Simulation of Wave front propagation with ZEMAX

48
Simulation of Wave front propagation with ZEMAX Sara Casalbuoni and Rasmus Ischebeck DESY

Transcript of Simulation of Wave front propagation with ZEMAX

Page 1: Simulation of Wave front propagation with ZEMAX

Simulation of Wave front propagation with ZEMAX

Sara Casalbuoni and Rasmus Ischebeck

DESY

Page 2: Simulation of Wave front propagation with ZEMAX

Sara Casalbuoni & Rasmus Ischebeck

Overview• Motivation

– FEL optics (S. Düsterer) λ = 6 nm

– TEO optics λ = 800 nm

– THz radiation λ = 1 mm

• Tool: ZEMAX– Optics

– Usage

• First results– TEO optics

– Free Propagation in Near Field

– CTR on paraboloid mirror

• Future plans

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Sara Casalbuoni & Rasmus Ischebeck

Motivation

The TEO experiment

• EO vacuum chamber

Probe laser

Beam axis

M2 M1

EO crystal

• Pockels effect: Er of e--bunch rotates laser polarization

Er

Principal oftemporal-spatial

correlationLine image

camera

Present resolution limit ~ 100 fs(limited by laser in tunnel)

Experiment prepared by Univ. Michigan, D. Reis, A .CavalieriSLAC, with contributions from DESY

Holger Schlarb

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Motivation

Optics for the TEO experiment

additionally, some planes are rotated by 45°

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Motivation• Beam diagnostics with coherent THzspectroscopy:

• Coherent Transition Radiation (CTR)• Coherent Diffraction Radiation (CDR)• Coherent Synchrotron Radiation (CSR)• Design of transfer line for THz coherent radiation from source to interferometer

• Calculate the transfer function

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Motivation

TTF2 scheme with placing of the interferometers

CSR @30m CDR @80m CTR/CDR @140m

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Coherent radiationcontains bunch lengthinformation in the

form factor

Fourier transform of themeasured intensity

]|)f(| 1)-(N N [N )I( )(I 2tot ω+ω=ω

dtt)p(ixe )ct(cdzz/c)p(ixe )z()f( ωρ=ωρ=ω ∫∫∞

∞−

∞−

Normalized longitudinal charge distribution

)(I )T( )(I tot meas ωω=ω

Motivation

Transfer function

T(ω) can be obtained by :•Calibrating the system with a known source•Calculate it by ZEMAX

At λ>bunch length => Coherent Emission

Page 8: Simulation of Wave front propagation with ZEMAX

Sara Casalbuoni & Rasmus Ischebeck

Overview• Motivation

– FEL optics (S. Düsterer) λ = 6 nm

– TEO optics λ = 800 nm

– THz radiation λ = 1 mm

• Tool: ZEMAX– Optics

– Usage

• First results– TEO optics

– Free Propagation in Near Field

– CTR on paraboloid mirror

• Future plans

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Sara Casalbuoni & Rasmus Ischebeck

Optics

• Commercial optics

• Perfect lens optics

• Ray optics

• The Slowly Varying Amplitude approximation

• Gaussian optics

• Near field and far field

• Notion of the Rayleigh length and the Fresnel number

• Propagation of a wave front

• Far field (Fraunhofer diffraction propagation)

• Near field (Fresnel diffraction propagation)

• called “far field” in the ZEMAX manual

• Very near field (angular spectrum propagation)

• called “near field” in the ZEMAX manual

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Ray Optics (Geometrical Optics)

• In vacuum, light propagates on a straight line

• Refraction at the surfaces according to Snell’s Law

• No diffraction

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Geometrical Optics

• ZEMAX takes into account

• “thick” lenses

• spherical aberration at the surfaces of the lens

• wavelength-dependent index of refraction (chromatic aberration)

• and calculates

• beam positions and angles

• spherical aberrations, coma, chromatic aberrations

• contribution of the various aberrations to the resolution

• optimization of parameters

• etc…

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The Slowly Varying Amplitude (SVA) approximation

Plan:

• Assume an electromagnetic field of the form

• Amplitude is assumed to vary slowly

• slowly as compared to the wavelength

• AND slowly as compared to the grid spacing

• Derive the development (propagation) of a wave front from Maxwell‘s Equations

• Find clever ways to solve the propagation numerically

• time-efficient

• minimize numerical errors

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Gaussian Optics

• Assume an amplitude of the form

• Assume a constant phase for z=0,corresponding to an infinite radius of curvature

• Often found in laser optics

• By solution of the Fresnel integral,one can show that the amplitude distribution will remain Gaussian when the beam propagates

• The behavior is governed by the Rayleigh length, defined as:

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Gaussian Optics

• The wave front will acquire a curvature for z>0:

