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1.INTRODUCTIONThe DARWIN mission [2] will search for “earth-like” planets in the vicinity of a central star. This means finding a weak scattering and small object near to a very bright light source. In order to cope with the contrast between the star and the planet a nulling interferometer is set up that shall cancel out the starlight by destructive interference of the receive beams. For improving the performance of interferometer the superimposed beams are coupled into an optical single mode fibre which acts as a modal filter. Two major challenges result from the DARWIN scenario:
2.FIBRE COUPLING ASPECTSThe efficiency of coupling light into a single-mode fibre strongly depends on the matching between the incident diffraction pattern and the principal mode of the fibre, see Fig. 1. A collimated circular beam of a top-hat intensity profile conventionally focussed on the fibre tip forms an Airy pattern which differs from the propagation function of the fibre, the fibre mode, and the coupling efficiency CE (η) cannot be better than 78%. That maximum of 78% is reached only at the cut-off frequency of the fibre, which corresponds to the shortest wavelength λc for single mode operation. The coupling efficiency drops, with increasing slope, at higher wavelengths. (red curve in Fig. 2) Fig. 2.Drop of the CE versus decreasing frequency V i.e. increasing wavelength λ, for 3 focal lengths.  By tuning the coupling parameters, and at costs of the maximum achievable CE, the wavelength sensitivity of the curve CE versus λ may be reduced such that at least over one octave λc-2λc one obtains a flat and almost constant curve. That is illustrated in Fig. 2. That figure plots the normalised CE versus the normalised frequency. Normalised CE meaning 1.0 equals 78%. The normalised frequency V is proportional to the inverse λ: where rk is the core radius and nco, ncl are the refractive indices of core and cladding, All of them are system constants1, and V varies only with 1/λ for a given fibre. A frequency of 2.405 is the cut-off-frequency, the limit of single mode regime. For maximum CE, ηmax, the focal length of the focussing optics would be tuned such that the diffraction Airy has the best match to the fibre mode at a λ corresponding to V=2.4. That is done in almost all practical applications. The red curve Vopt=2.4 shows the spectral behaviour. If the focal length is tuned such that the best match results at 2λc, (dotted blue curve Vopt=1.2), the CE is sub-optimal at shorter wavelengths. Within λc and 2λc, h varies only little between 0.84 and 0.89. 3.FIBRE COUPLING WITH IMPROVED EFFICIENCYAs mentioned above, there is a potential gain of 20% in CE if the mode mismatch can be resolved. This means that the uniform intensity of the incoming beam has to be transformed into an intensity distribution that matches the back-propagated fibre mode. This beam shaping must not affect the other properties of light, i.e. wave front error and polarisation. 3.1Optical design aspectsThe optical design has to provide two main functions, beam shaping and fibre coupling. In order to be prepared for operation in the DARWIN wavelength range, all optical surfaces shall be reflective to prevent from spectral dispersion. The spectral range for the breadboard was defined from 633 nm to 1550 nm in order to have suitable fibres available which can be implemented in a proof of concept demonstrator. The design wavelength is 1064nm. The intensity redistribution is performed by means of tailored free form surfaces. The approach was developed by the company OEC in Munich [4]. One surface also alters the optical path difference. Thus a second free form surface is needed to correct for the wave front error of the first surface. The two beam shaping surfaces (Beam Shaping Optics, BSO) receive and provide a collimated beam. A third parabolic mirror delivers the beam to a focus on the fibre tip (Fibre Coupling Optics, FCO) (Fig. 3). Additionally the reflections of the BSO mirror set fold the beam in two orthogonal planes in order to minimise polarisation degradation. For the same reason, the third mirror, which focuses the light onto the fibre tip, may be substituted by a refractive focusing optics if the application allows for the possible dispersion and transmission. Fig. 3 visualises the beam shaping effect: the first mirror receives a beam of equal ray density, which changes into a density profile with concentration in the middle. By increasing the beam size by three times on the secondary mirror and the parabola, the outer part of the fibre mode can also be used. Theoretically, this design reaches a maximum coupling efficiency of 95%. (100% CE can only be achieved for an infinite large coupling mirror) The optical design is based on the parameters of the fibre: an OFS Clearlite 630-11 with a cut-off wavelength of 580 nm. The nominal wavelength of operation would be 633 nm. The focal length (68 mm) is adjusted such that the best coupling efficiency is reached at 1064 nm (Vopt=1.27, see Fig. 2). Experimental operation was foreseen at laser lines of 633, 1064 and 1300 nm plus also incoherent “white” light. Further design evolution may eliminate the third mirror and combine the wave front recovery and the imaging function together in one single mirror. 