Holographic planar lightwave circuit for on-chip spectroscopy

Computer-generated planar holograms are a powerful approach for designing planar lightwave circuits with unique properties. Digital planar holograms in particular can encode any optical transfer function with high customizability and is compatible with semiconductor lithography techniques and nanoimprint lithography. Here, we demonstrate that the integration of multiple holograms on a single device increases the overall spectral range of the spectrometer and offsets any performance decrement resulting from miniaturization. The validation of a high-resolution spectrometer-on-chip based on digital planar holograms shows performance comparable with that of a macrospectrometer. While maintaining the total device footprint below 2 cm2, the newly developed spectrometer achieved a spectral resolution of 0.15 nm in the red and near infrared range, over a 148 nm spectral range and 926 channels. This approach lays the groundwork for future on-chip spectroscopy and lab-on-chip sensing. An on-chip spectrometer based on digital planar holograms offers a miniature alternative to conventional devices. Developed by three research team in California, USA, the spectrometer uses two computer-designed holograms as high-resolution gratings for separating different wavelengths of light in the spectral bands of 630–694 nm and 766–850 nm. The holograms are made by electron beam lithography and reactive ion etching of a Si/SiO2/Si3N4 substrate. The result is a semiconductor spectrometer chip that occupies a footprint of less than 2 cm2 and boasts a resolution of 0.15 nm and a bandwidth of 148 nm across the red and near-infrared regions. The researchers say that the device’s performance is comparable to much larger conventional instruments and will be a useful component for ‘lab-on-a-chip’ applications such as sensing. They also believe that it should be possible to make even smaller versions with higher performance in the future.


INTRODUCTION
Spectrometers are employed in a variety of applications spanning biomedicine to material characterization and product quality control. 1 The core component of spectrometers is a dispersive optical element, such as prisms or diffraction gratings. In conventional spectrometers, light is guided to the dispersive element by a series of mirrors and is ultimately projected onto a detector. These spectrometers can reach ultrahigh resolution and have broad spectral ranges, but their portability and high cost limit their applicability. While the readout electronics can be easily scaled down, the size of spectrometers still represent a bottleneck to the integration with micro/nanoelectromechanical systems 2 or optofluidic devices [3][4][5] for portable sensing and lab-on-chip capabilities. Thanks to the development of nanophotonic structures to control light at the nanoscale, a number of compact spectrometers have been proposed over the last few years. Although miniaturization of spectrometers was proved to be feasible down to the micrometer scale, performance drops as the device footprint becomes smaller, which generally results in a decrement of resolution or spectral range. [6][7][8][9] Integrated spectrometers based on arrayed-waveguide gratings, 10,11 photonic crystals, 12 silicon spiral waveguides, 13 Mach-Zender interferometers, 14 microrings 15 and microresonators 16,17 can reach relatively high resolutions, but their spectral range is narrow and often constrained by the number of output waveguides. Approaches that use planar diffraction gratings 18 and echelle gratings 19,20 are also capable of high resolution, but their working range is mainly limited by their free spectral range.
Conversely, spectrometers based on microelectromechanical systems, 21 filter arrays of Fabry-Perot cavities 22 and particular types of arrayed photonic crystals 23,24 exhibit broad spectral ranges but have a poor resolution. Each of the aforementioned approaches is also not sufficiently resilient to fabrication errors. This problem encouraged the development of a more recent high-resolution spectrometer based on disordered scattering media. 7 Unfortunately, this solution is not flexible and can only work on a narrow spectral range.
