SOLUTION SET. Chapter 11 LASER CAVITY MODES "LASER FUNDAMENTALS" Second Edition
|
|
- Edwin Dennis
- 6 years ago
- Views:
Transcription
1 SOLUTION SET Chapter 11 LASER CAVITY MODES "LASER FUNDAMENTALS" Second Edition By William T. Silfvast
2 Cl-I II 1. Show that the two expressions for ft of (11.12) and (11.16) are equivalent; that is, 1 show that y2 y Rei<Pl 2 = 10 (1- R) F' sin 2 (<P/2) \ I - ~ e ~ dl ) 2 -= ( 1- f2 e./ cl)( I- Re" qj) = 1-12 e_ A. l - r<. e-... / rj. + r<. "'-. ~ I- 2 r<. C.Q;t. ~ +- R~ s1., 2 l~)-= I- c.o-of 2 c-=-> ([_::: I - L S '"'- 2 (t) r, ) I - r< \. 1-: 2 R [I -z ~i.(fl,jj + R 2. ~ :: I - 2 I'< + '-{ R y;...'l@;i) + R. :=. I - L. le.. + R. " + L/ R. y;_.., t (.cl) -::: (1 - r<) L. t- 'i R ~ '(~) ' '(_I_ - R ) 'l I -1- ~ F I ::: '-( I<.. ll-r_j'- (_ ( _ ~),_ $,-., 'l~j] ~ J 1 - r<. e.,. ar1 '= u-12-jl, + c 's 1...\~,_)J I L~::: r T"- ' I I f" ( 1 - r<t ~ +- F 1 sl" ~(%)]
3 C.H II 2. Compute the FWHM frequency linewidth for a plane-parallel Fabry-Perot interferometer with two identical mirrors, separated by a distance of 1 cm, with air between : the mirrors. Assume mirror reflectivities of 99.99%, 95%, and 70%. Determine the cavity Q for these three cases if the output of a GaAs diode laser operating at 800 nm is transmitted through the interferometer. ol :: o, 0 I ~ A ::: <t l)l) VI IM_ r<--::: qc). 9 Cj i) q ~%, 7 (J lo 'v1 ~ I. D c ~ ~ AV:::-. ~ 3 x llj -::. /, r:x10 10 H 1.1..= 3 x; o 2 ~~ "2.. I D. O I ~ b t/ OfJ x 10-'I ''IH :::: 3/7S-X/D r Lj.?/ - F 3. I '-II '>( I f) '1 -- ~ A?' t"' F= Tl{,,~-- / -. ~/?"-::. (p /, 2 ltj 'a"..,.9 / 1 ~XIO t..;5'"'.xio fltt A YFWff-M -= - (.P /, '2.- Q :: ~, '7 S"' X I() I 'f vrx 10 ~ - /, ~ J X I 0 "' (CJ J. 7 r-xio''l - L1 11 XI().r - /.?I x101
4 t:. II II 3. A very narrow-frequency 10-mW cw single-mode He-Ne laser beam is transmitted through an air-spaced Fabry-Perot interferometer with the laser wavelength exactly corresponding to one of the looo/o transmission peaks of the interferometer, as indicated in Figure The reflecting surfaces of the interferometer, separated by a distance of 0.1 m, are dielectric coatings with a reflectivity at the laser wavelength of 99% and no absorption losses. What is the power of the beam inside of the Fabry-Perot cavity? Assume that the laser is instantly shut off in a time of the order of 1 ns or less. How long will it then take for the beam inside the Fabry-Perot cavity to decay to 1/ e of its steady-state value prior to the shutoff? ca> \.'. e r b),,,..,,.,;.,....- L - ' en.. e-l1... M. 1 v- *"'' Y' 1 '.J l}"t! V' 1 ff-;,.._,_ Tu- ~tt_ &M... ~, r v ~,..., a.a J2 tj Stll!. $ I lo t> v 1 s re dit ~do.,/ 71> 0 1?9 r/ /Ts. t ~(.,t~ LI~, l+f'cm"' N ~f/a:f/u~ it wrl/ be. y-e.,lu. '4~ n ~ v~ ~ (_ 0, 91) ~ fl-11-w IM.~~ pa s>e.s w/11 it n~ T',, ~- ve-k"-.,.1 TD Ye..? l (), <? '1) N = i = t'' 3 ~ q ~ N :: I O o Eac.k pc...s. s be.-t<»eem.. Vv\ t Y. v- o v- ~ i'~~ O, f IM.. = ix1o e1ct/s Hau~ ~ A t:~ 1i'~fl' t'_s ~ V - I"? "'., h s<<l Io D x 3. $3 ~ lb v -_j_>_ -~ _,{) 3,})Xlb ~
5 Cl/ I/ 4. A 0.1-m-long Nd:YAG laser rod is coated with a 99o/o reflector on one end and a 95% reflector on the other end. Determine the longitudinal mode spacing. How '. many modes could be operating if the gain bandwidth is a Lorentzian shape with a FWHM of 0.45 nm and a peak at 1.06 µm? (Assume the laser is mode-locked so that all possible modes are lasing.) Assume that the maximum small-signal gain is 10% at the peak of the emission spectrum and that the cavity losses (in addition to mirror losses) are 2 % per pass. The index of refraction of Nd: YAO at µm is Note: Since the transmission losses are different at each mirror, you must : consider the total round-trip gain and loss. \ ~-=- O, I~ R.,~ IJ,,, f<.,--;:. {),~~ V\-=- I. ~L. L::. ')) = c ~ :s )( 10~1-v.../5 - ('~ 2'1 x /fj g#e- V\_d 1..(1,C/l) (fj,/)~ - _~_, CA vi I~ lo c,s ~!> f2\( c../1.1. eil i'"'1...,-.,.,..,"" T.