Efficiency of evanescent excitation and collection of spontaneous Raman scattering near high index contrast channel waveguides

We develop and experimentally verify a theoretical model for the total efficiency η0 of evanescent excitation and subsequent collection of spontaneous Raman signals by the fundamental quasi-TE and quasi-TM modes of a generic photonic channel waveguide. Single-mode silicon nitride (Si3N4) slot and strip waveguides of different dimensions are used in the experimental study. Our theoretical model is validated by the correspondence between the experimental and theoretical absolute values within the experimental errors. We extend our theoretical model to siliconon-insulator (SOI) and titanium dioxide (TiO2) channel waveguides and study η0 as a function of index contrast, polarization of the mode and the geometry of the waveguides. We report nearly 2.5 (4 and 5) times larger η0 for the fundamental quasi-TM mode when compared to η0 for the fundamental quasi-TE mode of a typical Si3N4 (TiO2 and SOI) strip waveguide. η0 for the fundamental quasi-TE mode of a typical Si3N4, (TiO2 and SOI) slot waveguide is about 7 (22 and 90) times larger when compared to η0 for the fundamental quasi-TE mode of a strip waveguide of the similar dimensions. We attribute the observed enhancement to the higher electric field discontinuity present in high index contrast waveguides. ©2015 Optical Society of America OCIS codes: (130.0130) Integrated optics; (170.5660) Raman spectroscopy; (130.6010) Sensors; (230.6080) Sources. References and Links 1. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). 2. E. Ryckeboer, R. Bockstaele, M. Vanslembrouck, and R. 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Introduction
Integrated photonics has been established as a very promising platform for lab-on-a-chip sensing applications [1].An emergent type of photonic sensors is based on light-matter interaction with the evanescent wave of nanophotonic waveguide modes.This has led to the realization of on-chip absorption spectroscopy [2] and spontaneous Raman spectroscopy [3].These spectroscopic sensors, particularly Raman sensors, allow for direct detection and analysis of the target molecules by measuring their distinctive spectrum [4].In this paper we consider Raman sensors in which the molecules under study are evanescently excited through a high-index channel waveguide and the corresponding Raman signal is evanescently collected using the same single-mode photonic waveguide.This technique leads to a signal much stronger than collected by Raman microscopes, thanks to a long interaction length and the enhancement effects inherent to high-index-contrast waveguides [5].In the proposed technique, a single-mode waveguide carries the pump beam and also collects the Stokes light with the smallest possible étendue.Hence, it opens up the potential of integration with very compact photonic components, such as an Arrayed Waveguide Grating (AWGs) acting as an on-chip spectrometer [6].Furthermore, these nanophotonic chips are mass-producible at the wafer scale using CMOS-compatible process steps, which will pave the way towards low-cost, high performance and compact point-of-need tools for Raman analysis of chemical and biological materials.
To achieve the best performance of these sensors, it is crucial to optimize the various design parameters of the waveguide, such as geometry, dimensions, polarization of the mode and the index contrast.The corresponding problem can be modelled as a scattering problem or as an absorption/re-emission problem near a waveguide.The absorption and emission of light by the particles lying close to planar dielectric waveguides is studied extensively in the context of light sources and sensors [7][8][9][10].In this paper we complement these studies in the context of channel waveguides that are used extensively in integrated photonics.We will study the overall conversion efficiency (η 0 ) which is defined as the ratio between the total Stokes power (P wg ) collected (in both directions) by a waveguide of unit length to the pump power (P in ) in the same waveguide for unit scattering cross section when the particles are distributed uniformly in the vicinity of the waveguide with unit concentration [3].We will elaborate the preliminary theoretical analysis and experimental results reported earlier [3, 10 and 11].In particular, we will experimentally validate the key equation for η 0 in an absolute manner and investigate how η 0 is affected by the polarization of the mode, the refractive index contrast, and the waveguide geometry.
