Issue
Eur. Phys. J. Appl. Phys.
Volume 90, Number 3, June 2020
Disordered Semiconductors: Physics and Applications
Article Number 30502
Number of page(s) 10
Section Photonics
DOI https://doi.org/10.1051/epjap/2020190250
Published online 07 July 2020

© EDP Sciences, 2020

1 Introduction

Photonics, defined as a multidisciplinary domain dealing with light, encompassing its generation, detection and control, has been identified by the European Commission as one of the five Key Enabling Technologies (KETs). KETs are multidisciplinary, cutting across many technology areas with a focus on integration and service innovation [1]. Silicon photonics is an ultrahigh-density integration technology for optical devices using submicron-scale optical waveguides with a core composed of Si. Photonic Silicon integrated devices and circuits are fabricated on silicon-on-insulator (SOI) wafers consisting of crystalline Si (c-Si) and buried oxide (SiO2). Because of the large difference between the refractive index of silicon and silica it is possible to design miniaturized optical devices, where the waveguide dimension is only a few hundreds of nanometres.

The traditional argument in favour of silicon photonics is based on its compatibility with mature silicon IC manufacturing processes. Creating low-cost photonics for mass-market applications by exploiting the mighty IC industry has been a strong motivation for silicon photonics researchers [2,3]. The large expectations about low-cost photonics integrated circuits, in terms of monolithic integration with advanced CMOS transistors and cheap and simple packaging, has been somehow frustrated by the complexities introduced by reduced process geometries that can inversely impact manufacturability, optical power efficiency and fibre-optic packaging [4]. Recent ideas about silicon photonics, point out the need for reducing the complexity in the circuit design, avoiding placing all the focus on device miniaturization and instead searching for cost-effective solutions which can be readily transferred from the research laboratory to real-world applications. As microelectronics races to progressively smaller nodes, this new point of view considers the possibility for a leading photonics platform where bigger is better [5]. In such a scenario where the photonic devices need to be not as small as possible, but as accurate as you can make it, alternative methods of device production can pave the way to low cost devices and systems.

In this context, low-cost production materials, such as hydrogenated amorphous Silicon (a-Si:H) becomes an attractive material for use in photonic devices and has been reported by many authors as a possible candidate for being used in mass production of photonics circuits [610]. The amorphous phase of silicon has been intensively studied during the last decade of the XX century [11] and, nowadays, state of the art good quality a-Si:H can be easily deposited by the well-known method Pressure Enhanced Chemical Vapor Deposition (PECVD). This is a low-cost technique that has reached a stable maturity and quality, due to the large investment directed to mass production of a-Si:H solar cells [12] and thin film transistors for active matrix flat panel displays [13]. Also, good quality a-Si:H can be deposited by PECVD at low temperatures (between 200 and 400 °C), making the deposition of this material directly compatible with back-end CMOS processing.

It is well known that electronic and optical properties of the films are strongly influenced by the conditions of the deposition technique. Optimal refractive index of a-Si:H, measured by reflectometry [14], is approximatively 3.65 at 1550 nm, which is a higher value than the crystalline silicon correspondent. Anyway, the unavoidable presence of defects and dangling bonds in the lattice results in a high density of localized states at energies below the energy gap, producing photon absorption in the near IR range at telecommunication wavelengths. Hydrogen can passivate defects and its concentration is strongly dependent, among other factors, on the deposition temperature. Hydrogen concentration determines the sub-gap absorption coefficient and it may produce small variations of the amorphous silicon optical functions [15].

Dependence of the material characteristics on the specific deposition conditions should be considered and taken into account at the waveguide design stage, together with geometric variability. The optical constants of a-Si:H are substantially different from the crystalline counterpart and are generally represented by a Tauc-Lorentz model describing the real and imaginary part of the dielectric function [16], corrected by introducing an exponential term representing the Urbach tail (UTL model) [17]. Nevertheless, because of the reduced thickness of the typical a-Si:H solar cell (less than 1 μm), infrared absorption has never been considered important for solar cell development and was often neglected. As in waveguide systems the infrared absorption is indeed important, it can be described by an additional term, describing photon absorption based on a Gaussian defect distribution (GUTL model) [18]. The presence of defects in the network influences mainly light absorption in the infrared range which is interesting for photonic waveguides.