-.. u... ;~str.. : L. '4 /,.."s Th~ rot.ttae/ ;,_~P lo!i~lf~ (/-(.).'1~)+ {1- tj,.1~)+ ~,t>lj"-~.d2j () V' S ~ f er ~ p A 'o+ s ( o._ u-e.,,..,._,,e.-i) : ~ /a~c H.e"l ~ ~.? a.;"'- a~ L~ e:,t. (. e12jt- ~ I ~ s s es. ()trf..v ~ bam-..t w I el T l\ e "3 u i v 11. L.,..J ti 'f'i..e F W If M " f fi.t_ e ~ ' ~ $ '.. tri-t It'*~ w id!/,,. "'.. I lL_ F W-H M ~ f ~ ~w.t..ts >I tn<f I~ I$! - A -::: 3 )( I () ""t ""-/ s l (). '( f'x 10. ~..,_ /, 2 4 V- A,_ 4 0Dt..x11;- '')"'- /'4 ~ I ~<A. ~ vt L-t ~ b 4 Y' 0c f / trl:t.f! /T IA,/,';,,J l/u C,J.a,q 1 S (. '~ 20 ~!~ 1 'f,2 V' X IO ~ IJ x + 1) =: I Lf ~,.~ :: I lf ~ ~.A)~ 1\forA! ~ (~ a_j... u~q4 ~ ~~ f:!~st-1'6~ 1o''lf., VIA.--b cl.e ~~ ('k.o..~ a 1ttL S ft'i. G4 ~ be_( wee~ Wt~~,
6 Cl-I I/, 5. A helium-cadmium laser is operating at nm with a natural mixture of Cd in ; the discharge. Assume the laser has a gain of 6o/o per pass for the isotope 114 at / its maximum emission frequency. The laser mirrors are separated by a distance of 0.4 m and the mirrors have reflectivities of 96% and 99.9% at the laser wavelength. 1 Assume that there are scattering losses of 1 % per pass through the cavity. Also remember that the index of refraction within a gas laser is 1. How many longitudi- : nal modes would be lasing in this system? Refer to Figure 4-15(a) for information i about isotopes of Cd. \ d ~ (),'-{ ~ R,-::: (), lfe f(_l :- 0, ct 9~ Sc_t1.1tevi1',,~ /r;sse-s /~ ~pa_s5 c;r tj,ol/p~ss ~I.\_ c..e T4. V"b u ~'-c.e IV'~ p ( ~ s.se s, ct r-e '... (/- o,cffr) + (t - 0, 917) + 0,01.J. o,o/ = o,o~iv1.fti.1' A M--o..-e t._c.t.-vi... ~ w o... 1 ~ ca I c.m.. I q_. T, "'-"/ ~ I 5, [I - ( (),'/b)(o,9?) (O, 9'?')(o,crtJ= ~,OO<tx =. (p,dlt>, L~ {A.11'1, O? (L..e j;t.l Cl )(_ I ~ - '"' IM.. V,-0 la. "l d.. Tt' I ~ 'f 41 "\ (... I$ I L f[) Fr'"'t>~ Ft'v, '1-1rtt1.J, fr;.,,.. Ld 112 1a1 11= ~ 11?t,: /12,tJlo f~r Cf //D ffj ~ &lllj? ~4 i "< :.- /_,"2, y It.~.:: ~ ~ lo, 2.. f q Cf,-11. : 7, ~ I., % -:: s, 2. d/e y 2'(; ~ 0 /-.4'<u ~ ~//'- <!..~ Gf 11 'r wr// U'<.T,,.,);,,._(j. n la.s1"'-7., Frie~ Ftj L/-1.rt~) fz...e bcv-d t.-utdfl,_ fo.,., ~~ T'w o l $a TO p~ 15 ~ - pp Y'fJ x., J!tA.d--f:;el ~.. t11{= /.'-/~ &-H~ (~, Oep/"~w1ATL..) -= /, '-f' + /, I -=- "2, s~ t::r-h~
7
8 C. H II 7. Show that, for a TEMoo mode passing between two laser mirrors, the transverse ' I displacement - from the center axis, where (according to eqn ) the intensity : reaches a maximum, to the location where the intensity of the mode has a value I of 1/ e 2 of the maximum - corresponds to the value w in (11.53) (for a Gaussian. mode distribution). '-L~-::. w r 0 - e'2.. l.. l. L L.. ~"? f ~ vj
9 (, 1-1 I/ I 8. Write out the expressions for the transverse sp~tial distribution at the mirrors of! the TEMu, TEM20, and TEM22 modes. TDM, 1 ::o 'U11 (t,,) ~ H, (f'""2;) Hi(~) e - cx:i+tv')/wl. - 2 lf2_ x 7_ l['2:!i e_ -( X 2-+ ( 1y W '- r,{ )( J e. - (x1i-~ ry f wl w w
10 c 1-1 // 9. For a confocal cavity with a Fresnel number of 1, compare the losses per pass with those of a plane-parallel resonator for both TEM 00 and TEM 01 modes. What are the implications of having a Fresnel number of 1 for a visible laser operating at 500 nm and an infrared laser operating at 10 µm? ~fou.j. Ctui11 w irk F ~(> ""'- F1 7~ II - II , o o I
11 LH II 10. Assume an argon ion laser is operating at nm in a confocal cavity in the! TEM 00 mode with a mirror separation of 0.6 m. Assume that the gain medium is. '. 0.4 m long. What must the gain coefficient be for the laser to operate at threshold with mirror refiectivities of 99.99o/o at the laser wavelength? Assume that the beam radius (the effective limiting aperture) for the laser beam is 0.5 mm at each mirror. Assume also that the only losses in the cavity are the diffraction losses at, the mirrors. (The mirrors are mounted at the ends of the laser discharge tube such that there are no Brewster angle windows.) ~ '"::. L' i i, o V\ ~ a. -.:. a, tj () o $"" ~ N "" ~ -::. (_o, ti tlf.1 s ) -:::- O, e'( S"" I\(";\ '-- L/ft8x1c-'(!,&,) FV"a ~"' l=l,u~ I { - I I F <>.,... CAJ""- ft> ce.)_ CA- v; t7 T E IV( 6 0 ~o e1..a ~ d/hy--~{ib vi. /, s5 /rtt'~ 1 ~$ ~ C),tJO 2. :;- :::. 4 1 ) tt"- F~o IM-. (_7, ~o). ~~ :: tl fo{~, /C?..{1-&1,)(1-«l J +OL J:;wt rx. ~ 0 L "" o, '1 ~.,I. ((. I -:::. fl... :;. tj /11"1 1-rz..._ A-~ o.1"'~ == Ll(o,'f) )... (' -O.ao :g )';:.J ~, ~ X /'fj- "J, ::: (), ~ O &, ~/ lnt