In section 2, we outline the experimental methodology and compare the experimental results with the theoretical values of η 0 obtained for both quasi-TE (henceforth, TE) and TM (henceforth, TM) polarizations for silicon nitride (Si 3 N 4 ) strip [12] and slot [13] waveguides of several widths.In section 3 we discuss the experimental results with the help of more detailed simulation results.In section 3 we also extend the theoretical analysis to silicon-on-insulator (SOI) waveguide platform [14] and an emerging waveguide platform based on Titanium oxide (TiO 2 ) [15,16] to assess their performance as evanescent sensors or light sources.The derivation of the key equation for determining η 0 is elaborated in the Appendix.Fig. 1.Schematic of a dielectric a) strip and b) slot waveguides defined by a core of higher refractive index (Si3N4, TiO2 or silicon) patterned on a lower index bottom cladding (typically silicon dioxide).The scattering particles are assumed to be embedded with a uniform density in the upper cladding (colorless region).A particle at position r0 is shown for both cases for theoretical analysis in the Appendix.

Measurement of η 0 for strip and slot Si 3 N 4 waveguides
We consider a nanophotonic waveguide that is translationally invariant along its length L (z-axis in Fig. 1) and assume that the scattering particles with cross-section σ lie uniformly in the upper cladding with a density ρ.As discussed in [3], to measure the conversion efficiency η 0 for several waveguides it is convenient to define the guided power efficiency ζ (L) as the ratio of the spontaneous Stokes power collected by the waveguides P col. to the transmitted pump power P tx .The quantity η 0 is related directly to ζ (L) via: Where, on the right hand side, we have added a factor of ½ to account for the backward propagating signal that is not collected in the current configuration of our experimental setup.Δα= α(ω p ) -α(ω s ) is the difference between the waveguide losses α(ω p ) and α(ω s ) for pump and Stokes frequencies respectively.The term in brackets converges to L when Δα→0, as can be seen by expanding the exponent.The contribution due to the quantity Δα is generally small for small Stokes shifts and shorter waveguide lengths.
The measurement setup is similar to that reported in [3].A tunable Ti-Sapphire CW laser emitting at 785 nm is coupled to the waveguide by end-fire coupling using an aspheric lens of effective focal length 8 mm (NA=0.5).The incident polarization is set to the TE or TM mode of the waveguide using a half-wave-plate.The Raman signal (Stokes) collected in the waveguide and co-propagating with the pump is then collimated out of the chip via an achromatic objective (50x, NA=0.9).The Raman signal is filtered from the strong pump using an edge filter blocking light below 790 nm.The Raman spectrum is then focused to a singlemode optical fiber (cutoff =770 nm) using a parabolic mirror of 15 mm effective focal length (NA=0.2) and measured using a commercial spectrometer (AvaSpec-ULS2048XL).Because of the edge filter, the pump transmission is optimized and measured at 800 nm wavelength at the position of the spectrometer.The pump transmission at 800 nm is verified to be practically the same as for the pump wavelength 785 nm without the filter.An additional polarizer at the signal collection side is used so as to only collect light of a given polarization mode.
The input laser power is set at 40 mW, with an estimated 8±1 dB coupling loss per chipfacet.Si 3 N 4 strip waveguides of widths w = 550 nm and w = 700 nm, as well as Si 3 N 4 slot waveguides with slot width s =150 nm and total waveguide width w =700 and w = 800 are studied experimentally.The waveguides are wound as spirals (typical footprint: 800 μm x 500 μm) with bend radius 50 μm and 150 μm for strip waveguides and slot waveguides respectively, so that the bend losses are negligible.Fig. 2. Typical evanescently measured Raman spectra (normalized to 819/cm peak from slot waveguide) of IPA after background subtraction.The case shown is for excitation and collection by a TE-mode, pump power of 40 mW, 8 ± 1 dB coupling losses per facet and integration time of 5 s.The black spectrum is obtained using a w =700 nm slot waveguide with s = 150 nm.The blue spectrum is obtained by using 700 nm wide Si3N4 strip waveguides and is shifted vertically for clarity (with blue axes).We observe an enhancement of the signal by more than a factor six as expected theoretically for TE modes.
Si 3 N 4 waveguide circuits used for the experiments were fabricated on 200 mm silicon wafer containing a stack of 2.2 μm -2.4 μm thick high-density plasma chemical vapor deposition (HDP-CVD) silicon oxide (SiO 2 ) and 220 nm thick plasma-enhanced-CVD (PECVD) Si 3 N 4 [12].The structures were patterned with 193 nm optical lithography and subsequently etched by the fluorine based inductive coupled plasma-reactive ion-etch process to get the final structure.
