Development of high resolution arrayed waveguide grating spectrometers for astronomical applications: first results
Pradip Gatkine, Sylvain Veilleux, Yiwen Hu, Tiecheng Zhu, Yang Meng, Joss Bland-Hawthorn, Mario Dagenais
DDevelopment of high-resolution arrayed waveguide gratingspectrometers for astronomical applications: first results
Pradip Gatkine a , Sylvain Veilleux a,b , Yiwen Hu c , Tiecheng Zhu c , Yang Meng c , JossBland-Hawthorn d , and Mario Dagenais ca Department of Astronomy, University of Maryland, College Park, Maryland 20742, USA b Joint Space-Science Institute, University of Maryland, College Park, Maryland 20742, USA c Department of Electrical and Computer Engineering, University of Maryland, College Park,Maryland 20742, USA d Sydney Institute for Astronomy and Sydney Astrophotonic Instrumentation Labs, School ofPhysics, The University of Sydney, New South Wales 2006, Australia
ABSTRACT
Astrophotonics is the next-generation approach that provides the means to miniaturize near-infrared (NIR) spec-trometers for upcoming large telescopes and make them more robust and inexpensive. The target requirementsfor our spectrograph are: a resolving power of ∼ N in the core of our waveguides. Thewaveguide bending losses are minimized by optimizing the geometry of the waveguides. Our first generation ofAWG devices are designed for H band have a resolving power of ∼ ∼
10 nm arounda central wavelength of 1600 nm. The devices have a footprint of only 12 mm × ∼ -1 dB) and contrast ratio of about 1.5%(-18 dB). These results confirm the robustness of our design, fabrication and simulation methods. Currently,the devices are designed for Transverse Electric (TE) polarization and all the results are for TE mode. We aredeveloping separate J- and H-band AWGs with higher resolving power, higher throughput and lower crosstalkover a wider free spectral range to make them better suited for astronomical applications. Keywords:
Astrophotonics, Arrayed Waveguide Gratings (AWGs), near-infrared (NIR), H band, spectrometer
1. INTRODUCTION
The J- and H-bands of near-infrared (NIR) light are crucial in studying phenomena in the first billion years (z ∼ α ), characteristic of the starformation, is redshifted to NIR band. To obtain the NIR spectra of high redshift probes such as quasars andgamma ray burst (GRB) afterglows, large telescopes such as Keck 10-meter telescopes are required.The next-generation of ground-based extremely large telescopes (ELTs) in optical and NIR will have diametersin the range of thirty meters (eg. Thirty Meter Telescope). This necessitates the development of suitable seeinglimited spectroscopic instrumentation. The size of the optical components in a conventional spectrograph scalesroughly with the telescope diameter D, hence the volume, mass, and cost of the instrument scale roughly asdiameter cubed. This highlights the need for innovation to build instruments for upcoming Extremely LargeTelescopes (ELTs). Astrophotonics is a new approach that will miniaturize the next-generation spectrometersfor large telescopes by the virtue of its two-dimensional structure. As each pixel is a fiber at the slit, the
Further author information: (Send correspondence to P. Gatkine)E-mail: [email protected] a r X i v : . [ a s t r o - ph . I M ] J un ollimating lenses are no longer required. The light is guided through the fibers and waveguides into the 2-dimensional structure for dispersion, thus reducing the size of spectroscopic instrumentation to few centimetersand the weight to a few hundreds of grams. These devices are also much less expensive than conventionalastronomical spectrographs with commensurate specifications (resolution, efficiency and operating wavelengthrange). AWG device has originated from the need of increasing the data rate in the field of fiber-optic communication.This was achieved by using AWG as a wavelength separating and wavelength combining device. The pioneeringpaper by Meint Smit described the detailed theory of AWG design in 1996. The traditional uses of AWG involvedhigh power sources centered on a narrow band (5-10 nm) around wavelength 1550 nm, which is the standardin telecommunication industry. But in principle, the same theory can be used for spectroscopic purposes. Inparticular, some of the recent work towards making ultra-low loss AWG devices made it possible to explore theutility of AWG based spectrographs in astronomical instrumentation. There have also been successful preliminarytests of using modified commercial AWGs for astronomical spectroscopy.
