1 Lattice Filter for Wavelength De-multiplexing
Wavelength division multiplexing (WDM) is commonly adopted in optical communication systems and is considered an effective solution to counter the unprecedented bandwidth scalability of photonic technology. With rapid increasing market size in data ceter applications, 100 Gigabit Ethernet (GbE) has been standardized in which 4x25 Gbit/s WDM electro-optic transceiver solutions are commonly employed.
Optical de-multiplexers are the key functional components in WDM transceivers. Flattop optical filters are widely used in transceivers that separate an incoming spectrum into two complementary set of periodic spectra (odd and even channels) or combine them into a composite spectrum. Various types of optical filters are implemented in the bulk optics, but the lattice type flat-top filter has an edge over others in terms of reliability, ease of manufacturing, use of passive temperature compensation schemes, low polarization dependent loss, and zero chromatic dispersion without compensation. The chromatic dispersion is a critical factor in the \(40\)-Gb/s transmission systems and beyond. Thus, flat-top interleaver optical filters are an attractive choice in the high data rate applications and play a key role in the dense wavelength division multiplexing (DWDM) systems as in the dispersion compensation and channels add/drop applications.
2 Theory
In this article, we present a 1x4 channel wavelength division de-multiplexing optical filter based on work reported in [1-2]. The filter is centered around 1550 nm with a target to achieve a \(50\) GHz channel spacing as per the DWDM ITU channel grid in C-band. This optical filter comprises the directional couplers and the cascaded Mach-Zehnder Interferometers (MZIs) forming a lattice filter, whose schematic is shown in figure 1.
The key advantage of this lattice filter configuration is that it provides a flat-top passband type filter response and a wide \(3\)-dB bandwidth. The lattice filter comprises two stages. Stage 1 is an input stage, formed of cascaded MZIs, where the cross-coupled power for the directional couplers is \(0.5\), \(0.29\) and \(0.08\) as observed in the schematic. The unit delay length (\(\Delta L\)) is calculated based on the desired channel spacing (\(\delta \lambda\)), also known as the Free Spectral Range (FSR) through the following expression:
\[\begin{equation} \Delta L = \frac{\lambda^2}{2 n_g (\delta\lambda)} \end{equation}\]
where,
\(\lambda\) is the central wavelength of operation
\(n_g\) = group index of the waveguide forming the unit delay length
Stage 2 has two arms of cascaded MZIs formed by the directional couplers of cross-coupled power \(0.5\), \(0.29\), and \(0.08\) and unit delay lengths. The unit delay lengths in stage 2 are calculated based on the \(\Delta L\) from stage 1, as shown in figure 1. The four frequency channels are sent in through stage 1 which filters out and send the odd frequency channels to the upper arm and the even frequency channels to the lower arm. The unit delay lengths are halved in each arm of stage 2 to further separate the odd and even channels. Some extra length is added to the unit delay lengths (\(\Delta L\)) in the upper arm of the stage 2 to compensate for the phase shift. Another important characteristic of these channels is their absolute position on the wavelength axis. A given output has a periodic spectral response with the central passband wavelengths \(\lambda_{k,m}\) [2]:
\[\begin{equation} \lambda_{k,m} = \frac{n_{eff} \Delta L}{m log_2 N} + \delta \lambda(k-1), m \in N \end{equation}\]
where,
\(\delta \lambda\) is the channel spacing
\(k\) is the channel number from \(1\) to N
\(n_{eff}\) is the effective refractive index of the waveguide used in the optical filter
\(\Delta L\) is the unit delay length of the MZI.
3 Design
The 1x4 lattice filter is designed and simulated in the simulation tool S-edit from Siemens Tanner. The circuit is build using the building blocks from the PDK (version 6.5) of Fraunhofer HHI and the electro-optic devices from the OptiSPICE device library. All the HHI PDK devices used in this circuit, in stage 1 and stage 2, are modelled internally using the OptiSPICE devices via netlist. The devices used from the HHI PDK are: HHI_DirCoupE600 (directional couplers), HHI_PMTOE1700 (MZI unit delay length), HHI_WGTE600E1700 & HHI_WGTE1700E600 (waveguides to connect directional couplers and delay lengths). These devices are connected to other opto-electronic OptiSPICE devices to complete the simulation circuit, as shown in figure 2.
A laser from the OptiSPICE library is connected to the Stage 1 to send in the light signal. The frequency of the laser is set to \(193.1\) THz. A voltage source is connected to the laser to drive it. At the output of the stage 2, the even and odd frequency channels are detected using the photodiode from OptiSPICE library. A probe connected to the photodiode to measure the signal.
The HHI_DirCoupE600 is modelled analytically, such that its parameter coupling length (\(L_C\)) consequently sets the power coupling ratio. The L_C is set to \(3.5333\ \mu\)m, \(102.8399\ \mu\)m and \(118.502\ \mu\)m in order to set \(0.5\), \(0.29\), and \(0.08\) power coupling ratio, respectively. The unit delay length (\(\Delta L\)) is set to \(940\ \mu\)m in order to get the desired FSR of \(50\) GHz (\(0.4\) nm) near C-band. The remaining delay lengths in the circuit are evaluated and set as shown in Figure 1.
4 Simulation and Results
The AC analysis is carried out for this circuit where the frequency is swept linearly from \(193.269\) THz to \(193.5175\) THz. The flat-top transmission response of four even and odd frequency channels obtained at the photodiodes, is shown in figure 3.
Probe \(N_2\) and \(N_3\) represent the odd frequency channels and N_4 and N_5 represent the even frequency channels. The measured 3-dB bandwidth of a flat-top frequency response is around 48.3 GHz. The measured FSR is \(50\) GHz (\(0.4\) nm). The central passband frequency (wavelength) recorded at \(N_2\) probe is \(193.47\) THz (\(1549.55\) nm), at \(N_3\) probe is \(193.37\) THz (1550.35 nm), at \(N_4\) probe is \(193.32\) THz (\(1550.76\) nm), and at \(N_5\) probe is \(193.42\) THz (\(1549.96\) nm). The measured crosstalk from the neighbouring channel is ~ \(18.6\) dB. This crosstalk can be further improved by optimizing the phase shift by using thermal heaters. Therefore, a four channel de-multiplexing optical filter with a flat-top response, and the desired FSR of \(50\) GHz in C-band is designed and simulated using the building block devices from the HHI PDK.