12 Cl-I I/ 11. A C0 2 laser is operating at 10.6 µm in a confocal resonator having a mirror sep-. aration of 0.5 m such that both the TEMoo and TEMn modes are lasing. What is : the distance between the maximum intensity points of diagonally opposite lobes of the TEMu mode at the mirrors? i. [. CZ><~ _ (x' tto/w J "t =- I u,, / -:: -w"i e. ~ ~... 10'- e w"' eal'a.; ~p d.1~c.tl("-:j) e _ t.cj( 1..,..v" f'w'" - 'f X~W'- '1:: x
13 C.N I/ 12. A Nd:YAG laser has a homogeneously broadened gain profile with a FWHM of J 120 GHz. The laser is fiashlamp pumped to operate cw with a single-pass small- : signal gain at the center of the gain profile of 8 o/a. Mirrors are coated on the ends of the 0.1-m-long Nd:YAG rod with a reflectivity of 98% each. What is the maximum number of longitudinal modes that could be lasing? (Assume that the laser is operating under mode-locked conditions such that all possible modes are lasing.) iz~ dat~/p~s s l:u.. Th f"-i" p Y1> fr-~ I~ M""""'~"~ ~ ~ ~re..ex.. p re $ s.e.,( e:l4, /L/ rr,_ 5 (} f ~ fi>vi L1 v-= -v.- tjo vj ~ 11-=- o ,02-::.. 'DC.'( 'i it;7t'- a. i - C4 -V.. + l"rv rr )~ t> r
14 C /-1 II 13. An argon ion laser beam operating at 488 nm is passed through a Fabry-Perot cav- I I ity in air at normal incidence with no reduction in its intensity. The cavity has a.: mirror separation of 0.3 m, mirror refiectivities of 95o/o at the laser wavelength, and no absorption losses. What is the minimum distance the mirror separation would have to be changed in order to reduce the transmitted intensity to one half of the input intensity? r<;:: (),qi;- I<:::: rj. q s- (u.3~) 0,3M l ( I - '2.\ '-TT V\_cA fr /,, f'\ o\,.. C>. Y1 -::.. 7- "\ d, 1. b..y, - ol, A "I ~I Ao( I -:: L Y\' (_,_ "'\ '0_ C. - C D.. -v, = A -VFWHM I -::.. L/, D ~ x1ot.?/.lt V\, - {). 3 LM-- I'- ~1 :;_ L.[ '616 )(I o- 1 V'-' ( 0,.J, )( '-/, D'iXI 0 ~ /-/~) (~'l!xllf'i,.._) ~ I, 1'1 XI 0 -'t IM. L\ t?f I -::.. 3 X. l 0 'a ~/s
SOLUTION SET. Chapter 8 LASER OSCILLATION ABOVE THRESHOLD "LASER FUNDAMENTALS" Second Edition
SOLUTION SET Chapter 8 LASER OSCILLATION ABOVE THRESHOLD "LASER FUNDAMENTALS" Second Edition By William T. Silfvast - 1. An argon ion laser (as shown in Figure 10-S(b)) operating at 488.0 nm with a gainregion
More informationSOLUTION SET. Chapter 6 RADIATION AND THERMAL EQUILIBRIUM - ABSORPTION AND STIMULATED EMISSION "LASER FUNDAMENTALS" Second Edition
SOLUTION SET Chapter 6 RADIATION AND THERMAL EQUILIBRIUM - ABSORPTION AND STIMULATED EMISSION "LASER FUNDAMENTALS" Second Edition By William T. Silfvast Cll ~ 1. Calculate the number of radiation modes
More informationSOLUTION SET. Chapter 9 REQUIREMENTS FOR OBTAINING POPULATION INVERSIONS "LASER FUNDAMENTALS" Second Edition. By William T.
SOLUTION SET Chapter 9 REQUIREMENTS FOR OBTAINING POPULATION INVERSIONS "LASER FUNDAMENTALS" Second Edition By William T. Silfvast C.11 q 1. Using the equations (9.8), (9.9), and (9.10) that were developed
More informationLaser Types Two main types depending on time operation Continuous Wave (CW) Pulsed operation Pulsed is easier, CW more useful
Main Requirements of the Laser Optical Resonator Cavity Laser Gain Medium of 2, 3 or 4 level types in the Cavity Sufficient means of Excitation (called pumping) eg. light, current, chemical reaction Population
More informationStimulated Emission Devices: LASERS
Stimulated Emission Devices: LASERS 1. Stimulated Emission and Photon Amplification E 2 E 2 E 2 hυ hυ hυ In hυ Out hυ E 1 E 1 E 1 (a) Absorption (b) Spontaneous emission (c) Stimulated emission The Principle
More information(b) Spontaneous emission. Absorption, spontaneous (random photon) emission and stimulated emission.
