Relative contributions of scattering, diffraction and modal diffusion to focal ratio degradation in optical fibres

D. M. Haynes 1 2 M. J. Withford 2 J. M. Dawes 2 J. S. Lawrence 1 2 R. Haynes 0 1 0 Present address: innoFSPEC, Astrophysikalisches Institut Potsdam , An der Sternwarte 16, Potsdam 14482 , Germany 1 Australian Astronomical Observatory , PO Box 296, Epping, New South Wales 1710 , Australia 2 MQ Photonics Research Centre, Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), Department of Physics and Engineering, Macquarie University , North Ryde, New South Wales 2109 , Australia Focal ratio degradation (FRD) is a major contributor to light loss in astronomical instruments employing multimode optical fibres. We present a powerful diagnostic model that uniquely quantifies the various sources of FRD in multimode fibres. There are three main phenomena that can contribute to FRD: scattering, diffraction and modal diffusion. We propose a Voigt FRD model where the diffraction and modal diffusion are modelled by the Gaussian component and the end-face scattering is modelled by the Lorentzian component. The Voigt FRD model can be deconvolved into its Gaussian and Lorentzian components and used to analyse the contribution of each of the three major components. We used the Voigt FRD model to analyse the FRD of modern astronomical grade fibre for variations in (i) end-face surface roughness, (ii) wavelength, (iii) fibre length and (iv) external fibre stress. The elevated FRD we observed was mostly due to external factors, i.e. fibre end effects such as surface roughness, subsurface damage and environmentally induced microbending caused by the epoxy, ferrules and fibre cable design. The Voigt FRD model has numerous applications such as a diagnostic tool for current fibre instrumentation that show elevated FRD, as a quality control method for fibre manufacture and fibre cable assembly and as a research and development tool for the characterization of new fibre technologies. 1 I N T R O D U C T I O N Multimode optical fibres have been used as light pipes in astronomical instrumentation for the past 30 yr because of their unique ability to take light from the telescope focal plane and spatially reformat it at a distant image plane. This has revolutionized spectroscopy by enabling a remotely mounted highly stable single object, multi-object and integral-field unit spectrographs. Future applications of fibres in astronomy require a better understanding of how light propagates and evolves in a multimode fibre. One major manifestation of light loss in systems employing multimode optical fibres is focal ratio degradation (FRD; Nelson 1988; Ramsey 1988). In a perfect fibre, the light would emerge at the same f -ratio as it entered (for a straight length of fibre, i.e. no bends); however, due to minor imperfections in the fibres the emergent light is more divergent (faster f -ratio) than the input beam. This beam spreading can result in a loss either in throughput or in resolution in astronomical spectroscopic applications (Parry 1998, 2006). In order to reduce the possible light losses in multimode fibre-based systems, instrument designers need to quantify FRD and minimize its impact prior to designing the instrument components such as the spectrograph collimator. If the FRD is such that the beam spreads out beyond the collimator, then there will be a loss in throughput and potential scattered light contamination in the spectrograph if the baffling is insufficient. Researchers have been performing FRD measurements on fibres ever since the first multifibre systems were used in astronomy over 30 yr ago (Angel, Adams & Boroson 1977; Barden 1998; Ramsey 1988). However, there have been some inconsistencies in the results reported by different researchers, even for fibres from the same manufacturer and the same type. Much of this has been attributed to varying measurement techniques and fibre end preparation techniques (Avila 1998) indicating a need to standardize measurement techniques. There are three main phenomena that can contribute to FRD: scattering, diffraction and modal diffusion. These effects are influenced by various factors, including material irregularities (impurities and variations in the density of the glass), fibre geometry irregularities (changes in concentricity, variations in circularity and diameter of the fibre), macrobending, microbending, end-face surface roughness, subsurface damage caused by the lapping/polishing process (Hed & Edwards 1987; Collier & Schuster 2005) and fibre geometry. Some of these contributions to FRD can be very sensitive to the external environment and are likely responsible for the diverse results reported by researchers (Craig & Hailey 1988; Avila 1998). Two FRD measurement techniques commonly used are the cone (Lee, Haynes & Skeen 2001; Murphy et al. 2008) and the parallel laser beam methods (Ferwana et al. 2004; Haynes et al. 2004, 2008). In the cone technique a cone of light, set to a particular f -ratio, is injected into the fibre and the FRD is measured from the encircled energy (EE) within a given f -ratio at the output. This technique gives a good estimate of the total light loss that might be expected in a fibre-based system, but it is sensitive to alignment errors and does not provide information about the possible causes of the FRD. The parallel laser beam technique uses a collimated laser beam to inject light into the fibre at selected angles (f -ratios) and the FRD is determined from the radial profile width on output (Haynes et al. 2004). This technique is highly sensitive to small changes in FRD and is commonly used as a rapid diagnostic technique. In the past, this method has been used to quantify FRD by assuming the radial profile to be Gaussian and measuring the full width at half-maximum (FWHM). However, this method can underestimate the FRD if the output distribution deviates away from a Gaussian profile due to effects such as scattering (Haynes 2008). In this paper, we use the parallel laser beam technique and methodology and present a Voigt FRD model that simulates an FRD distribution in the presence of scattering, diffraction and modal diffusion. We show, in a step-wise fashion, how this model can be used as a diagnostic tool to identify, quantify and potentially minimize sources of FRD and improve the fibre system performance. We first concentrate on the scattering contribution caused by the fibre endface surface roughness in order to model its contribution to FRD. This then permits deconvolution of the other contributions due to modal diffusion and diffraction. 2 B AC K G R O U N D 2.1 Scalar scattering theory Scalar scattering theory, otherwise known as surface roughness scattering theory, is often used to determine the ratio of specular transmittance/reflectance to diffuse (scattering) transmittance/reflectance for a given surface roughness (Bennett & Mattsson 1999; Lindstrom & Ronnow 2000). It does not provide any information on the angular distribution of the diffuse (scattered) light. Scalar sc (...truncated)