Polarization-maintaining Fiber Optics

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Polriztion-mintining Fier Optics Stle fier-optic setups from the ultrviolet to the infrred Anj Krischke, Christin Knothe nd Ulrich Oechsner A stle mesurement setup is fundmentl for ny successful

1 Polriztion-mintining Fier Optics Stle fier-optic setups from the ultrviolet to the infrred Anj Krischke, Christin Knothe nd Ulrich Oechsner A stle mesurement setup is fundmentl for ny successful mesurement. A mjor cuse of frustrtion nd error is the need to continuously redjust optomechnicl equipment ecuse of continuous instilities. The use of fier optics hs proven to increse oth stility nd convenience significntly when compred with stndrd free-em setups. These modulr, complex nd self-contined setups lso often increse lser sfety nd reduce the lser sfety clssifiction. The defined interfce etween lser source nd the more sensitive environment of the mesurement setup provides the physicl seprtion tht enles mechnicl nd therml decoupling, suppressing mutully negtive effects. Singlemode fiers re specilized fiers tht trnsmit light in the trnsverse fundmentl mode LP 01. The field distriution (mode field) of the light exiting the fier is close to Gussin. For stndrd singlemode fiers the light is guided in two principle sttes of polriztion. Imperfections in the fier do led, however, to rndom power trns fer etween the two principle sttes of polriztion so tht the polriztion is not mintined. Singlemode fiers re chrcterized y their numericl perture NA, their mode field dimeter MFD nd their cut-off wvelength λ o. It is only t wvelengths ove this cut-off tht the coupled light is guided in single mode nd not in multiple modes, where the em nd intensity profiles re no longer stle nor Gussin. The MFD is wvelength-dependent nd inversely proportionl to the fier NA. While fiers used for telecommuniction in the infrred region, round wvelengths of 1550 nm, re chrcter- Fig. 1 Components nd tools for polriztion-mintining fier optics. The lser em coupler couples the rdition into PM fiers with high coupling efficiency. The polriztion Anlyzer SK0101PA is utilized to perform the polriztion lignment quickly nd efficiently. ized y firly lrge mode field dimeters of round 10 µm, the MDF in the UV is smll, e. g. 3 µm for 405 nm nd fier with NA = Polriztion-mintining singlemode fiers (PM fiers) re rottionlly non-symmetric ecuse of integrted stress elements, for exmple, tht rek the degenercy of the two principle sttes of polriztion (SOP). Light is guided either in the so-clled fst or the slow xis nd linerly polrized light coupled into one of these xes is mintined. If light is guided prtly in the other xis then the coherence of the light source determines the resulting polriztion. For sources where the coherence length is lrger thn the opticl pth difference etween the light in the two principle SOPs of the fier, the outcome polriztion is ellipticl. However, strin nd temperture vritions, chnge this ritrry ellipticl stte. If the coherence length of the lser is smller thn the opticl pth difference then there is no defined phse etween the light guided in the two principle SOPs nd, s result, the exciting light is prtly depolrized. For well-defined polriztion stte, it is extremely importnt to lign the polriztion xis of the PM fiers precisely with the liner polriztion xis of the source. The mximum power tht cn e guided within fier is minly restricted y the power density t the fier end fces, when not considering nonliner opticl effects, such s Brillouin scttering. Extreme power densities cn cuse scorching of the end fce or photo-contmintion y the genertion of dipole trp, phenomenon used to good effect in opticl tweezers. These detrimentl effects cn e ovited using fier 40 Optik&Photonik 4/ WILEY-VCH Verlg GmH & Co. KGA, Weinheim

