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Introduction

Unstable confocal optical resonators with high magnification (about 100x) are commonly used with Metal Vapor Lasers (MVL) with high-aperture active media. The main problem in modeling these devices is the large single-pass loss, which requires an accurate resampling process. Other problems include modelling hard apertures when using Fast-Fourier Transform (FFT) calculations, as sharp edges produce a high-frequency drift of the resulting field.

This article will demonstrate how to handle both these problems. Here is the specification of the laser to be modelled:

Specifications:

Laser:

* Copper vapor (CVL)

* Wavelengths: 510.6 nm and 578.2 nm

* Active medium length: 600 mm

* Active medium diameter: 14 mm

Resonator:

* Confocal with output coupler represented by afocal meniscus with reflective coating of 3 mm in diameter

* Primary mirror: R2032mm

* Secondary (output) mirror: R20.04mm

* Distance: 1005.98mm

The Resonator Geometry

Experimental and previous theoretical investigations have shown the output radiation to be independent of starting beam characteristics after at least 2 passes through the resonator. Only diffraction effects and manufacturing and adjustment errors are significant . The following model may be used for system sensitivity analysis of these factors.

ZEMAX Model of the Unstable Laser Cavity

The file resonator.zmx is included in the zip archive that may be downloaded from the last page of this article. Note that it has the following system parameters:

System unit to mm (System > General > Units)

Wavelength to 0.5106um and 0.5782um (System > Wavelengths)

Set one field with values X=0 and Y=0 (System > Fields)

Set system aperture as Entrance Pupil Diameter of 0.14 mm (System > General > Aperture)

It is set to the geometry equaling to 2 full passes in sequential mode:

The LDE fo rthe attached file

On the surfaces 2, 3, 7, 8, 10, 11, 15, 16 are set circular apertures with semi-diameters 7mm representing the apertures of the active medium.

Surface 17 is a user-defined surface which is supplied with Zemax. It represents a soft edged aperture on the central mirror at output lens. The optical density function is given by D = 0.5Dmax (1.0 + cos(πr )), where r is the radial coordinate normalized to the semi-diamater of the surface.

Surfaces 18 and 19 represent the output coupler and may be omitted. The distance 5e4mm at the19th surface is used for analysis at far field (actually it is not real far field, but the distance is good for analysis).

Coordinate breaks are inserted to model the primary mirror misalignment. Note that if this mirror is decentered, then the chief ray will miss the center of the output surface (this is usually compensated by adjustment and there is no case when only offset of tilt only is present). So the needed tilt may be found by simple optimization. For modelling of significant offset is must be changed iteratively or also by optimization. Operands of merit function are the following:

The merit function

Here REAY controls the needed tilt and PMVA must be modified to desired target offset (shown +10mm).

Adding Physical Optics

Unstable confocal optical resonators with high magnification (about 100x) are commonly used with Metal Vapor Lasers (MVL) with high-aperture active media. The main problem in modeling these devices is the large single-pass loss, which requires an accurate resampling process. Other problems include modelling hard apertures when using Fast-Fourier Transform (FFT) calculations, as sharp edges produce a high-frequency drift of the resulting field.

This article will demonstrate how to handle both these problems. Here is the specification of the laser to be modelled:

Specifications:

Laser:

* Copper vapor (CVL)

* Wavelengths: 510.6 nm and 578.2 nm

* Active medium length: 600 mm

* Active medium diameter: 14 mm

Resonator:

* Confocal with output coupler represented by afocal meniscus with reflective coating of 3 mm in diameter

* Primary mirror: R2032mm

* Secondary (output) mirror: R20.04mm

* Distance: 1005.98mm

The Resonator Geometry

Experimental and previous theoretical investigations have shown the output radiation to be independent of starting beam characteristics after at least 2 passes through the resonator. Only diffraction effects and manufacturing and adjustment errors are significant . The following model may be used for system sensitivity analysis of these factors.

ZEMAX Model of the Unstable Laser Cavity

The file resonator.zmx is included in the zip archive that may be downloaded from the last page of this article. Note that it has the following system parameters:

System unit to mm (System > General > Units)

Wavelength to 0.5106um and 0.5782um (System > Wavelengths)

Set one field with values X=0 and Y=0 (System > Fields)

Set system aperture as Entrance Pupil Diameter of 0.14 mm (System > General > Aperture)

It is set to the geometry equaling to 2 full passes in sequential mode:

The LDE fo rthe attached file

On the surfaces 2, 3, 7, 8, 10, 11, 15, 16 are set circular apertures with semi-diameters 7mm representing the apertures of the active medium.

Surface 17 is a user-defined surface which is supplied with Zemax. It represents a soft edged aperture on the central mirror at output lens. The optical density function is given by D = 0.5Dmax (1.0 + cos(πr )), where r is the radial coordinate normalized to the semi-diamater of the surface.

Surfaces 18 and 19 represent the output coupler and may be omitted. The distance 5e4mm at the19th surface is used for analysis at far field (actually it is not real far field, but the distance is good for analysis).

Coordinate breaks are inserted to model the primary mirror misalignment. Note that if this mirror is decentered, then the chief ray will miss the center of the output surface (this is usually compensated by adjustment and there is no case when only offset of tilt only is present). So the needed tilt may be found by simple optimization. For modelling of significant offset is must be changed iteratively or also by optimization. Operands of merit function are the following:

The merit function

Here REAY controls the needed tilt and PMVA must be modified to desired target offset (shown +10mm).

Adding Physical Optics

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