We report on the first demonstration of guiding light in vertical slot-waveguides on silicon nitride/silicon oxide material system. Integrated ring resonators and Fabry-Perot cavities have been fabricated and characterized in order to determine optical features of the slot-waveguides. Group index behavior evidences guiding and confinement in the low-index slot region at O-band (1260–1370nm) telecommunication wavelengths. Propagation losses of <20 dB/cm have been measured for the transverse-electric mode of the slot-waveguides.
©2007 Optical Society of America
Integrated optical waveguides are essential elements in photonic integrated circuits (PICs) because they constitute photonic wires for light distribution among the different devices (switches, modulators, filters, add-drops, polarizers, attenuators, etc) contained in a PIC, and they are the basic building element for those devices. Conventional strip  and rib  waveguides are commonly used for those purposes. In these waveguides, the guiding mechanism is based on total internal reflection (TIR) in a high-index material (core) surrounded by a low-index material (cladding); the TIR mechanism can strongly confine light in the high-index material. The use of high-index-contrast material systems, such as Si/SiO2, has permitted the implementation of highly integrated photonic structures . There are also integrated waveguides non-based on TIR, such as hollow-core waveguides , which are employed to guide light in low-index materials. In these guides, interference is involved and therefore they are strongly wavelength dependent.
A recently introduced waveguide configuration called slot-waveguide  is able to guide and to confine light in a nanometric-size low index material by using TIR. A slot-waveguide consists of two strips of a high index material separated by a sub-micrometer low index region (slot region). The principle of operation of this structure is based on the discontinuity of the electric field at the high-index-contrast interface. For an electromagnetic wave propagating in the z direction as shown in Fig. 1(a), the electric field component of the quasi-TE mode (which is aligned in the x direction) undergoes a discontinuity that is proportional to the square of the ratio between the refractive indices of the high-index material [silicon nitride in Fig. 1(a)] and the low-refractive-index slot material [silicon oxide in Fig. 1(a)]. This discontinuity is such that the field is much more intense in the low-refractive-index slot region than in the high-index rails. Given that the width of the slot is comparable to the decay length of the field, the electrical field remains high across the slot, resulting in a power density in the slot that is much higher than that in the high index regions. The calculated optical field distribution of the structure shown in Fig. 1(a) for the quasi-TE mode is presented in Fig. 1(b) and it illustrates the field enhancement in the slot region. Since TIR mechanism is employed and there is no interference effect involved, the slot-structure exhibits very low wavelength sensitivity . Potential applications of devices built with slot-waveguides are, for example, high performance active devices [6–9] and ultra-sensitive sensors , where high light-matter interaction is desirable.
Hitherto, experimental demonstration of slot-waveguides has been achieved in the silicon/silicon oxide material system [11, 12]. Due to the high index contrast between Si and silicon oxide, strong optical confinement and high integration can be achieved. However, for the same reason, a Si/SiO2 slot-waveguide is more sensitive to interface roughness between the high-index-contrast materials, and the slot region must be on the order of 100 nm or less at telecomm wavelengths, which makes fabrication challenging. Silicon nitride has lower refractive index than Si but still higher than that of SiO2, allowing the implementation of photonic devices less sensitive to surface roughness and higher tolerance to dimensions deviations during fabrication while keeping a reasonable level of integration (small size). In particular, the use of silicon nitride instead of Si as the high-index material in a slot-waveguide would allow defining a wider slot region due to a weaker optical confinement in the rails as compared to Si. The possibility of using a larger slot region would facilitate filling the slot volume with, for example, non-linear or electroluminescent materials or fluids for sensing applications. In this work, we demonstrate for the first time slot-waveguide devices using silicon nitride and silicon oxide as the high-index and low-index materials, respectively, operating at O-band (1260–1370 nm) telecomm wavelengths.
A schematic cross-sectional view of the fabricated slot-waveguides is shown in Fig. 1(a). A 5-μm-thick bottom cladding layer of SiO2 was thermally grown on a Si wafer. Then, a 300-nm-thick silicon nitride layer was deposited by low pressure chemical vapor deposition (LPCVD). Slot-waveguide rings and Fabry-Perot resonators schematically illustrated in Fig. 2(a) and Fig. 2(b), respectively, were defined in the silicon nitride layer by using electron-beam lithography and inductively coupled plasma (ICP) etching. The radius of the ring resonators was 70 μm and different coupling distances (d) were considered. Fabry-Perot cavities consisted of a slot-waveguide of length Lcav = 140 μm flanked by two Bragg reflectors with different number of periods defined in a silicon nitride strip waveguide. Different slot widths (wslot) were also considered for both rings and Fabry-Perot devices. The width of the silicon nitride rails [see Fig. 1(a)] was kept to wrail= 400 nm. Finally, a 3-μm-thick top cladding SiO2 layer was deposited by LPCVD. Figures 3(a) and 3(b) show scanning electron microscope (SEM) pictures of fabricated ring and Fabry-Perot resonators, respectively.
