Birefringence and optical power confinement in horizontal multi-slot waveguides made of Si and SiO 2

Through simulations and measurements, we show that in multi-slot thin film waveguides, the TM polarized modes can be confined mostly in the low refractive index layers of the waveguide. The structure consisted of alternating layers of a-Si and SiO2, in the thickness range between 3 and 40 nm, for which the slots were the SiO2 layers. Simulations were performed using the transfer matrix method and experiments using the m-line technique at 1.55 μm. The dependence of the birefringence and of the power confinement in the slots was studied as a function of the waveguide thickness, the Si and SiO2 layer thicknesses, and the SiO2 / Si layer thickness ratio. We find a large birefringence—a refractive index difference between TE and TM modes—as large as 0.8. For TM polarized modes, up to ∼ 85% of the total power in the fundamental mode can be confined in the slots. © 2008 Optical Society of America OCIS codes: (130.2790) Guided waves; (130.3120) Integrated optics devices; (230.7390) Waveguides, planar; (230.7400) Waveguides, slab References and links 1. P. G. Kik, M. L. Brongersma and A. Polman, “Strong exciton-erbium coupling in Si nanocrystal-doped SiO2,” Appl. Phys. Lett. 76, 2325–2327 (2000). 2. X. W. Zhao, S. Komuro, H. Isshiki, Y. Aoyagi and T. Sugano, “Fabrication and stimulated emission of Er-doped nanocrystalline Si waveguides formed on Si substrates by laser ablation,” Appl. Phys. Lett. 74, 120–122 (1999). 3. V. Y. Timoshenko, M. G. Lisachenko, B. V. Kamenev, O. A. Shalygina, P. K. Kashkarov, J. Heitmann, M. Schmidt and M. Zacharias, “Highly efficient sensitizing of erbium ion luminescence in size-controlled nanocrystalline Si/SiO2 superlattice structures,” Appl. Phys. Lett. 84, 2512–2514 (2004). 4. J. H. Shin, W.-H. 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Introduction
The goal of achieving optical gain at the telecommunication wavelengths using a silicon platform is driving research on erbium incorporation in CMOS-compatible host materials and structures.Erbium luminescence at 1.55 μm is especially strong if the Er ions reside in a silicon oxide host and are excited by energy transfer from silicon nanocrystals (nc-Si) placed in close proximity [1][2][3][4][5][6].An attractive structure is a stratified multilayer film of alternating thin layers of nc-Si and Er-doped SiO 2 [3,4].One of the major hindrances to achieving lasing using Er is the confined (or free) carrier absorption by nc-Si and thus there has been a marked interest in minimizing this type of loss [7,8].
One of the possible ways to minimize loss is to tailor the light distribution in the film such that light interacts with Er in the SiO 2 layers only and avoids the nc-Si layers.Simulations have shown that for a waveguide consisting of ultra-thin slots of low refractive index n L (e.g., SiO 2 ) embedded between high refractive index n H regions (e.g., Si), the intensity of TM-polarized light-the direction of its H-field parallel to the slot-can be enhanced in the slots [9,10].Power confinement factors in the slot(s) of ∼ 30% for a single-slot vertical waveguide [10,11] and ∼ 56% for a three-slot horizontal waveguide [12] have been reported.This high power confinement in the low-index regions is due to the D-field continuity across the interface.Since the E-field strength differs by a factor of n H 2 /n L 2 immediately across the interface between the two regions, the larger the material index contrast is, the stronger the power confinement in the low-index region is.This effect has been verified by measuring the effective modal index via thermo-optic coefficient measurements [13], angle-resolved attenuated total reflectance [14] and cladding field intensity measurements [15].
In this letter, we present simulations and experiments on horizontal multilayer films consisting of alternating nanometer-thin amorphous Si (a-Si) and SiO 2 layers.Since the material index of nc-Si is similar to that of a-Si overall [16], our results are also applicable to multilayer films of alternating polycrystalline Si and SiO 2 layers, which can be formed by post-deposition thermal annealing [17,18].Simulations show that a birefringence of up to 0.8 and a power confinement of up to ∼ 85% can be achieved.It ought to be noted that these effects should also be observable in any multilayer film made of alternating ultra-thin layers with a large material index contrast.Films containing layers of a-Si and SiO 2 were deposited by computer-controlled reactive ion RF magnetron sputtering at room temperature on Si substrates covered by a 5-μm thick thermal oxide layer (Fig. 1).The layer thicknesses L Si and L SiO 2 of the two materials varied from ∼ 3 to ∼ 40 nm and the number of periods P ranged from 13 to 160, to keep the total film thickness L Film close to 1 μm, ensuring the presence of multiple guiding modes.Two sets of five films were fabricated: in one set the thickness ratio L SiO 2 /L Si was kept close to 1, whereas the ratio in the other set ranged between 0.7 and 11.5.

Simulations & experimental methods
Simulations were carried out using the transfer matrix method [19]-equivalently, the Abeles matrix method [20]-for stratified multilayer films.For the refractive index of the deposited and thermal oxide layers and that of a-Si, we used the values of 1.44 and 3.44 obtained from ellipsometric measurements at 1.55 μm.
To experimentally verify the higher power confinement in the lower index layers (slots)-defined as the ratio of the power in the low-index layers to the total power-the modal indices were obtained using a prism coupler instrument (Metricon 2010) via the m-line measurement [21].The indices were measured at 1.55 μm.A 1/2 waveplate and a linear polarizer were employed to select the polarization (TE or TM).As shown in Fig. 2(a), the incident light was coupled evanescently into the multilayer film through a prism, establishing a bound guiding mode at certain incident angles.A germanium detector measured the intensity of the reflected light from the interface between the sample and prism base.The film's modal indices were evaluated by treating the multilayer stack as a single film with an effective material index  n Film sandwiched between the 5-μm thermal oxide and air.
Figure 2(b) shows the reflected light intensity as a function of modal index for a multilayer film consisting of 34 periods of 15.2-nm a-Si and 19.7-nm SiO 2 .For this sample, a total of three TE modes and two TM modes were found.When a bound mode is established, the reflected light intensity becomes significantly smaller, as marked with arrows on the figure.Two prisms were used to cover a wide range of effective modal indices-one covering 1.0 ∼ 1.8 and the other 1.9 ∼ 2.9.Measured (dots) and calculated (curves) modal index difference between the fundamental TE and TM modes as a function of layer thickness ratio for total film thicknesses between 0.4 and 0.9 μm.The maximum difference of ∼ 0.8 is obtained if the thickness ratio is around 0.5 and 0.6.

Modal index & birefringence
Our simulations indicated that as long as the multilayer thickness is less than 8% of the wavelength, the modal indices for a fixed thickness primarily depend on the SiO 2 / Si thickness ratio and little on the number of periods or the individual layers' thicknesses.
Figure 3(a) compares the calculated and measured modal indices of the first and second order TE and TM modes as a function of the layer thickness ratio for a 1-μm thick film.As the fraction of SiO 2 increases, the modal index decreases and the second order TM mode is no longer supported.The experiments and calculations are in good agreement.The deviations between the measurement and calculation are primarily due to variations in the actual film thickness between 0.93 to 1.19 μm.Simulations performed with actual film thicknesses resulted in less than 2% of discrepancy.
As expected, the TM modal indices are substantially lower than the TE ones, indicating a strong birefringence.Figure 3(b) shows the modal index difference between the fundamental TE and TM modes as a function of layer thickness ratio at various total film thicknesses.A maximum difference of ∼ 0.8 is obtained over a wide range of layer thickness ratios and total film thicknesses.To determine whether the lower effective mode indices of the TM polarized light is simply due to a higher evanescent field intensity in the air and substrate layer, we calculated the power profile for both polarizations.Figure 4 shows that the TM-polarized light intensity is highly localized in the SiO 2 layers and that power in the cladding is small in all cases.Hence the modal index disparity between the two polarizations is due to the higher field confinement in the SiO 2 layers.As explained in Ref. [10], the higher field concentration in the lower index regions for TM modes due to the continuity of the transverse D-field component across an interface is possible if the light wavelength is substantially greater than the layer thicknesses.

Confinement factor & optimum layer thickness ratio
In Fig. 5(a), the power confinement factor in the SiO 2 layers for the fundamental TM mode is plotted as a function of layer thickness ratio for various total film thicknesses.At any given layer thickness ratio, the confinement factor in the SiO 2 layers rises as the total film thickness increases, approaching the absolute maximum of ∼ 85% ( ), which can be reached for 0.90-μm or thicker films provided that the thickness ratio is greater than 1.72.
Furthermore, the figure shows that for each film thickness there is an optimum layer thickness ratio at which the confinement in the SiO 2 layers is maximum.The confinement factors  for thicker films reach their maxima at higher thickness ratios than for thinner films.The optimum layer thickness ratio for a given film thickness follows an empirical linear relationship (Fig. 5(b)).For example, if the film thickness is 0.50 μm, then the optimum ratio is ∼ 0.83.The shaded region in Fig. 5(b) denotes the layer thickness ratio and total film thickness where only one TM mode exists.If a film is to be a single-mode waveguide for TM polarization and to provide the highest SiO 2 confinement, then its thickness should be set to 0.80-μm.This thickness is larger than the one producing the largest birefringence (Fig. 3(b)).
Finally, we note that for large SiO 2 / Si thickness ratios, the confinement factor decreases.This decrease is the result of the increasingly large evanescent tails in the air and the SiO 2 substrate, which are produced by the decreasing effective refractive index of the multilayer.

Conclusions
Simulations and experiments have shown that multilayer films with high contrast material indices exhibit a high birefringence and confine more TM-polarized light in the low-index layers than in the high-index layers.For a given total thickness, there is an optimum SiO 2 / Si layer thickness ratio that yields the maximum light confinement in the SiO 2 layers.This optimum ratio is linearly proportional to the total film thickness.This demonstrates that using TM polarization it is possible to reduce the confined carrier absorption loss in a nc-Si / Er-doped SiO 2 multilayer film via modal profile shaping such that most of the light is confined in the Er-doped SiO 2 regions.

Fig. 1 .
Fig. 1.(a) SEM of a structure made of alternating a-Si and SiO 2 layers.(b) Schematic of sample structure with P periods of L Si thick a-Si and L SiO 2 thick SiO 2 layers on a 5-μm thick thermal oxide layer.(c) Sample structure as viewed by the prism coupler for m-line measurement.The multilayer film is replaced by a single film with an effective material index of n Film and thickness L Film = P(L Si + L SiO 2 ).

Fig. 2 .
Fig. 2. (a) Schematic of m-line measurement.(b) Graph of reflected light intensity as a function of the modal index for a multilayer film of 34 periods of 15.2-nm a-Si and 19.7nm SiO 2 .The arrows show the modal indices greater than 1.44 at which a bound mode is established (2.43, 2.16 and 1.75 for TE; and 1.74 and 1.55 for TM).Modal indices between 1.8 and 1.9 were not measurable because of the two prisms used.

Fig. 3 .
Fig. 3. (a) First and second order modal indices versus SiO 2 / a-Si layer thickness ratio for both polarizations.The curves represent the calculation for 1.00-μm thick film and the dots represent the measured values for film thicknesses ranging from 0.93 to 1.19 μm.(b)Measured (dots) and calculated (curves) modal index difference between the fundamental TE and TM modes as a function of layer thickness ratio for total film thicknesses between 0.4 and 0.9 μm.The maximum difference of ∼ 0.8 is obtained if the thickness ratio is around 0.5 and 0.6.

Fig. 4 .
Fig. 4. The power profile of the first order TE and TM modes in a 0.60-μm thick film consisting of 10 periods of alternating 30-nm thick a-Si and SiO 2 layers.The SiO 2 substrate layer is positioned below the 0.0-μm mark and the air above the 0.6-μm mark.The shaded areas represent the SiO 2 layers.For TM polarization, the transverse E-field component in the low-index n L region is greater by a factor of n H 2 /n L 2 than that in the high-index n H region immediately across the interface.

Fig. 5 .
Fig. 5. (a) The power confinement factor in the SiO 2 layers for first order TM mode as a function of layer thickness ratio at various total film thicknesses.(b) The linear relationship between the total film thickness and its optimum layer thickness ratio.The shaded area represents the region where only one TM mode exists.