We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm 2 . Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm. In a typical configuration, a waveguide array of MachZehnder interferometers (MZIs) with increasing path differences are used to implement the SHS concept [9,10]. For such a geometry, the source power spectrum and the output interferogram are related by the cosine FT. A similar MZI array geometry, including phase-correction circuits using independent heaters for each MZI, has also been demonstrated [13]. However, when long optical path delays are required for high spectral resolution, similar configurations yield prohibitively large devices.In this Letter, we present a compact FT spectrometer chip, in which a high spectral resolution of 40 pm with a compact device size is achieved by using tightly coiled spiral waveguide structures in an MZI array. Furthermore, a spectral retrieval algorithm with phase and amplitude error compensations is demonstrated for the first time to the best of our knowledge, obviating the need for dedicated phase correction circuits. The FT spectrometer is implemented as an array of N MZIs in silicon-on-insulator (SOI) waveguides (Fig. 1). Each MZI comprises a reference arm of constant length and a delay arm with a spiral waveguide. The length of the delay arm, i.e., spiral length, linearly increases by ΔL across the array. The high refractive index contrast of the SOI platform and the waveguide bend radius of ∼5 μm readily allows the making of spirals with geometrical lengths of over a centimeter within an area only a few hundred micrometers in diameter.For a given input spectral distribution, the dispersive property of the MZI array results in a wavelengthdependent spatial interferogram at the outputs of the array. The relation between the input spectral distribution and the interferogram Ix i is unambiguous within

We demonstrate compressive-sensing (CS) spectroscopy in a planar-waveguide Fourier-transform spectrometer (FTS) device. The spectrometer is implemented as an array of Mach-Zehnder interferometers (MZIs) integrated on a photonic chip. The signal from a set of MZIs is composed of an undersampled discrete Fourier interferogram, which we invert using l₁-norm minimization to retrieve a sparse input spectrum. To implement this technique, we use a subwavelength-engineered spatial heterodyne FTS on a chip composed of 32 independent MZIs. We demonstrate the retrieval of three sparse input signals by collecting data from restricted sets (8 and 14) of MZIs and applying common CS reconstruction techniques to this data. We show that this retrieval maintains the full resolution and bandwidth of the original device, despite a sampling factor as low as one-fourth of a conventional (non-compressive) design.

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Subwavelength grating (SWG) structures are an essential tool in silicon photonics, enabling the synthesis of practical metamaterials with controllable refractive index. Here we propose, for the first time, tilting the grating elements to gain control over the anisotropy of the metamaterial. Rigorous FDTD simulations demonstrate that a 45°tilt results in an effective index variation on the fundamental TE mode of 0.23 refractive index units, whereas the change in the TM mode is 20 times smaller. Our simulation predictions are corroborated by experimental results. We furthemore propose an accurate theoretical model for designing tilted SWG structures based on rotated uniaxial crystals, which is functional over a wide wavelength range and for both the fundamental and higher order modes. The proposed structures open up promising venues in polarization management of silicon photonic devices.

The design and fabrication of an ultracompact silicon-on-insulator polarization converter is reported. The polarization conversion with an extinction ratio of 16 dB is achieved for a conversion length of only 10 μm. Polarization rotation is achieved by inducing a vertical asymmetry by forming in the waveguide core two subwavelength trenches of different depths. By taking advantage of the calibrated reactive ion etch lag, the two depths are implemented using a single mask and etching process. In this Letter, we report the design and fabrication of an ultracompact dual-trench polarization rotator in SOI, with a conversion length as short as 10 μm, for a wavelength of 1.5 μm. The converter schematic is shown in Fig. 1. The converter exploits the asymmetry induced by two adjacent subwavelength trenches, resulting in two orthogonal hybrid modes (Fig. 1, inset) with optical axes rotated 45º with respect to the x and y axes, that is, hybrid modes consisting of 50% TE and 50% TM polarization. This geometry allows both hybrid modes to be excited with equal efficiency by a TE (or TM) polarized input. The two hybrid modes propagate with different propagation constants along the device, resulting in a 90°polarization rotation at each half-beat length L 1∕2 :

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We present two techniques for mitigating the effects of temperature drifts in waveguide spatial heterodyne Fourier--transform on--chip spectrometers. In high--resolution devices, large optical path length differences result in an increased sensitivity to temperature variations and impose stringent requirement on the thermal stabilization system. In order to overcome this limitation, here we experimentally demonstrate two new temperature mitigation techniques based on a temperature--sensitive calibration and phase errors correction. The spectrometer chip under analysis comprises an array of 32 Mach--Zehnder interferometers fabricated on a silicon--on--insulator platform. The optical path delays are implemented as microphotonic spirals of linearly increasing length up to 3.779 cm, yielding a spectral resolution of 17 pm. We demonstrate that the degradation in retrieved spectra caused by temperature drift is effectively eliminated by temperature--sensitive calibration and phase errors correction. [5, 6], and cascaded micro--ring resonators [7, 8] can achieve sub--nanometer spectral resolution and compact chip sizes. However, the optical throughput (étendue) of these devices is fundamentally limited by the need for a single--mode input waveguide. On the contrary, spatial heterodyne Fourier--transform (SHFT) spectrometers can provide a substantially larger étendue due to the possibility of multiple input waveguide apertures [9]. In an SHFT system, multiple interferometric measurements are performed in parallel using an array of interferometers each with a different optical path length difference (OPD) [10]. The input spectrum is calculated by the Fourier transform (FT) of the stationary spatial interferogram, which can be captured by a detector array in a single shot.SHFT spectrometers have been successfully implemented on silicon--on--insulator (SOI) platform [9]. The high refractive index contrast of SOI provides a high modal confinement with a correspondingly reduced bend radius which ultimately allows to achieve a larger spectral resolution on a smaller chip footprint, The SHFT spectrometer can be implemented on an SOI platform as an array of N waveguide Mach--Zehnder interferometers (MZIs) [9]. In such configuration, the spectral resolution (δλ) is determined by the OPD of the most unbalanced interferometer while the free spectral range (FSR) is set by the numbers of interferometers (N) [9, 11]:(2) where λ0 is the device central wavelength, ΔLmax is the maximum MZI geometrical path difference and ng is the waveguide group index. For an arbitrary input signal, all the interferometer outputs (each corresponding to a different optical path difference) are

Polarization management is of paramount importance in integrated optics, particularly for highly birefringent photonic platforms such as silicon-on-insulator. In this paper, we present a polarization beam splitter based on a multimode interference coupler incorporating tilted subwavelength gratings. The tilt provides accurate control of the structural anisotropy and enables independent selection of the beat length for two orthogonal polarization states. As a result, device length is reduced to less than 100 μm while simultaneously achieving broadband operation through subwavelength grating dispersion engineering. Insertion losses below 1 dB and an extinction ratio higher than 20 dB are demonstrated through three-dimensional FDTD simulation in a 131-nm bandwidth.