The devices were characterized by coupling light from a tunable laser source (1260–1370 nm) through a lensed optical fiber into the guides. The experiments were achieved at a nominal output power from the laser source of 10 mW. An inverted taper configuration  was used to match the optical modes of the fiber and the input waveguide. Polarization of the input light was controlled using a paddle style fiber polarization rotator. By imaging the top of the chips onto an InGaAs CCD camera, we were able to observe light from the resonators and waveguides while in operation. The output light was collimated by an objective, filtered by a polarizer and collected by a photodetector.
3. Results and discussion
3.1. Ring resonators
The loaded quality factor of a ring resonator, Q1, is given by :
where λFWHM is the full bandwidth at half maximum of the dropped power or transmitted power, λ0 is the resonance wavelength, r is the field transmission coefficient at the waveguide resonator coupling, a = exp-(αring L/2), where a is the inner circulation factor and αring is the total loss in the ring, L is the ring length, and ng is the group index given by:
where ne is the effective refractive index of the waveguide. The group index can be obtained from the difference between two contiguous resonance wavelengths, that is, from the free-spectral range (FSR), as
Q1 can also be written as
where Qe relates to the coupling of optical power from the bus waveguide to the ring and Qi is the unloaded (intrinsic) quality factor. They are given, respectively, by :
where Tmin is the minimum in the normalized transmission spectrum; and Qi equals Ql for r=1, that is:
Figure 4 shows the experimental transfer function of a 70-μm-radius silicon nitride/silicon oxide slot-waveguide ring resonator for TE polarization at the resonance wavelength λ=1298.81 nm. The experimental curve has been fitted by a well-known analytical equation :
where a and r are the values extracted from the measured curve and the previous equations. In the fitting, the product Lne has been assumed to be equal to Lng obtained from the experimental FSR [Eq. (3)]. This approximation is based on the assumption of small dispersion in the wavelength range around the resonance wavelength shown in Fig. 4.
The measured loaded quality factor equals Ql= 9,224 and the unloaded quality factor results to be Qi=15,701. The obtained values of the inner circulation factor and transmission coefficient are a= 0.8875 and r=0.9198, respectively, demonstrating that favorable critical coupling (a = r) has nearly been achieved. Therefore, a significant throughput attenuation of -15 dB at resonance is observed. The field enhancement factor at critical coupling is given by FEcritical = (1-a 2)-1/2 , which results to be equal to 2.17. Good agreement between the experimental and the fitting curve indicates that the aforementioned approximation (Lne ≅ Lng) in the considered wavelength range is acceptable. From the value of a, the total loss in the ring is determined as αring= -2(ln a)/L = 23.3 dB/cm. This value includes slot-waveguide losses and radiation loss due to bending. The latter contribution was estimated to be 3.6 dB/cm from beam propagation method (BPM) simulations . The measured loss are higher than that in the Si/SiO2 material system , which we attribute to fabrication imperfections such as excessive sidewall roughness or void formation during the top cladding deposition. An optimized process should reduce significantly these losses. Insertion losses were estimated to be -20 dB.
Figure 5 shows the group indexes for TE and TM polarization obtained from experimental FSR (Eq. 3) for different slot widths (wslot). Semi-empirical values of the group indexes are also shown in Fig. 5. These values have been calculated by using an approximated expression of Eq. 2, given by:
where λ0 and λ1 are two contiguous resonance wavelengths obtained from measurements, whereas ne(λ) is the effective refractive index of the slot-waveguide at the wavelength λ calculated by using the finite difference BPM . It is observed in Fig. 5 that for both, the experimental and the semi-empirical values, ng is higher for TE polarization than for TM polarization. This suggests that no polarization conversion occurs at the ring resonator. Polarization conversion may be originated by surface imperfections such as roughness and angled sidewalls or particular device geometries . It is also seen that ng decreases as wslot increases. Note that when no slot is present (wslot=0), the group index of the quasi-TE mode, ng= 1.974, is much higher than that of the quasi-TM mode, ng= 1.834, indicating that the power of the quasi-TE mode is mostly confined in the silicon nitride core. When the slot is introduced, a strong decrease in the group index of the quasi-TE mode is measured, whereas the group index of the quasi-TM mode is less affected. This behavior is direct evidence that, for the quasi-TE mode, light is indeed concentrated in the low-index region because of the field discontinuity .