To overcome all of these limitations, we have designed and fabricated a novel miniaturized spectrometer based on digital planar holograms (DPHs) that is capable of high resolution over a customizable spectral bandwidth. DPH technology belongs to the class of computergenerated holograms 25 and can encode any specific optical transfer function by manipulating the light in the spectral and spatial domains. In applications like integrated spectroscopy, DPH technology provides several decisive advantages over competing technologies in terms of resolution, bandwidth, robustness to fabrication errors and technology flexibility. As opposed to other approaches where light is dispersed in a continuous spectrum, a DPH spectrometer splits the source light in a discrete number of spectral components and focuses them onto different focal points (Figure 1). We have previously reported the fabrication of the DPH in different waveguide core (SiO 2 Ge x , HfO 2 and Si 3 N 4 ) in order to demultiplex the light in the visible wavelength range. [26][27][28][29][30] Over the years, we have demonstrated that one single planar hologram can reach a high resolution (down to 0.015 nm) in a very narrow spectral range 28 (1 nm) or be designed to work over multiple narrow bands 26 (up to 4). Here, we extend these results and demonstrate for the first time that DPHs can be used to build up a high-resolution, broadband spectrometer-on-chip with performance that are similar to conventional spectrometers. Our strategy consists of integrating multiple planar holograms on the same device and connects them with an optical circuitry ( Figure 1). Each DPH works in one specific spectral bandwidth, whereas the integrated circuitry includes several functionalities (taper, splitter, waveguide) to efficiently manipulate the light and guide it to the holograms. This geometry overcomes the limitations of devices with one single DPH, and makes it possible to further integrate the optical chip with external optical components, like an input optical fiber and output photodetectors. In this publication, we report the design, the fabrication and the characterization of one photonic device that integrates two DPHs with an optical circuitry, each of them being etched with a different depth in order to maximize their respective efficiency. The spectrometer chip works in two separate spectral bands (630-694 nm and 766-850 nm) for a total spectral bandwidth of 148 nm and 0.15 nm resolution. To the best of our knowledge, this is the first validation of a miniaturized spectrometer with spectral range and resolution that are comparable to conventional spectrometers. This opens a wide range of new opportunities for compact biosensors, lab-on-chip and portable medical diagnostic devices.

MATERIALS AND METHODS
The fundamental idea behind DPH is to exploit the focusing properties of elliptical Bragg gratings 31 and superimpose several elliptical gratings in a miniature supergrating. The supergrating is synthesized by performing a mathematical superposition of the refractive index modulation functions of the multiple sub-gratings, which define the structure. Considering the Fourier components f in (x,y,v) and f out (x,y,v) of the incoming and outgoing waves propagating through a planar waveguide, it can be shown that to transform f in (x,y,v) into f out (x,y,v), the variation of the effective refractive index must be computed as Dn eff (x,y)5#f in (x,y,v)f out (x,y,v)dv. This equation can also be expressed as Dn eff (x,y)5A(x,y)n eff (x,y), where n eff (x,y) is the effective refractive index of the planar waveguide core for the operating propagation mode, transverse electric or transverse magnetic. A(x,y) is an analog-generating function that describes the modulation of the effective refractive index and delineates the superposition of different interference fringes of diverging and converging light beams. The practical implementation of A(x,y) would imply that the device is fabricated with a multilevel relief and have nanometer resolution, which is impractical and time-consuming with existing lithography techniques. To overcome this complexity, the function A(x,y) is converted into a binary function B(x,y) by using a threshold algorithm to assign 1 s and 0 s. B(x,y) is a spatial map of two-leveled features, corresponding to etched and non-etched areas in the actual fabrication. The algorithm and the device simulations are simplified by replacing curved features of the function B(x,y) with rectangular grooves of the same width. This operation can be regarded as a quantization of the binary function B(x,y). The binarization and quantization of A(x,y) are strongly nonlinear processes that introduce detrimental phenomena like interference between the hologram outputs, scattering to cladding modes or second order core reflections. These problems are minimized by using a specifically developed design code, which dramatically reduces the incoherent scattering. More details about the simulation and design of the DPHs can be found in the Ref. 32.
