Editing Group delay and phase delay (section)

== Group delay in optics ==
Group delay is important in [[physics]], and in particular in [[optics]].

In an [[optical fiber]], group delay is the transit [[time]] required for optical [[Power (physics)|power]], traveling at a given [[Transverse mode|mode]]'s [[group velocity]], to travel a given distance. For optical fiber [[dispersion (optics)|dispersion]] measurement purposes, the quantity of interest is group [[Propagation delay|delay]] per unit length, which is the reciprocal of the group velocity of a particular mode. The measured group delay of a [[signal]] through an optical fiber exhibits a [[wavelength]] dependence due to the various [[dispersion (optics)|dispersion]] mechanisms present in the fiber.

It is often desirable for the group delay to be constant across all frequencies; otherwise there is temporal smearing of the signal. Because group delay is <math display="inline"> \tau_g(\omega) = -\frac{d\phi}{d\omega}</math>, it therefore follows that a constant group delay can be achieved if the [[transfer function]] of the device or medium has a [[linear]] phase response (i.e., <math>\phi(\omega) = \phi(0) - \tau_g \omega </math> where the group delay <math>\tau_g </math> is a constant). The degree of nonlinearity of the phase indicates the deviation of the group delay from a constant value.

{{anchor|Differential}}The '''differential group delay''' is the [[Difference (mathematics)|difference]] in [[phase velocity|propagation time]] between the two [[eigenmode]]s ''X'' and ''Y'' [[Polarization (waves)|polarizations]].  Consider two [[eigenmodes]] that are the 0° and 90° [[Linearity|linear]] [[polarized light|polarization]] states.  If the state of polarization of the input signal is the linear state at 45° between the two eigenmodes, the input signal is divided equally into the two eigenmodes.  The power of the [[Transmitter|transmitted signal]] ''E''<sub>''T'',total</sub> is the combination of the transmitted signals of both ''x'' and ''y'' modes.

: <math>E_T  =  (E_{i,x} \cdot t_x)^2 + (E_{i,y} \cdot t_y)^2 \, </math>

The differential group delay ''D''<sub>''t''</sub> is defined as the difference in propagation time between the eigenmodes: ''D''<sub>''t''</sub>&nbsp;=&nbsp;|''t''<sub>''t'',''x''</sub>&nbsp;&minus;&nbsp;''t''<sub>''t'',''y''</sub>|.