• The width of the beam will evolve as:

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Near Field and Far Field

Fresnel number

• For a beam that has a radius R, propagatedby a distance L

• equal to the number of Fresnel rings on the source plane that can be seen from any point on the detection plane

• is a position of both the source and the detection plane

• Far field:

• Near field:

• Very near field:

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Propagation of an Arbitrary Wave Front

• Assume a wave with an arbitrary amplitude given numerically on agrid

• Propagation along the z axis can be calculated in three domains:

• Far field (Fraunhofer diffraction propagation)

• Near field (Fresnel diffraction propagation)

⇝ Peter’s and Bernhard’s talk

• Very near field (angular spectrum propagation)

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Fraunhofer Diffraction

• Propagation from the source plane (index 0) to the observation plane (index 1)

• The electric field amplitude on the observation plane can be calculated by a superposition of the wavelets originating from all points in the source plane

• In the far field, one may make the following approximations:

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Fresnel Diffraction

• If the far field approximation cannot be made, one has to use the second order expansion:

• The near field effects can be essential:far field simulation near field simulation measurement

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Numerical Considerations

• The integrals are represented as sums.

• The number of terms in the sum is very large, and time-intensive functions have to be computed

• If the separation of the grid points is too large, the transition is not smooth

⇒ Aliasing occurs

⇒ Increase the number of grid points

• This problem is especially serious for large Fresnel numbers, asthe phase changes rapidly in the outer Fresnel zones

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Angular Spectrum Propagation

• Assume an electric field amplitude on a grid

• Let the Fourier transform of the field be

• The inverse Fourier transform is

plane waves propagating in the direction

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Angular Spectrum Propagation

• The wave can be regarded as a superposition of plane waves,the field is the angular spectrum.

• Using the approximation that

the wave propagates at a small angle to the z axis,

• Thus, the angular spectrum evolves as

• Solving the Maxwell equations is reduced to a simple multiplication.

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Limitations of the Angular Spectrum Propagator

• The size of the grid on which the field is given remains constant as the beam evolves.

⇒ If the beam expands a lot during the propagation, it exceeds thegrid

⇒ The angular spectrum propagator is suitable for cases where the beam diameter does not change significantly, i.e. near the focus

• The use of the Fourier transform implicitly assumes a periodic source.

⇒ There is an interferencewith rays that comefrom the mirror sources:

⇒ One has to make thegrid large enough(⇒ high demands onprocessor & memory)Sara Casalbuoni & Rasmus Ischebeck

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Usage of the Algorithms in ZEMAX

Usage (examples)Usage (examples)Usage (examples)Usage (examples)AlgorithmAlgorithmAlgorithmAlgorithm

Physical Optics Propagation for large Fresnel numbers

Angular spectrum propagation

Physical Optics Propagation for small Fresnel numbers

Fresnel diffraction

Calculation of the Point Spread Function in the focus

Fraunhofer diffraction

Geometrical optics: find the position of the focus

Ray tracing

Decision on the Fresnel numbers is based on a Gaussian pilot beam

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Tool:ZEMAX• What is ZEMAX?

`ZEMAX is a program which can model, analyze and assist in the design of optical systems, but is NO substitute for good engineering practices´

• What do we do with ZEMAX?

• Plug in an optical design (lenses, THz:mirrors )

• Ray tracing as first check (focal point @right positions)

• PHYSICAL OPTICS PROPAGATION

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Tool:ZEMAXTransferline for the Martin-Pupplet interferometer @TTF1

CTRscreen

Detector

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PHYSICAL OPTICS PROPAGATION:Usage

• ZEMAX input: Fourier Transform of the Electric field on the first surfacein the 2 polarization directions

• Example for CTR:Fourier Transform of the radial Electric field of a uniformbunch charge distribution moving with velocity v in straight line uniform motion from M. Geitz PhD Thesis

Rr;)(kb/I)(kb/K

)(kR/I)(kr/IR)(kr/K )(kR/IRr)(k,E~

Rr;)(kb/I)(kb/K

)(kR/I)(kr/IR)(kR/K )(kr/I rr)(k,E~

c//2kradius pipebradius beamRcoordinate radialr

0

01111

0

01111

>γγγ⋅γ⋅+γ⋅γ⋅=

<γγγ⋅γ⋅+γ⋅γ⋅=

ω=λπ====

ϕ⋅=ϕ⋅=

sinE~ E~cosE~ E~atan(y/x)

ryrx

yx E~,E~

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PHYSICAL OPTICS PROPAGATION:Usage

• Source field (J. Menzel implemented .DLL for CTR and CDR)

