How to make a (better?) light bulb Nick Vamivakas Journal Club

An ideal incandescent light bulb u FS (ω,T) = X T(i) How do we calculate?? Emitted energy density of a black body u FS (ω,T) visible T(i) = 3000K

The Planck formula version 1 cavity of oscillators in thermal equilibrium with EM field oscillator frequency ω cavity mode emitted light What is the spectral content of the light escaping the cavity? u FS (ω,T) = EM mode density X average energy per mode (ω,T) = T average energy -> Boltzmann Distribution for oscillators

The Planck formula version 1 cavity of oscillators in thermal equilibrium with EM field oscillator frequency ω cavity mode emitted light What is the spectral content of the light escaping the cavity? u FS (ω,T) = EM mode density X average energy per mode T u FS (ω,T) = X u FS (ω,T) = ρ FS (ω) X (ω,T)

The Planck formula version 2 cavity of oscillators in thermal equilibrium with EM field cavity mode is an oscillator of frequency ω emitted light What is the spectral content of the light escaping the cavity? u FS (ω,T) = EM mode density X average energy per mode u FS (ω,T) = X u FS (ω,T) = ρ FS (ω) X (ω,T) T everything is attributed to field modes

An nonideal incandescent light bulb How can we calculate?? g FS (ω,T) = ε(ω,T) x u FS (ω,T) Emitted energy density of a gray body T(i) g FS (ω,T) visible T(i) = 3000K emissivity

Kirchoff’s Radiation Law Putting this is in a more suggestive form “When a body is in thermodynamic equilibrium its emissivity is equal to its absorptivity” In other words g FS (ω,T) = ε(ω,T) x u FS (ω,T) = α(ω,T) x u FS (ω,T) g FS (ω,T) = α(ω,T) x ρ FS (ω) x (ω,T)

To make a (better?) light bulb To repeat: g FS (ω,T) = α(ω,T) x ρ FS (ω) x (ω,T) Tailor the material’s absorption spectrum Modify the density of electromagnetic modes Change the particle statistics?? Can we recover the original BB spectrum?

Modify EM Mode Density g FS (ω,T) = α(ω,T) x ρ FS (ω) x (ω,T) Introduce a 1D Photonic Crystal 5 period gray body measure g FS (ω,T) on-axis T n s =3+.03in 1 =sqrt(2) /n 2 =2 Tune Midgap black gray PBG Tune Below Gap resonances 1 ~ λ o =4n 1 a=4n 2 b

What if the emitter is a semiconductor and there is an energy gap in the electronic excitation spectrum? Tailor the Absorption Spectrum g FS (ω,T) = α(ω,T) x ρ FS (ω) x (ω,T) α(ω,T) proportional to ρ electron (ω) x (f h (E 1,T)-f e (E 1 +hν,T )) plot g FS (ω,T) = norm(α(ω,T)) x norm(u FS (ω,T)) visible Singularity in α 1D (ω,T) leads to ideal BB behaviour

What if there is more than 1D emitter? Tailor the Absorption Spectrum g FS (ω,T) = α(ω,T) x ρ FS (ω) x (ω,T) Just sum each of g FS (ω,T)-> Inhomogeneous Broadening visible

seen how to modify the Blackbody spectrum by manipulating either the emitter’s electronic excitation spectrum or the emitter’s environment (not both together!) Conclusions To answer whether we can make a better incandescent light bulb need to define an efficiency (optical power out versus input excitation power), book keep the constants and compare Neglected all other material excitations contribution to the absorption coefficient Electronic and EM resonances lead to narrowband BB behaviour broadband resonances?

References Planck formula Theory of Heat, Planck Theory and Application of Quantum Mechanics, Yariv Kirchoff Law On the Validity of Kirchoff’s Law in Nonequilibrium Environment D.G Burkhard, J. V. S. Lockhead & C.M Oenchina AJP v40 p1794 (1972) EM DOS Tailoring Modification of Planck Blackbody by PBG C.M. Cornelius & J.P. Dowling Phys Rev A v59 p4736 (1999) Electronic DOS Tailoring 3D -> Laser Electronics, Verdeyen dD -> did not find any discussion

References cavity of oscillators in thermal equilibrium with EM field oscillator frequency ω cavity mode emitted light What is the spectral content of the light escaping the cavity? u FS (ω,T) = EM mode density X average energy per mode u FS (ω,T) = X u FS (ω,T) = ρ FS (ω) X (ω,T) T