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AWGs, along with other advancesin the field of astrophotonics, such as photonic lanterns to convert multimode fibers to single mode fibers,Bragg gratings (in-fiber as well as on-chip ) to suppress unwanted OH-emission background (in NIR) andhigh-efficiency fiber bundles for directly carrying the light from the telescope focal plane, offer a complete highefficiency miniaturized solution for astronomical spectroscopy in NIR. This has a potential to be a paradigmshifting development for future ground-, balloon- and space-based telescopes.The analogy between AWGs and a conventional grating spectrograph is shown in Fig. 1. Light propagates inconfined guided paths by the principle of total internal reflection. The focusing lenses are replaced by on-chipfree propagation regions (FPR) and the gratings are replaced by the array of waveguides guiding the light alongthe lines with a fixed desired path differences by linearly increasing the waveguide length from bottom to top.The fixed path difference between adjacent waveguides depends on the spectral order. The output light from thearray propagates through the output FPR and different wavelengths constructively interfere at different positionson the concave output facet. The dispersed light can be collected in output waveguides or sent to the detectorthrough free space. A sample light path with AWG used as a spectrograph is shown in Fig. 2. Figure 1. Analogy between conventional grating spectrograph (left) and arrayed waveguide gratings (right)
The requirements for the spectrograph are set by the science goals. The main science goals we are considering hereare: (1) precise measurement of the metallicity of high-z GRB hosts and the intervening systems by measuringthe equivalent widths of a few metal-diagnostic lines and (2) a proper characterization of red damped wingof Lyman- α in GRB afterglow spectrum for constraining HI column density (N H I ) and intergalactic mediumroperties. Achieving these goals requires a spectral resolving power ( λ /∆ λ ) of ∼ ∼ Figure 2. A sample light path with AWG used as a spectrograph in an astronomical setupTable 1. Preliminary and future target specifications for the proposed AWG device in the order of importance
Parameters Preliminary Target Future Target
1. On-chip Throughput 80% 90%2. Peak Overall Throughput(including coupling + propagation) 15% 35%3. Operating Waveband H band (1450-1700 nm) H band (1450-1700 nm)J-band (1150-1400 nm)4. Resolving Power (R) ∼ ∼ ∼ contrast ratio) ∼ ∼
2. METHODS
The target specifications in astronomy are very different from the traditional narrowband, high power applicationsof AWGs in telecommunication industry from where the concept of AWGs originate. The book by Okamoto explains the principles of operation and fundamental characteristics of AWGs. The pioneering paper by MeintSmit dwells upon the design procedures, geometrical layout and various practical issues of AWGs. The firsttheoretical and experimental work towards proving the capabilities and limitations of an astronomical AWGspectrograph was conducted by Lawrence et al. Buried silicon nitride platform is the leading solution forlow-loss AWGs. The photonics group at UC Santa Barbara have performed several experiments with thisplatform for applications in telecommunication industry.
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These results are also useful for the development ofan astronomical AWG spectrometer.eveloping a photonic AWG spectrometer involves 4 broad steps: design, simulation, fabrication and character-ization of the instrument. In our first design we are developing an AWG spectrometer for H band (1450-1650nm). In this section, we will describe the design methodology followed, the simulations performed and fabricationtechniques developed to achieve our preliminary target specifications.
For developing low-loss AWGs, the selection of material profile is crucial. We use Si N waveguides buried inSiO as shown in Fig. 3 since it is the most suitable configuration for low on-chip transmission loss. The mostimportant sources of loss in AWG (in the order of importance) are:1.
Coupling loss from fiber to waveguide and vice versa due to mismatch between fiber mode and waveguidemode2.
Sidewall scattering loss : The fabrication processes limit the smoothness of sidewalls of the waveguides,thus leading to a loss of guided light through scattering from the sidewalls. This loss can be mitigated by makingvery thin waveguides to reduce the sidewall area.3.
Bending loss due to radiation-leaking of light from the curved waveguides in AWG. A weakly confined modeloses light more easily than a strongly confined mode.4.
