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detection of terrestrial - mass extra - solar planets ( exoplanets ) requires extremely stable and precise instruments . in the strive to reach extreme levels of doppler precision , a number of previously uncharacterized instrumental effects will begin to dominate instrument error budgets . dedicated doppler radial velocity ( rv ) instruments must be able to measure shifts in stellar spectra at precisions approaching 10 cm s@xmath0 in order to detect true earth twins orbiting nearby stars . in the pursuit of reaching this bold precision goal , a number of previously uncharacterized instrument noise sources must be studied and mitigated at unprecedented levels . in the past decade , much attention has been paid to maximizing detection sensitivity by using optical fibers to deliver light from the telescope to the spectrograph . typical multi - mode fibers ( mmfs ) used in current generation seeing - limited doppler instruments have the convenient ability to scramble light , producing an output illumination that is significantly , though not perfectly , decoupled from the incident flux distribution @xcite . however , these fibers do suffer from mode interference effects , commonly referred to as modal - noise , which can impose a fundamental limit on achievable measurement precision if not addressed properly @xcite . this has been shown to severely limit both achievable signal - to - noise on stellar targets @xcite , and ability to realize the full potential of coherent frequency calibration sources @xcite . it is important to note that insufficient image scrambling and fiber modal noise can both limit measurement precision , but are fundamentally different phenomena , as described in @xcite . as precision goals approach 10 cm s@xmath0 , a number of subtle and largely unexplored instrumental systematics will begin to dominate overall performance error budgets . more recently , the use of smfs for compact doppler spectrometers has been suggested as a method of minimizing instrument size while overcoming many of these systematics @xcite . these fibers support only a single spatial propagation mode and therefore do not suffer from the classical modal interference effects of mmfs . the output intensity distribution of a smf is entirely decoupled from input illumination variations , yielding a fundamentally stable instrument point - spread function ( psf ) with perfect radial and azimuthal scrambling . these qualities make smfs an attractive choice when designing compact , stabilized doppler velocimeters for instruments on small telescopes @xcite , where mode - matching is relatively efficient , and for larger telescopes with high performance adaptive optics ( ao ) systems working near the diffraction limit @xcite . while these fibers can produce a stable and perfectly scrambled output illumination , typical smfs do support two fundamental polarization modes . similarly to mmfs , imperfections and internal stresses in the fiber can lead to variable coupling between these two polarization modes @xcite . in smfs , this leads to an effective polarization change of propagating light . in fact , a single fiber cable can very efficiently rotate or circularize any arbitrary input polarization to an arbitrary output polarization . as such , stressed single - mode fiber cables are frequently used as in - line wave - plates for polarization rotation of monochromatic sources @xcite . 10% ) polarized supercontinuum source . top : effective polarization rotation induced by variable twisting of the fiber cable . bottom : bend - induced polarization rotation measurement . in both cases , the effective polarization angle exiting the fiber varied by 10 s of degrees with minimal stress applied.,width=326 ]    here we study the impact of polarization rotation in single - mode fibers on radial velocity measurements by examining the polarization sensitivity of the primary disperser ( in this case , an echelle reflection grating ) used in most doppler spectrometers . the purpose of this study is to emphasize the scope and magnitude of this effect , and show specifically how this affects high precision rv measurements . this is of particular importance since there are several instruments currently being designed or built that utilize smf delivery systems , including minerva - red @xcite , ilocator @xcite , and tests of an extreme precision doppler spectrometer for the subaru telescope @xcite . with any fiber - fed instrument , the internal stresses within the fiber will change as the fiber is perturbed ( e.g. due to telescope tracking , temperature variations , etc . ) this variable stress can change the intrinsic fiber birefringence , which alters the polarization distribution exiting the fiber . the consequences of this variable birefringence have been studied for interferometric applications ( e.g. @xcite ) , as birefringent effects in standard smfs can degrade fringe contrast @xcite , but they have yet to be thoroughly studied in the context of precision doppler spectroscopy . the goal of this study is to estimate how these birefringence effects propagate to spectroscopic velocity errors . as such , we do not present a rigorous mathematical model of fiber birefringence in typical smfs , as this has been abundantly documented and studied in the literature over the past several decades ( e.g. @xcite ) . instead , we present a brief summary of the scope of the problem and the relevance to astronomical spectroscopy .    