gtrace.beam

gtrace.beam

A module to define GaussianBeam class.

Module Contents

Classes

GaussianBeam

This is a class to represent a Gaussian beam.

Functions

optFunForStartPointR(phi, Mrot, R, q0, k, sigma, side)

A function to return the distance between the point on

optimStartPointR(theta, R, q0, k, sigma)

Caltulate optimal starting point.

optFunForEndPointR(phi, Mrot, R, q0, k, sigma, side)

A function to return the distance between the point on

optimEndPointR(theta, R, q0, k, sigma)

Caltulate optimal end point.

optFunForFlat(a, Mrot, q0, k, sigma, side)

A function to return the distance between the point on

optimCrossPointFlat(theta, q0, k, sigma)

Caltulate optimal cross point.

Attributes

pi

array

sqrt

__author__

__copyright__

__credits__

__license__

__version__

__maintainer__

__email__

__status__

gtrace.beam.pi
gtrace.beam.array
gtrace.beam.sqrt
gtrace.beam.__author__ = Yoichi Aso
gtrace.beam.__copyright__ = Copyright 2011-2021, Yoichi Aso
gtrace.beam.__credits__ = ['Yoichi Aso']
gtrace.beam.__license__ = BSD
gtrace.beam.__version__ = 0.2.1
gtrace.beam.__maintainer__ = Yoichi Aso
gtrace.beam.__email__ = yoichi.aso@nao.ac.jp
gtrace.beam.__status__ = Beta
class gtrace.beam.GaussianBeam(q0=1j * 2 * pi / 1064 * nm * 1e-06 / 2, q0x=False, q0y=False, pos=[0.0, 0.0], length=1.0, dirAngle=0.0, dirVect=None, wl=1064 * nm, P=1 * W, n=1.0, name='Beam', layer='main_beam')

Bases: traits.api.HasTraits

This is a class to represent a Gaussian beam. A GaussianBeam object has its origin (pos) and a propagation direction (dirVect or dirAngle). A GaussianBeam is characterized by q-parameter(s) at its origin. The beam can be either circular or elliptic. In order to deal with elliptic beams, some parameters are stored in pairs like (q0x, q0y). x and y denote the axes of the cross section of the beam. x-axis is parallel to the paper and the y-axis is perpendicular to the paper.

A beam object can be propagated through a free space or made to interact with an optics.

As a beam propagate through optical system, optical distance and Gouy phase are accumerated.

q

q-parameter of the beam. If the beam is eliptic, q is the q-parameter of the best matching circular mode.

Type

complex

qx

q-parameter of the beam in the x-direction.

Type

complex

qy

q-parameter of the beam in the y-direction.

Type

complex

pos

Position of the beam origin (x, y).

Type

array

dirVect

Propagation direction vector.

Type

array

dirAngle

Propagation direction angle measured from the positive x-axis.

Type

float

length

Length of the beam (used for DXF export)

Type

float

layer

Layer name of the beam when exported to a DXF file.

Type

str

name

Name of the beam

Type

str

wl

Wavelength in vacuum. Not the wavelength in the medium.

Type

float

n

Index of refraction of the medium the beam is passing through.

Type

float

P

Power.

Type

float

wx

Beamwidth in x-direction.

Type

float

wy

Beamwidth in y-direction.

Type

float

optDist

Accumulated optical distance.

Type

float

Gouyx

Accumulated Gouy phase in x-direction.

Type

float

Gouyy

Accumulated Gouy phase in y-direction.

Type

float

Mx

ABCD matrix in x-direction. This is a 2x2 matrix representing the product of ABCD transformations applied to this beam. It defaults to an identity matrix. Whenever a beam experience an ABCD matrix transformation, such as propagation in the space or reflection by a curved mirror, the applied ABCD matrix is multiplied to this matrix, so that we can keep track of what kind of transformations were made during beam propagation.