Absorption loss : The waveguide material has a finite absorption co-efficient which leads to absorption of asmall amount of guided light.In our first design we focused on sidewall loss and bending loss. We used a waveguide width of 2.8 µ m and aheight of 0.1 µ m in order to minimize the bend loss as demonstrated in Ref and sidewall roughness loss, sinceAWGs have extended curved waveguides. This waveguide geometry is shown in Fig. 3. The waveguide geometryand the design was modified in the second version for better coupling efficiency (as explained in results section).The dispersed light for all the spectral orders is received by the output channels (i.e. output waveguides) andguided to the edge of the chip, called facet, where it can be coupled with the output fiber for characterization.We chose to sample the focal plane of dispersed light at 5 discrete uniformly spaced points to ensure sufficientcharacterization. Thus the design has 5 output waveguides, each sampling a specific region of the output planeand the output spectrum. We developed a code to automate the process of design as shown in Fig. 4. Selection of spectral order :A spectral order m = 165 (at λ = 1600 nm) is used in this design to maximize the free spectral range and atthe same time keeping the incremental path difference between adjacent arrayed waveguide and thereby, the sizeof the chip small. Using a higher spectral order results into a higher incremental path difference and increasedchip-size. Also, if the order is too small, the center to center distance between adjacent waveguides at the freepropagation region (FPR) interface reduces, thus making the FPR overcrowded and leading to higher crosstalkbetween adjacent waveguides. Therefore, a spectral order m = 165 is used to strike a balance between freespectral range (FSR) and chip-size for the first design. In future, we plan to push the boundaries to increaseFSR to the target specification of 30 nm. Figure 3. Geometry and material profile of the waveguide cross-section. .2 Simulations
We simulate the design obtained in the step above using RSoft CAD and AWG utility of BeamPROP software. The CAD for the first AWG design is shown Fig. 5 and the simulation result is shown in Fig. 6. There are straightand curved reference waveguides below the AWG (in the CAD), which are used to calibrate the output. Theoverall size of the AWG chip is 8mm × λ ∼ Figure 4. AWG Design procedure. For details, please see Ref Figure 5. CAD of AWG (first design). Note the vertical cleaving marks near the four corners to aid cleaving the edgesto expose optical quality cross-section of waveguides for fiber coupling. The extra waveguides at the bottom are forcalibration
To fabricate AWG chip, we use silicon substrate with 10 µ m of thermal silica (SiO ) pre-deposited on it. Wedeposit 0.1 µ m silicon nitride (Si N ) on top of that using LPCVD (Low Pressure Plasma Enhanced Deposition).The processes followed to fabricate buried Silicon Nitride AWG device (in the sequence) are: Electron-beamlithography, electron-beam Chromium metal deposition, Chromium lift-off leaving only the Chromium mask foretching, reactive ion etching (RIE) to a depth of 0.1 µ m, Chromium etching to dissolve the mask and finally,PECVD (Plasma Enhanced Chemical Vapor Deposition) of 6 µ m of SiO as the upper cladding layer of thedevice. After fabrication, the sample is cleaved at precise locations from left end and right end to expose facetsof the input and output waveguides for coupling the light. The facets are of optical quality, since the samplebreaks along the crystal plane of the chip. The fabrication sequence is briefly shown in Fig. 7. avelength (nm) T r an s m i ss i on i n l og sc a l e Channel 1Channel 2Channel 3Channel 4Channel 5
Figure 6. Simulated transmission of 5 output channels of AWG (4 spectral orders shown here)Figure 7. Fabrication sequence for AWG. Here, PMMA is a chemical used as photoresist (a material which changesproperty when it is exposed to electron beam) and is washed out when the exposed area is developed with a chemicaldeveloper (called MIBK).
To characterize the transmission spectrum of the AWG, a broadband superluminescent diode source by Throlabs(S5FC1550P- A2) operating in a waveband of 1450 nm - 1650 nm is used. A polarization maintaining (PM) fiber,PM1550-XP is connected to this light source and is optically coupled to the AWG input waveguide. AnotherPM fiber is optically coupled to one of the output waveguides and the other end of the fiber is connected tothe Optical Spectrum Analyzer (OSA, YOKOGAWA AQ6370C). The optical coupling is achieved by carefulalignment of the fibers and the AWG chip. The characterization setup is illustrated in Fig. 8. The output fiber iscoupled to all the output channels of AWG one by one and the transmission response of each channel is recorded.Similarly, the transmission response of the straight reference waveguide is obtained by coupling the fibers toit. The reference waveguide transmission response is used to normalize the AWG response to obtain the trueon-chip response. The normalization process makes the characterization independent of the input intensity andfiber to chip coupling losses. The broadband light source is measured to be steady within 0.05 dB (within 1%)as a function of time.