2 Fier Optics Rel. Efficiency [%] Entrnce Bem Tilt / mrd Fig. 2 Reltive coupling efficiency plotted ginst the entrnce em tilt of lser em coupler for focl length of 4 mm, fier NA 0.12 nd 400 nm (green) nd 1550 nm (lue). A mislignment of 0.2 mrd (0.01 ) cuses decrese in coupling efficiency for 1550 nm of < 5 % compred with out 30 % for 400 nm. end cp, in which short length of fier (< 500 µm) without core is connected to the polriztion-mintining fier. Without fier core, the mode field dimeter of the em diverges to out ten times its prior size nd the power density decreses y fctor of hundred, while hrdly ffecting the numericl perture of the fier or the polriztion of the lser em. Stle fier coupling even t short wvelengths When coupling into singlemode fiers, the lser em couplers should produce diffrction-limited spot tht mtches the mode field dimeter nd the numericl perture of the fier in order to chieve mx. coupling efficiency. It is only when this condition is met tht fier coupling with high coupling efficiencies of up to 85 % re chieved. A focl length chosen too lrge is inefficient, since the focussed lser spot is lrger thn the mode field dimeter. When using focl length too smll, the convergence ngle of the focussed lser spot is lrger thn the mximlly cceptle divergence ngle α of the fier the coupling efficiency is diminished. For n optimlly chosen focl length, prt from losses due to Fresnel reflection t oth fier ends of out 4 % ech, n idel Gussin em is coupled lmost completely. The high pointing-stility required for fier coupling into polriztionmintining fier cn e visulized with n exmple (see Fig. 2): for focl length of 4 mm, n ngulr mislignment of the coupler of only 0.2 mrd (0.01 ) results in lterl displcement of 0.8 µm etween the lser spot nd the mode field of the fier nd decreses coupling efficiency for 400 nm nd NA 0.12 y s much s 30 %. The fier coupling is much less sensitive for 1550 nm where the decrese in coupling efficieny is < 5 %. For λ = 400 nm nd NA 0.12, displcement of 0.4 µm lone is lredy sufficient to decrese the coupling efficiency y s much s 10 %. It is self-evident tht high coupling efficiencies nd long-term stility require su-micron precision nd pointing stility for the coupling optics, especilly in the ultrviolet rnge. Proven stility The high stility of fier-coupling using lser em coupler is demonstrted in temperture-stility tests using different focl lengths nd wvelengths. The test setup is depicted in Fig. 3. The light emitted y the temperture-stilized lser diode em source 48TE (with integrted Frdy isoltor) is guided to the test setup using polriztion-mintining fier, collimted y lser em coupler, nd then coupled ck into polriztion-mintining fier using second lser em coupler, with oth plced 12 mm prt. The recoupled power is monitored using photodetector. The coupling setup is plced on thermo-controlled plte, to vry the temperture etween 15 C nd 35 C in successive cycles with rte of 0.5 C per minute. The temperture of the coupling system is monitored y temperture sensor plced on one of the two lser em couplers. In order to minimize ny temperture impct on the mesurement equipment, the lser source s well s the photo detector nd the dt logger re ll plced on Lser Source 48TE 405 nm reltive Power [%] Fl Temperture Cycling Lser Bem Coupler Lser Bem Coupler Photo Detector Time [min] Temperture [ C] reltive Power [%] c Temperture [ C] Fig. 3 Test setup for mesuring the stility of two lser em couplers (f = 4.5 mm, λ = 405 nm) (). The reltive power () shows repetitive pttern following the temperture (elow). The reltive power curves (c) re lmost coincident nd confirm the high reproduciility of the pointing stility during temperture cycling WILEY-VCH Verlg GmH & Co. KGA, Weinheim Optik&Photonik 4/

Fst nd high-qulity polriztion lignment Mesurement of polriztion extinction rtio Connector key Core Good Polriztion Alignment Bd Fig.

Time-consuming lignment tsks re completed efficiently for lser sources with lrge nd smll coherence length. thermo-controlled plte t constnt temperture of 25 C. Fig.

The power is normlized with respect to the men power cquired over ll mesurement cycles. The power devition from the men power is ±1.5 %.