Lecture 10 Stimulated Emission Devices Lasers Stimulated emission and light amplification Einstein coefficients Optical fiber amplifiers Gas laser and He-Ne Laser The output spectrum of a gas laser Laser
More information~,. :'lr. H ~ j. l' ", ...,~l. 0 '" ~ bl '!; 1'1. :<! f'~.., I,," r: t,... r':l G. t r,. 1'1 [<, ."" f'" 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'..
,, 'l t (.) :;,/.I I n ri' ' r l ' rt ( n :' (I : d! n t, :?rj I),.. fl.),. f!..,,., til, ID f-i... j I. 't' r' t II!:t () (l r El,, (fl lj J4 ([) f., () :. -,,.,.I :i l:'!, :I J.A.. t,.. p, - ' I I I
More informationA L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
More information176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
More informationWhat Makes a Laser Light Amplification by Stimulated Emission of Radiation Main Requirements of the Laser Laser Gain Medium (provides the light
What Makes a Laser Light Amplification by Stimulated Emission of Radiation Main Requirements of the Laser Laser Gain Medium (provides the light amplification) Optical Resonator Cavity (greatly increase
More informationAPPH 4200 Physics of Fluids
APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I $T1P#(
More informationCHAPTER FIVE. Optical Resonators Containing Amplifying Media
CHAPTER FIVE Optical Resonators Containing Amplifying Media 5 Optical Resonators Containing Amplifying Media 5.1 Introduction In this chapter we shall combine what we have learned about optical frequency
More informationChapter-4 Stimulated emission devices LASERS
Semiconductor Laser Diodes Chapter-4 Stimulated emission devices LASERS The Road Ahead Lasers Basic Principles Applications Gas Lasers Semiconductor Lasers Semiconductor Lasers in Optical Networks Improvement
More informationLaser Types Two main types depending on time operation Continuous Wave (CW) Pulsed operation Pulsed is easier, CW more useful
What Makes a Laser Light Amplification by Stimulated Emission of Radiation Main Requirements of the Laser Laser Gain Medium (provides the light amplification) Optical Resonator Cavity (greatly increase
More informationSome Topics in Optics
Some Topics in Optics The HeNe LASER The index of refraction and dispersion Interference The Michelson Interferometer Diffraction Wavemeter Fabry-Pérot Etalon and Interferometer The Helium Neon LASER A
More informationMEFT / Quantum Optics and Lasers. Suggested problems Set 4 Gonçalo Figueira, spring 2015
MEFT / Quantum Optics and Lasers Suggested problems Set 4 Gonçalo Figueira, spring 05 Note: some problems are taken or adapted from Fundamentals of Photonics, in which case the corresponding number is
More informationEE485 Introduction to Photonics
Pattern formed by fluorescence of quantum dots EE485 Introduction to Photonics Photon and Laser Basics 1. Photon properties 2. Laser basics 3. Characteristics of laser beams Reading: Pedrotti 3, Sec. 1.2,
More informationLaser Basics. What happens when light (or photon) interact with a matter? Assume photon energy is compatible with energy transition levels.
What happens when light (or photon) interact with a matter? Assume photon energy is compatible with energy transition levels. Electron energy levels in an hydrogen atom n=5 n=4 - + n=3 n=2 13.6 = [ev]
More information3.1 The Plane Mirror Resonator 3.2 The Spherical Mirror Resonator 3.3 Gaussian modes and resonance frequencies 3.4 The Unstable Resonator
Quantum Electronics Laser Physics Chapter 3 The Optical Resonator 3.1 The Plane Mirror Resonator 3. The Spherical Mirror Resonator 3.3 Gaussian modes and resonance frequencies 3.4 The Unstable Resonator
More informationA novel scheme for measuring the relative phase difference between S and P polarization in optically denser medium
A novel scheme for measuring the relative phase difference between S and P polarization in optically denser medium Abstract Yu Peng School of Physics, Beijing Institute of Technology, Beijing, 100081,
More informationS. Blair September 27,
S. Blair September 7, 010 54 4.3. Optical Resonators With Spherical Mirrors Laser resonators have the same characteristics as Fabry-Perot etalons. A laser resonator supports longitudinal modes of a discrete
More informationEE 119 Introduction to Optical Engineering Fall 2010 Final Exam
EE 119 Introduction to Optical Engineering Fall 2010 Final Exam Name: ------~~~~----------------------------------- SID: _ CLOSED BOOK. THREE 8 112" X II" SHEETS OF NOTES, AND SCIENTIFIC POCKET CALCULATOR
More informationLasers... the optical cavity
Lasers... the optical cavity history principle, intuitive aspects, characteristics 2 levels systems Ti: Helium Al2O3 - Neon model-locked laser laser VCSEL bragg mirrors cleaved facets 13 ptical and/or
More informationAr and Kr ion lasers
Types of Lasers Ar and Kr ion lasers Nd:YAG and Nd:YLF lasers CO 2 lasers Excimer lasers Dye lasers Transition metal lasers Optical parametric amplification Ar and Kr ion lasers Noble gas ions are created
More informationP a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
More informationECE 484 Semiconductor Lasers
ECE 484 Semiconductor Lasers Dr. Lukas Chrostowski Department of Electrical and Computer Engineering University of British Columbia January, 2013 Module Learning Objectives: Understand the importance of
More informationQuantum Electronics Laser Physics PS Theory of the Laser Oscillation
Quantum Electronics Laser Physics PS407 6. Theory of the Laser Oscillation 1 I. Laser oscillator: Overview Laser is an optical oscillator. Resonant optical amplifier whose output is fed back into its input
More informationThe Generation of Ultrashort Laser Pulses
The Generation of Ultrashort Laser Pulses The importance of bandwidth More than just a light bulb Two, three, and four levels rate equations Gain and saturation But first: the progress has been amazing!
