Sources (Sec. 3.5) Mar. 27, 2018

• Monochromatic source: Laser or LED. They can be external modulated or more conveniently direct modulated with a time varying current.
• Diode: Laser diode and LED are diodes. Require forward biasing to emit light from active (depletion) layer at the PN junction.
Unbiased PN junction\

Forward biased PN junction\

They are devices that convert electrons to photons.

• Comparison:
Output power P_{out} - laser (LD) P_{out} = eta_{slope} (I-I_{th}) where eta_{slope} (W/A) is the slope efficiency and I_{th} is the threshold current.
LED P_{out} = eta_{\t\o\t} h nu I/q where eta_{\t\o\t} = eta_{ext} eta_{\i\nt} is the total quantum efficiency, eta_{ext} is the external quantum efficiency and eta_{\i\nt} is the internal quantum efficiency.
Threshold current - LD has it but not LED. I_{th} temperature dep.
Spectral width - LD has very narrow peaks. It can be single or multiple longitudinal modes.
LED has wide spectral width Delta nu which is temp dep Delta nu = {3.3 kT}/h and has maximum freq f_{max} = {E_g + kT}/h
Note: {kT}/q = 26meV at 300K.
Modulation - LD requires biasing current above I_{th}
LED requires positive modulation current.
Modulation bandwidth - LD has Delta f = 0.35 /{tau_t} where tau_t is the rising time of LD.
LED has Delta f = 0.35 /{tau_t} or Delta f = 1/{2 pi tau_c} where tau_c is the electron-hole recombination time.
Divergence angle - LD has theta = {2 lambda}/{pi w_o}
LED has angle proportional to physical size.
Temp. dep. - LD has I_{th}, lambda and P_{\o\u\t} temp. dep.
LED has P_{\o\u\t}, lambda and Delta nu temp. dep.

• Temp. control: Thermoelectric cooler with thermistor providing temp. feedback.
Power monitoring with built-in photodetector.
Aging drives up I_{th}
• 3 radiative process for laser:
absorption

spontaneous emission

and stimulated emission
.
Lasing generated by electron-hole recombination in stimulated emission.

• Semiconductor materials: Radiation freq. determined by the bandgap energy E_g = E_c -E_v By choosing appropriate materials, we generate certain wavelength, e.g. (Al_x Ga_{1-x})As has E_{g} (x) = 1.414 + 1.27x (eV).
3 Lasing requirements : A pumping source (current injection), positive feedback (FP cavity) and special device structure to enhance stimulated emission (heterojunctions, quantum wells).

Laser in action

• Lasing conditions: Ampl condition -> threshold gain coef. g = alpha + 1/{2d} ln (1 /{R_1 R_2})
Phase condition -> resonant freq f_m = m c/{2nd} and Delta f_{FSR} = c/ {2nd}
Example for calculations with lasing conditions