Pure Isopropyl Alcohol (IPA) with a density ρ =7.87x10 21 molecules/cm 3 is used as an analyte to compare the Raman signal strength for several waveguide geometries.IPA droplets are drop-casted with a pipette on top of the waveguides and cover the entire waveguide region of interest as seen with a camera from top.The Raman spectra are extracted by fitting the background spectrum with truncated polynomials as explained in [3,17] and then subtracting it.Figure 2 shows a typical Raman spectrum of IPA obtained using such a procedure for w = 700 nm strip waveguide and w = 700 nm slotted waveguides with s =150 nm.As a main highlight, we observe enhanced signal for slotted waveguides, while we can clearly distinguish all the major peaks of IPA in both spectra.The IPA peak corresponding to the C-C-O vibration at 819 cm -1 wavenumber (839 nm, for 785 nm pump) is used as reference to compare the values of η 0 for several waveguides.The η 0 is estimated by first converting the total analog to digital converter (ADC) counts to the corresponding power in units of Watts.This is done by dividing the ADC counts with the corresponding integration time (typically 1-5 seconds) and the measured sensitivity (19x10 6 counts/ms/μW) of the spectrometer near the wavelength corresponding to the IPA peak.We take σ = 7.9x10 -31 cm 2 /sr/molecule for the 819 cm -1 line which is calculated by using the value measured at 488 nm in [18] and applying the 1/λ 0 4 dependence of the scattering cross-section [4].Four chips containing different waveguide dimensions and geometries were diced from different locations on a wafer and measured three times for the experiments.Figure 3 shows the experimental data for the guided power efficiency ζ(L) normalized with ρσ, the product of density and the cross section of IPA.The normalization with ρσ renders the curve directly related to η 0 .A considerable spread in the experimental values of ζ(L) can be observed for a given waveguide length.This spread comes mainly from variation of the waveguide properties among the several waveguides on several chips and from the variation of the transmitted power caused by mechanical instability of the stages used for coupling, shot-noise of the laser and laser power drifts.The variation is particularly high for slotted waveguides due to variability of the slot width during the etching process.Variations in the thickness of SiO 2 and Si 3 N 4 across the wafer during deposition also leads to a spread in the observed ζ(L).
Another important source of variation is side-wall roughness of the waveguides due to imperfect waveguide etching which has not been taken into account in our theory, but which may affect the coupling of the Raman signal to the waveguide.
We implemented a Least Square Error (LSE) fitting algorithm to compare the measured data with the theoretical model.The average guided power efficiencies ζ(L) can be fitted with the model described by Eq. ( 1) with mean R 2 value of 0.96 indicating a good fit [19].The LSE fit yields estimated values of η 0 very close to the theoretically predicted values.In Fig. 4, the estimated values of η 0 obtained for various waveguide geometries and polarizations are compared with the theoretically determined values using Eq. ( 13) in the Appendix.The theoretical curves of η 0 as a function of waveguide width w are within the error margin of the experimental data for both polarizations and the waveguide types studied.Assuming statistically independent measurement errors, the total experimental error Δ tot is estimated by: where, Δ(σ)( = ± 10% ) is the error in the cross-section value [18], Δ(P tx ) (= ± 20%) is the error in the measurement of transmitted power, Δ(P col ) (= ± 25%) is the error in the measurement of the sensitivity of the spectrometer.The last term in Eq. ( 2) approximates the error due to the fit [19].
For 700 nm wide Si 3 N 4 strip waveguides, the average efficiency η 0 for TM polarization is approximately 2.5 times larger than for TE excitation.For 700 nm wide Si 3 N 4 slot waveguides (s = 150 nm) excited with TE polarized light, about 6 fold enhancement of the estimated η 0 compared to strip waveguides of the same width.Note that the wider waveguides lead to reduced η 0. In the next section, we will investigate and explain these results using the model just validated.

