b) Estimate the relevant electro-optical coefficient in the material (0.7p)

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1 Exam. Advaned Optis and Lasers 8-5- (-8) Allowed tools: Textbook, your own notes, a alulator, your favourite physis and mathematis tables & formulas. Some plots and tables are shown on a separate sheet Eah of the 6 assignments gives a maximum point. The maximum is 6. points. A total of. points is needed for a passing grade, 4. points (inluding FRED points) for grade 4 and 5. points (inluding FRED points for grade 5.. In the Lund Terawatt Laser the strethed pulse transmitted trough a set-up with a pokels-ell in order to remove unwanted pre- and post-pulses. It is plaed between rossed polarisers. The laser operates at 8 nm and the ring anode is supplied with 8 kv pulses relative to the ring athode. The pokelsell is shown in the figure below. a) How should the KDP Pokels ell be oriented with respet to the diretion of propagation and with respet to the polarization vetor of the light transmitted through the first polarizer in order to enable a omplete extintion when inative and % transmission when ative? Motivate your answer!(.p) b) Estimate the relevant eletro-optial oeffiient in the material (.7p) Note for the interested: The material is in fat KD*P where the hydrogen has been replaed by deuterium a) The pokelsell should work as a halfwaveplate when 8kV is applied and be inative when no voltage is applied. KDP is a uniaxial rystal. Let the optial axis be parallel to the diretion of propagation. Then there will be no rotation without voltage beause the refrative index is the same for all polarisation omponents in the plane perpendiular to the optial axis. When a voltage is applied along the optial axis the refrative index is modified by n +/- 45 degrees to the rystal axis. In one diretion (n= no-n) whereas in the other (n= no+n). Hene the inoming beam should be parallel to one of the other axis (x or y in Fig.-). When the pokelsell is ative one polarisation omponent will be retarded by L*n/ d L b See example.-6 V r n r n n n n o From the red urve we an read n o for KDP to be.5 ( r 6 ( r6)) n r6.5 V n V. A linearly (horizontally) polarized laser beam (6 nm) has a top-hat profile (uniform beam intensity) with a mm beam diameter and a power of 8 mw.

2 a) Calulate the magnitude E of the E-field of the laser in vauum. (.p).8 W W I P / A 5. m m E I E I 4V / m Where the impedane of vauum 77 has been used. b) The beam enters glass at normal inidene. Calulate the magnitude of the E-field inside the glass? (.p) Fig 6.- gives an amplitude refletivity of % and thus an intensity refletivity of 4%. 96% of the E-field enters the glass and the amplitude an be written as E I E I The impedane in glass is va 5 n E=.kV/m ) The beam goes through an unknown optial omponent. The power is still 8 mw after the omponent but the state of polarisation has been hanged. We analyze the state of polarisation with a lossless polarizer. When we orient it horizontally it transmits 4 mw. When aligned vertially it also transmits 4 mw. When the polariser is rotated the minimum transmission is found to be mw. Write down the normalized Jones vetor for the light. State how you define the x and y axis. (.4p) For an angle of 45 degrees to horizontal we obtain minimum transmission (6.-6). We have not said if this is lokwise of ounter-lokwise. Let s define it as being lokwise and view as if the beam is approahing us. This is roughly fig 6.-. In our ase, tan, r sin sin( artan( )) artan( ) The Jones matrix is: i e Please turn page for next assignement

3 . A sound wave propagates along the y axis of a ubi ZnTe rystal. S i S o e ( tqx). Various material parameters for ZnTe an be found in the table below. The light wave originates from a He-Ne laser. It has a wavelength of 6.8 nm and makes a.5 degree angle with the z-axis with a small omponent parallel to the diretion of the aousti wave. The rystal is a ube with a m side. The strain-opti tensor P IK is: a) What frequeny should the sound wave have in order to fulfil the Bragg ondition (.4p) vs vs nsin sin f 9MHz n nsin b) What amplitude should the beam have in order to obtain % diffration effiieny (% refletivity in power), Neglet the refletions at the boundaries between the rystal and air. Hint: Whih dimension will limit the interation length? (.6p) Review 9.-4 in order to find whih strain-opti onstant to use n pn S L L R n pn S Z pn sin sin 6 6 S R.5 Zpn Z denotes the length of the rystal in the diretion of propagation whih is m, L is also m, but Z is the limiting dimension. 4. A diode laser operates at a wavelength of 6 nm. The bandwidth is. nm FWHM. The spetrum is Gaussian. a) Calulate the oherene time. (.p) g (.p) b) Sketh the time-dependene of the normalized oherene funtion ) At what delay has g dropped to 5% (.p) d) What resolution ould be obtained if optial oherene tomography was used inside medium with refrative index n=.5 (.p) S

4 .nm 75,6GHz.66. ps (Defined as power-equivalent width) g( ) e g( ) / ln ln 8.8 ps In a medium with refrative index.5, the veloity of light is e8 m/s, and the light has to go forward and bak. The resolution is given by e8*8.8e-/=8.8e-4. The resolution is.88mm 5. A short-pulse laser produing radiation entered around 8 nm is haraterized. An intensity autoorrelation is measured and the FWHM of the autoorrelation funtion is found to be 4 fs. The spetrum is measured and the FWHM of a nearly Gaussian spetrum was found to be 8 nm. a) Calulate the hirp fator of the omplex amplitude. (.7p) b) The beam goes through a fused silia glass plate and the intensity autoorrelation is found to be 8 fs. What was the sign of the hirp in a) (p)

5 ) Motivate your answer in b) (.p) 8nm.75THz FWHM.44 7 fs a a FWHM 7 fs a 7 fs a 7 fs Beause the seond derivative of the refrative index with respet to wavelength is positive the dispersion is positive whih gives an up-hirping filter. If an uphirping filter gives a shorter pulse, the pulse was downhirped to begin with. This means that the negative solution was the orret one. 6. We are studying the frequeny mixing of a 6 nm beam and a 8 nm beam in BBO. The duration of the pulses are suffiiently long so that we an onsider the waves to be stationary (ontinuous wave) a) Calulate the phasemathing angle for effiient frequeny mixing in BBO, for Type ooe (.4p) b) Calulate the phasemathing angle for effiient frequeny mixing in BBO, for Type II oee (.p) ) Do you think Type I or Type II will be most effiient? (p) d) Motivate your answer from! (.p)

6 ZnTe Property Value Refrative index at 6.8 nm.986 Photoeletri onstants: P.44 P.94 P 44 =.5 Mass density 5.66 g/m Speed of sound* 55 m/s *The sound speed depends on the diretion of propagation but we give the longitudinal speed along a rystal axis, whih is the wave to onsider Fused silia d n/d (m) - d n/d (m) - Please turn over for other diagram

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8 Reservuppgift We set out to frequeny double a fs pulse and want to maintain the pulse duration reasonable well.. We are trying to deide if we should use a BBO rystal or a KDP rystal. We are also ontemplating if we should use type I or type II phasemathing. Deide whih type of rystal to order, whih length of the rystal we should speify to the manufaturer and finally whih thikness should the rystal have?