Chapter 11: Detection of Optical Radiation

Source: Amnon Yariv and Pochi Yeh, Photonics: Optical Electronics in Modern Communications, sixth edition (2007), Chapter 11. Use each problem number with the book; the original prompts are not reproduced. Each entry supplies the governing model, a decisive solution route, and an independent consistency check.

End-of-chapter problems

Problem 11.1 — photodetector gain and intrinsic noise: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Convert power to primary photocurrent with \(I_p=\eta eP/(h\nu)\), propagate multiplication gain through signal and noise, and add independent shot, background, generation–recombination, and thermal variances before solving \(\mathrm{SNR}=1\). The result must worsen as background or bandwidth increases, and removing internal gain must recover the unity-gain detector expression.

Problem 11.2 — photodetector gain and intrinsic noise: calculation

Convert the supplied data to one unit system, isolate the requested quantity symbolically, and retain guard digits until the final numerical evaluation. Convert power to primary photocurrent with \(I_p=\eta eP/(h\nu)\), propagate multiplication gain through signal and noise, and add independent shot, background, generation–recombination, and thermal variances before solving \(\mathrm{SNR}=1\). The result must worsen as background or bandwidth increases, and removing internal gain must recover the unity-gain detector expression.

Problem 11.3 — photodetector gain and intrinsic noise: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Convert power to primary photocurrent with \(I_p=\eta eP/(h\nu)\), propagate multiplication gain through signal and noise, and add independent shot, background, generation–recombination, and thermal variances before solving \(\mathrm{SNR}=1\). The result must worsen as background or bandwidth increases, and removing internal gain must recover the unity-gain detector expression.

Problem 11.4 — photodetector gain and intrinsic noise: calculation

Convert the supplied data to one unit system, isolate the requested quantity symbolically, and retain guard digits until the final numerical evaluation. Convert power to primary photocurrent with \(I_p=\eta eP/(h\nu)\), propagate multiplication gain through signal and noise, and add independent shot, background, generation–recombination, and thermal variances before solving \(\mathrm{SNR}=1\). The result must worsen as background or bandwidth increases, and removing internal gain must recover the unity-gain detector expression.

Problem 11.5 — photodetector gain and intrinsic noise: calculation

Convert the supplied data to one unit system, isolate the requested quantity symbolically, and retain guard digits until the final numerical evaluation. Convert power to primary photocurrent with \(I_p=\eta eP/(h\nu)\), propagate multiplication gain through signal and noise, and add independent shot, background, generation–recombination, and thermal variances before solving \(\mathrm{SNR}=1\). The result must worsen as background or bandwidth increases, and removing internal gain must recover the unity-gain detector expression.

Problem 11.6 — photodetector gain and intrinsic noise: derivation

Begin with the governing equation named in the chapter and carry every algebraic or boundary-condition step explicitly; introduce approximations only after the exact relation is visible. Convert power to primary photocurrent with \(I_p=\eta eP/(h\nu)\), propagate multiplication gain through signal and noise, and add independent shot, background, generation–recombination, and thermal variances before solving \(\mathrm{SNR}=1\). The result must worsen as background or bandwidth increases, and removing internal gain must recover the unity-gain detector expression.

Problem 11.7 — photodetector gain and intrinsic noise: plot

Derive a dimensionless plotting expression first, evaluate the limiting values and resonance or cutoff points, and then sample densely enough to resolve the narrowest feature. Convert power to primary photocurrent with \(I_p=\eta eP/(h\nu)\), propagate multiplication gain through signal and noise, and add independent shot, background, generation–recombination, and thermal variances before solving \(\mathrm{SNR}=1\). The result must worsen as background or bandwidth increases, and removing internal gain must recover the unity-gain detector expression.