ICPY471 19 Laser Physics and Systems November 20, 2017 Udom Robkob, Physics-MUSC
Topics Laser light Stimulated emission Population inversion Laser gain Laser threshold Laser systems
Laser Light LASER= Light Amplification by Stimulated Emission of Radiations Some history 1917 Einstein treatment of stimulated emission 1951 C.H. Townes develop the first MASER 1960 T.H. Maimandevelop the first LASER, ruby laser 1961 Invention of He-Ne laser 1962 Invention of semiconductor laser 2014 ShunjiNakamura, Hiroshi Amano and Isamu Akaskiwon the Nobel Prize for invention of blue-light laser
Laser Light Basic properties: Monochromaticity Directionality Brightness (spectral) Coherence, both spatial and temporal coherences
Stimulated Emission Spontaneous and stimulated emissions:
Stimulated Emission Einstein s A and B coefficients: Two level system with N 1 and N 2 population: Stimulated absorption (12) Spontaneous emission (21) Stimulated emission (21) - dn dt dn dt 1 2 1 = B ( ) 12N 1u ν dn = = A ( ) 21N2 u v dt dn dt 2 = B ( ) 21N2 u v
Stimulated Emission Equilibrium processes at finite temperature T B N u( v) = A N + B N u( v) 12 1 21 2 21 2 N 2 B 12u( v) g 1 e hv / kt = N A + B u( v) g 1 21 21 2 g1, g1 degeneracy factors e
Stimulated Emission From this relation, we can solve for spectral function, then compare to the Boltzmann function: 3 g 2 A 21 8 π hv 1 u ( v ) = hv/ kt 3 hv/ kt g B e g B c e 1 1 12 2 21
Stimulated Emission From this relation, we can solve for spectral function, then compare to the Boltzmann function: 3 g 2 A 21 8 π hv 1 u ( v ) = hv/ kt 3 hv/ kt g B e g B c e 1 12 2 21 3 8π hv g B = g B and A = B c 1 12 2 21 21 3 21 1 A21 << B21 A21 = τ 1
Population Inversion To get LASER, we need a condition B N u( v) >> B N u( v) 21 2 12 2 g N >> N or N >> N 2 2 1 2 1 g 1 It is called population inversion condition, as some people say, it corresponds to negative temperature condition Please note that, if the condition satisfied, this will be a highly non-equilibrium situation
Laser Gain Population inversion is a necessary condition for LASER Let us determine the atomic radiations, with a spectral line shape function g(ν)
Laser Gain The rate equations read dw = B N u( v) g( v) dv 12 21 1 W = 12 0 21 1 B N u ( v ) g ( v ) dv
Laser Gain The rate equations for stimulated absorption read Let dw = B N u( v) g( v) dv 12 21 1 W = 12 21 1 0 u( v) = u δ ( v v ) for a narrow band emission of LASER v B N u ( v ) g ( v ) dv laser
Laser Gain Then we have W12 = B12 N1 g( vlaser ) u ν The same argument is derived for stimulated emission rate equation W21 = B21 N2 g ( ν laser ) u ν
Laser Gain Then we have W12 = B12 N1 g( vlaser ) u ν The same argument is derived for stimulated emission rate equation W21 = B21 N2 g ( ν laser ) u ν The light source is considered to have delta function spectrum at frequency νwith energy density u ν The intensity of optical beam is I = u c ν
Laser Gain From a given relation between B 12 and B 21, on can write the net rate equation for stimulated emission as net I W21 = ( W21 W12 ) = NB21 g ( ν ) c where g N = N N 2 2 1 g1
Laser Gain From a given relation between B 12 and B 21, on can write the net rate equation for stimulated emission as net I W21 = ( W21 W12 ) = NB21 g ( ν ) c where g N = N N 2 2 1 g1 The net emission rate of photon energy hνis W net hν (energy density) 21
Laser Gain The corresponding beam intensity in x- direction is net I di = W21 hν dx = NB21 g( ν ) hν dx c
Laser Gain The corresponding beam intensity in x- direction is net I di = W21 hν dx = NB21 g( ν ) hν dx c Let us define gain coefficient γ from intensity equation I( x + dx) = I( x) + γi( x) dx = I( x) + di di = γ Idx I( x) = I(0) e γ x
Laser Gain We can find the gain coefficient as 2 I λ γ = NB21 g( ν ) hν = N g( ν ) c 8πτ after an expression of B 21 is inserted. Note that γ N, λ, τ, g( ν ) This is the required condition of the medium to relate to population inversion N
Laser Threshold LASERs are classified as being 3-and 4-level systems, i.e., He-Ne and Nd:YAGare 4-level systems For any 4-level system, the LASER mechanism For any 4-level system, the LASER mechanism are
Laser Threshold Let the system has a constant pumping rate The population equations for level 1 and 2, with the assumption that No pumping rate for N 1 Only radiativetransition from level 2 to 1, read dn2 N2 net = W + R dt τ dn N net N = + + W21 dt τ 21 2 1 2 1 τ R 2
Laser Threshold Let us rewrite net W21 = W N In steady state condition, the population equations become N = R τ, N = R W N ( ) We can solve this equation for N to be τ 1 2 1 2 2 2 = R2 g2τ 1 N 1 W + 1/ τ 2 g 1τ 2 Note that N > 0 τ > ( g / g ) τ 2 2 1 1
Laser Threshold Let us define R = R2 (1 g τ 2 1 / g τ 1 2) We can identify the laser threshold in term of the population inversion threshold N th as th N = th τ 2 R τ It is also the threshold of the pumping rate, and it is also the threshold for the laser gain coefficient γ th
Laser Threshold What is the laser threshold?
Laser Cavity How can we increase pumping rate? Using laser cavity, longitudinal mode frequency ν = nc / 2L
Laser operations Laser Cavity
Laser Cavity Laser operations Single mode operation
Multimode operation Laser Cavity
Laser Systems Examples of laser Infrared laser: CO 2 (10.6µm), erbium (1.55µm), Nd:YAG(1.064µm), Nd:glass(1.054µm) Visible light laser: ruby (693nm), He-Ne (633nm), argon ion (514nm), HeCd(442nm) Ultraviolet laser: nitrogen (337nm), excimerlaser (308, 248, 193, 150nm)
He-Ne laser Laser System
Laser Systems Ruby laser (Cr +3 :Al 2 O 3 )