More informationChapter9. Amplification of light. Lasers Part 2
Chapter9. Amplification of light. Lasers Part 06... Changhee Lee School of Electrical and Computer Engineering Seoul National Univ. chlee7@snu.ac.kr /9 9. Stimulated emission and thermal radiation The
More informationrhtre PAID U.S. POSTAGE Can't attend? Pass this on to a friend. Cleveland, Ohio Permit No. 799 First Class
rhtr irt Cl.S. POSTAG PAD Cllnd, Ohi Prmit. 799 Cn't ttnd? P thi n t frind. \ ; n l *di: >.8 >,5 G *' >(n n c. if9$9$.jj V G. r.t 0 H: u ) ' r x * H > x > i M
More informationModern optics Lasers
Chapter 13 Phys 322 Lecture 36 Modern optics Lasers Reminder: Please complete the online course evaluation Last lecture: Review discussion (no quiz) LASER = Light Amplification by Stimulated Emission of
More informationT h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
More informationSOUTHWESTERN ELECTRIC POWER COMPANY SCHEDULE H-6.1b NUCLEAR UNIT OUTAGE DATA. For the Test Year Ended March 31, 2009
Schedule H-6.lb SOUTHWSTRN LCTRIC POWR COMPANY SCHDUL H-6.1b NUCLAR UNIT OUTAG DATA For the Test Year nded March 31, 29 This schedule is not applicable to SVvPCO. 5 Schedule H-6.1 c SOUTHWSTRN LCTRIC POWR
More informationLasers PH 645/ OSE 645/ EE 613 Summer 2010 Section 1: T/Th 2:45-4:45 PM Engineering Building 240
Lasers PH 645/ OSE 645/ EE 613 Summer 2010 Section 1: T/Th 2:45-4:45 PM Engineering Building 240 John D. Williams, Ph.D. Department of Electrical and Computer Engineering 406 Optics Building - UAHuntsville,
More informationr(j) -::::.- --X U.;,..;...-h_D_Vl_5_ :;;2.. Name: ~s'~o--=-i Class; Date: ID: A
Name: ~s'~o--=-i Class; Date: U.;,..;...-h_D_Vl_5 _ MAC 2233 Chapter 4 Review for the test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the derivative
More informationImproving the stability of longitudinal and transverse laser modes
Optics Communications 239 (24) 147 151 www.elsevier.com/locate/optcom Improving the stability of longitudinal and transverse laser modes G. Machavariani *, N. Davidson, A.A. Ishaaya, A.A. Friesem Department
More information3rd Year Mini Project - The Helium Neon LASER
3rd Year Mini Project - The Helium Neon LASER Kylie J MacFarquharson May 11, 2018 Abstract In this experiment we built a large He-Ne LASER with an open cavity. We then investigated various properties of
More informationEE 472 Solutions to some chapter 4 problems
EE 472 Solutions to some chapter 4 problems 4.4. Erbium doped fiber amplifier An EDFA is pumped at 1480 nm. N1 and N2 are the concentrations of Er 3+ at the levels E 1 and E 2 respectively as shown in
More informationTentative Schedule: Date, Place & Time Topics Sep.4 (Mo) No classes Labor Day Holiday Exam 1 Exam 2 Over Chapters 4-6
Tentative Schedule: Date, Place & Time Topics 1 Aug. 8 (Mo) 394; 5:00-6:15 Introduction, Spontaneous and Stimulated Transitions (Ch. 1) Lecture Notes Aug. 30 (We) 394; 5:00-6:15 Spontaneous and Stimulated
More informationi;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s
5 C /? >9 T > ; '. ; J ' ' J. \ ;\' \.> ). L; c\ u ( (J ) \ 1 ) : C ) (... >\ > 9 e!) T C). '1!\ /_ \ '\ ' > 9 C > 9.' \( T Z > 9 > 5 P + 9 9 ) :> : + (. \ z : ) z cf C : u 9 ( :!z! Z c (! $ f 1 :.1 f.
More informationExecutive Committee and Officers ( )
Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r
More informationR e p u b lic o f th e P h ilip p in e s. R e g io n V II, C e n tra l V isa y a s. C ity o f T a g b ila ran
R e p u b l f th e P h lp p e D e p rt e t f E d u t R e V, e tr l V y D V N F B H L ty f T b l r Ju ly, D V N M E M R A N D U M N. 0,. L T F E N R H G H H L F F E R N G F R 6 M P L E M E N T A T N T :,
More informationOptoelectronics ELEC-E3210
Optoelectronics ELEC-E3210 Lecture 3 Spring 2017 Semiconductor lasers I Outline 1 Introduction 2 The Fabry-Pérot laser 3 Transparency and threshold current 4 Heterostructure laser 5 Power output and linewidth
More informationEdward S. Rogers Sr. Department of Electrical and Computer Engineering. ECE426F Optical Engineering. Final Exam. Dec. 17, 2003.
Edward S. Rogers Sr. Department of Electrical and Computer Engineering ECE426F Optical Engineering Final Exam Dec. 17, 2003 Exam Type: D (Close-book + one 2-sided aid sheet + a non-programmable calculator)
More informationEXTREME ULTRAVIOLET AND SOFT X-RAY LASERS
Chapter 7 EXTREME ULTRAVIOLET AND SOFT X-RAY LASERS Hot dense plasma lasing medium d θ λ λ Visible laser pump Ch07_00VG.ai The Processes of Absorption, Spontaneous Emission, and Stimulated Emission Absorption
More informationTausend Und Eine Nacht
Connecticut College Digital Commons @ Connecticut College Historic Sheet Music Collection Greer Music Library 87 Tausend Und Eine Nacht Johann Strauss Follow this and additional works at: https:digitalcommonsconncolledusheetmusic
More information::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2...
