Final Exam Spring 2014 SOLUTION

Transcription

1 Appled Opts H-464/564 C 594 rtland State nverst A. La Rsa Fnal am Sprng 14 SOLTION Name There are tw questns 1%) plus an ptnal bnus questn 1%) 1. Quarter wave plates and half wave plates The fgures belw shw a alte rstal plate lated at the rdnate =. Calte a brefrngent materal whse prnpal ndes f refratn are n e = n = The thness d f the plate n eah f the dfferent ases nsdered belw rrespnds t ether a quarter wave plate QW n )d n e ) r a half wave plate HW n n e )d ). Here s the wavelength n vauum. The ptal as s rented alng the as. In ths questn we anale the dfferent effet the alte plate has n ndent lght f dfferent plaratns. 1A. Case: Indent lght s lnearl plared. The alte materal s a half wave plate. S r ut r ut X OA Calte HW Seth ur answer here als

2 ) rvde an epressn fr the felds t) and t) n the regn <. rvde an epressn fr the felds t) and t) n the regn >d. ) valuate the felds and at = and use the dagram abve t seth ther shape and rentatn n whh var as tme prgresses. valuate the felds and at =d and use the dagram abve t seth ther shape and rentatn n whh var as tme prgresses. Slutn n n > n e n e X OA ) < > = COS [ /) t ] = COS [ /)n e d + /) -d) t ] = COS [ /) t ] = COS [ /)n d + /) -d) t ] Lnear plaratn ) At = At = d = COS [ t ] = COS [ /)n e d t ] = COS [ t ] = COS [ /)n d t ] sng HW n )d n e = COS [ /)n e d + t ] Rewrtng n term f +t fr nvenene

3 = COS [ t ] = COS [ t /)n e d ] = COS [ t ] = COS [ t - /)n d ] t Ths gves 1. Case: Indent lght s lnearl plared. The alte materal s a quarter wave plate. S r ut r ut X OA Calte QW Seth ur answer here als ) rvde an epressn fr the felds t) and t) n the regn <.

4 rvde an epressn fr the felds t) and t) n the regn >d. ) valuate the felds and at = and use the dagram abve t seth ther shape and rentatn n whh var as tme prgresses. valuate the felds and at =d and use the dagram abve t seth ther shape and rentatn n whh var as tme prgresses. ANSWR ) It s dental t 1 abve ) At = At = d = COS [ t ] = COS [ /)n e d t ] = COS [ t ] = COS [ /)n d t ] sng QW n )d n e = COS [ /)n e d + t ] Rewrtng n term f +t fr nvenene = COS [ t ] = COS [ t /)n e d ] = COS [ t ] = COS [ t - /)n d ] t Ths gves

5 1C. Case: Indent lght s lnearl plared. The alte materal s a quarter wave plate. S X OA Calte QW Seth ur answer here als ) rvde an epressn fr the felds t) and t) n the regn <. rvde an epressn fr the felds t) and t) n the regn >d. ) valuate the felds and at = and use the dagram abve t seth ther shape and rentatn n whh var as tme prgresses. valuate the felds and at =d and use the dagram abve t seth ther shape and rentatn n whh var as tme prgresses.

6 ) < > = COS [ /) t ] = COS [ /)n e d + /) -d) t ] = - COS [ /) t ] = - COS [ /)n d + /) -d) t ] Lnear plaratn ) At = At = d = COS [ t ] = COS [ /)n e d t ] = - COS [ t ] = - COS [ /)n d t ] sng QW n )d n e = - COS [ /)n e d + t ] Rewrtng n term f +t fr nvenene = COS [ t ] = COS [ t /)n e d ] = COS [ t ] = - COS [ t - /)n d ] t Ths gves

7 1D. Case: Indent lght s rularl plared. The alte materal s a half wave plate. S r ut r ut X OA Calte HW Seth ur answer here als ) rvde an epressn fr the felds t) and t) n the regn <. rvde an epressn fr the felds t) and t) n the regn >d. ) valuate the felds and at = and use the dagram abve t seth ther shape and rentatn n whh var as tme prgresses. valuate the felds and at =d and use the dagram abve t seth ther shape and rentatn n whh var as tme prgresses. ) < >

8 = COS [ /) t ] = COS [ /)n e d + /) -d) t ] = COS [ /) t + ] = COS[ /)n d +/) -d) t+ ] Crular plaratn t Seth ur ) At = At = d = COS [ t ] = COS [ /)n e d t ] = COS [ t + ] = COS[ /)n d t + ] sng HW n )d n e = COS[ /)n e d + t + ] 3 = COS[ /)n e d t + ] Rewrtng n term f +t fr nvenene = COS [ t ] = COS [ t - /)n e d ] 3 = COS [ t - ] = COS [ t - - /)n e d ] t

9 Seth ur answer here als. T-plaratn radatn has the fllwng frm ) ) ) ) t t r r A Calulate. Als use the Mawell equatns t btan the fllwng relatnshp ) = Answer det j ˆ ˆ ˆ ) Answer ) ) ) = Calulate. Als use the Mawell equatns t btan the fllwng relatnshp:

10 = j = j Answer: det ˆ ˆ ˆ j ) Answer: ) = = ) = = C Frm the results n A and demnstrate that the T mde must satsf the fllwng wave equatn ω ε ε Answer sng = gves = = = sng A ) = ) = The left sde an be alulated frm

11 the result abve - = + + = OTIONAL QSTION 1%) The eletr suseptblt s defned thrugh the epressn where N p s the ttal dple mment per unt vlume. results frm the ndvdual atm dples ntrbutn p -e. T fnd we need t fgure ut hw hanges wth tme under the effet f an eletr feld t). A smple mdel nsders the eletrn mtn equvalent t a mehanal fred harmn mtn. That s ) the harge s bund t the atm b a restrng fre - m. ) sne the aelerated harge lsses energ a d phenmenlgal dampng fre s nsdered - mγ. dt The rrespndng equatn f mtn s m d d γ dt dt ω ) -e t) t Assumng the eletr feld t) vares harmnall n tme wth frequen as e - and that N s the number f atms per unt vlume slve epltl the equatn abve t prvde an epressn fr a) The ampltude f sllatns b) The phase relatve t the feld). ) The eletr suseptblt. Slutn

12 e 1 p -er dple mment per atm m - ) Hwever an atm has dfferent resnane frequenes... These resnant 1 3 etatns ma als have dfferent strengths f 1 f f3...the latter are numbers f the rder 1 magntude.) e f p -er dple mment per atm m - ) If N s the number f atms per unt vlume the plaratn vetr s gven b whh gves N e f N p = ) m - ) N e f ) eletr suseptblt 1) m - )