3. RESULTS
We fabricated the AWG devices as described in the previous section and characterized them. For the first AWGdevice we used 2.8 µ m width for waveguides and 0.1 µ m height. There are three transmission responses that areimportant: (1) Transmission from PM fiber to PM fiber : This defines the input power that is fed to the AWG chip. (2) Transmission response of the reference waveguide : This incorporates the fiber to waveguide couplingefficiency (at input and output side) and the propagation loss of the waveguide (3) On-chip AWG throughput : This is the efficiency of the AWG structure and thus incorporates loss due tocurvature of the waveguides, insertion loss between the waveguides and free propagation region (FPR) interfacesand additional propagation loss due to excess length of waveguides in the array. igure 8. A schematic of the characterization setup with its main constituents and degrees of freedom. In this section, we will present the results from our first AWG and further improvement in the overall throughputby adding mode transforming taper between waveguide and fiber and tweaking the waveguide dimensions in thesecond AWG.
Fig. 9 shows PM fiber to PM fiber transmission response and reference waveguide transmission (for TE polar-ization). Fiber to fiber response is equivalent to input light intensity because the fiber attenuation is very small( < Table 2. Key Spectral parameters of the TE polarization transmission response for the first AWG λ (nm) Full width at halfmaximum (FWHM) in nm Free Spectral Range(nm) Resolving Power(R = λ /FWHM) igure 9. Comparison of PM fiber to PM fiber transmission response (red) with reference waveguide transmission response(blue) for TE polarization for 1st AWG. Most of the loss is due to fiber to waveguide coupling loss. Wavelength (nm) T r an s m i ss i on N o r m a li z ed t o r e f e r en c e w a v egu i de ( i n % ) Channel 1Channel 2Channel 3(Central channel)Channel 4Channel 5
Figure 10. TE polarization normalized transmission response of all 5 output channels of AWG in the wavelength rangeof 1450 to 1660 nm
As explained earlier, the most important contribution to the overall loss comes from fiber to waveguide couplingloss. The coupling loss occurs due to mismatch between mode profiles of the fiber and the waveguide. One way tosolve this problem is using narrow waveguides which tend have very large mode size (squeezed-out modes). Butdue to their weakly confined modes, we cannot directly use them in AWG. Therefore, we use narrow waveguidesat the coupling ends and then lateral adiabatic tapers to slowly increase the waveguide width to the desiredvalue. Then this wide waveguide is used for the AWG structure. This concept is illustrated in Fig. 12.To balance the trade-off between using a weakly confined mode for better coupling efficiency and a stronglyconfined mode for low AWG losses, we designed an AWG with 2 µ m width (as opposed to previous width of2.8 µ m) and 0.1 µ m thickness (same thickness as previous). In addition to that we added tapered geometry atthe fiber coupling ends of the input and output waveguides (as shown in Fig. 12). Since 2 µ m waveguide hasless confined mode than 2.8 µ m, the on-chip throughput slightly decreases (from ∼
80% to ∼ ∼
8% to ∼
26% ). The crosstalk (contrast ratio) has slightly increased for 2 µ m AWG (from ∼
2% to ∼ avelength (nm)1604 1605 1606 1607 1608 1609 1610 1611 1612 T r an s m i ss i on N o r m a li z ed t o r e f e r en c e w a v egu i de ( i n % ) Channel 1Channel 2Channel 3Channel 4 Channel 5
Crosstalk:~ 1.5%
43 % 63% 68 % 63 % 49 %1.6nm1.6nm1.6nm 1.6nm
Figure 11. TE mode transmission response of AWG in range 1604 nm to 1612 nm. Center to center wavelength separationbetween adjacent channels as well as peak values of normalized transmission for all channels are shown. The small rippleson the peaks are due to inherent spatial variation in the refractive index of the material leading to small phase variations,ultimately causing ripples in the transmission.Figure 12. Illustration of the concept of tapered modification of mode index. The taper geometry (top view) is exponential.From left to right, the mode size slowly decreases before finally converging to the mode profile of the waveguide.