Math 3298 Exam 1 NAME: SCORE: l. Given three points A(I, l, 1), B(l,;2, 3), C(2, - l, 2). (a) Find vectors AD, AC, nc. (b) Find AB+ DC, AB - AC, and 2AD. -->,,. /:rf!:,-t- f1c =-
More informationfur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.
OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te
More informationLasers & Holography. Ulrich Heintz Brown University. 4/5/2016 Ulrich Heintz - PHYS 1560 Lecture 10 1
Lasers & Holography Ulrich Heintz Brown University 4/5/2016 Ulrich Heintz - PHYS 1560 Lecture 10 1 Lecture schedule Date Topic Thu, Jan 28 Introductory meeting Tue, Feb 2 Safety training Thu, Feb 4 Lab
More informationQuantum Electronics Laser Physics. Chapter 5. The Laser Amplifier
Quantum Electronics Laser Physics Chapter 5. The Laser Amplifier 1 The laser amplifier 5.1 Amplifier Gain 5.2 Amplifier Bandwidth 5.3 Amplifier Phase-Shift 5.4 Amplifier Power source and rate equations
More informationWhat do we study and do?
What do we study and do? Light comes from electrons transitioning from higher energy to lower energy levels. Wave-particle nature of light Wave nature: refraction, diffraction, interference (labs) Particle
More information. ~ ~~::::~m Review Sheet #1
. ~ ~~::::~m Review Sheet #1 Math lla 1. 2. Which ofthe following represents a function(s)? (1) Y... v \ J 1\ -.. - -\ V i e5 3. The solution set for 2-7 + 12 = 0 is :---:---:- --:...:-._",,, :- --;- --:---;-..!,..;-,...
More informationLecture 8 Con,nuous- Wave Laser*
Lecture 8 Con,nuous- Wave Laser* Min Yan Op,cs and Photonics, KTH 24/04/15 1 * Some figures and texts belong to: O. Svelto, Principles of Lasers, 5th Ed., Springer. Reading Principles of Lasers (5th Ed.):
More informationMODERN OPTICS. P47 Optics: Unit 9
MODERN OPTICS P47 Optics: Unit 9 Course Outline Unit 1: Electromagnetic Waves Unit 2: Interaction with Matter Unit 3: Geometric Optics Unit 4: Superposition of Waves Unit 5: Polarization Unit 6: Interference
More informationThe laser oscillator. Atoms and light. Fabry-Perot interferometer. Quiz
toms and light Introduction toms Semi-classical physics: Bohr atom Quantum-mechanics: H-atom Many-body physics: BEC, atom laser Light Optics: rays Electro-magnetic fields: Maxwell eq. s Quantized fields:
More information,\ I. . <- c}. " C:-)' ) I- p od--- -;::: 'J.--- d, cl cr -- I. ( I) Cl c,\. c. 1\'0\ ~ '~O'-_. e ~.\~\S
Math 3306 - Test 1 Name: An d {"0v\ ( _ roj ~ ed Date: l'( ~0 { 1\ Fall 2011 1. (to Pts) Let S == {I, 2, 3,4, 5,6,7,8,9, 10}. of each of the following types of mappings, provide justification for why the
More informationThe laser oscillator. Atoms and light. Fabry-Perot interferometer. Quiz
toms and light Introduction toms Semi-classical physics: Bohr atom Quantum-mechanics: H-atom Many-body physics: BEC, atom laser Light Optics: rays Electro-magnetic fields: Maxwell eq. s Quantized fields:
More informationMetal Vapour Lasers Use vapoured metal as a gain medium Developed by W. Silfvast (1966) Two types: Ionized Metal vapour (He-Cd) Neutral Metal vapour
Metal Vapour Lasers Use vapoured metal as a gain medium Developed by W. Silfvast (1966) Two types: Ionized Metal vapour (He-Cd) Neutral Metal vapour (Cu) All operate by vaporizing metal in container Helium
More informationEngineering Medical Optics BME136/251 Winter 2017
Engineering Medical Optics BME136/251 Winter 2017 Monday/Wednesday 2:00-3:20 p.m. Beckman Laser Institute Library, MSTB 214 (lab) Teaching Assistants (Office hours: Every Tuesday at 2pm outside of the
More informationnecessita d'interrogare il cielo
gigi nei necessia d'inegae i cie cic pe sax span s inuie a dispiegaa fma dea uce < affeandi ves i cen dea uce isnane " sienzi dei padi sie veic dei' anima 5 J i f H 5 f AL J) i ) L '3 J J "' U J J ö'
More informationo C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco
> p >>>> ft^. 2 Tble f Generl rdnes. t^-t - +«0 -P k*ph? -- i t t i S i-h l -H i-h -d. *- e Stf H2 t s - ^ d - 'Ct? "fi p= + V t r & ^ C d Si d n. M. s - W ^ m» H ft ^.2. S'Sll-pl e Cl h /~v S s, -P s'l
More informationIn a metal, how does the probability distribution of an electron look like at absolute zero?
1 Lecture 6 Laser 2 In a metal, how does the probability distribution of an electron look like at absolute zero? 3 (Atom) Energy Levels For atoms, I draw a lower horizontal to indicate its lowest energy
More informationPhysical Optics. Lecture 8: Laser Michael Kempe.