in smfs , any stresses induced on the fiber core , e.g. due to variations in applied pressure on the cable @xcite , bends @xcite , twists @xcite , thermal fluctuations @xcite , or even variations in external magnetic fields @xcite , will lead to variable polarization mode coupling in the fiber core . this variable coupling will , in effect , rotate the polarization of light propagating through the fiber . since most smfs typically support two polarization modes , this variable mode coupling can lead to a manifestation of fiber modal noise . for astronomical instruments utilizing dedicated calibration fibers , any variations in the spectral profile due to variable polarization will not be traced with a calibration source , as the polarization state is specific to the source and fiber pair . it is important to note that any polarization rotation will also have a wavelength dependence , which depends strongly on the polarization beat length of the fiber in question @xcite and the internal and external stresses applied to the fiber core @xcite . polarization - maintaining ( pm ) fibers have the ability to maintain a single polarization with a high polarization extinction ratio , but rely on stable and precise alignment of the incident polarization with the fast axis of the fiber for efficient mode propagation . this generally requires the incident illumination to be strongly linearly polarized , which is usually an impractical choice for most astronomical applications due to the associated efficiency losses . while ample amounts of literature exists that studies the effects of stress - induced polarization rotation in smfs ( see previous references ) , we perform a series of simple laboratory tests to show the magnitude of possible polarization fluctuations expected from typical stresses associated with astronomical telescope fiber feeds ( namely twists and bends effects ) illuminated by a weakly polarized continuum source , meant to emulate a possible astrophysical target .    a 2 meter commercial smf cable ( corning smf-28 ) is illuminated by a supercontinuum source that is intrinsically weakly polarized ( degree of polarization is approximately 10% , as measured by our polarimeter ) . the output polarization of the fiber cable is then recorded using a commercial pmi - nir meadowlark polarimeter . an h - band interference filter ( 1.5 - 1.65 @xmath1 m ) is inserted at the fiber exit to ensure the illumination bandpass is restricted to wavelengths where the fiber supports a single spatial mode ( 1.26 - 1.65 @xmath1 m ) . the fiber is coiled onto a linear translation stage , which allows for a variable stress to be induced in the cable , and terminated with standard telecommunication fc connectors on either side . a schematic of the experimental setup is shown in figure  [ fig : setup ] . the cable is then perturbed by both translating the linear stage ( inducing a mild bend ) and twisting the fiber by hand . for twist measurements , the cable was periodically twisted by hand between 0 and 90 degrees across a 0.5 meter section of the cable . for bend measurements , the cable was bent between two fixed mounting points , separated roughly 0.3 meters apart , using a mechanical stage . this varied the overall fiber bend radius by several inches . we find that , even for low - levels of added stress , the effective output polarization angle of light exiting the fiber is highly variable . measurements of the fiber output polarization are shown in figure  [ fig : lab_data ] . mild twists and bends of the fiber cable can induce effective polarization rotations of over 10 degrees . to estimate the direct effects of polarization variations on measured radial velocities , we focus on the polarization sensitivity of the primary dispersive element in the spectrograph : in this case , an r4 echelle grating . we use measured @xmath2 and @xmath3 polarization curves for two newport rgl gratings , manufactured with two different grating masters : mr 160 , used on harps @xcite , and mr 257 , used on hpf @xcite and carmenes @xcite instruments , to modulate simulated stellar spectra ( see figures  [ fig : grating_response_vis ] & [ fig : grating_response_nir ] ) . the modulation is a linear combination of different ratios of the measured grating blaze functions for the two orthogonal incidence polarizations , for a variety of spectral orders in the visible and near - infrared ( nir ) . model spectra are assumed to be noiseless , and are generated at an effective instrument resolution of @xmath4=100,000 . for the mr160 grating , we use a synthetic g2 spectrum ( t@xmath5 = 5700 k ) for radial velocity calculations for four spectral orders between 350 and 700 nm . for the mr257 grating , where our available data is centered in the nir , we use a synthetic m - dwarf spectrum as a stellar template ( in this case a 3000 k bt - settl model ) . the variable blaze modulation due to changing polarization can induce apparent velocity offsets . on the smallest scale , it can introduce a variable gradient across individual spectral features , although this is likely a negligible change . across an order , it changes the relative chromatic weighting of lines , and shifts the center of the cross - correlation peak in that wavelength range . most importantly , it changes the shape of the aggregate cross - correlation function , and the final determination of radial velocity from a single observation . these effects are similar to what would be observed due to variable atmospheric refraction effects ( e.g. due to airmass changes , variations in atmospheric dispersion correction , etc . ) . relative velocity offsets are calculated using weighted mask cross - correlation method ( similar to the methods described in @xcite and @xcite ) with a custom stellar template mask built specifically for this purpose for each spectral class considered ( approximately g2 and m5 ) . for the latter , telluric contamination is neglected since a synthetic spectrum is used , but this could be easily adapted for use with an observed spectrum with a slightly more rigid selection procedure for mask lines . velocity offsets at all effective polarization combinations are then compared to spectra modulated by an unpolarized blaze function ( average of @xmath2 & @xmath3 ) . spectra for each order were purposely not continuum normalized when calculating velocity offsets , as the blaze functions contain important information relating to the weights of various spectral features used for the cross - correlation .    