While photonic integrated circuits (PICs) have the potential to generally bring the photonic methods and technologies to the mass market in several segments, PECVD thin film technology is particularly attractive for low-cost devices in low frequency applications. Integrated biophotonic applications, for example, are a very interesting field where the PECVD thin film approach have the potential of paving the way toward the cost reduction of bulky and expensive life science systems, producing a massive generalized access to health care based on the Point-of Care paradigm. PECVD thin film technology widens the application horizon allowing the design of biophotonic devices working not only in the telecommunication wavelengths but also in the mid-infrared and in the visible range [19]. Within this context, Surface Plasmon Resonance (SPR) sensors find extensive use for biomedical applications [20]. They can achieve higher sensitivity when compared to other evanescent wave sensors, can be made at nanoscale, providing a route to miniaturization [21], offering the potential to move proteomic biology into the clinical setting as a routine diagnostic procedure. Many different SPR configurations have been proposed, based on different schemes for SPP generation and interrogation methods, leading to the production of highly sensitive sensors including miniaturized optical waveguide structures [22]. Also, higher sensitivity in detection of small size biomolecules can be achieved with waveguide interferometers [23]. One key point common to all the SPR sensor configurations is allowing, under the right conditions, coupling of the excitation field to the propagating Surface Plasmon Polariton (SPP). Small imperfections caused by waveguide wall roughness can undermine the coupling efficiency and compromise the performance. It is of major importance to understand the tolerance of a specific device design on imperfections due to lithographic roughness and finite lithographic resolution.

The sensor structure hereby considered for computer simulation analysis is based on a sensing region operated by a plasmonic interferometer composed by an a-Si:H waveguide covered by a thin gold layer. The light power propagating inside the waveguide is inherently low, just like expected photocurrents measured at the output. This limitation can be mitigated by using a 1 × 2 power splitter at the input and calibrating the sensor using a reference arm. Therefore, the sensor is composed by two arms, one working as a reference while the other, which is directly in contact with the analyte, acts as sensing element. Two different splitter configurations are considered: an MMI (multimode interference) and a directional coupler. The two alternative device structures are depicted in Figure 1. The main point hereby analysed is the waveguide wall roughness that can be expected when the structures are produced by PECVD method. The waveguide quality, light coupling, multimode interference in the near IR range will be analysed in the scenario of an integrated plasmonic biosensor. The different components are analysed separately, using the RSOFT package based on FDTD and Beam Propagation methods [24].

thumbnail Fig. 1

Plasmonic interferometer composed by an a-Si:H Waveguide covered by a thin gold layer. The sensing analysis is performed by equally splitting the input light into two arms, allowing the sensor to be calibrated by a reference arm. The 1 × 2 power splitter can be built upon two configurations: (a) Based on a directional coupler. (b) Based on multimode interference (MMI).

2 Device physics and simulation results

2.1 The directional coupler

Slab waveguides have the advantage that can be realized in a multilayer structure, avoiding the need for an expensive high-resolution mask process. The layer thickness corresponds to the waveguide width, and it can be easily controlled by the deposition time. This approach only permits the realization of simple photonic structures, but it can be robust enough for the development of biosensing devices based on the waveguiding phenomenon. The directional coupler is a method for splitting and combining light in photonic systems, consisting of two parallel waveguides enabling the transfer of light from one waveguide to another through evanescent wave coupling. The fraction of the power coupled from one waveguide to the other is controlled by the waveguide material and size (i.e. through the modal effective index), the spacing between the waveguides and the length of the coupler (L) [25]. It can be expressed as:(1) (2) (3)

where P0 is the input optical power, Pcross is the power flux coupled across the coupler and PThrough is the not-crossing power flux. The coupling coefficient (C) for a slab symmetrical coupler formed by two identical waveguides with width w and refractive index n1, separated by a distance d with a cladding material with refractive index n2 and without losses, can be theoretically calculated for both TE and TM modes (CTE and CTM, respectively) with an extension of the Marcatili coefficients model [26,27]:(4) (5)where , , k0 is the free space wave number, and b = neff k0 is the propagation constant of the mode. It should be noted here that in the same waveguide the coupling coefficient may assume different values for different mode orders.

