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ABCD Matrix

Emission Spectrum

Emission spectrum (often called the optical spectrum of a source) is the distribution of emitted optical power or photon energy versus wavelength, frequency, or wavenumber. In lasers and photonics it is the map of which wavelengths a gain medium or device actually radiates when electrons, ions, or molecules drop from higher to lower energy states.


The photon energy of each line or band equals the energy difference between those states:


E=hν=hc/λ ​


Each species has a characteristic set of allowed transitions, so the emission spectrum is a fingerprint of the emitter.


Technical picture:


  • Spontaneous emission produces the intrinsic spectrum of the material (fluorescence, electroluminescence, gas-discharge lines). Transitions that are well isolated give line spectra; dense vibrational/rotational structure or inhomogeneous broadening in solids and dyes gives band spectra. 


  • In a laser the gain medium has a finite gain bandwidth set by that emission spectrum (plus homogeneous and inhomogeneous broadening). The resonator then selects one or more modes inside that band. The actual laser output is usually much narrower than the gain band: a single-frequency laser can have a linewidth of hertz to megahertz, while the same medium’s fluorescence band may be nanometers to hundreds of nanometers wide.


  • Line shape is often Lorentzian (homogeneous lifetime / Schawlow–Townes broadening) or Gaussian (Doppler or inhomogeneous effects). Mode-locked lasers produce a broad comb spanning much of the gain spectrum.


  • Typical examples:

    • HeNe: narrow line at 632.8 nm (gain bandwidth ~1.5 GHz).

    • Nd:YAG: strongest line 1064 nm (other lines at 946, 1319 nm, etc.).

    • Ti:sapphire / dye / Yb-fiber: tunable bands of tens to hundreds of nm.

    • Semiconductor lasers / LEDs: band-to-band recombination whose peak wavelength is set by the bandgap.


The measured quantity is usually spectral power density (W/nm or dBm/nm) recorded with a grating spectrometer, Fabry–Pérot interferometer, or heterodyne setup.



Applications in lasers and photonics:


  • Choosing and designing the source: the emission spectrum of the gain medium (Nd, Yb, Er, Tm, semiconductors, gases, dyes) determines available wavelengths, tunability, and whether the laser can be single-frequency, multi-line, or ultrafast.


  • Identification and spectroscopy: atomic/molecular emission lines identify species; laser-induced fluorescence uses a narrow laser to excite a transition and then records the emission spectrum.


  • Communications and sensing: telecom lasers and EDFAs sit on the 1.5 µm Er emission band; LIDAR, interferometry, and frequency metrology need known, narrow emission lines.


  • Diagnostics of the laser itself: optical spectrum analyzers check mode structure, side-mode suppression, ASE, and linewidth.


  • Nonlinear optics and frequency conversion: knowing the emission band tells you which harmonics, OPOs, or supercontinua you can generate.


  • Lighting and displays: LED and laser-diode emission spectra set color, efficiency, and eye-safety class.


The emission spectrum is both the raw spectroscopic signature of the active material and the starting point from which resonators, filters, and nonlinear processes produce the highly controlled spectra used in photonics.

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