Analysis of η 0 for Si 3 N 4, TiO 2 and SOI channel waveguides
Having established the relevance of our model, we elaborate the experimental results obtained in the previous section with the theory and extend the theoretical analysis to TiO 2 and SOI waveguides.To be in line with the experimental parameters used for the experiments with the Si 3 N 4 waveguides, we perform simulations with an excitation wavelength λ 0 = 785 nm.The refractive indices of the core , SiO 2 undercladding and IPA upper cladding are respectively taken to be n sin = 1.89, n ox = 1.45 and n ipa = 1.37.In case of SOI waveguides, λ 0 = 1550 nm was chosen because of a low optical absorption.The refractive index of silicon is taken to be n si =3.44.As for TiO 2 waveguides, the refractive index n TiO2 = 2.4 reported in [15] is used.For the TiO 2 case we study η 0 at λ 0 = 785 nm and also at λ 0 = 1064 nm.The latter choice of λ 0 corresponds to a material wavelength comparable to that of SOI (at λ 0 = 1550 nm) and Si 3 N 4 (at λ 0 = 785 nm).The aforementioned choice of the comparable material wavelengths ensures similar fabrication constraints and practical waveguide dimensions for single mode operation.The height of the waveguides is fixed at h = 220 nm for all waveguide types, which is a typical deposition thickness during the fabrication of Si 3 N 4 and TiO 2 waveguides, and also a typical silicon thickness for SOI waveguides.The conversion efficiency η 0 was calculated using Eq. ( 13) with COMSOL finite elements mode solver.In Fig. 5 we show theoretical conversion efficiency η 0 for randomly distributed particles lying uniformly in the upper cladding of Si 3 N 4 , TiO 2 and SOI strip waveguides of several waveguide widths w corresponding to the single mode operation of the waveguides.As the waveguide width is increased, initially η 0 increases to a maximum corresponding to an optimal mode confinement in the core and the cladding.Once this condition is reached, further increase in the width leads to a decrease in η 0 owing to more confinement of the modal field in the core.We observe this irrespective of the waveguide type, polarization or core material.This is because the increase in the waveguide width increases the confinement of the mode in the core thereby reducing the interacting field in the upper cladding region of the analytes.For strip waveguides, TM polarization generally performs better than TE polarized modes and its sensitivity to the waveguide width is smaller.The discontinuity of the electric field at the core -top cladding interface of the TM modes leads to higher field at the analyte location.The increased field and larger interaction volume present on the top cladding for TM modes (owing to high width-height aspect ratio) results in higher η 0 .Since the electric field in the TM mode is discontinuous in the perpendicular direction, only substantial changes in waveguide height h vary the TM field significantly.For a typical 600 nm wide strip waveguide, TM excitation in comparison to the TE excitation, leads to more than 2.5, 4 and 5 times more efficiency respectively for Si 3 N 4 (at λ 0 = 785 nm), TiO 2 (λ 0 = 1064 nm), and Si (λ 0 =1550 nm) waveguides.
In Fig. 6, η 0 for slotted waveguides with various slot widths s = 10 nm, 50 nm, and 150 nm, and waveguide widths w (inclusive of the slot) is shown for Si 3 N 4 , TiO 2 and SOI waveguides.In case of TE polarized modes, slotted waveguides generally perform much better than strip waveguides and the value of η 0 increases as s decreases.This can be attributed to the enhancement of the TE-field in the slot region as s is decreased.However, there is an optimum s whence η 0 starts to decrease.This originates from a reduction in the interaction volume within the slot region as s is decreased.The optimum s is near 50 nm, 30 nm and 10 nm for respectively Si 3 N 4 (operating at λ 0 = 785 nm), TiO 2 waveguides (λ 0 =1064 nm) and SOI waveguides (λ 0 =1550 nm).As expected, due to the continuity of the electric field, the field enhancement in the slot is much less in case of TM polarization (Fig. 7); hence, the effect of s is not significant in case of TM polarization.
In Fig. 8 we compare the conversion efficiency η 0 of TiO 2 waveguides for λ 0 = 785 nm and λ 0 = 1064 nm.η 0 is generally higher for λ 0 = 1064 nm because the field is confined more to the cladding where analyte is located.Due to a shorter material wavelength, the modal field is more confined to the high index TiO 2 region when excited at 785 nm, compared to excitation at 1064 nm.Consequently, the optimal slot width for TiO 2 (λ 0 = 785 nm) is narrower: about 10 nm compared to about 30 nm λ 0 = 1064 nm.For λ 0 = 785 nm η 0 also increases weakly for wider slots (such as 150 nm > s > 100 nm).This can be understood with the help of Fig. 7.