Physical Optics Lecture 8: Laser 2018-12-13 Michael Kempe www.iap.uni-jena.de Physical Optics: Content 2 No Date Subject Ref Detailed Content 1 18.10. Wave optics G Complex fields, wave equation, k-vectors,
More informationLecture 20. Wind Lidar (2) Vector Wind Determination
Lecture 20. Wind Lidar (2) Vector Wind Determination Vector wind determination Ideal vector wind measurement VAD and DBS technique for vector wind Coherent versus incoherent Detection Doppler wind lidar
More information1. Consider the biconvex thick lens shown in the figure below, made from transparent material with index n and thickness L.
Optical Science and Engineering 2013 Advanced Optics Exam Answer all questions. Begin each question on a new blank page. Put your banner ID at the top of each page. Please staple all pages for each individual
More informationOH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
More information35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3
- - - - ff ff - - - - - - B B BB f f f f f f f 6 96 f f f f f f f 6 f LF LZ f 6 MM f 9 P D RR DD M6 M6 M6 M. M. M. M. M. SL. E 6 6 9 ZB Z EE RC/ RC/ RC/ RC/ RC/ ZM 6 F FP 6 K KK M. M. M. M. M M M M f f
More information,.*Hffi;;* SONAI, IUERCANTII,N I,IMITDII REGD- 0FFICE: 105/33, VARDHMAN GotD[N PLNLA,R0AD No.44, pitampura, DELHI *ffigfk"
$ S, URCT,,MTD RGD 0C: 10/, VRDM G[ LL,R0D.44, ptmpur, DL114 C: l22ldll98l,c0224gb, eb:.nlmernte.m T, Dte: 17h tber, 201 BS Lmted hre ]eejeebhy Ter Dll Street Mumb 41 The Mnger (Ltng) Delh Stk xhnge /1,
More informationI N A C O M P L E X W O R L D
IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e
More informationComputer Modelling and Numerical Simulation of the Solid State Diode Pumped Nd 3+ :YAG Laser with Intracavity Saturable Absorber
Copyright 2009 by YASHKIR CONSULTING LTD Computer Modelling and Numerical Simulation of the Solid State Diode Pumped Nd 3+ :YAG Laser with Intracavity Saturable Absorber Yuri Yashkir 1 Introduction The
More informationB 2 P 2, which implies that g B should be
Enhanced Summary of G.P. Agrawal Nonlinear Fiber Optics (3rd ed) Chapter 9 on SBS Stimulated Brillouin scattering is a nonlinear three-wave interaction between a forward-going laser pump beam P, a forward-going
More informationUsing the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl --
Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl -- Consider the function h(x) =IJ\ 4-8x 3-12x 2 + 24x {?\whose graph is
More information< < or a. * or c w u. "* \, w * r? ««m * * Z * < -4 * if # * « * W * <r? # *» */>* - 2r 2 * j j. # w O <» x <» V X * M <2 * * * *
- W # a a 2T. mj 5 a a s " V l UJ a > M tf U > n &. at M- ~ a f ^ 3 T N - H f Ml fn -> M - M. a w ma a Z a ~ - «2-5 - J «a -J -J Uk. D tm -5. U U # f # -J «vfl \ \ Q f\ \ y; - z «w W ^ z ~ ~ / 5 - - ^
More informationLaser Excitation Dynamics of Argon Metastables Generated in Atmospheric Pressure Flows by Microwave Frequency Microplasma Arrays
Physical Sciences Inc. Laser Excitation Dynamics of Argon Metastables Generated in Atmospheric Pressure Flows by Microwave Frequency Microplasma Arrays W.T. Rawlins, K.L. Galbally-Kinney, S.J. Davis Physical
More informationFree-Electron Lasers
Introduction to Free-Electron Lasers Neil Thompson ASTeC Outline Introduction: What is a Free-Electron Laser? How does an FEL work? Choosing the required parameters Laser Resonators for FELs FEL Output
More informationFigure 1 Relaxation processes within an excited state or the ground state.
Excited State Processes and Application to Lasers The technology of the laser (Light Amplified by Stimulated Emission of Radiation) was developed in the early 1960s. The technology is based on an understanding
More informationγ c = rl = lt R ~ e (g l)t/t R Intensität 0 e γ c t Zeit, ns
There is however one main difference in this chapter compared to many other chapters. All loss and gain coefficients are given for the intensity and not the amplitude and are therefore a factor of 2 larger!
More informationThe Generation of Ultrashort Laser Pulses II
The Generation of Ultrashort Laser Pulses II The phase condition Trains of pulses the Shah function Laser modes and mode locking 1 There are 3 conditions for steady-state laser operation. Amplitude condition
More information- Outline. Chapter 4 Optical Source. 4.1 Semiconductor physics
Chapter 4 Optical Source - Outline 4.1 Semiconductor physics - Energy band - Intrinsic and Extrinsic Material - pn Junctions - Direct and Indirect Band Gaps 4. Light Emitting Diodes (LED) - LED structure
More informationis: 3o>« P 6 Jsgg E 2 si O j= o ocq O o & s r 3 O O K O r " CD r cd as c 3 ^th ^ "OU a 5 " c ?.53 drag S.S pqc O r OT3 4J o >> o.- X h 5 c o o C C :_
& Q f*
More informationParts Manual. EPIC II Critical Care Bed REF 2031
EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4
More informationPropagation losses in optical fibers
Chapter Dielectric Waveguides and Optical Fibers 1-Fev-017 Propagation losses in optical fibers Charles Kao, Nobel Laureate (009) Courtesy of the Chinese University of Hong Kong S.O. Kasap, Optoelectronics
More informationLASERS. Amplifiers: Broad-band communications (avoid down-conversion)
L- LASERS Representative applications: Amplifiers: Broad-band communications (avoid down-conversion) Oscillators: Blasting: Energy States: Hydrogen atom Frequency/distance reference, local oscillators,
More informationExhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No
xhibit 2-9/3/15 Invie Filing Pge 1841 f Pge 366 Dket. 44498 F u v 7? u ' 1 L ffi s xs L. s 91 S'.e q ; t w W yn S. s t = p '1 F? 5! 4 ` p V -', {} f6 3 j v > ; gl. li -. " F LL tfi = g us J 3 y 4 @" V)
More informationThe helium-neon laser Luuk Vermunt
The helium-neon laser Luuk Vermunt (Dated: 9 April 2015) In this paper a detailed description of the physical properties of the helium-neon laser is presented. Aspects like the energy level scheme, broadening
More informationI-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. l"l. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S l"l. \ (?