3 Fst nd high-qulity polriztion lignment Mesurement of polriztion extinction rtio Connector key Core Good Polriztion Alignment Bd Fig. 4 SK010PA polriztion nlyzer for the djustment of polriztion-mintining fiers s well s free em pplictions such s the lignment of fier collimtors with integrted qurter-wve plte. Time-consuming lignment tsks re completed efficiently for lser sources with lrge nd smll coherence length. thermo-controlled plte t constnt temperture of 25 C. Fig. 3 shows the typicl results of the reltive trnsmitted power over five mesurement cycles using focl length of 4.5 mm nd wvelength of 405 nm. The power is normlized with respect to the men power cquired over ll mesurement cycles. The power devition from the men power is ±1.5 %. The repetitive pttern in the reltive power cused y the temperture cycling is demonstrted more clerly in Fig. 3c, in which the reltive power (normlized to the mximum) is plotted ginst the temperture of the Adjustle qurter-wve plte Adjustment of 45 right nd lefthnded circulr polriztion lser em couplers. The mximum coupling efficiency is reched little ove 25 C nd it decreses fster towrds lower tem pertures thn higher tempertures, with the smllest slope ner the requested operting point (25 C). The respective power curves for ech mesurement cycle re lmost coincident nd the power vrition t points with equl tempertures is < 1 %, which demonstrtes the reproduciility of the pointing stility during temperture cycling nd the long-term stility of the fier-coupling. The mximum devition with respect to the mximum power here is 3 %. Stle long-term stle coupling efficiencies re only prt of the success when coupling into PM fiers. Linerly polrized light tht is not coupled completely into one of the polriztion xes is not mintined, nd the polriztion chnges with temperture nd vritions in strin on the fier. The SK010PA polriztion nlyzer (Fig. 4) hs een specilly designed to perform fier lignment tsks s well s to determine the polriztion stte quickly nd efficiently. The mesurement principle is sed on rotting qurter-wve plte nd sttic polrizer in front of photodiode. A detiled nlysis of the photodiode signl nd the time/position informtion of the qurter-wve plte revels e. g. the stte of polriztion, which is then depicted on the Poincré sphere. Liner polriztion sttes re found on the equtor wheres circulrly polrized light is locted t the poles. An indictor of the mintennce of the polriztion stte is the rtio of the coupled power into the two xes: the polriztion extinction rtio (PER in db). A high PER indictes successful preservtion of the polriztion stte. The fiers used in the stility mesurement setup (Fig. 3) for exmple, hve polriztion extinction rtio of more thn 32 db (mesured t 405 nm). The polriztion nlyzer dditionlly evlutes the degree of polriztion (DOP) the rtio of trnsmitted polrized light reltive to the totl trnsmitted power. A Compny Schäfter+Kirchhoff Hmurg, Germny Schäfter+Kirchhoff hs ccumulted lot of experience in the development of optomechnicl nd optoelectronic systems for use in reserch, vition nd in spce, s well s for demnding medicl nd industril pplictions. Schäfter+Kirchhoff designs nd mnufctures their own CCD line scn cmer systems, lser sources, em-shping optics nd fier-optic components, including lser em couplers, fier collimtors nd fier port clusters for customers worldwide. Fig. 5 Adjustment of PM fier. The im is to minimize the dt circle rdius. With poor fier lignment, the stte of polriztion vries significntly e.g. when ending the fier (). With etter ngulr lignment of the fier, the chnge in polriztion nd the rdius of the dt circle ecome smller (). 42 Optik&Photonik 4/ WILEY-VCH Verlg GmH & Co. KGA, Weinheim

4 DOP of 1 indictes fully polrized light, totlly unpolrized em produces DOP vlue of zero. When fier is strongly jigged, the stte of polriztion jumps wildly over section of the Poincré sphere, wheres more defined mient chnge, such s gentle ending of the fier, produces dt circle. This circle represents ll possile sttes of polriztion for the current lignment, with the center representing the men polriztion extinction rtio. For n idel polriztion-mintining fier, the men PER should e locted t the equtor. The dt point tht is frthest from the equtor revels the worst possile polriztion extinction rtio for the current lignment. When djusting the coupling of the fier, the rdius of the circle on the Poincré sphere indictes the qulity of the lignment, s it shows the ngle devition etween fier polriztion xis nd the polriztion xis of the source. The circle rdius is lrge for poorly ligned fiers the polriztion chnges significntly with the mient conditions nd is smll for precisely ligned fiers. For n optimlly ligned idel fier, the dt circle converges to single point on the equtor of the Poincré sphere. When djusting the fier coupling, series of mesurement points is cquired while chnging the temperture or crefully ending the fier to generte circulr cloud of dt points. A circle is utomticlly fitted to the dt points nd the men nd miniml PER re displyed (Fig. 5). The fier xis is now rotted with respect to the polriztion xis of the source until the rdius of the circle reches minimum (Fig. 5). If it is the stility of the stte of polriztion tht is of mjor importnce nd not the PER itself, simply swpping the fier input nd output nd performing nother PER mesurement will revel the most stle fier configurtion (ssuming tht ny disturnces only occur in the fier connector). The most stle configurtion is the one hving the smller dt circle. When swpping the fier input nd output, the distnce of the center of the circle from the equtor (the men polriztion rtio) ecomes the new rdius of the circle, nd the former circle rdius (the ngulr devition) ecomes the new distnce of the center of the circle from the equtor. Stle, complex fier-optic setups the fier port cluster Fier port clusters re compct optomechnicl units tht comine or split the rdition from one or more polriztionmintining fiers into one or multiple output polriztion-mintining fier cles with oth high efficiency nd vrile splitting rtio. The em delivery system consists of compct, modulr optomechnicl units (Fig. 6). A sic component in these fier port clusters is the lser em coupler, which is used oth s n input nd n output, nd collimtes the fier-coupled rdition tht enters the system nd lunches the split rdition into the output fier cles. The modulrity ensures tht lmost ny desired system cn e ssemled tht is oth compct nd enclosed. Becuse of the polriztion sensitive properties of some of the opticl components within the fier port cluster, PM fiers re used to trnsport the light to the cluster with defined liner polriztion. There re severl wys to chieve em splitting into severl output ports. When working with one input wvelength, rdition splitting is chieved y using cscde of rotry hlf-wve pltes in comintion with polriztion em splitters. Integrted photodiodes, for exmple, provide dt tht llow insightful monitoring of the input powers. By rotting the hlf-wve pltes, lmost ny desired splitting rtio cn e relized. If using severl inputs with multiple wvelengths, the wvelength difference etween the input ports determines how the comintion cn e chieved. For two lser sources with lrge wvelength difference, dichroic em cominer is used (Fig. 6). If the wvelength difference is too smll for dichroic em comintion, polriztion em splitter nd susequent dichroic wve pltes llow multiplexing (Fig. 6c). Fier collimtors cn then e used to collimte the exciting em. The optiml collimtion focl length is determined y the em dimeters required y the experiment nd cn e clculted from the NA of the fier nd the trget em dimeter. Specil collimtors with n integrted qurter-wve plte, for exmple, trnsform the liner output rdition into circulrly polrized light for 2014 WILEY-VCH Verlg GmH & Co. KGA, Weinheim