In Fig. 9, we show the conversion efficiency η 0 of slot waveguides with s = 100 nm, as a function of the total waveguide width w for different material systems.We observe a strong enhancement in η 0 with the increase in the index contrast of the waveguide.Higher index contrast leads to a lower mode area, higher modal field intensity and higher field discontinuity, thus giving rise to a stronger evanescent field for interaction.From the simulation data presented in Fig. 5 and Fig. 9, we can conclude that a slot of width s = 100 nm leads to about 90, 20 and 7 fold higher efficiency respectively for SOI (excited at λ 0 = 1550 nm), TiO 2 (λ 0 = 1064 nm), Si 3 N 4 (λ 0 = 785 nm) slot waveguides of w = 600 nm compared to the strip waveguide of the same dimension.When comparing different waveguide systems operating at different excitation wavelengths, however, the corresponding change in the scattering cross-section also has to be taken into account.As the scattering cross-section varies approximately as 1/λ 0 4 [4], the total collected power also varies in a similar manner.We can include this correction factor and compare the respective net efficiencies for slot waveguides (w = 600 nm and s = 100 nm), Si 3 N 4 waveguides (λ 0 = 785 nm), TiO 2 waveguides (λ 0 = 1064 nm) and the SOI waveguides (λ 0 = 1550 nm).After the 1/λ 0 4 correction at these respective operating wavelengths, SOI is about twice as efficient, and TiO 2 is about 30% more efficient than Si 3 N 4 waveguides owing to their higher index contrast.Note that in Fig. 6 and Fig. 9, η 0 > 4π sr, for SOI waveguides in a certain range of waveguide dimensions.This is a result of high importance.To appreciate this, we apply Eq. ( 12) for free space beams with η 0 = 4π and integrate dz arbitrarily.This is possible in an ideal situation when we can collect the scattered light perfectly from total solid angle of 4π sr, and if particles are excited with a diffraction-less beam so that dz in Eq. ( 12) can be integrated arbitrarily.Thus, we conclude that due to enhanced excitation and emission (Purcell enhancement) near the high index contrast waveguides, the overall efficiency of excitation and collection of a practical single mode waveguide can be higher than the ideal free space excitation and collection.For a realistic diffraction-limited free-space microscope system, however, the collection and excitation depth of focus are limited due an inverse relationship between the collection angle and the depth of focus.Hence, waveguide systems, in general, perform much better than realistic free space optical systems [5].
Although the current experiments and simulations are performed for IPA as the analyte in the upper cladding, the experimental and theoretical assessments have also been performed using other analytes such as acetone, dimethyl sulfoxide, their aqueous solutions and also clinically relevant solutions, such as glucose solution.If the upper cladding refractive index varies, the confinement properties of the waveguide mode also changes.Consequently, the conversion efficiency will vary via Eq.( 9) in the Appendix.Nevertheless, the qualitative conclusions discussed in this article are applicable for analytes with refractive index in the range 1.3-1.44.For analytes with refractive indices significantly different from IPA (n=1.37),η 0 can be calculated using Eq. ( 9) and Eq. ( 13).

Conclusion
Based on our measurements of evanescently collected Raman signals with Si 3 N 4 slot and strip waveguides, we have been able to validate a theoretical model for the collection efficiency of generic channel waveguides.Using the model, we have investigated the effect of waveguide geometry, core refractive index and polarization on the overall efficiency of evanescent excitation and collection of spontaneous Raman scattering.Due to enhanced excitation and emission near the high index contrast waveguides, the overall efficiency of excitation and collection of a practical single mode waveguide can be higher than the ideal free space excitation and collection.We have shown that when excited with TE polarized modes, slot waveguides have the highest efficiency.Specifically, we have shown that a slot of width s = 100 nm leads to approximately 90, 22 and 7 fold more efficiency respectively for SOI (excited at λ 0 = 1550 nm), TiO 2 (λ 0 =1064 nm), Si 3 N 4 (λ 0 =785 nm) for slot waveguides compared to the strip waveguides of the similar dimensions.In case of strip waveguides of typical dimensions, excitation and collection of Raman signal using TM polarized modes leads to higher collection efficiency than for TE polarization.Specifically, for 600 nm wide strip waveguides, TM excitation leads to more than 2.5, 4 and 5 times more efficiency for Si 3 N 4, TiO 2 and Si core compared to TE excitation.The investigated slot and strip waveguides for this result can be fabricated with current Deep-UV lithography technology.The results of this paper can also be used for integrated light sources based on evanescent interaction of the waveguide modes with quantum dots [20], rare-earth dopants [21] or III-V epitaxial layers [22].Finally, we conclude that owing to their higher index contrast, SOI waveguides excited with 1550 nm and emerging TiO 2 waveguide platform operating at 1064 nm are good candidates for evanescent Raman or fluorescence sensing and light generation.