measured velocity offsets between polarization angles are shown in figure  [ fig : rv_offset ] . we note that effective shifts of several m s@xmath0 are seen between orthogonal polarizations for nearly all measured echelle orders . even for weakly polarized light , low - level polarization rotation due to variable mode coupling can still introduce errors at the 10 s of cm s@xmath0 level . for strongly polarized , coherent sources , such as laser frequency combs , this effect will be even more pronounced . if not dealt with , this systematic error could conceivably compromise the exquisite stability capabilities of dedicated smf doppler velocimeters . periodic mechanical agitation of the fiber cable will change the polarization mode coupling of incident radiation . this method is frequently used to temporally vary the phase distribution of modes in mmfs , which can significantly reduce classical mode interference effects @xcite . in smfs , this agitation could conceivably scramble the effective mode coupling . this could reduce the effective degree of polarization over typical astronomical integration times , though may result in an efficiency drop due to increased bend losses depending on the amplitude and frequency of agitation . it has been shown that using long fiber cables can effectively act as depolarizers for strongly polarized sources @xcite , though likely not at the level required to completely mitigate this issue for precise rv measurements . in addition , it may be possible to mitigate this effect post factum through continuum normalization or `` deblazing '' of the spectrum before calculating rvs . for example , using the continuum normalization routines included in the _ reduce _ package @xcite , we are able to mitigate the rv disparity by about an order of magnitude . depending on the precision level desired , this might be the most convenient solution , but will remain sensitive to the normalization procedure , and might produce rv offsets as the fits to the varying order response functions change . additionally , important spectral weighting information , such as absolute chromatic flux level across a given spectral order , is omitted by dividing by a estimated blaze function . while we have focused entirely on standard smfs in this study , it is import to note that the polarization effects discussed here could conceivably affect multi - mode fiber delivery systems at the cm s@xmath0 level . this is particularly true for instruments using small diameter , asymmetric core geometry fibers . these fibers can significantly improve scrambling performance over standard circular - core fibers , but may also be prone to maintaining measurable levels of residual polarization @xcite . harps has observed subtle , though measurable , variations in measured blaze functions at the @xmath610@xmath7 level @xcite . while these variations could be attributed to a number of error sources ( such as seeing variations , telescope focus drifts , airmass variations , etc . ) , residual polarization in the instrument delivery fiber could also be a contributing factor , and should be considered along with more commonly examined sources of variability . we present a cautionary note that variable coupling of polarization modes in single - mode fibers can cause systematic shifts in measured radial velocities for spectrographs using standard echelle reflection gratings as the primary disperser . this effect is comparable to classical modal interference in multi - mode fibers , though it manifests in a more subtle manner . we perform a simple laboratory test to explore the effects of external stresses on polarization mode coupling by measuring the output polarization of a commercial smf illuminated by a weakly polarized continuum source under external stress . to quantify the magnitude of this effect on rv measurements , we calculate the effective doppler shift of a template spectrum modulated by measured echelle grating response functions for several spectral orders for two different manufactured gratings . we use a linear combination of these response functions to span a wide range of effective polarizations incident on the grating . we show that , even for low - level rotation of weakly polarized light , rv offsets of 10 s cm s@xmath0 are entirely possible for instruments using smfs . this subtle effect is not traced with a simultaneous calibration source , and can therefore lead to insidious systematic shifts in stellar radial velocity measurements . in the era of extreme precision doppler spectrometers striving towards 10 cm s@xmath0 precision , this effect could conceivably dominate measurement error for smf - based instruments .                                  , m. , tozzi , a. , sanna , n. , zangrilli , l. , & oliva , e. 2014 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 9147 , society of photo - optical instrumentation engineers ( spie ) conference series , 66    , n. , guyon , o. , martinache , f. , schwab , c. , & cvetojevic , n. 2014 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 9147 , society of photo - optical instrumentation engineers ( spie ) conference series , 7          , s. , ramsey , l.  w. , terrien , r. , et  al . 2014 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 9147 , society of photo - optical instrumentation engineers ( spie ) conference series , 1        , k.  s. , ramsey , l. , mahadevan , s. , halverson , s. , & redman , s.  l. 2012 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 8446 , society of photo - 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exploring the use of single - mode fibers ( smfs ) in high precision doppler spectrometers has become increasingly attractive since the advent of diffraction - limited adaptive optics systems on large - aperture telescopes . 
 spectrometers fed with these fibers can be made significantly smaller than typical seeing - limited instruments , greatly reducing cost and overall complexity . 
 importantly , classical mode interference and speckle issues associated with multi - mode fibers , also known as modal noise , are mitigated when using smfs , which also provide perfect radial and azimuthal image scrambling . 
 however , these fibers do support multiple polarization modes , an issue that is generally ignored for larger - core fibers given the large number of propagation modes . since diffraction gratings used in most high resolution astronomical instruments have dispersive properties that are sensitive to incident polarization changes , any birefringence variations in the fiber can cause variations in the efficiency profile , degrading illumination stability . here 
 we present a cautionary note outlining how the polarization properties of smfs can affect the radial velocity measurement precision of high resolution spectrographs . 
 this work is immediately relevant to the rapidly expanding field of diffraction - limited , extreme precision rv spectrographs that are currently being designed and built by a number of groups .