Input 1 Input 1 Fig. 6 Fier port cluster (). For lser sources with lrge wvelength dif ference (), dichroic em cominer is used.

The retrdtion plte is integrted into the divergent em nd cn e rotted with respect to the liner input polriztion producing right-hnded s well s left-hnded circulr polriztion.

5 C per minute) ws performed for fier port cluster splitting one input into six output ports.

This is especilly smll considering tht the loworder wve pltes used within the cluster themselves lredy exhiit strong temperture sensitivity.

systems. The stility of ny fier-optic system strongly depends on the long-term stility of the lser em couplers used for oth coupling in nd out of PM fiers.

5 Input 1 Input 1 Fig. 6 Fier port cluster (). For lser sources with lrge wvelength dif ference (), dichroic em cominer is used. If the wvelength difference is too smll for dichroic em comintion (c), polriztion em splitter nd su sequent dichroic wve pltes llow multiplexing. uses such s in mgneto-opticl trp. The retrdtion plte is integrted into the divergent em nd cn e rotted with respect to the liner input polriztion producing right-hnded s well s left-hnded circulr polriztion. Similr to the test setup proving the long-term stility of the lser em coupler, test demonstrting the stility during temperture cycling (here etween 20 C nd 26 C in successive cycles with rte of 0.5 C per minute) ws performed for fier port cluster splitting one input into six output ports. The reltive power (@ 780 nm) trnsmitted in one of the six output ports while the temperture of the cluster ws vried, revels power devition from the men power of ±1.0 %. This is especilly smll considering tht the loworder wve pltes used within the cluster themselves lredy exhiit strong temperture sensitivity. Conclusion c Input 2 Input 2 Fier optics cn significntly increse the stility nd convenience of mesurement setups nd llows lrge redord setups to e replced y stle, compct, trnsportle, seled fier-optic systems. The stility of ny fier-optic system strongly depends on the long-term stility of the lser em couplers used for oth coupling in nd out of PM fiers. Power stility during temperture cycling, with typicl mximum devition of 3 % ws chieved in test setup for lser em couplers with focl length of 4.5 mm t 405 nm nd t tempertures etween 15 nd 35 C. This high stility is fundmentl for the successful use of fieroptic equipment. Fier port clusters - more complex compct modulr units tht cn e used to split rdition into multiple polriztion-mintining fiers lso exhiit very good long-term stility s well. Time-consuming lignment tsks cn e completed efficiently for free em s well s fier-optic pplictions y using polriztion nlyzer. Specil routines llow the precise coupling of linerly polrized light into polriztion-mintining fiers nd help identifying the configurtion with the most stle polriztion. DOI: /opph Authors Anj Krischke studied Physics t the University of Würzurg with focus on the description of ultrshort lser pulses nd quntum control. She joined Schäfter+Kirchhoff in 2011 nd now works in optics development. Christin Knothe first studied Physics t the University of Freiurg i.br. with focus on lserspectroscopy efore completing his doctorl thesis in fier optics t the Technicl University of Hmurg-Hrurg. Since he joined Schäfter+Kirchhoff in 2005, he hs een responsile for the dvnced fier optic pplictions. Ulrich Oechsner studied Physics efore completing his doctorl thesis t the University of Hmurg. After reserch in the fields of electrophysiology nd physiologicl optics, he joined Schäfter+Kirchhoff in 2000 where he is responsile for opticl design nd system development. Anj Krischke, Dr. Christin Knothe nd Dr. Ulrich Oechsner, Schäfter+Kirchhoff GmH, Kieler Str. 212, Hmurg, Germny, E-mil: info@sukhmurg.de 44 Optik&Photonik 4/ WILEY-VCH Verlg GmH & Co. KGA, Weinheim

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus 7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e