The optimal 3  dB splitter length (L), for the fundamental TE and TM modes, calculated with the model described by equations (1)(5) is reported in Figure 2. As can be observed in the figure, even not considering losses in guided mode propagation, a fine tuning of all the coupler parameters is needed for an optimal performance, as a very large variation of this optimal length can be expected for waveguide size fluctuations that are at the lower limit of standard UV lithography.

Minimization of wall roughness requires complex nanotechnology steps. While this limitation is one of the main limiting factors to obtain efficient photonic waveguides, the PECVD process permits the production of homogenous layers with good uniformity especially in small areas, just like in this case study. The simulation is directed to describe how the texture of the waveguide walls will affect the optimal length of the waveguide for a 3  db splitter function, analysing a waveguide with perfectly flat walls and comparing with a roughness of 10 nm, 50 nm and the worst case with 100 nm layer roughness. In the coupler design, the two waveguide cores have an average width of 1 μm, and are separated by 0.5 μm, but along the coupling region the interfaces between core and cladding are designed with imperfections. The deviation of the interfaces from their mean positions is described by a random function representing the sidewall roughness introduced by the lithographic process. The simulation monitors the transmitted power along the pathway of the two splitter arms and calculates the optimal waveguide length necessary to obtain the 3 dB splitter function. In Figure 3 is depicted the simulation domain for a coupler with ideally smooth waveguides and with a roughness wall of 50 nm, outlining the different propagation behaviour induced by the roughness in the waveguide walls. While in the smooth waveguide structure the light splitter divides exactly in two equal parts, for an optimal coupling length, as described by the theory [28], the degradation of the splitter efficiency is not only limited to a different optimal length of the coupling region, but also includes a strong attenuation of the output light and an overall degradation of the device efficiency. In Table 1 is reported the calculated optimal length of the coupler for different dimensions and separation of the waveguides with different wall roughness. All the simulations are performed with a wavelength of 1550 nm.

We have observed in our simulations that when the roughness is too high (up to 100 nm) it is not possible to obtain useful coupling between the two waveguides. This is due to the fact that a large sidewall roughness introduces backscattering effects and radiation losses [29] limiting the maximum propagation of the signal to lengths that are smaller than the minimum needed to support the coupling exchange.

For lower levels of wall roughness (up to 10 nm) there is little difference from the optimal condition. For intermediate levels, coupling is only possible when the separation between the two arms is lower than 500 nm. The special case of the monomodal waveguide presents a small tolerance to the wall irregularity, producing a strongly attenuated output even for the case of 10 nm roughness.

thumbnail Fig. 2

Optimal length for an ideal 3B a-Si:H waveguide coupler with SiO2 cladding, with increasing waveguide distance between the two coupling arms. Calculation is based on the Marcatili Coupling coefficients described in equations (1)(5).

thumbnail Fig. 3

Simulation domain for an ideal directional splitter (a), an equivalent device with accentuated wall roughness, described by a random function (b) and the correspondent beam propagation simulations (c,d). Separation between the coupling arms is 50 μm in both cases, bit the sidewall roughness is causing losses in the guided node propagation.

Table 1

calculated optimal length of the coupler for different dimension (W) and separation (D) of the waveguides and with different wall roughness. Light wavelength is 1550 nm.

2.2 The MMI splitter

Multimode interference structures are able to provide two identical electromagnetic field profiles when operating as a 3 dB power splitter. Device integration of one or many of these structures are attainable given minute dimensions and design simplicity.

