Grating and diode laser 劉子維 指導老師 鄭王曜

Grating Equation m = d (sin  + sin  ), Gm = sin  + sin , where G = 1/d is the groove frequency or groove density, more commonly called "grooves per millimeter". (When (  =  ) ， this is called Littrow configuration)

Overlapping of diffracted spectra For any grating instrument configuration, the light of wavelength diffracted in the m = 1 order will coincide with the light of wavelength /2 diffracted in the m = 2 order, etc.

Free Spectral Range The free spectral range of a grating is the largest wavelength interval in a given order which does not overlap the same interval in an adjacent order  +Δ = (m+1/m) F = Δ = /m

Angular dispersion The angular spread d  of a spectrum of order m between the wavelength and + d can be obtained by differentiating the grating equation, assuming the incidence angle  to be constant. The change D in diffraction angle per unit wavelength is therefore D = = =Gm sec  = meaning that the angular separation between wavelengths increases for a given order m

Linear dispersion For a given diffracted wavelength in order m (which corresponds to an angle of diffraction  ), the linear dispersion of a grating system is the product of the angular dispersion D and the effective focal length r' (  ) of the system: r'D= r‘ =Gmr' sec .

Resolving power R= (  is the limit of resolution) R=mN From grating equation R= If the groove spacing d is uniform over the surface of the grating, and if the grating substrate is planar, the quantity Nd is simply the ruled width W of the grating, so R= |sina + sinb | < 2,so Rmax=

The structure of a laser diode

Output power vs injection current for a typical laser.

Tuning characteristics i.Band gap of the semiconductor material ii. Temperature iii. Injection current

appendix

Principal maxima: Minima:

Angular dispersion:

Transverse mode: Longitudinal mode: