We describe a polarization rotator based on an off-axis double-core structure consisting of a silicon wire waveguide and a silicon-oxinitride waveguide. The rotator can be made by planar fabrication technology and do not require complex processes, such as three-dimensional structure formation. A rotator with 35-µm long provides the polarization rotation angle of 72 degrees and the polarization extinction ratio of 11 dB with the excess loss of about 1 dB. Our polarization rotator represents a significant step towards accomplishing an optical circuit with polarization diversity based on silicon wire waveguides.
©2008 Optical Society of America
Silicon wire waveguides have great potential as a platform for ultra-small photonic circuits [1–3]. Their bending radius with negligible loss is as small as several micrometers because of their large refractive index contrast. Several kinds of functional devices based on Si wire have been demonstrated [4–6]. However, polarization mode dispersion (PMD), polarization dependent loss (PDL), and polarization dependent wavelength characteristics (PDλ) caused by large structural birefringence are not negligible. These drawbacks narrowly limit their application range.
There are several approaches to making a polarization-independent photonic circuit. The simplest way is to use a square core. However, for high-index-contrast waveguides, such as silicon wire, fabrication errors of just a couple of nanometers are critical and result in birefringence. For instance, for waveguide length of 5 cm, the differential group delay between cores with 300±5-nm width and 300-nm height reaches 6.6 ps, which degrades high-speed signals, i.e., those with data rates of 40 Gbps. Then again, the fluctuation of core width varies the group index and results in PDλ of wavelength filters. The difference in the resonant wavelength between the transverse electric (TE) and transverse magnetic (TM) modes is larger than 100 GHz for a 10-µm-radius ring resonator with a 300±1-nm-wide core. Therefore, accuracy of under a nanometer is required for devices used in polarization-independent dense wavelength division multiplexing systems. This is a big obstacle to mass production.
Another solution is the use of a polarization diversity system consisting of polarization splitters and rotators. If TE andTM components are separated by the splitter, and the TM component is rotated 90 degrees by the rotator, we need to fabricate functional devices (e.g., a filter) for the TE mode only, not for both modes. Several key components for accomplishing the polarization diversity have been presented [7–14]. D. Tailaert et al. developed a two-dimensional grating coupler, which couples orthogonal modes from a fiber into identical modes of two waveguides . This device is efficient for polarization splitting, although the coupling efficiency is as small as approximately -7 dB. M. R. Watts et al. demonstrated a polarization splitter and rotator with an asymmetric core cross section for SiN waveguides [9–12].
In this paper, we describe the principle of a polarization rotator based on an off-axis double-core structure consisting of a short Si photonic wire and an SiOxNy waveguide. Our polarization rotator is just a short waveguide with low insertion loss. In addition, the rotator is easy to fabricate because there is no need for complex fabrication processes for three-dimensional structure formation. We show experimental results for the wavelength characteristics, polarization rotation angle, and polarization extinction ratio. The fabrication tolerance of our rotator is also discussed.
2. Principle and design
A schematic diagram of our polarization rotator is shown in Fig. 1(a). A Si wire with a square core is embedded in a second waveguide whose core is larger than the Si wire’s. The waveguides have offsets both horizontally and vertically, and the left- and down-side edges of the Si wire close up the corresponding edges of the second waveguide. The eigen-axes of such a double-core structure are tilted towards the substrate as shown in Fig. 1(b). Therefore, propagation through the waveguide produces a rotation of the polarization plane when the polarization of an incident light is parallel (TE) or orthogonal (TM) to the substrate.
Design parameters are the material of the second core and the sizes of the Si core and second core. Polarization rotation is described by πLΔn/λ, where L is the propagation length, Δn the difference in the effective indices between two orthogonal eigenmodes, and λ the operation wavelength. The efficient wavelength range thus becomes wider for a device with shorter propagation length. The rotator length to accomplish 90-degree rotation L π/2 is described by λ/2Δn. The second core with large refractive index makes Δn large and ensures a sufficient angle of polarization rotation even for a short device. Here we assumed that the material of the second core is SiOxNy with the refractive index of 1.60, which can be formed by plasma-enhanced chemical vapor deposition.
The L π/2 also depends on the Si core’s size and the second core’s size. The cross-section of the Si core has to be just square to split the optical power into two eigenmodes equally. Moreover, the core ought to be a little smaller than that of a normal Si wire waveguide because the geometry and the materials surrounding the Si core determine Δn. In the calculation, the cross-section of the Si core was set to 200-nm square because the input and output waveguides are normal Si wires with a height of 200 nm and width of 400 nm.
We calculated the effective indices of two orthogonal modes as a function of the second core’s size using a mode solver  for the operating wavelength of 1552.52 nm. The L π/2 estimated by the effective indices is shown in Fig. 2(a). The required length is shorter for a larger second core. However, for core size of over 850 nm, the rotator length again becomes longer, because the mode-field spreads into the second core’s area and Δn becomes small since the contribution of the Si core decreases. Therefore, the cross-section of the second core was set to 840-nm square.
The eigenmodes calculated from the conditions just mentioned above are shown in Fig. 2(b). The effective indices of the two orthogonal eigenmodes are 1.542 and 1.525. Under these conditions, a device less than 50 µm-long provides a polarization rotation of 90 degrees. Even a device this short exhibits wideband characteristics, with the bandwidth being over 100 nm.
We confirmed the polarization rotation in our rotator by propagation simulation. The field intensities with TE and TM polarization calculated by a three-dimensional FDTD simulation are shown in Fig. 3(a). Transmittances calculated by the eigenmode expansion method (EME) as a function of L are plotted in Fig. 3(b). In both results, the TE component decreases along the rotator, and the TM component gradually increases. And as expected, a 48-µm-long rotator produces a rotation of 90 degrees. The polarization extinction ratio (PER), defined as the difference in transmittance between TE and TM lights, is over 30 dB for a 48-µm-long rotator.
Next, we estimated the excess loss and bandwidth of our rotator. Figure 4(a) shows the excess loss calculated by EME as a function of the second core’s size. A large second core produces a large excess loss, which would be caused by the reflection at its start and end points. The difference in the effective indices between the rotator and the simple Si wire waveguide produces impedance mismatching, which results in a reflection loss at the interfaces. The excess loss for the second core of 840-nm square is 1.3 dB, which can be reduced by introducing a tapered connection between the rotator and the oblong cores.
The wavelength characteristics for a 48-µm-long rotator calculated by EME are shown in Fig. 4(b). The PER of over 10 dB is indeed maintaine in the S-, C-, and L-bands. Moreover, the PER exceeds 20 dB in the wavelength range of 1530-1580 nm. That means that the off-axis double-core structure we devised can actually be used to make an ultrasmall rotator with wideband characteristics and a low loss.
3.1. Sample preparation and experimental setup
Devices were fabricated on silicon-on-insulatorwafer with a 200-nm-thick Si layer and a 3-µm-thick SiO2 buried layer. The Si wire waveguides for the input and output are 400-nm wide. For efficient coupling between the Si wire and external fiber, we made spot-size converters (SSCs) at the ends of the Si wires . Si wires and SSCs were fabricated by electron beam lithography and electron cyclotron resonance plasma etching. An 840-nm-thick silicon oxynitride film with a refractive index of 1.60 is deposited by plasma-enhanced chemical vapor deposition and the second core is formed by reactive ion etching with fluoride gas. The propagation loss was measured by the cutback method and found to be 2.2 dB/cm for the TE mode and 1.7 dB/cm for the TM mode.
A schematic diagram of a fabricated rotator is shown in Fig. 5. The Si wires for the input and output are 200-nm high and 400-nm wide. Their cores are adiabatically connected to the 200-nm square Si core by 10-µm-long tapers. The polarization of the input light was TM.
3.2. Transmission spectra
The transmission spectra filtered for the TE and TM components are shown in Fig. 6. When the length of the rotator is 35 µm, the TM component is greatly suppressed, and the TE component is transmitted with an excess loss of about 1 dB. When the length is 60 µm, the TM component is larger than the TE component because of excessive polarization rotation. The measured rotator length for sufficient rotation is about 10 µm shorter than the simulated one. It seems that the tapers work as rotators with an efficiency of about 50%. The spectral ripples are caused by the polarization rotation of the ordinary Si wire waveguides used for input and output. These ripples may be caused by slight misalignment of the polarization plane of the input light and they complicate the estimation of the actual extinction ratio.
3.3. Polarization rotation angle
To obtain the actual extinction ratio, we measured the state of polarization with a Poincaré sphere. A schematic diagram of a Poincaré sphere is shown in Fig. 7(a). The red line shows the polarization rotation by the rotator when the input light is TM. If the rotation is insufficient (φ<90 degrees), the polarization at output becomes elliptical. The output waveguide equiped with the rotator is normal Si wire with large birefringence. Thus the polarization changes through the Si wire and the final polarization state depends on the wavelength. The blue circle in Fig. 7(a) shows a trace of the polarization state when the wavelength is swept. Therefore, we can easily separate the polarization rotation in the rotator (φ) from that in the Si wire.
A measured Poincaré map is shown in Fig. 7(b). The point of the polarization state of the input light is located at the right end of the sphere, and those of the outputs are the circles. The circle for a 35-µm-long rotator exhibits the largest rotation.
Figure 8 shows the rotation angle calculated from the Poincaré map and the extinction ratio estimated from the rotation angle as a function of rotator length. The wavelength ranges are the C- and L-band for the left and right graphs, respectively. For the C-band, the maximum rotation angle is 72 degrees, and the maximum extinction ratio is about 11 dB, when the rotator length is 35 µm. A rotator for longer wavelengths requires greater length. The maximum extinction ratio of 9 dB is obtained for a 50-µm-long rotator for the L-band.
3.4. Fabrication tolerance
For a practical device, it is important to estimate the fabrication tolerance. The most critical parameter for fabrication is the offset between the Si core and the second core (Fig. 9(a)). If it is too large, it results an insufficient polarization rotation. The excess loss for the polarization diversity system caused by an insufficient polarization rotation is described by 10log10(sin2 φ). We fabricated rotators with various offsets. Figure 9(b) shows the insertion loss of the polarization diversity systems estimated from the rotation angle of the rotator. When a rotator is 30 or 40 µm long, the insertion loss is less than 1 dB, even when the offset is around 30 nm. Therefore, we can conclude that the fabrication tolerance of our devices is around 30 nm. This value is practical for current fabrication technology.
We demonstrated a polarization rotator based on an off-axis double-core structure consisting of a Si wire waveguide and a SiOxNy waveguide. A 35-µm-long rotator provides the polarization rotation angle of 72 degrees and the polarization extinction ratio of 11 dB with the excess loss of about 1 dB. Our polarization rotator is suitable for mass production because it requires just planar fabrication and allow fabrication error of around 30 nm, which is practical for current fabrication technology.
This work was partly supported by the SCOPE program of the Ministry of Internal Affairs and Communications, Japan.
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