One of the main properties of DPH technology is its flexibility. Just as computer logic consists of a series of 1 s and 0 s, optical transfer functions associated with any two-dimensional optical device can be generated by the combination of a limited set of holographic symbols defining a two-dimensional diffraction grating. In the specific case of a spectrometer, the DPH would implement a function to demultiplex the input light in the spectral domain, and reflect its components to different focal points (output channels) in the spatial domain. The hologram is embedded into a planar waveguide structure, which consists of a 158-nm-thick silicon nitride film deposited on top of an 8-mm-thick SiO 2 lower cladding on silicon. A high refractive index contrast between the core and the cladding (,25% for Si 3 N 4 wafers) further reduces scattering-related propagation losses from the DPH to the cladding modes. Figure 2a shows a low-magnification optical picture and a scanning electron microscope image of a digital hologram. Light entering the DPHs passes through a gradual variation of the refractive index achieved by lowering the periodicity of the hologram lines on the edge

Reference RWGs
Output channels Figure 1 Schematic of an integrated DPH spectrometer. The spectrometer-on-chip integrates one or multiple digital planar holograms and optical circuitry for coupling and wave-splitting operations. The light is brought to the chip with an optical fiber and coupled through a planar taper; light is guided with low losses by ridge waveguides and split based on its bandwidth by directional couplers; once directed to the hologram operating in the relative band, light is demultiplexed and focused on several different output channels at the edge of the chip. DPH, digital planar hologram.
Holographic circuit for on-chip spectroscopy G Calafiore et al 2 (Figure 2a), resulting in the elimination of spurious harmonics 30 that would otherwise be generated. As the light goes through the hologram, it gets reflected according to its wavelength towards different output focal points (channels) spaced 5.25 mm from each other. The depth of the DPHs is kept shallow, typically 10 to 20 nm (Figure 2b), in order to minimize refractive index perturbation and ultimately, increase the spectrometer's resolution. The linewidth of the DPH grooves is fixed to be l c /4n eff , l c being the central wavelength of the DPH. Each hologram is optimized to reach high performance on one spectral band of about 100 nm. Thus, in order to build broadband and/or multipleband spectrometer-on-chips, we have developed a specific type of optical architecture that couples several single-band DPHs in parallel on the same chip ( Figure 1). The solution that we designed consists of an optical circuit that connects the entire device and expands its functionalities. Light is introduced from a single mode fiber to the chip by means of a taper 33 to reduce coupling losses by matching the mode profiles in the horizontal direction. The input light is then split by directional couplers 34,35 according to its spectral band ( Figure 3) and directed through two distinct ridge waveguides (RWGs) to the two holograms, which are working in the separate spectral bands 630-694 nm (436 channels) and 766-850 nm (490 channels) respectively for a total bandwidth of 148 nm and 0.15 nm spectral resolution. Figure 3a and 3b shows the response of the splitter in case of l5662 nm and l5805 nm, respectively. At these wavelengths, the splitting ratio is maximum and the light is fully directed to the correspondent DPH. The dashed area in Figure 3c indicates the light that is sent to the opposite DPH, when the splitting efficiency is not maximum. Part of this light is transmitted through the hologram, the remaining part is dispersed upwards to the upper cladding, and consequently does not contribute to the output channel intensities since it is not reflected by the hologram that receives it. All of the optical elements that belong to the circuitry are optimized for the highest efficiency in the visible light range, and, unlike the DPHs, are etched through the full thickness of the waveguide core to reach a higher confinement of the light and reduce the losses in tight turns (Figure 2b).
