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Design and optimization of compact freeform lens array for laser beam splitting

Milan MaksimovicFocal - Vision and Optics,

Enschede, The Netherlands

Brussels, Belgium, 14 - 17 April 2014

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Outline

• Introduction: free-form optics and beam shaping• Motivation: laser beam multiplexing• Design Method• Design Examples: simulations results and analysis• Concluding remarks

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Introduction• Freeform optics: no rotational invariance, surfaces with arbitrary shape and regular or

irregular global or local structure:• enhanced flexibility in design,• boost in optical performances, • combining multiple functionalities into single component, • simplifying complex optical systems by reducing element count,• lowering costs in manufacturing, • reducing stray-light • easing system integration and assembly

• Laser beam shaping (splitting) to achieve parallelism• Lens array archives this purpose by the geometrical aperture splitting using the pupil division by

individual lenslets residing within sub-apertures• Other optical elements are used and needed to obtain functions such as beam focusing,

combining or collimating

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Motivation: design of 1x laser diode to 3x fibers coupler

• High-power LD (elliptical) beam splitting into 3 fibers with equalized energy per channel

• System components: Individual lenses• Collimator lens• Single focusing lens element per spot

• Manufacturing cost high (number of components)• Assembly tolerances (for many elements) are critical

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Element representation: • Low order aspheric + specific aperture on input• Low order aspheric lenslet in the focusing lens array

Design and optimization (using standard software package Zemax):• Custom merit function using real ray coordinates: explicit specification of in-out

relationship per each channel (spot)• Pupil sampling (grid) define sampling rays f0r merit function• Multi-parameter optimization• Local optimizer (DLS or OD):

-> Initial starting point critical !

• Free-form surface representation: 2 2

2 2 2

( )( , ) ,1 1 ( )

i ii

c x yz x y w x yKc x y

where c=1/R is base curvature, K is base conic constant, wi is weight in expansion and Φ is suitable basis function in expansion

Compact beam splitter: design method

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Compact beam splitter: design method

Compact beam splitter with regular lens array: 1x3 (left) and 1x 5 (right)

Optical layouts for: collimator (left), single lenslet (center) and 1x3 lens array (right).

Fixed input parameters (example):• Object and image distance : 50mm • Entrance pupil diameter: 30mm • Rectangular aperture of 10x30 mm • Lens array 10x10 mm, (replicated in vertical direction)

Merit Function based onreal ray position @ image plane!

Pupil sampling grid defines input ray position sampling !

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Different pupil sampling grids used to compute merit function

Fibonacci sampling grid:

• Deterministic algorithm based on Fibonacci spiral

• Uniform and isotropic resolution

• Equal area (contribution) per each grid point

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Compact design of 1x3 beam splitter using regular lens array

Composite Fibonacci pupil sampling grid used in merit function , layout with rays generated in the merit function, 3D model and multi-spot surface plot in the image pane (left to right respectively).

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Compact design of 1x3 beam splitter using regular lens array

Surface sag map (left) and cross-section (right) of lens array surface

Optimization with radius and conic as variables : -> R=-22.9954mm and K=-2.1314

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Compact beam splitter design using general freeform surface

Extended Polynomial surface representation

Surface sag map (left) and sag cross-section (right) (Extended Polynomial surface after the optimization with 150 variables)

2 2

2 2 2,

( )( , )1 1 ( )

m nmn

m n

c x yz x y c x yKc x y

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Compact beam splitter design using general freeform surface

Merit function vs. number of variables used in optimization with different size of pupil sampling grids:

0 50 100 1500.5

1

1.5

2

2.5

3

Number of Variables

Merit

Func

tion

Extended Polynomial Representation

17 points per segment

51 points per segment

153 points pr segment

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Compact beam splitter design using general freeform surface

Zernike surface representation :

Surface sag map (left) and sag cross-section (right) of Zernike surface after the optimization with 37 variables

2 22

2 2 21...8 1..37

( )( , ) ( , )1 1 ( )

ii j j

i j

c x yz x y r A ZKc x y

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Compact beam splitter design using irregular lens arrayMotivation/ Application: different power ratio per spot!Beam splitter 1x3 design with irregular lens array: layout (left) and 3D model (right)

Surface intensity plot in the entrance pupil (left) and multi-spot surface intensity plot in the image plane (right)

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Compact beam splitter design using irregular lens array: smoothing using image processing technique

Surface sag map of irregular lens array after smoothing

Sharp transitions removal:

Gaussian filter followed by Median filterin the transition region (local smoothing!)

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Compact beam splitter design using irregular lens array: CAD model smoothing

CAD model post-processing• heuristic approach• CAD surface representation often implies less

accurate ray tracing!• Iterative procedure: (Zemax->CAD->Zemax)

Example of successful design iteration:

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Concluding remarks• We demonstrated feasibility of freeform design of compact beam splitting element

that combines both functions of collimation and beam splitting into one (both regular and irregular structure is possible)

• Design relaying on multi-parameter optimization + custom design merit function based on real ray coordinates at target location works, but:• Standard free-form surfaces often fail to produce design directly and with small number

of variables-> inefficient design process!• Open questions: optimal free-form representation

• Pupil sampling method based on Fibonacci grid (highly structured grid and having features usually associated with random grids) improves convergence in local optimization procedure

• Designs often require post-processing for manufacturing constraints (smoothing)• Application of local filtering techniques borrowed from image processing produce

smoothed versions of surfaces with discontinuities

• Possible applications of similar designs are in laser fiber coupling and off-axis multi-spot generation where power splitting ratio can be arbitrarily predefined.

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Thank you for the attention!