A s the field of integrated optics has expanded 1 , small-scale silicon-based modulators and filters have been studied and demonstrated, consequently motivating exploration at both the transmitter and receiver sides 2,3. In many...
moreA s the field of integrated optics has expanded 1 , small-scale silicon-based modulators and filters have been studied and demonstrated, consequently motivating exploration at both the transmitter and receiver sides 2,3. In many applications, specific frequencies or electrical responses are desired 4-6 : in radio-frequency (RF) applications, linear transmission is typically required to provide a large spurious-free dynamic range (SFDR) 7. Detecting digitally modulated optical signals requires an optical comparator that can be realized by a device having a square-wave shape 8. A square-like behaviour, this time in the frequency domain, is also encountered when considering a bandpass 'box-like' filter in high-capacity optical links such as wavelength-division multiplexing (WDM) 9. WDM-based devices can be used in dense WDM (DWDM) systems through multiplexing/de-multiplexing odd and even channels by employing a so-called interleaver filter 10,11. The separation of channels , obtained by the interleaved shaped waveform, is also needed to facilitate traffic routing within a relay station. The above-mentioned response shapes are commonly realized by complex optical circuits, often comprising several optical elements. In the case of analog RF applications, a chain of Mach-Zehnder interferometers (MZIs) was required to obtain a high SFDR 12 ; ring-assisted MZIs (RAMZIs) with multiple electrodes have also been widely explored 13-15. Several complex designs were suggested 8,16,17 for detecting digitally modulated optical signals using an optical comparator. These designs require multiple electrodes and a large footprint. To obtain a sharp box-like filter response, five cascaded rings were devised 9 while several rings coupled to a MZI have also been reported 5,6,18. For an interleaver, a flat-top spectral response is required, otherwise the transmission efficiency will be sensitive to a slight shift in wavelength (for example, laser quality or temperature). Consequently, the sinusoidal response of a single crossbar MZI is not adequate. This motivated analysis of circuits comprising MZIs in a serial configuration made of directional couplers (DC) or multimode interferometer (MMI) elements to obtain a flat-top response 10,19. An interleaver for Nyquist-WDM (super-channel) based on RAMZI circuits with additional coupled rings has recently been demonstrated 20. The above-mentioned solutions exhibit similar characteristics, such as large footprint, fabrication sensitivity and a multiplicity of electrodes. A large free spectral range (FSR) is required in a variety of applications. These include some sensing applications, tunable filters, and WDM architectures where a large FSR is required to avoid cross-talk among channels. The increase in FSR is typically achieved by reducing the resonator length; however, this also reduces the electrode length, consequently increasing the required operating voltage. Small-scale optical structures, such as photonic crystals 21 and rather complex ring resonator-based designs 22-24 , have been suggested to increase the FSR and may, in theory, be able to operate under low voltage. However, these are more complicated to fabricate and harder to integrate with an electrical control. Optical circuits based on ring resonators are very sensitive to fabrication deviations. A small variation in the coupling or loss coefficients may drastically decrease the extinction ratio (ER) of the transmission. A three-dimensional finite difference (FDTD) sensi-Modern systems often provide complex functionality that can be realized by tailoring together elements of simpler functional-ity. Multiplicity of simple optical functions (response shapes), when densely fabricated on a chip, can promote the concept of a field-programmable optical array. Shaping of the frequency response, or otherwise an electrical-to-optical response, is studied and demonstrated by means of a racetrack-shaped ring resonator designed and fabricated in the so-called double injection configuration. This configuration possesses a unique property that allows two free spectral range states (regular, 2 × regular) to exist for a single ring length. Shaping is realized by properly selecting different coupling coefficients that provide a variety of interesting responses. Here, we demonstrate various shapes including: sinusoidal, triangular (linear), square (bandpass), dips and peaks (two states), spikes (tangent-like), interleaver and a so-called 20dB-min parameters-insensitive-response modula-tor. The transmission responses were experimentally realized, fabricated in a silicon-on-insulator platform and characterized at wavelengths around 1,550 nm. Su bs tra te E il E i2 E in E t2