3.2. Fabry-Perot cavities
The quality factor of a Fabry-Perot cavity, QFP, is given by :
where R is the power reflection coefficient and A is the power loss coefficient in the cavity. R and A are also related through the following equation :
where Tmax is the maximum transmittivity of the Fabry-Perot cavity.
Similarly to the ring resonator analysis, from the direct measurement of FSR and Eq. (3) (with L=2Lcav), ng can be known, whereas from the measurement of QFP and Tmax, and the value of ng, R and A can be obtained from Eq. (9) and Eq. (10).
Figure 6 shows the experimental transfer function of a 140-μm-long slot-waveguide Fabry-Perot resonator for TE polarization at the resonance wavelength λ=1269.44 nm. The experimental curve has been fitted by the basic relation of a Fabry-Perot etalon :
where A and R are the values extracted from the measured curve and the previous equations. The measured quality factor is QFP= 8,677, while R=0.9477 and A=0.9117. This means slot-waveguide losses of αFP=-(lnA)/(Lcav)= 28.4 dB/cm. This value includes slot-waveguide losses and losses due to optical mode mismatch between the slot-waveguide cavity and the strip-waveguide Bragg reflectors, which explains the higher value of αFP as compared to that obtained for the ring resonators. Insertion losses were estimated to be -31.8 dB. Note that this attenuation is much higher than that for the ring resonators (-20 dB), which is attributed to mode mismatch between the Bragg reflectors and the slot-waveguide cavity and diffraction losses at the Bragg reflectors.
Figure 7 shows the experimental and semi-empirical values of the slot-waveguide cavities group indexes for TE polarization and various slot widths (wslot), obtained from Eq. (3) and Eq. (8), respectively. As observed for the ring resonators, it is seen that a significant decrease of ng occurs when the slot is introduced, suggesting light concentration in the low-index slot region. No significant resonances were observed for TM polarization in the scanned wavelength range. This is expected from the theoretical analysis of the device: the designed Bragg reflectors do not show significant stop-band for the quasi-TM mode in the considered wavelength range. This also indicates that no polarization conversion effects occur since the device was designed to show resonances only for the quasi-TE propagation mode. Note that the group indexes shown in Fig. 7 are slightly higher than those illustrated in Fig. 5. This is because the values in Fig. 7 were obtained at shorter wavelengths (around 1269 nm) than those in Fig. 5 (around 1300 nm). The optical field is more confined in the high index regions at shorter wavelengths and, therefore, the effective index increases as the wavelength decreases. Thus, according to Eq. (2) and assuming similar wavelength dispersion, the group index results to be higher at shorter wavelengths, as shown in Fig. 7.
Nonlinearities in response to input power  were not observed. This is expected due to the weak nonlinear properties of Si3N4 and SiO2 and the modest quality factors exhibited by the fabricated devices. For applications based on a nonlinear material response, such as photonic switching, the slot region could be filled with a proper non-linear material such as Si-nanocrystals  or polymers .
Silicon nitride/silicon oxide vertical slot-waveguide ring and Fabry-Perot microresonators have been demonstrated for the first time. The behavior of the group indexes of slot-waveguides with different slot widths indicates that light is concentrated in the low-index slot region for the quasi-TE mode, as predicted by theory. Near critical coupling is obtained for the fabricated ring resonators which exhibit intrinsic quality factor of 15,701. Propagation losses of <20 dB/cm for the quasi-TE mode are extracted from the devices optical characteristics. This promising first demonstration of vertical silicon nitride/silicon oxide slot-waveguide devices makes this material system an appropriate trade-off between high integration and ease access to the slot region (larger dimension) for the implementation of active and sensing photonic devices based on integrated slot-waveguides.
C.A. Barrios acknowledges support from the Spanish Ministry of “Educación y Ciencia” under Program “Ramón y Cajal”. K.B. Gylfason would like to acknowledge support of the Steinmaur Foundation, Lichtenstein. This work is done within the FP6-IST-SABIO project (026554), funded by the European Commission.
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