Modulation bandwidth

Modulation bandwidth ($f_{3dB}$) states how fast a device can follow an electrical signal. It is read from the small-signal frequency response $|H(f)|^2$: the point where response has dropped by half.

For a directly modulated laser, the response is that of a second-order resonant system. Photons and carriers exchange energy through stimulated emission, producing a resonance at the relaxation-oscillation frequency $f_r$ with a peak height set by damping. In the low-damping regime the two figures relate as $f_{3dB} \approx 1.55\, f_r$, and $f_r$ itself grows with the square root of output power (equivalently $\sqrt{I - I_{th}}$). Pushing bandwidth therefore means driving harder, shrinking the cavity (higher photon density), and increasing differential gain, until damping, thermal limits, or parasitics intervene. The package matters as much as the chip: bond-wire inductance and pad capacitance form a parasitic low-pass that can cap an otherwise fast laser. Uncooled datacom DMLs run tens of GHz; research devices with optimized cavities exceed 100 GHz.

For a photodiode, bandwidth is the interplay of carrier transit time across the depletion region and RC time of junction capacitance against load. Thinner absorbers are faster but less responsive, the classic bandwidth-efficiency tradeoff.

For electro-optic modulators, the limits are RC (lumped devices) or velocity and loss walk-off between RF and optical waves (traveling-wave devices).

Measurement is standard S-parameter work: a calibrated vector network analyzer drives the device and reads the opto-electronic response ($S_{21}$) through a reference photodetector, de-embedding cables and fixtures. Quote bandwidth with its bias point: it is a strong function of operating current in lasers and of reverse bias in photodiodes.