The substrate consists of Si/SiO 2 (8 mm)/Si 3 N 4 (158 nm), from Lionix BV. 36 The planar holograms and the optical circuitry are fabricated by a twofold electron beam lithography (EBL) and reactive ion etching process, over two successive steps, for the optical circuitry and the holograms, respectively. Direct EBL writing is performed at 100 kV and 500 pA using a Vistec VB-300 EBL system. ZEP 520A is the resist used for the lithography with variable thickness: 200 nm and 60 nm for the optical circuitry and the DPHs, respectively. This is covered by a 100 nm thick conductive polymer, Aquasave ZA. This process is carefully reported in Ref. 37. Specific EBL proximity corrections are applied with CATS software from Synopsis. 38 Plasma etching processes are carried out with a Reactive Ion Etching tool (Oxford Plasmalab 80) and optimized for slow etching, high vertical sidewalls and minimum edge roughness. The optical circuitry is etched through the full thickness of the waveguide core with a mixture of 50 sccm CHF 3 -4% O 2 at 55 mT of pressure and 50 W of radio frequency power. The same recipe is used for etching the DPH grooves with power reduced to 25 W to have more precise control over the etching depth. The planar structure of DPHs makes them compatible with high-volume manufacturing by standard complementary metal oxide semiconductor lithography techniques and nanoimprint lithography, as shown in our previous work. 39 After the lithography step, the chip is covered with a 2-mm-thick SiO 2 upper cladding that is deposited by plasma enhanced chemical vapor deposition at 350 6 C to protect the DPH structure and minimize light scattering. 27

RESULTS AND DISCUSSION
The holographic spectrometers were tested using the optical set-up described in detail in Ref. 27. A micro-objective system is used to project the demagnified image of the output fiber from the light source to the input of the DPH chip. In experiments an optical parametric oscillator with a 0.2-nm-bandwidth that is tunable in the range of 400-2700 nm is used, unless otherwise specified. The power and spectrum of light at the DPH input is monitored with the Avantes-2048 spectrometer, 40 which has a spectral resolution of 0.4 nm. Simulations of the light propagation and reflection into the planar hologram are performed with the proprietary code Spectroplan. 41 The upper section of the Figure 4 maps the simulated geometrical distribution of the hologram's reflectivity for the DPH that operates in the red wavelength range, when it is illuminated at l5660.59 nm. Simulations show that the reflectivity of the hologram in one output channel is around 35%65%. To determine the actual reflective power of our holograms, a second directional coupler, that is located in proximity of the RWG end, splits the light with a splitting ratio of 10%. The main portion of light is directed towards the hologram via a single-mode RWG, while the rest is coupled into a reference RWG (Figure 1). By comparing the signals at the reference RWGs to the output of the hologram, the actual coupling efficiency of the splitters and reflectivity  Holographic circuit for on-chip spectroscopy G Calafiore et al 4 of the holograms can be calculated. In good agreement with our simulations, the reflection of the DPHs was evaluated to be 40%615%, depending on several parameters, including hologram depth. The value of reflection is calculated, accounting for material losses along free space propagation, which were measured to be around 2 dB cm 21 for wavelengths in the range of 600-900 nm. The losses associated with the vertical edge roughness of the RWGs are found to be around 6 dB m 21 (at 660 nm wavelength) due to the high field amplitude at the edge of the waveguides. These losses are reduced by adiabatically widening the RWG linewidths up to 5 mm over long straight paths. 42,43 The total output/input ratio is around 215 dB, mostly due to material losses and the low coupling efficiency measured to be around 20% for wavelengths from 600 to 800 nm. The stray light due to imperfect coupling of the fiber with the input RWG is visible in Figure 5a. In spite of these losses, an input spectral intensity as low as 50 pw nm 21 is sufficient for signal detection (3s level) with an integration time of 10 ms.
The lower section of Figure 4 shows the simulated variation of the beam phases at the output of the hologram. The phases that light beams with the same wavelength acquire when reflected by the DPH are assigned accounting for the different optical paths from the DPH to the output channel. With the correct phase shift, light will constructively interfere at the focal points, maximizing the output intensities. A representation of the output light profile and output intensities is shown in Figures 5b. The intensity distribution at the output plane of the DPH is recorded using a charge-coupled device camera (50 frames per second).