Type

array

My

ABCD matrix in y-direction. The meaning is the same as Mx.

Type

array

departSurfAngle

The angle formed by x-axis and the normal vector of the surface from which the beam is departing. Default is None. Used by the drawing routine.

Type

None

departSurfInvROC

Inverse of the ROC of the surface from which the beam is departing. The ROC is positive for a concave surface seen from the beam side. Default is None. Used by the drawing routine.

Type

None

incSurfAngle

The angle formed by the x-arm and the normal vector of the surface to which the beam is incident. Default is None. Used by the drawing routine.

Type

None

incSurfInvROC

Inverse of the ROC of the surface to which the beam is incident. The ROC is positive for a concave surface seen from the beam side. Default is None. Used by the drawing routine.

Type

None

stray_order

An integer indicating if this beam is a stray light or not. The default value is 0. Every time a beam is reflected by an AR surface or transmits an HR surface, this couter is increased by 1.

Type

int

name
wl
P
q
qx
qy
qrx
qry
Gouyx
Gouyy
wx
wy
n
pos
length
layer
dirVect
dirAngle
optDist
Mx
My
copy(self)

Make a deep copy.

propagate(self, d)

Propagate the beam by a distance d from the current position. self.n is used as the index of refraction. During this process, the optical distance traveled is added to self.optDist. self.Goux and self.Gouyy are also updated to record the Gouy phase change.

Parameters

d (float) – Distance.

ABCDTrans(self, ABCDx, ABCDy=None)

Apply ABCD transformation to the beam.

Parameters

  • ABCDx (array) – ABCD matrix for x-direction.

  • ABCDy (array or None, optional.) – ABCD matrix for y-direction. Defaults None. If None, set to ABCDx.

rotate(self, angle, center=False)

Rotate the beam around ‘center’. If center is not given, the beam is rotated around self.pos.

Parameters

  • angle (float) – Rotation angle in radians.

  • center (array or boolean.) – Center of rotation. Should be an array of shape(2,). Defaults False.

translate(self, trVect)

Translate the beam by the direction and the distance specified by a vector.

Parameters

trVect (array) – A vector to specify the translation direction and distance. Should be an array of shape(2,)

flip(self, flipDirVect=True)

Change the propagation direction of the beam by 180 degrees. This is equivalent to the reflection of the beam by a spherical mirror with the same ROC as the beam.

If optional argument flipDirVect is set to False, the propagation direction of the beam is not changed.

Parameters

flipDirVect (boolean, optional) – Flip propagation direction. Defaults True.

width(self, dist)

Returns the beam width at a distance dist from the origin of the beam. The width is the radius where the light power becomes 1/e^2.

Parameters

dist (float) – Distance.

Returns

The width of the beam in x and y direction.

Return type

(float, float)

R(self, dist=0.0)

Returns the beam ROC at a distance dist from the origin of the beam.

Parameters

dist (float, optional) – Distance.

Returns

Beam ROC.

Return type

(float, float)

waist(self)

Return the tuples of waist size and distance

Returns

{“Waist Size”: (float, float), “Waist Position”: (float, float)}

Return type

dict

draw(self, cv, sigma=3.0, mode='x', drawWidth=True, fontSize=False, drawPower=False, drawROC=False, drawGouy=False, drawOptDist=False, drawName=False, debug=False)

Draw the beam into a DXF object.

Parameters

  • cv (gtrace.draw.draw.Canvas) – gtrace canvas.

  • sigma (float, optional) – The width of the beam drawn is sigma * (1/e^2 radius of the beam). The default is sigma = 3. sigma = 2.7 gives 1ppm diffraction loss. Defaults 3.

  • mode (str, optional) – ‘avg’, ‘x’, or ‘y’. A beam can have different widths for x- and y- directions. If ‘avg’ is specified, the average of them are drawn. ‘x’ and ‘y’ specifies to show the width of the respective directions. Defaults ‘x’.