3.2Simulation3.2.1ImplementationFor performance analysis the tailored surfaces are implemented to optical design software CodeV via NURBS representation and a user defined interface or ASAP via conversion to Rational Bicubic Splines. Additionally the ESA proprietary software “beam warrior” was used to simulate the full interferometer performance of DARWIN. The rays can be traced as in any conventional optical system. For purpose of coupling efficiency analysis, the last step from the last parabolic mirror to the image needs the diffractive beam propagator. 3.2.2Sensitivity and tolerancesThe simulations investigated the sensitivity of the optical set-up to misalignments and surface shape errors. The tolerances result in more stringent requirements compared to conventional optics. Concerning the practical purpose of Darwin, the operation wavelengths are longer by a factor of at least 7, and the tolerances scale up accordingly. Table 1:Alignment and stability tolerances, λ=1064nm
The simulation results show that beam shaping improves the fibre coupling efficiency significantly to the cost of the alignment and manufacturing tolerances. For the proof-of-concept demonstrator the requirements are challenging but feasible 3.2.3Spectral performanceThe simulations also verified whether the beam shaping would change the spectral behaviour provided in- Fig. 2. Normally, both the Airy radius and the fibre mode field diameter increase with the wavelength. The beam shaping is made geometrically and does not scale with the wavelength. The mode matching was designed for 1064 nm. In fact, Fig. 2 could be reproduced for the normalised effects of the beam shaping with CodeV as shown in Fig. 4. The graphs from Fig. 2 correspond to the dotted lines in Fig. 4, i.e. without the beam shaping. The effect of the beam shaping is shown with the solid lines, which are all above the dotted lines. For the beam shaping optics, this means both the focal length and the beam shaping are optimized for this specific wavelength. In the simulation, only the wavelength changes, the fibre remains the same with V=2.4 at 580 nm. The blue curve for Vopt=1.2 is almost flat between V=1.2 and V=1.4. As can be seen from Fig. 4, the degradation of Vopt=1.2 in comparison to the ideal V=2.4 is identical to the non-shaped system, i.e. the blue solid and dotted curves reach the same value for V=2.4. At all longer wavelengths towards the left the solid curve is always above the dotted. Thus there is even a relative improvement compared to the non-shaped system. For later experimental verification the curves of Fig. 4 were converted into the absolute coupling efficiency curves in Fig. 5. The absolute improvements by beam shaping become obvious: The distance between the dotted (no BS) and the solid (with BS) lines of one color means the gain in coupling efficiency that can be achieved by beam shaping. 4.EVALUATIONIn order to verify the theoretical findings, a demonstrator was built and a verification programme was set up to evaluate the achievable gain in coupling effiviency, the wavelength sensitivity, the impact of aberrations of the input wavefront 4.1Opto-mechanical design of the demonstratorThe POCD consists of four sections (Fig. 12) of three building blocks:
4.2MAITThe MAIT process had to face challenges in each discipline:
The intensity redistribution was measured by feeding the POCD core reversely with light out of the fibre. As the fibre generates an ideal fibre mode intensity distribution the beam exiting the POCD core should then show a top-hat profile. This could be verified by beam profiler measurements, see Fig 8. The above measurements prove that beam shaping works in theory and in the real life: The intended intensity redistribution was achieved and the wavefront could be maintained as good as the BSO were flat mirrors. From test results on component level, the performance of the POCD was predicted in order to verify that the later verification programme would give meaningful results. The simulations based on the as-is components showed that the BSO’s CE should be 