User Interview: Development of spectrometer for High-order Harmonic Generation (HHG)

**Contents**

## 5-1. Toroidal Diffraction Gratings

A toroidal diffraction grating is a sort of concave gratings. The toroidal shape is defined by two curvature radii at each central axis. Toroidal shapes where *R _{h}* is a horizontal curvature radius and

*R*is a vertical curvature radius. The toroidal shapes are expressed in the following equation.

_{v}(14)

The paraxial focal positions of a toroidal grating in Fig.9 are defined by equations (15) and (16). Here *r* is the entrance length, *r' _{h}* is the horizontal focal length, and

*r'*is the vertical focal length.

_{v}*α*and

*β*satisfy the grating equation (2)'.

Fig.9 The different focus of the Spherical diffraction grating

(15)

(16)

The spherical diffraction gratings are formed on spherical blanks( *R _{h}*=

*R*) that has two focal lengths(

_{v}*r'*,

_{h}*r'*) has astigmatisms, The toroidal diffraction gratings are formed on toroidal (aspheric) blanks(

_{v}*R*≠

_{h}*R*) that can correct astigmatisms.

_{v}