Appendix: Theoretical model of scattering near waveguides
An electromagnetic field E induces a dipole moment d 0 = α E for a particle with scalar polarizability α.In the context of off-resonance, non-degenerate and adiabatic vibrational transitions corresponding to a pump frequency ω p and a Stokes frequency ω s , d 0 = α (ω p ,ω s ) E and α (ω p ,ω s ) is called Placzek polarizability [4].α (ω p ,ω s ) can be expressed in terms of the more familiar scattering cross-section σ using  , where 2πc/λ 0 ≈ ω p ≈ ω s and k ν =1.26 x10 23 C -2 V 2 m 2 is a universal constant related to the fine structure constant characterizing the coupling between electronic charge and the electromagnetic field [4].Then we can write: We assume that the particle is located at the position r 0 in the neighborhood of a channel photonic waveguide defined by a dielectric function ε(r) (Fig. 1).Consider its interaction with a guided mode traveling with group velocity v g and carrying a power P pump .For simplicity, we also assume that the waveguide core has a sufficiently small cross-section area so that only fundamental guided modes exist.If the power-normalized modal field distribution is e m (r), then the electric field component due to the mode is given by [23]:

Fig. 4 .
Fig. 4. The theoretical and experimental values of η0 obtained for a) TE modes and b) TM modes of Si3N4 waveguides.The markers represent the estimated experimental values obtained from the LSE fit of the experimental data of Fig 3 with Eq. (1).The error bars represent the measurement and estimation errors.Lines represent the theoretical curves obtained from Eq. (A.11).The red solid lines are the theoretical curve for slot waveguides with s = 150 nm.The blue and black dashed lines are the theoretical curves for TE and TM polarizations respectively for strip waveguides.Circle: TE polarization, strip waveguides.Left handed triangles: TM polarization, strip waveguides.Right handed triangles: TM polarization, slot waveguides.Square: TE polarization, slot waveguides.

Fig. 5 .
Fig. 5. Theoretical conversion efficiency curves for strip waveguides as a function of total waveguide width w for different material systems and the corresponding excitation wavelengths.Blue, red and magenta colors are respectively for SOI, TiO2 and Si3N4 cores.Solid lines: TE polarized excitation and collection.Dashed lines: TM polarized excitation and collection.Only the curve segments corresponding to single mode operation from the cut-off width are shown.Note that y-axis in log scale.

Fig. 6 .
Fig. 6.Theoretical conversion efficiency curves for slot waveguides for a) Si3N4 core with λ0=785 nm, b) TiO2 core with λ0 = 1064 nm c) silicon core with λ0=1550 nm.The solid lines: TE polarized excitation and collection.Dashed lines: TM polarized excitation and collection.Green, magenta and red lines are respectively for slot width of 150 nm, 50 nm and 10 nm.Only the curve segments corresponding to single mode operation from the cut-off width are shown.

Fig. 8 .
Fig. 8. Theoretical conversion efficiency curves for TiO2 a) strip b) slot waveguides with λ0=785 nm (dashed lines) and λ0=1064 nm (solid lines).Black and blue curves: strip waveguides.Green: slot waveguides, s = 150 nm.Magenta: slot waveguide, s = 50 nm.The values of η0 for TM polarization for all the slot widths (data not shown) do not differ significantly from the values for strip waveguides.Only the curve segments corresponding to single mode operation from the cut-off width are shown.

Fig. 9 .
Fig. 9.The conversion efficiency η0 of slot waveguides with s = 100 nm as a function of total waveguide width w for different material systems and corresponding excitation wavelengths.Note that y-axis in log scale.