The operation of MMI devices relies on the self-imaging principle which states that single or multiple images, of a given input field profile, are replicated periodically in space as the electromagnetic field propagates through the waveguide. These devices usually consist on two main waveguiding sections: − the access waveguides (input and output), that are often single mode structures, and the wider MMI guiding structure. Moreover, being the actual device a 3D structure, an analysis of the propagating modes within the multimode section requires proper handling methods, that convert a complex 3D dielectric structure into a simpler 2D equivalent model.

There are mainly two of these problem simplifying techniques, namely the Marcatili [26] and the Effective Index [30] methods. Both analytical approximation methods can provide a precise enough 2D model for further study of the modes propagating characteristics, in a multimode waveguide. Nevertheless, Marcatili's method is more adequate to be applied on channel waveguides, which delegates the Effective Index Method (EIM) for rib and more complex structures.

The obtained 2D structure is then characterized by a core refractive index ncore, of a given width W M , and a substrate/cladding effective refractive index nclad. To substantiate our description, a propagating modes analysis has been conducted on a structure with the following parameters:

  • Operating wavelength, λ = 1550 nm;

  • Core width, W M  = 2.1μm;

  • Core refractive index, ncore = 3.65 (a-Si:H refractive index at the operating wavelength);

  • Substrate/cladding effective refractive index, nclad = 1 (refractive index of air).

Figure 4 presents the modes supported by a structure characterized by previous parameters. The results obtained reflect only the transverse magnetic (TM) even modes, for those are the modes required by the intended operation of the MMI device, as part of our already mentioned plasmonic detection platform.

This structure supports five lateral TM even modes (m = 0, … , n − 1) at the free space operating wavelength λ 0 = 1550 nm. The electromagnetic energy profile, at a given plane along its propagation direction, results from a superposition of all supported modes. Its dispersion equation relates the lateral wavenumber k my and the propagation constant β m , with the core refractive index ncore, as described in the following:(6) with , is the lateral standing wave condition and W eff is the effective width of the multimode waveguide section. The W eff considers the penetration of the propagating field beyond the boundaries imposed by the side walls of the guiding structure. To each propagating mode lateral penetration (polarization dependent), is associated a Goos-Hähnchen shift in the propagating direction. Nevertheless, when considering high dielectric contrast structures, this shift is practically non-existent, as one may infer through the analysis of equation (7), and this width can be approximated by the effective width of the fundamental mode (W eff   ≅ W e0).(7)where σ = 0 or 1 for TE or TM polarized propagating fields. By simplifying equation (6) and assuming that , one may conclude that the propagation constant of a mode βm (m = 0, 1, 2, ), propagating in a high contrast step index multimode device, shows an approximate quadratic dependence to the mode number m [31].(8) Defining the beat length (L π ) between the two lowest order modes propagating in a step index multimode waveguide as:(9)then, propagation constants spacing may be written in terms of L π as:(10)

Hence, single mirrored and direct images from the input field profile, can be respectively obtained at 3Lπ and 2(3Lπ), while two-fold images are formed at 1/2(3Lπ) and 3/2(3Lπ). Single images are, approximately, the same amplitude as the input EM field and each of the two-fold images is affected by a 3 dB distribution factor in each output waveguide, thus offering the ideal conditions for a power splitter device.

Moreover, quarter length MMI sections can be designed through the usage of an interference mechanism designated as symmetric interference. This mechanism relies on avoiding the excitation of odd order modes, within the multimode section of the structure. This can be accomplished by positioning the input waveguide, with a launching symmetric field profile (e.g. a Gaussian beam or a fundamental mode even profile), at the width center of the MMI section [32]. This will result in N linear combinations of the input profile beam located at:(11)where p ≥ 0, N ≥ 1, p and N are integers with no common divisor and p/N represents 1st, 2nd, …, nth single and N-fold images at location L; a denotes the type of coupler (for a 1 × N structure, a = 4).

