17-Phys-A7 Optics · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
17-Phys-A7, Optics — National Exams, December 2018. 3 hours; closed book (approved Sharp/Casio calculator only). Total 78 marks. Questions 1–6 are mandatory; the paper then offers a choice of Question 7 or 8, and a choice of Question 9 or 10. Every question is solved in full below as a complete study resource, including both members of each either/or pair.
Reference texts. Hecht, Optics, 5th ed.; Pedrotti, Pedrotti & Pedrotti, Introduction to Optics, 3rd ed.; Griffiths, Introduction to Electrodynamics, 4th ed. (Ch. 9, EM waves in matter, for Maxwell's equations).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Selected source: the semiconductor (diode) laser.
(a) Physical characteristics. A semiconductor laser is a forward-biased p–n junction diode built from a direct-bandgap III–V compound (commonly GaAs or an AlGaAs/InGaAsP heterostructure). The active region is a thin layer at the junction, sandwiched between p-type and n-type cladding layers of slightly lower refractive index than the active layer — this index step confines the optical mode to the active region exactly as the core/cladding step confines light in the fibre of Question 2. The two cleaved end facets of the semiconductor crystal act as partially reflecting mirrors (the large refractive-index mismatch with air, $n\approx3.5$, gives $\sim30\%$ reflectivity from Fresnel reflection alone, enough for laser feedback without external mirrors), forming a Fabry–Perot optical cavity of length a few hundred microns. Electrical contacts on the top and bottom inject current directly into the junction.
(b) Optical processes required for lasing. Three processes must occur together. (1) Spontaneous emission seeds the process: electrons injected into the conduction band recombine with holes in the valence band across the direct bandgap, each recombination releasing a photon of energy $h\nu\approx E_g$. (2) Population inversion is established once the forward-bias current exceeds a threshold value, pumping more electrons into the conduction band (and holes into the valence band) at the junction than exist in thermal equilibrium, so that stimulated emission outweighs absorption for photons near $E_g$. (3) Stimulated emission and optical feedback: a photon travelling through the inverted active region stimulates further identical (same phase, direction, and wavelength) photons from other excited electron–hole pairs; the Fabry–Perot cavity formed by the two facets reflects this growing photon field back and forth through the gain region on each pass, and above threshold the round-trip gain exceeds the round-trip loss (facet transmission plus internal loss), so coherent light builds up and a fraction escapes through the partially transmitting output facet as the laser beam.
(c) Engineering applications. (1) Optical-fibre telecommunications — diode lasers (typically at 1310/1550 nm, the fibre's low-loss/low-dispersion windows) are the standard transmitter for long-haul and metro fibre-optic links, directly modulated or externally modulated to encode digital data. (2) Optical storage — CD/DVD/Blu-ray read/write heads use diode lasers (progressively shorter wavelengths, from $\sim780$ nm to $\sim405$ nm, to shrink the diffraction-limited spot size and raise storage density). (3) Laser rangefinding, barcode scanning and machine vision — the diode laser's compactness, low power draw, and direct electrical modulation make it the standard source for surveying rangefinders, industrial barcode/QR readers, and structured-light 3-D sensors. (4) Pump sources — high-power diode lasers pump solid-state lasers (e.g. Nd:YAG) and fibre amplifiers, replacing bulkier flashlamp pumping in industrial cutting/welding lasers.