55%±5% and the non-BSO giving 42%±5% leaving a minmium difference of 3% between the measurements with both systems at the design wavelength of 1064 nm. 4.3Verification programmeThe verification programme assessed the impacts of various parameters on the performance, i.e. on fibre coupling efficiency in the first degree. The introduced variations were optical aberrations and field angle. Originally the programme intended to test for effects of polarisation, wavelength, and central obscuration on power coupling efficiency, complex coupling efficiency and nulling performance. For reasons of the required resolution of introduced changes and the achievable performance of the POCD build from the “as-is” components in order to get meaningful measurements, the verification programme was reduced to basically test the beam shaping performances. It should be noted that the spectral transmission of the selected fibre did not allow for tests at longer wavelengths as 1064nm. The simulations could not take into account the spectral material properties of the fibre because they are not public. The measurements of the set-up with beam shaping optics will be compared to those of the set-up with two folding mirrors which replace the beam shaping surfaces. 4.4Verification test results4.4.1Power coupling efficiencyThe power coupling efficiency values which result from the predictions and from the measurements with the POCD are compared in Table 2. The measured coupling efficiency of both POCD versions, with and without beam shaping, range well above the expectations including all losses like fibre transmission, back-reflection at the fibre tip, etc. Table 2Power coupling efficiency predictions and measurements
Table 3Comparison of the fibre coupling gain
The comparison between the measured coupling efficiencies shows the gain provided by the beam shaping to range at approximately 1dB which could be verified despite the limitations of experiment (residual misalignments, losses, etc.). 4.4.2Impact of aberrationsAfter having set up the deformable mirror (DM) to deliver a flat wavefront to the entrance of the beam shaping optics, the deformable mirror was operated to introduce additional wavefront aberrations in their definition as Zernike coefficients. Each Zernike coefficient up to the 11th was generated individually with an amplitude of up to 2 rad. The resulting measured coupling efficiency curves are displayed in Fig. 9 and Fig. 10 4.4.3Impact of tilt of the input beamIn particular for DARWIN the sensitivity of the receive optics to tilts of the input beam within the field of view is of special importance because the light of the planet will come at a different angle of incident as the light of the star. This angular separation cannot be resolved the receiving telescope(s). Therefore the enhanced coupling efficiency shall be available for the planet’s light. As stated above the improved coupling efficieny by beam shaping is on cost of the sensitivity to deviations from the design parameters, here deviations from the on-axis beam at zero field angle. For the POCD the coupling efficiency with beam shaping shall remain higher than the CE without beam shaping up to an angle of incidence of 80 microrad in order to cover the DARWIN requirements. Fig. 11 shows the results of the beam warrior simulations (dashed curves) in comparison to the measured values (solid curves) where systematic biases have been removed. Fig. 11Gain in CE of the BSO (red) against the unshaped beam (blue); solid lines are the approximations to the measurements, dashed lines are the Beam Warrior simulations  Again, the simulations could be verified by the experiment. 5.CONCLUSIONSThe measurements performed with the Proof-Of-Concept Demonstrator proved the concept of beam shaping for improved coupling efficiency. The measured gain in coupling efficiency of 1.0 dB is close the theoretical limit of 1.09 dB. The optical simulations are in good agreement with the measurements. On-the-edge manufacturing technology of today allows for figuring optical free form surfaces for applications at wavelength greater and equal 1064 nm. 6.ACKNOWLEDGEMENTSThe work presented above is performed in the frame of the ESA project “Fibre Optic Wave front Filtering” (FOWF) (ESA contract no. 18773/04/NL/HE). We like to thank ESA and their technical officer, Mr. J. M. Perdigues-Armengol for supporting this activity. For their contribution in hardware we thank the LFM (Laboratory for Precision Machining) and their project manager, Mr. K. Rickens. 7.7.REFERENCESVoland, Ch., Weigel, Th., Dreischer, Th., Wallner, O., Ergenzinger, K., Ries, H., Jetter, R., Vosteen, A.,
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