In summary, we developed preliminary AWG spectrometer devices for H band with performance close to thepreliminary target specifications. Most importantly, we achieved a peak on-chip throughput of 80% in one deviceand a peak overall throughput of 13% in the second device using our design and fabrication techniques. Thecomparison between target specifications and achieved specifications (for TE polarization) is described in Table3. The coupling efficiency significantly increased from first AWG to the second due to the use of taper geometry.The on-chip performance slightly declined from first to the second due to weaker confinement of the waveguidemode leading to slightly higher bending losses and higher interaction between adjacent waveguides, causing ahigher crosstalk. But even with this decline, the overall throughput significantly increased from first AWG to thesecond, since major source of loss is the coupling loss. Current results are very encouraging but more experimentsare required to attain an optimum point between coupling and on-chip throughput.These results confirm the robustness of our design, fabrication and simulation methods and set the path forfurther improvements. We have achieved the operating waveband of almost entire H band (1450 – 1650 nm). Tocharacterize the device beyond 1650 nm we need to use a wider band source in the future. igure 13. Summary of comparison between measured performance of first (w = 2.8 µ m AWG, shown in red) and second(w = 2 µ m AWG, shown in blue) AWG design. Clearly, the overall throughput (box 3) has significantly increased in thesecond design, mainly due to better coupling (box 1), but the on-chip performance (box 2) has slightly declined. Thelower overall throughput in 1450 – 1550 nm range is due to unwanted Si-H bond in the SiO cladding. This problemis addressed in Section 4. Crosstalk (box 4) has slightly increased for 2 µ m AWG, which is mainly due to the weakerconfinement of the mode. Here, each point refers to the central wavelength of each order.
4. FUTURE WORK
The future work will be mainly focused on increasing the throughput at moderate resolution and then goingto higher resolution. At present, there are following practical ways to increase the throughput which will beexplored in future. able 3. Comparison between target parameters and measured parameters
Parameters TargetSpecifications 1st AWGw=2.8 µ m 2nd AWG(w=2 µ m with taper)
1. On-chip Throughput 80% ∼
80% (Peak) ∼
60% (Peak)2. Peak Overall Throughput(including coupling +propagation) 15% 6% 13%3. Resolving Power(at 1600 nm) 1500 1600 17754. Crosstalk(Contrast Ratio) 1% ∼ ∼ Using better taper geometries : Currently, we are using 0.9 µ m to 2 µ m taper. Further reducing the initialwidth will make the mode size larger, thus matching the fiber mode profile better. Our beam propagationsimulations using BeamPROP software (using Beam Propagation Method), indicate that a starting width of0.6 µ m comes closest to the fiber mode profile. Therefore, it is expected to give a higher coupling efficiency. Increasing throughput in 1450 - 1550 nm range using annealing : The increased attenuation in the range1450 to 1550 nm (see Fig. 13) is due to presence of unwanted Si-H bond in the cladding SiO that is depositedusing PECVD (Plasma Enhanced Chemical Vapor Deposition) in the last step of fabrication (see Fig. 7). Thisbond absorbs in NIR with peak absorption at 1400 and 1520 nm. Annealing the sample in a certain heatingprofile to 1200 C after PECVD step is a potential solution to alleviate this problem by liberating the hydrogen. Improving on-chip throughput : Reducing the thickness of the waveguides has been demonstrated as a way toachieve better on-chip throughput. With a reduced thickness, the width of the waveguides need to be increasedto maintain the same confinement of the mode. With a wide waveguide, the mismatch between the waveguideand the free propagation region on the chip is reduced, thus improving the on-chip throughput. Also, due toreduced height, the sidewall scattering area is reduced, thus reducing the scattering loss.Apart from these improvements, it is important to improve the Transverse Magnetic (TM) polarization responseof the AWG since most of the astronomical light to be observed with this device is largely going to be unpolarized.Making a polarization-independent AWG over such a wide band is a challenging problem due to the inherentbirefringence of the waveguide geometry. One way to solve this problem is by using a polarization splitter to feedTE light to one AWG and TM light to another AWG (specifically designed for TM mode). The other way willbe to develop a geometry of the waveguides that is polarization independent over a wide band. A square-shapedgeometry is more suited for this purpose, but there are other constraints such as single-mode (fundamental TEand TM) propagation condition, sidewall roughness for deeper etches and wideband performance. Therefore,currently it is challenging to achieve.
ACKNOWLEDGMENTS
The authors thank the University of Maryland NanoCenter and Fablab for providing all the fabrication equip-ment. In particular, we thank Jonathan Hummel, Tom Loughran and Mark Lecates for fabrication processtraining and advice. The authors thank Prof. Stuart Vogel for his suggestions. The authors acknowledge thefinancial support for this project from the W. M. Keck Foundation.