>. 1! = * l >'r : ^, : - fr). ;1,!/!i ;(?= f: r*. fl J :!= J; J- >. Vf i - ) CJ ) ṯ,- ( r k : ( l i ( l 9 ) ( ;l fr i) rf,? l i =r, [l CB i.l.!.) -i l.l l.!. * (.1 (..i -.1.! r ).!,l l.r l ( i b i i '9,
More information'NOTAS"CRITICAS PARA UNA TEDRIA DE M BUROCRACIA ESTATAL * Oscar Oszlak
OVí "^Ox^ OqAÍ"^ Dcument SD-11 \ 'NOTAS"CRTCAS PARA UNA TEDRA DE M BUROCRACA ESTATAL * Oscr Oszlk * El presente dcument que se reprduce pr us exclusv de ls prtcpntes de curss de Prrms de Cpctcón, se h
More information~ ~ 1 ~ ~ ;il&h.u iv ~/.iu?
Charlotte-Mecklenburg Schools &-~ fjajy ~ ~ ~iffrv~ 1-0 ~ ~ tn/ Jh~~ t~~ NMJi pit,ma.j ~ '.1~~ iv"j.w ~ V>'(i..;.J( o,,.l-,,,;)e ~ [,,._v,,,,.f HUAA!-t1/z,,.,..
More informationP a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
More informationOi ir\ o CM CM ! * - CM T. c *" H - VO - a CM - t - T - j. Vv VO r t- CO on *- t- «- - ** <* - CM CM CM b- f - on on. on CM CVJ t - o.
292 b» CJ «n :T * v j U n n C l * n t l f VL. n n W n V ' n Ln fv C ), C n e. t f *" T V n! * t t T j t Vv V t l / n * t «** n Pk Q * Ph t * b T~! ^ v n f n n N n T n l f P n t. n pn «n =f LPv j t t n
More informationMPM 2D Final Exam Prep 2, June b) Y = 2(x + 1)2-18. ~..: 2. (xl- 1:'}")( t J') -' ( B. vi::: 2 ~ 1-'+ 4 1<. -t-:2 -( 6! '.
MPM 2D Final Exam Prep 2 June 2017 1. Express each equation in standard form and factored form: ~ ~ +et's 'leu t W (.. ".>tak( a) y = (x + 5)2 + 1 on ::t~'t.{1'" ~heeh v 1' K 1 C'. T.) '. (J. lr lov J
More informationEM waves and interference. Review of EM wave equation and plane waves Energy and intensity in EM waves Interference
EM waves and interference Review of EM wave equation and plane waves Energy and intensity in EM waves Interference Maxwell's Equations to wave eqn The induced polarization, P, contains the effect of the
More informationStimulated Emission. Electrons can absorb photons from medium. Accelerated electrons emit light to return their ground state
Lecture 15 Stimulated Emission Devices- Lasers Stimulated emission and light amplification Einstein coefficients Optical fiber amplifiers Gas laser and He-Ne Laser The output spectrum of a gas laser Laser
More informationChemistry Instrumental Analysis Lecture 5. Chem 4631
Chemistry 4631 Instrumental Analysis Lecture 5 Light Amplification by Stimulated Emission of Radiation High Intensities Narrow Bandwidths Coherent Outputs Applications CD/DVD Readers Fiber Optics Spectroscopy
More information1 Longitudinal modes of a laser cavity
Adrian Down May 01, 2006 1 Longitudinal modes of a laser cavity 1.1 Resonant modes For the moment, imagine a laser cavity as a set of plane mirrors separated by a distance d. We will return to the specific
More informationLecture10: Plasma Physics 1. APPH E6101x Columbia University
Lecture10: Plasma Physics 1 APPH E6101x Columbia University Last Lecture - Conservation principles in magnetized plasma frozen-in and conservation of particles/flux tubes) - Alfvén waves without plasma
More informationOptical Gain and Multi-Quantum Excitation in Optically Pumped Alkali Atom Rare Gas Mixtures
Physical Sciences Inc. Optical Gain and Multi-Quantum Excitation in Optically Pumped Alkali Atom Rare Gas Mixtures Kristin L. Galbally-Kinney, Wilson T. Rawlins, and Steven J. Davis 20 New England Business
More information-74- Chapter 6 Simulation Results. 6.1 Simulation Results by Applying UGV theories for USV
Chapter 6 Simulation Results 6.1 Simulation Results by Applying UGV theories for USV The path planning with two obstacles by utilizing algorithms which are developed and tested for UGV is given below.
More informationLaser Physics OXFORD UNIVERSITY PRESS SIMON HOOKER COLIN WEBB. and. Department of Physics, University of Oxford
Laser Physics SIMON HOOKER and COLIN WEBB Department of Physics, University of Oxford OXFORD UNIVERSITY PRESS Contents 1 Introduction 1.1 The laser 1.2 Electromagnetic radiation in a closed cavity 1.2.1
More information34. Even more Interference Effects
34. Even more Interference Effects The Fabry-Perot interferometer Thin-film interference Anti-reflection coatings Single- and multi-layer Advanced topic: Photonic crystals Natural and artificial periodic
More information