  • fontSize (float, optional) – Size of the font used to show supplemental informations. Defaults False.

  • drawWidth (boolean, optional) – Whether to draw width or not. Defaults True.

  • drawPower (boolean, optional) – Whether to show the beam power. Defaults False.

  • drawROC (boolean, optional) – Whether to show the ROC or not. Defaults False.

  • drawGouy (boolean, optional) – Whether to show the Gouy phase or not. Defaults False.

  • drawOptDist (boolean, optional) – Whether to show the accumulated optical distance or not. Defaults False.

  • drawName (boolean, optional) – Whether draw the name of the beam or not. Defaults False.

  • debug (boolean, optional) – Debug.

drawWidth(self, cv, sigma, mode)

Draw width on canvas.

Parameters

  • cv (gtrace.draw.draw.Canvas) – The canvas.

  • sigma (float) – The width of the beam drawn is sigma * (1/e^2 radius of the beam). The default is sigma = 3. sigma = 2.7 gives 1ppm diffraction loss.

  • mode (str) – ‘avg’, ‘x’, or ‘y’. A beam can have different widths for x- and y- directions. If ‘avg’ is specified, the average of them are drawn. ‘x’ and ‘y’ specifies to show the width of the respective directions.

_dirAngle_changed(self, old, new)
_dirVect_changed(self, old, new)
_qx_changed(self, old, new)
_qy_changed(self, old, new)
_qrx_changed(self, old, new)
_qry_changed(self, old, new)
_n_changed(self, old, new)
gtrace.beam.optFunForStartPointR(phi, Mrot, R, q0, k, sigma, side)

A function to return the distance between the point on the spherical surface at an angle phi and the beam width at the same z.

Parameters

  • phi (float) – phi

  • Mrot (array) – Rotational transformation.

  • R (float) – R

  • q0 (complex) – Beam parameter.

  • k (float) – k

  • sigma (float) – Beam width

  • side – side

Returns

Distance between the point on the spherical surface at an angle phi and the beam width at the same z.

Return type

float

gtrace.beam.optimStartPointR(theta, R, q0, k, sigma)

Caltulate optimal starting point.

thetafloat

theta

Rfloat

R

q0complex

Beam parameter.

kfloat

k

sigmafloat

Beam width.

Returns

Optimal starting point.

Return type

(float, float)

gtrace.beam.optFunForEndPointR(phi, Mrot, R, q0, k, sigma, side)

A function to return the distance between the point on the spherical surface at an angle phi and the beam width at the same z.

Parameters

  • phi (float) – phi

  • Mrot (array) – Rotational transformation.

  • R (float) – R

  • q0 (complex) – Beam parameter.

  • k (float) – k

  • sigma (float) – Beam width

  • side – side

Returns

Distance between the point on the spherical surface at an angle phi and the beam width at the same z.

Return type

float

gtrace.beam.optimEndPointR(theta, R, q0, k, sigma)

Caltulate optimal end point.

thetafloat

theta

Rfloat

R

q0complex

Beam parameter.

kfloat

k

sigmafloat

Beam width.

Returns

Optimal end point.

Return type

(float, float)

gtrace.beam.optFunForFlat(a, Mrot, q0, k, sigma, side)

A function to return the distance between the point on the spherical surface (flat?) at an angle phi and the beam width at the same z.

Parameters

  • a (float) – a

  • Mrot (array) – Rotational transformation.

  • q0 (complex) – Beam parameter.

  • k (float) – k

  • sigma (float) – Beam width

  • side – side

Returns

Distance between the point on the spherical surface at an angle phi and the beam width at the same z.

Return type

float

gtrace.beam.optimCrossPointFlat(theta, q0, k, sigma)

Caltulate optimal cross point.

thetafloat

theta

Rfloat

R

q0complex

Beam parameter.

kfloat

k

sigmafloat

Beam width.

Returns

Optimal end point.

Return type

(float, float)