Like in the previously analysed case of the directional coupler, lithographic mask resolution has an adverse impact on output waveguides power imbalance and may lead to practical results different from the optimal condition described by the theory. The simulation considers two increasing roughness levels of the MMI lateral walls and analyses how far the MMI output will be driven from the optimal condition of a perfectly flat wall. In Figure 5 is reported the simulation of the MMI operation with different wall roughness. In the ideal situation of an MMI structure with perfectly flat walls, the splitter, dimensioned as indicated by the MMI theory, produces two perfectly equal output branches. By increasing the wall roughness, we may see a reduction in the output intensity and an increasing of the power unbalancing. In Figure 6 is depicted power monitoring as a function of the wall roughness of the two output channels. It may be observed here that power unbalancing does not have a monotonic variation with increasing wall roughness, but it remains limited to acceptable values up to 40 nm. These results demonstrate, when compared with the standard directional coupler, an additional tolerance of the MMI coupler efficiency to the quality of the deposition process.

thumbnail Fig. 4

Top: − Supported TM even modes (calculated with the help of Matlab) by a 2.1 μm wide a-Si:H waveguide, surrounded by air and at the 1.55 μm operating wavelength. TM polarization is imposed by the SPR phenomenon and by using symmetric restricted interference (only even modes are excited) in the MMI device, enables the design of multimode sections with one quarter of the length. Bottom: profiles of each of the propagating modes along the 2.1 μm wide a-Si:H waveguide. The total EM field profile propagating in the a-Si:H waveguide is a superposition of all modes (not represented). Also, one may observe a higher penetration depth beyond the a-Si:H/air interface on the last (5th) mode, which is due to the proximity of the mode and cut-off wavenumbers.

thumbnail Fig. 5

Simulation of the MMI structure with different standard deviations of a random distribution of defects along the edge walls of the device; from left to right: − ideal geometry, 10nm and 40 nm; operating wavelength is 1550 nm. Top row: − geometry and refractive indices of the devices. Bottom row: − power distribution inside the device and monitoring of input and each output powers. As the standard deviation of random defects increases, so does the power imbalance between the output waveguides.

thumbnail Fig. 6

Power monitoring (values normalized to the input power value) as a function of the wall roughness of the two MMI output channels (a) power evolution verified at each of the output waveguides as the standard deviation of the random distribution of defects is iterated from 1 to 40 nm; (b) evolution of power imbalance between the output waveguides as the standard deviation of the random distribution of defects is iterated from 1 to 40 nm (in this particular case of the independent random distribution of defects in each longitudinal edge of the MMI device, the power imbalance “re-zeroes” at the ∼30 nm standard deviation mark).

2.3 Plasmonic interferometer sensor

In order to further illustrate the potential of amorphous silicon materials, produced by PECVD, for building photonic sensor devices, we have used FDTD simulations to study the performance of the waveguide plasmonic interferometer. The sensor layout, as proposed by Debackere et al. [33], is presented in Figure 7a. If the coupling conditions are appropriate, the waveguide mode excites two surface plasmon polariton (SPP) modes, one on each side of the metal film. Both SPPs propagate to the end of the metal film and re-excite the waveguide mode. The transfer of energy from the SPP modes to the output guided mode is strongly dependent on the SPPs phase difference. The guided mode power is maximized when interference occurs with the SPPs in phase and minimized when occurs in phase opposition. The SPPs phase difference is given by equation (12):(12)

where L is the length of the metal film, β1SPP is the SPP propagation constant on the interface between the metal and the sensing region and β2SPP is the SPP propagation constant on the opposite metal interface. The propagation constant is dependent on the electric permittivity of the materials, which in the semi-infinite media approximation is given by [20]:(13)where εm is the complex permittivity of the metal, εd the permittivity of the material that interfaces the metal, ω the angular frequency and c the velocity of light. The key point is that while β2SPP is constant in our setup, since the relevant refractive indexes are invariable, β1SPP depends on the electric permittivity of the sensing region. Variation of the refractive index in this region is reflected both on β1SPP, and on the SPP phase difference and ultimately on the waveguide output power.

In our study the original c-Si waveguide core was replaced by a-Si:H. In Figure 7b we can observe that the output power drops considerably as a function of the refractive index of the sensing region, thus providing an effective sensing mechanism [22]. The minimum output power occurs exactly when the refraction index of the sampling medium is such that Δφ = π. Note that the length of the interferometer L, also affects the phase difference, we have set L = 6.2 µm, but it could be changed to tune the phase opposition to a different refractive index. In this figure we also present the performance of the interferometer using a low and high density defect model for a-Si:H [18], the output is very similar using both models. The device's transversal H field is presented in Figure 8, where we can clearly see the constructive and destructive interference conditions obtained by changing the refractive index of the sensing region. The simulations indicate that this type of device can be successfully produced employing a-Si:H and other PECVD thin film materials.

thumbnail Fig. 7

Inteferometric waveguide sensor structure (a). The simulation considers the following components: a-SiH (red), SiO2 (green), gold (yellow), water (blue), analyte solution (grey). If the coupling conditions are appropriate, the waveguide mode excites two SPP modes, one on each side of the metal film. Both SPPs propagate to the end of the metal film and re-excite the waveguide mode, whose intensity depends on the phase difference between the two SPPs. (b) While no significative dependence on the a-Si:H density of states can be observed, the sensor output power depends on the refractive index of the analyte.

thumbnail Fig. 8

Simulation of the EM wave propagation in the interferometric plasmon waveguide. When the interference of the plasmonic modes at the output is destructive (analyte refractive index n = 1.225) the power output is strongly reduced (a) while a constructive interference (analyte refractive index n = 1.13) produces a measurable output (b). Light wavelength is 1550 nm.

3 Discussion

A discrepancy between the simulation and the experimental measurement of waveguide photonic device performance has been reported by several authors, and the excess loss attributed to the sidewall roughness of SOI waveguides [3436]. Modelling studies of the roughness as a quasi-grating sidewall shape report that a grating period of 100 nm remains within tolerance limits for 1550 nm wavelength applications [37]. Nevertheless, recent results about silicon waveguides report signal attenuations below 3  dB for roughness larger than 30 nm [38], in agreement with our simulation results. While requirements for high speed silicon photonics applications are much more restrictive, an attenuation of this order of magnitude is tolerable in a sensing application structure, mainly if accompanied by a clear advantage in the production costs.

The impact of irregularities in the waveguide walls, expected by using PECVD production technique, has been outlined by simulating the devices in different conditions. While the overall efficiency foreseen by the simulation is, as expected, lower than the optimal behaviour that can be obtained by standard crystalline silicon photonics, the a-Si:H MMI splitter produced by PECVD shows an interesting tolerance to the wall roughness up to 40 nm. FDTD simulations shows that plasmonic effects can be excited in the interferometric waveguide structure, allowing a sensing device with enough sensitivity to support the functioning of a bio sensor for high throughput screening system.

4 Conclusion

It has been presented a simulation study about a photonic sensing device composed of a splitter and an interferometric plasmonic waveguide, entirely based on amorphous silicon deposited by PECVD method and outlining the effects of the waveguide sidewall roughness as a major negative effect caused by deposition imperfections. The simulation results point out that the PECVD deposition technique is a reliable option for the overall sensor system to be produced as a low-cost system. Whenever the simulation results are to be confirmed by an experimental prototype, this will open the possibility to extend the system project to larger area geometries, to multiplexed analysis of multiple biomarkers and to alternative methods of output reading, capable of improving the tolerance to fabrication defects.

Author contribution statement

Paulo Lourenço, as a PhD student, has elaborated the MMI analysis under the supervision of Manuela Vieira. João Costa has been committed with the analysis of the interferometers while Alessandro Fantoni have been studying the directional coupler. The overall synthesis of the manuscript has been edited by Alessandro Fantoni.

Acknowledgments

Research supported by EU funds through the FEDER European Regional Development Fund and by Portuguese national funds by FCT −Fundação para a Ciência e a Tecnologia with projects PTDC/NAN-OPT/31311/2017, UID/EEA/00066/2019. and by IPL IDI&CA/2018/aSiPhoto.

