Optics¶

Instrumental’s Optics package is useful for exploring and scripting basic gaussian optics using the ABCD matrix approach. The package is split up into three main categories: optical elements, beam tools, and beam plotting tools.

Optical Elements¶

Instrumental’s optical elements are based on simple numerical ABCD matrix representations and include Mirrors, Lenses, Spaces, and Interfaces. Each provides a useful constructor to create them in a way that’s conceptually simple and clear.

class instrumental.optics.optical_elements.ABCD(A, B, C, D)¶

A simple ABCD (ray transfer) matrix class.

ABCD objects support mutiplication with scalar numbers and other ABCD objects.

Methods

elems() Get the matrix elements.

__init__(A, B, C, D)¶

Create an ABCD matrix from its elements.

The matrix is a 2x2 of the form:

[A B]
[C D]

Parameters:

A,B,C,D : Quantity objects

A and D are dimensionless. B has units of [length] (e.g. ‘mm’ or ‘rad/mm’), and C has units of 1/[length].

elems()¶

Get the matrix elements.

Returns:

A, B, C, D : tuple of Quantity objects

The matrix elements

class instrumental.optics.optical_elements.Interface(n1, n2, R=None, aoi=None, aot=None)¶

An interface between media with different refractive indices

__init__(n1, n2, R=None, aoi=None, aot=None)¶

Parameters:

n1 : number

The refractive index of the initial material

n2 : number

The refractive index of the final material

R : Quantity or str, optional

The radius of curvature of the interface’s spherical surface, in units of length. Defaults to None, indicating a flat interface.

aoi : Quantity or str or number, optional

The angle of incidence of the beam relative to the interface, defined as the angle between the interface’s surface normal and the _incident_ beam’s axis. If not specified but aot is given, aot will be used. Otherwise, aoi is assumed to be 0, indicating normal incidence. A raw number is assumed to be in units of degrees.

aot : Quantity or str or number, optional

The angle of transmission of the beam relative to the interface, defined as the angle between the interface’s surface normal and the transmitted beam’s axis. See aoi for more details.

class instrumental.optics.optical_elements.Lens(f)¶

A thin lens

__init__(f)¶

Parameters:

f : Quantity or str

The focal length of the lens

class instrumental.optics.optical_elements.Mirror(R=None, aoi=0)¶

A mirror, possibly curved

__init__(R=None, aoi=0)¶

Parameters:

R : Quantity or str, optional

The radius of curvature of the mirror’s spherical surface. Defaults to None, indicating a flat mirror.

aoi : Quantity or str or number, optional

The angle of incidence of the beam on the mirror, defined as the angle between the mirror’s surface normal and the beam’s axis. Defaults to 0, indicating normal incidence.

class instrumental.optics.optical_elements.Space(d, n=1)¶

A space between other optical elements

__init__(d, n=1)¶

Parameters:

d : Quantity or str

The axial length of the space

n : number, optional

The index of refraction of the medium. Defaults to 1 for vacuum.

Beam Tools¶

instrumental.optics.beam_tools.find_cavity_modes(elems)¶

Find the eigenmodes of an optical cavity.

Parameters:

elems : list of OpticalElements

ordered list of the cavity elements

Returns:

qt_r, qs_r : complex Quantity objects

1/q for the tangential and sagittal modes, respectively. Has units of 1/[length].

instrumental.optics.beam_tools.get_w0(q_r, lambda_med)¶: Get waist size w0 of light with in-medium wavelength lambda_med and reciprocal beam parameter q_r

instrumental.optics.beam_tools.get_z0(q_r)¶: Get z-location z0 of the focus from reciprocal beam parameter q_r

instrumental.optics.beam_tools.get_zR(q_r)¶: Get Rayleigh range zR from reciprocal beam parameter q_r

Beam Plotting¶

instrumental.optics.beam_plotting.plot_profile(q_start_t_r, q_start_s_r, lambda0, elems, cyclical=False, names=(), clipping=None, show_axis=False, show_waists=False, zeroat=0, zunits='mm', runits='um')¶

Plot tangential and sagittal beam profiles.

Parameters:

q_start_t_r, q_start_s_r : complex Quantity objects

Reciprocal beam parameters for the tangential and sagittal components. They have units of 1/[length].

lambda0 : Quantity

Vacuum wavelength of the beam in units of [length].

elems : list of OpticalElements

Ordered list of optical elements through which the beams pass and are plotted.

Other Parameters:

cyclical : bool

Whether elems loops back on itself, i.e. it forms a cavity where the last element is immediately before the first element. Used for labelling the elements correctly if names is used.

names : list or tuple of str

Strings used to label the non-Space elements on the plot. Vertical lines will be used to denote the element’s position.

clipping : float

Clipping loss level to plot. Normally, the beam profile plotted is the usual spot size. However, if clipping is given, the profile indicates the distance from the beam axis at which knife-edge clipping power losses are equal to clipping.

show_axis : bool

If show_axis is True, sets the ylim to include the beam axis, i.e. y=0. Otherwise, y limits are automatically set by matplotlib.

show_waists : bool

If True, marks beam waists on the plot and labels their size.

zeroat : int

The index of the element in elems that we should consider as z=0. Useful for looking at distances from some element that’s in the middle of the plot.

zunits : str or Quantity or UnitsContainer

Units to use for the z-axis. Must have units of [length]. Defaults to ‘mm’.

runits : str or Quantity or UnitsContainer

Units to use for the radial axis. Must have units of [length]. Defaults to ‘um’.