D. Bodenmüller

Generation of an astronomical optical frequency comb in three fibre-based nonlinear stages

The generation of a broadband optical frequency comb with 80 GHz spacing by propagation of a sinusoidal wave through three dispersion-optimized nonlinear stages is numerically investigated. The input power, the dispersion, the nonlinear coefficient, and lengths are optimized for the first two stages for the generation of low-noise ultra-short pulses. The final stage is a low-dispersion highly-nonlinear fibre where the ultra-short pulses undergo self-phase modulation for strong spectral broadening. The modeling is performed using a Generalized Nonlinear Schrodinger Equation incorporating Kerr and Raman nonlinearities, self-steepening, high-order dispersion and gain. In the proposed approach the sinusoidal input field is pre-compressed in the first fibre section. This is shown to be necessary to keep the soliton order below ten to minimize the noise build-up during adiabatic pulse compression, when the pulses are subsequently amplified in the next fibre section (rare-earth-doped-fibre with anomalous dispersion). We demonstrate that there is an optimum balance between dispersion, input power and nonlinearities, in order to have adiabatic pulse compression. It is shown that the intensity noise grows exponentially as the pulses start to be compressed in the amplifying fibre. Eventually, the noise decreases and reaches a minimum when the pulses are maximally compressed. A train of 70 fs pulses with up to 3.45 kW peak power and negligible noise is generated in our simulations, which can be spectrally broadened in a highly-nonlinear fibre. The main drawback of this compression technique is the small fibre length tolerance where noise is negligible (smaller than 10 cm for erbium-doped fibre length of 15 m). We finally investigate how the frequency comb characteristics are modified by incorporating an optical feedback. We show that frequency combs appropriate for calibration of astronomical spectrographs can be improved by using this technique.

Astronomical optical frequency comb generation and test in a fiber-fed MUSE spectrograph

We here report on recent progress on astronomical optical frequency comb generation at innoFSPEC-Potsdam and present preliminary test results using the fiber-fed Multi Unit Spectroscopic Explorer (MUSE) spectrograph. The frequency comb is generated by propagating two free-running lasers at 1554.3 and 1558.9 nm through two dispersionoptimized nonlinear fibers. The generated comb is centered at 1590 nm and comprises more than one hundred lines with an optical-signal-to-noise ratio larger than 30 dB. A nonlinear crystal is used to frequency double the whole comb spectrum, which is efficiently converted into the 800 nm spectral band. We evaluate first the wavelength stability using an optical spectrum analyzer with 0.02 nm resolution and wavelength grid of 0.01 nm. After confirming the stability within 0.01 nm, we compare the spectra of the astro-comb and the Ne and Hg calibration lamps: the astro-comb exhibits a much larger number of lines than lamp calibration sources. A series of preliminary tests using a fiber-fed MUSE spectrograph are subsequently carried out with the main goal of assessing the equidistancy of the comb lines. Using a P3d data reduction software we determine the centroid and the width of each comb line (for each of the 400 fibers feeding the spectrograph): equidistancy is confirmed with an absolute accuracy of 0.4 pm.

Precise control of dispersion flatness in silicon nitride waveguides by cladding refractive index engineering

A technique for flattening the chromatic dispersion in silicon nitride waveguides with silica cladding is proposed and numerically investigated. By modifying the transversal dimensions of the silicon nitride core and by adding several cladding layers with appropriate refractive indices and thicknesses, we demonstrate dispersion flattening over large spectral bandwidths in the near infrared. We analyze several cladding refractive index profiles that could be realistically fabricated by using existing materials and doping procedures. We show that cladding engineering allows for much more dispersion control (and flattening) in comparison with optimizing only the core transversal dimensions. For the latter case it is demonstrated that while the zero dispersion wavelength can be shifted to a great extent, the effect of the cross-section adjustment in the flatness is very limited. In sharp contrast, by adding two cladding layers and decreased refractive index values, the dispersion ripple can be strongly reduced. By further adding one more layer and by adjusting their refractive indices it is possible to obtain nearly constant chromatic dispersion (only +/- 3 ps/nm-km variation) over the spectral region from 1.8 to 2.4 microns. In our calculations, the analyzed change in the silica or silicon nitride refractive index is up to +/-3%. Our technique should open new avenues for the demonstration of high-performance nonlinear devices on a chip. Furthermore highly dispersive integrated photonic components can be envisaged for slow light applications and integrated photonics spectrographs.