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Cite this article as: Alessandro Fantoni, João Costa, Paulo Lourenço, Manuela Vieira, Computer simulation study about the dependence of amorphous silicon photonic waveguides efficiency on the material quality, Eur. Phys. J. Appl. Phys. 90, 30502 (2020)

All Tables

Table 1

calculated optimal length of the coupler for different dimension (W) and separation (D) of the waveguides and with different wall roughness. Light wavelength is 1550 nm.

All Figures

thumbnail Fig. 1

Plasmonic interferometer composed by an a-Si:H Waveguide covered by a thin gold layer. The sensing analysis is performed by equally splitting the input light into two arms, allowing the sensor to be calibrated by a reference arm. The 1 × 2 power splitter can be built upon two configurations: (a) Based on a directional coupler. (b) Based on multimode interference (MMI).

In the text
thumbnail Fig. 2

Optimal length for an ideal 3B a-Si:H waveguide coupler with SiO2 cladding, with increasing waveguide distance between the two coupling arms. Calculation is based on the Marcatili Coupling coefficients described in equations (1)(5).

In the text
thumbnail Fig. 3

Simulation domain for an ideal directional splitter (a), an equivalent device with accentuated wall roughness, described by a random function (b) and the correspondent beam propagation simulations (c,d). Separation between the coupling arms is 50 μm in both cases, bit the sidewall roughness is causing losses in the guided node propagation.

In the text
thumbnail Fig. 4

Top: − Supported TM even modes (calculated with the help of Matlab) by a 2.1 μm wide a-Si:H waveguide, surrounded by air and at the 1.55 μm operating wavelength. TM polarization is imposed by the SPR phenomenon and by using symmetric restricted interference (only even modes are excited) in the MMI device, enables the design of multimode sections with one quarter of the length. Bottom: profiles of each of the propagating modes along the 2.1 μm wide a-Si:H waveguide. The total EM field profile propagating in the a-Si:H waveguide is a superposition of all modes (not represented). Also, one may observe a higher penetration depth beyond the a-Si:H/air interface on the last (5th) mode, which is due to the proximity of the mode and cut-off wavenumbers.

In the text
thumbnail Fig. 5

Simulation of the MMI structure with different standard deviations of a random distribution of defects along the edge walls of the device; from left to right: − ideal geometry, 10nm and 40 nm; operating wavelength is 1550 nm. Top row: − geometry and refractive indices of the devices. Bottom row: − power distribution inside the device and monitoring of input and each output powers. As the standard deviation of random defects increases, so does the power imbalance between the output waveguides.

In the text
thumbnail Fig. 6

Power monitoring (values normalized to the input power value) as a function of the wall roughness of the two MMI output channels (a) power evolution verified at each of the output waveguides as the standard deviation of the random distribution of defects is iterated from 1 to 40 nm; (b) evolution of power imbalance between the output waveguides as the standard deviation of the random distribution of defects is iterated from 1 to 40 nm (in this particular case of the independent random distribution of defects in each longitudinal edge of the MMI device, the power imbalance “re-zeroes” at the ∼30 nm standard deviation mark).

In the text
thumbnail Fig. 7

Inteferometric waveguide sensor structure (a). The simulation considers the following components: a-SiH (red), SiO2 (green), gold (yellow), water (blue), analyte solution (grey). If the coupling conditions are appropriate, the waveguide mode excites two SPP modes, one on each side of the metal film. Both SPPs propagate to the end of the metal film and re-excite the waveguide mode, whose intensity depends on the phase difference between the two SPPs. (b) While no significative dependence on the a-Si:H density of states can be observed, the sensor output power depends on the refractive index of the analyte.

In the text
thumbnail Fig. 8

Simulation of the EM wave propagation in the interferometric plasmon waveguide. When the interference of the plasmonic modes at the output is destructive (analyte refractive index n = 1.225) the power output is strongly reduced (a) while a constructive interference (analyte refractive index n = 1.13) produces a measurable output (b). Light wavelength is 1550 nm.

In the text

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