EFERENCES [1] Bland-Hawthorn, J. and Horton, A., “Instruments without optics: an integrated photonic spectrograph,” in[
SPIE Astronomical Telescopes+ Instrumentation ], 62690N–62690N, International Society for Optics andPhotonics (2006).[2] Bland-Hawthorn, J. and Kern, P., “Astrophotonics: a new era for astronomical instruments,”
Optics Ex-press (3), 1880–1884 (2009).[3] Cvetojevic, N., Jovanovic, N., Bland-Hawthorn, J., Haynes, R., and Lawrence, J., “Miniature spectro-graphs: characterization of arrayed waveguide gratings for astronomy,” in [ SPIE Astronomical Telescopes+Instrumentation ], 77394H–77394H, International Society for Optics and Photonics (2010).[4] Smit, M. K. and Van Dam, C., “Phasar-based wdm-devices: Principles, design and applications,”
IEEEJournal of Selected Topics in Quantum Electronics, 2 (2) (1996).[5] Bauters, J. F., Heck, M. J., John, D., Tien, M.-C., Leinse, A., Heideman, R. G., Blumenthal, D. J., andBowers, J. E., “Ultra-low loss silica-based waveguides with millimeter bend radius,” in [
Proceedings of the36th European Conference on Optical Communication ], (2010).[6] Dai, D., Wang, Z., Bauters, J. F., Tien, M.-C., Heck, M. J., Blumenthal, D. J., and Bowers, J. E., “Low-loss silicon nitride arrayed-waveguide grating (de) multiplexer using nano-core optical waveguides,”
Opticsexpress (15), 14130–14136 (2011).[7] Akca, I. B., Ismail, N., Sun, F., Driessen, A., Worhoff, K., Pollnau, M., and de Ridder, R. M., “High-resolution integrated spectrometers in silicon-oxynitride,” in [ CLEO: Applications and Technology ], JWA65,Optical Society of America (2011).[8] Cvetojevic, N., Jovanovic, N., Lawrence, J., Withford, M., and Bland-Hawthorn, J., “Developing arrayedwaveguide grating spectrographs for multi-object astronomical spectroscopy,”
Optics express (3), 2062–2072 (2012).[9] Cvetojevic, N., Jovanovic, N., Betters, C., Lawrence, J., Ellis, S., Robertson, G., and Bland-Hawthorn,J., “First starlight spectrum captured using an integrated photonic micro-spectrograph,” Astronomy &Astrophysics , L1 (2012).[10] Leon-Saval, S. G., Argyros, A., and Bland-Hawthorn, J., “Photonic lanterns: a study of light propagationin multimode to single-mode converters,”
Optics Express (8), 8430–8439 (2010).[11] Trinh, C. Q., Ellis, S. C., Bland-Hawthorn, J., Lawrence, J. S., Horton, A. J., Leon-Saval, S. G., Shortridge,K., Bryant, J., Case, S., Colless, M., et al., “Gnosis: the first instrument to use fiber bragg gratings for ohsuppression,” The Astronomical Journal (2), 51 (2013).[12] Zhu, T., Hu, Y., Gatkine, P., Veilleux, S., Bland-Hawthorn, J., and Dagenais, M., “Arbitrary on-chip opticalfilter using complex waveguide bragg gratings,”
Applied Physics Letters (10), 101104 (2016).[13] Lawrence, J., Bland-Hawthorn, J., Bryant, J., Brzeski, J., Colless, M., Croom, S., Gers, L., Gilbert, J.,Gillingham, P., Goodwin, M., et al., “Hector: a high-multiplex survey instrument for spatially resolvedgalaxy spectroscopy,” in [
SPIE Astronomical Telescopes+ Instrumentation ], 844653–844653, InternationalSociety for Optics and Photonics (2012).[14] Okamoto, K., [
Fundamentals of optical waveguides ], Academic press (2010).[15] Lawrence, J., Bland-Hawthorn, J., Cvetojevic, N., Haynes, R., and Jovanovic, N., “Miniature astronomi-cal spectrographs using arrayed-waveguide gratings: capabilities and limitations,” in [
SPIE AstronomicalTelescopes+ Instrumentation ], 77394I–77394I, International Society for Optics and Photonics (2010).[16] RSoft Photonics, C., “Layout user guide, rsoft design group, inc,”
Physical Layer Division .[17] BeamPROP. https://https://optics.synopsys.com . AWG Utility from Synposys.[18] Henry, C. H., Kazarinov, R., Lee, H., Orlowsky, K., and Katz, L., “Low loss silicon nitride – silica opticalwaveguides on silicon,”
Applied optics26