The physical position of the activated output channel is univocally determined by the wavelength of the input light. Figure 5b illustrates the intensity profile of the output channels when a laser beam with 10 pm bandwidth illuminates the device input; as expected, only one channel is activated. By comparing adjacent channel intensities (Figure 5c), the device cross-talk can be measured. The cross-talk is defined as the ratio between the light intensity in one channel and the intensity of the interfering light in lateral channels. In our spectrometer, it is evaluated to be around 10 dB over the entire spectral range, which is adequate to allow the analysis of complex spectra. Figure 5c shows the response to six different wavelengths and the relative correspondence to the output channel number. Reporting wavelengths to wavenumbers, their association with relative channel numbers is plotted in Figure 5d, which shows the linearity of the device dispersion curve with accuracy better than 20% of channel spacing, as expected by design. In addition to the bandwidth and resolution, the dispersion curve of a DPH spectrometer can be customized to assume any specific profile, allowing resolution changes over different bands of interest for specific applications. Initial attempts to integrate the spectrometer with an electronic readout were performed. A temperature monitor of the DPH-detector assembly was provided in the integration. As a result, after the proper temperature-wavelength calibration, the device showed strong resistance to temperature variation and enabled the identification of isolated narrow laser lines with an accuracy of about 20 pm. The spectral emission of a laser diode was measured by our spectrometer and compared with the response from a standard spectrometer that is commercially available (Figure 6). The edge view of the light coming out of the channels is taken by a charge-coupled device array and reported in Figure 6 (upper section; the gray profile plots the actual channel light intensities). Light between the maxima of the grey curve in Figure 6 is concentrated into the nearby peaks. The spline interpolation of this 'quantized' reading constitutes the spectrum of the incoming light (in green) as seen by our spectrometer, while the red curve is the spectrum of the same laser diode measured by the Avantes spectrometer. Both spectrometers present similar optical responses. This result validates DPH technology as a competitive candidate to the development of on-chip spectroscopy, and opens a wide range of unexplored opportunities for lab-on-chip development.

CONCLUSIONS
We have reported a novel solution to integrate multiple digital planar holograms on the same chip and demonstrated the first spectrometeron-chip that presents performance that is competitive with conventional macro-spectrometers. While the area occupied by a DPH is below 3 mm 2 and the overall device footprint is smaller than 2 cm 2 , the spectrometer has a resolution as low as 0.15 nm over 148 nm spectral range and 926 channels. Integration of multiple DPHs based on the ideas reported here promises development of an even broaderband compact spectrometer. The sensitivity, resolution, dispersion curve and spectral region of spectrometers can be easily customized exploiting the flexibility of our DPH design code to cover a large wavelength range, from visible light to mid-wavelength infrared, and can be produced at a low cost by nanoimprint lithography. The already small footprint can be further reduced by monolithically integrating photodetectors on chip, in order to shorten the distance between the output plane and the holograms, and minimize the required volume. We believe that DPH technology offers a unique platform for developing a miniaturized, broadband, high resolution and on-demand spectrometer for a new variety of lab-on-chip applications and sensors. Comparison between the optical responses to a laser diode input light beam of a DPH spectrometer-on-chip (green) and a commercial conventional spectrometer (red). The gray line represents the actual profile of the light exiting the 26 output channels spread over the 137.5 mm DPH chip edge. Meaningful information of the input spectrum can be determined by interpolation of the channel peaks. A third-order spline is used to outline the DPH spectrum, reported in green. The resolution of the DPH spectrometer used in this experiment is 0.15 nm/channel whereas the other spectrometer has 0.4 nm resolution. Light emitted by the laser diode is split and sent to the compact and conventional spectrometers for analysis; responses are then overlapped and compared. From the similarity of the two curves, we can conclude that performances of DPH spectrometer-on-chip can compete with that of a traditional spectrometer (within the reading tollerance of the two devices). DPH, digital planar hologram.
Holographic circuit for on-chip spectroscopy G Calafiore et al