Astronomical optical frequency comb generation in nonlinear fibres and ring resonators: optimization studies

We here discuss recent progress on astronomical optical frequency comb generation at innoFSPEC-Potsdam. Two different platforms (and approaches) are numerically and experimentally investigated targeting medium and low resolution spectrographs at astronomical facilities in which innoFSPEC is currently involved. In the first approach, a frequency comb is generated by propagating two lasers through three nonlinear stages – the first two stages serve for the generation of low-noise ultra-short pulses, while the final stage is a low-dispersion highly-nonlinear fibre where the pulses undergo strong spectral broadening. In our approach, the wavelength of one of the lasers can be tuned allowing the comb line spacing being continuously varied during the calibration procedure – this tuning capability is expected to improve the calibration accuracy since the CCD detector response can be fully scanned. The input power, the dispersion, the nonlinear coefficient, and fibre lengths in the nonlinear stages are defined and optimized by solving the Generalized Nonlinear Schrodinger Equation. Experimentally, we generate the 250GHz line-spacing frequency comb using two narrow linewidth lasers that are adiabatically compressed in a standard fibre first and then in a double-clad Er/Yb doped fibre. The spectral broadening finally takes place in a highly nonlinear fibre resulting in an astro-comb with 250 calibration lines (covering a bandwidth of 500 nm) with good spectral equalization. In the second approach, we aim to generate optical frequency combs in dispersion-optimized silicon nitride ring resonators. A technique for lowering and flattening the chromatic dispersion in silicon nitride waveguides with silica cladding is proposed and demonstrated. By minimizing the waveguide dispersion in the resonator two goals are targeted: enhancing the phase matching for non-linear interactions and producing equally spaced resonances. For this purpose, instead of one cladding layer our design incorporates two layers with appropriate thicknesses. We demonstrate a nearly zero dispersion (with +/- 4 ps/nm-km variation) over the spectral region from 1.4 to 2.3 microns. The techniques reported here should open new avenues for the generation of compact astronomical frequency comb sources on a chip or in nonlinear fibres.

Model-based calculations of fiber output fields for fiber-based spectroscopy

The accurate characterization of the field at the output of the optical fibres is of relevance for precision spectroscopy in astronomy. The modal effects of the fibre translate to the illumination of the pupil in the spectrograph and impact on the resulting point spread function (PSF). A Model is presented that is based on the Eigenmode Expansion Method (EEM) that calculates the output field from a given fibre for different manipulations of the input field. The fibre design and modes calculation are done via the commercially available Rsoft-FemSIM software. We developed a Python script to apply the EEM. Results are shown for different configuration parameters, such as spatial and angular displacements of the input field, spot size and propagation length variations, different transverse fibre geometries and different wavelengths. This work is part of the phase A study of the fibre system for MOSAIC, a proposed multi-object spectrograph for the European Extremely Large Telescope (ELT-MOS).

Dispersion Engineering in Silicon Nitride

As part of ongoing efforts towards development of integrated optoelectronic platforms on a single chip, specifically integrated photonic spectrographs for Astronomy, we report numerical and experimental results from dispersion engineering in integrated silicon nitride waveguides.

Numerical investigation of propagation constant in silicon nitride waveguides with different refractive index profiles

The engineering of the propagation constant in integrated silicon nitride waveguides is numerically investigated. We compare several geometrical designs and show that fairly large chromatic dispersion control is obtained when the transversal dimensions are modified.

Silicon nitride waveguides and micro ring-resonators for astronomical optical frequency comb generation

Silicon nitride ring resonators with diameter of 250 and 500 μm are fabricated and their spectral characteristics investigated with the ultimate goal of optical frequency comb generation for astronomical spectrograph calibration. A continuously tunable laser was used to evaluate the spectral characteristics (propagation losses and transmission properties) of PECVD silicon nitride waveguides and ring-resonators. Losses were measured to be smaller than 0.75 dB/cm over the range between 1500 nm and 1620 nm. The transmission properties of the fabricated ring resonators were assessed for the TE and TM modes, showing promise for the ultimate goal of astronomical optical frequency comb generation.