation depth e on the performance of optimized LPGs for the three investigated sensor systems. The fundamental mode is launched into the LPGs and the mode power ratio P0/(P0 + P1) after the grating is given for bimodal systems.
4. Summary
Bimodal interferometers have been compared in terms of sensitivity with sensor concepts based on single mode waveguides, such as the Mach-Zehnder interferometer. Although the theoretical sensitivity of bimodal waveguides is smaller than that of single mode waveguides, bimodal grating-assisted interferometers feature improved referencing and simultaneous access to the power in both waveguides mode, which benefits the sensor performance in real applications. Designs for long period gratings for mode conversion were presented and discussed for three different material systems.
Interferometers made from bimodal waveguides have already proven their suitability as sensitive biosensor. The grating-assisted bimodal interferometer further enhances this concept with an improved outcoupling concept using two photodiodes for collecting the power in both waveguide modes, as well as a simplified fabrication with a single etch step. The long period gratings give full control over the power distribution in the modes and implement a nearly lossless mode conversion mechanism. Therefore, increased transmission, higher stability and a simplified readout system can be expected from grating-assisted bimodal interferometers.
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