### Hermite-Gauss mode conversion

#### Introduction

Arbitrary solutions of the paraxial Helmholtz equation can be expressed as combinations of Hermite-Gaussian modes (whose amplitude profiles are separable in x and y using Cartesian coordinates).

For many applications, it is useful to convert the fundamental laser mode TEM00 to a higher order of Hermite-Gaussian beams:

 Phase Element Output Intensity Phase Element Output Intensity TEM00 TEM20 TEM01 TEM12 TEM10 TEM21 TEM11 TEM22 TEM02

Each mode HGlm is denoted by two indices, l & m, which represent the number of modes in the x & y directions, respectively.

Typical Applications

• Communication
• Scientific & research
• Scanning applications
• STED microscopy
• Optical tweezing
• Optical trapping

Feature

• Aberration free
• High efficiency

Typical Optical set-up:

Typical Operating Principle

The operating principle is quite straight-forward – a Fourier Transform (FT) is applied on the initial field amplitude and phase to obtain the desired field (or intensity) at far-field. In this way, the fundamental Gaussian beam TEM_00 is converted to a higher order of Hermite-Gaussian modes. For example – conversion of TEM_00 to TEM_10:

For the phase-plate element, the height of the step is defined as:

where n is the refractive index of the material.

Design Considerations:

For a high-quality performance, the laser output should be Single Mode (TEM00 with an M2 value <1.3. If the M2 is larger, it may still be possible to reduce the M2 value by inserting a spatial filter in between the laser and the DOE lens component.

All optics in the beam path should be of high quality, i.e. have a low irregularity figure, in order not to introdcue wav-front errors which would degrade the diffractive phase element’s performance.

General Specifications:

 Materials: Fused Silica, Sapphire, ZnSe, Plastics Wavelength range: 193[nm] to 10.6[μm] DOE design: Binary (2-level) Element size: Few mm to 100 [mm] Coating (optional): AR/AR Coating Custom Design: Available

### π Phase-Plate

Introduction:

For many applications, it is necessary to use a phase element with a π-phase at the center. For imaging purposes using this element will result in an increased depth-of-focus, and for particle manipulation purpose, using this element will result in optical tweezing\trapping.

Standard Products:

 Part Number Diameter [mm] Aperture size [mm] Material Description PE-202 25.4 23.6 Fused Silica Half-space π difference mode converter, TEM01 (or TEM10) PE-230 25.4 23.6 Fused Silica Quarter-space π difference mode converter, TEM11 PE-215 11 9.2 Fused Silica Round π phase at the center, diameter 4817 μm PE-216 23.6 9.2 Fused Silica Round π phase at the center, diameter 5680 μm PE-217 20 23.6 Fused Silica Round π phase at the center, diameter 6200 μm PE-218 25.4 18.2 Fused Silica Round π phase at the center, diameter 8428 μm PE-219 25.4 23.6 Fused Silica Round π phase at the center, diameter 10838 μm PE-220 25.4 23.6 Fused Silica Round π phase at the center, diameter 7224 μm PE-221 11 9.2 Fused Silica Round π phase at the center, diameter 3612 μm PE-222 11 9.2 Fused Silica Round π phase at the center, diameter 4214 μm PE-223 11 9.2 Fused Silica Round π phase at the center, diameter 3000 μm PE-224 11 9.2 Fused Silica Round π phase at the center, diameter 5400 μm PE-225 25.4 23.6 Fused Silica Round π phase at the center, diameter 6384 μm PE-226 12.5 10.7 Fused Silica Round π phase at the center, diameter 6840 μm PE-227 25.4 23.6 Fused Silica Round π phase at the center, diameter 8900 μm PE-228 11 9.2 Fused Silica Round π phase at the center, diameter 1200 μm PE-229 11 9.2 Fused Silica Round π phase at the center, diameter 1800 μm PE-241 25.4 22.9 Fused Silica Round π phase at the center, diameter 3860 μm

For a quotation of an above Part Number, please specify the wavelength used.