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\
PN junction animation
Forward biased PN junction\
Biased PN junction animation
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 = 26`meV 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 animation
spontaneous emission
spontaneous emission animation
and stimulated emission
stimulated emission animation.
Lasing generated by electron-hole recombination in stimulated emission.

Electron-hole generation animation
• 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
Laser oscillation animation
• 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

Last Modified: March 26, 2018
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