Sara Casalbuoni & Rasmus Ischebeck

Page 28: Simulation of Wave front propagation with ZEMAX

Sara Casalbuoni & Rasmus Ischebeck

Overview• Motivation

– FEL optics (S. Düsterer) λ = 6 nm

– TEO optics λ = 800 nm

– THz radiation λ = 1 mm

• Tool: ZEMAX– Optics

– Usage

• First results– TEO optics

– Free Propagation in Near Field

– CTR on paraboloid mirror

• Future plans

Page 29: Simulation of Wave front propagation with ZEMAX

HELMHOLTZ GEMEINSCHAFT VUV FEL

thethe real real focusfocus –– usingusing real real lenslens telescopestelescopes

50 µm

all calculations for M2 =1!!!

encircled energy

50% of energy within 9 µm diametergeometrical focus variation

through focus diagram

logarithmic focus image

1-D cut - 9µm focus 1-D cut - logarithmic

800 µm

Stefan Düsterer

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Optics for the TEO experiment

Optics (simplified)

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Optics for the TEO experiment

Imaging of a Point on the Crystal

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Optics for the TEO experiment

Envelope of the Laser

⇝ beam expander optics

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Sara Casalbuoni & Rasmus Ischebeck Sara Casalbuoni & Rasmus Ischebeck

Optics for the TEO experiment

ZEMAX simulations

• Point Spread Function

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Optics for the TEO experiment

Reverse the first doublet

• Distribute the refraction evenly over all surfaces

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Optics for the TEO experiment

Improved resolution

• The reversal of the first doublet improves the resolution:

Sara Casalbuoni & Rasmus Ischebeck

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Optics for the TEO experiment

ZEMAX Simulations

Further studies (Stefan Düsterer)

• Optimization of the distances

• Optimization of the tilt of the camera

• Calculation of the PSF with Fresnel diffraction

• Limitation of the resolution: spherical aberrations

⇒ It does not help to increase the diameter of the lens

• Calculation of the resolution for off-axis points

• Studies on the required alignment precision

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CTR Free Propagation in Near Field• Comparison with MATLAB code

0 5 1 0 1 5 2 0 2 5 3 0 3 50 .0 0 0

0 .0 0 1

I (a.

u.)

x (m m )

M A T L A B Z E M A X

λ = 1 m m ; γ = 2 7 0 ; s c re e n ra d iu s = 2 0 m m ;d is ta n c e s o u rc e - im a g e = 1 0 0 m m

Sara Casalbuoni & Rasmus Ischebeck

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CTR on flat mirrorComparison with Bernhard‘s code

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

Mathematica ZEMAX

λ=1 mm; γ=270; screen radius=20 mm;distance mirror-image=200 mm;f = 100mm FLAT

I (a.

u.)

x (mm)

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CTR on paraboloid mirror: crestComparison with Bernhard‘s code

0 5 10 15 20 25 30 350.0

0.2

0.4

0.6

0.8

1.0

1.2

Mathematica ZEMAX ZEMAX paraxial

λ=1 mm; γ=270; screen radius=20 mm;distance mirror-image=200 mm;f = 100mm crest

I (a.

u.)

x (mm)

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0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

1.2

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

1.2

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

d is tan c e m ir ro r - im a ge= 3 00 m m

x (m m )

I (a.

u.)

d is ta nc e m ir ro r - im age = 500 m m

d is ta nc e m irro r-im a g e = 5 0 m m

I (a.

u.)

d istanc e m ir ro r - im ag e= 10 0 m m

d istanc e m ir ro r - im ag e= 20 0 m m

d is ta nc e m ir ro r - im age = 100 0 m m

x (m m )

x (m m )

CTR on paraboloid mirrorComparison with Bernhard‘s code

CTRscreen

Image

λ=1mm; ϒ=270; screen radius=20 mm; f = 50mm

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Transmission through a 10m beam line

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Re-focusing of the wave

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CTR on paraboloid mirrorExperimental setup at SPPS

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CTR on paraboloid mirrorComparison with measurements

-30 -20 -10 0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

1.2 Measurement ZEMAX

λ=0.3 mm; γ=55772; screen radius=20 mm; distance mirror-image=320 mm; f = 75mm

I (

a.u.

)

x (mm)

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Future plans

• Check the resolution of the TEO optics experimentally

• Check the transfer function for the interferometer in TTF1 (CTR)

• BC3 Frascati transfer line (CDR)

• Implement Surface.DLL (with J. Menzel) for elliptical and paraboloid mirrors for design optimization (at the moment impossible)

• Implement CSR source from O. Grimm calculations

• Check O. Grimm (CSR) transfer line

• Comparison with JLab (CSR) transfer line

• Transfer line for the interferometer @ 140m

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Jlab transfer line

M1

M2 M3

M4

Sara Casalbuoni & Rasmus Ischebeck

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Transfer line with parallel beamfor the interferometer at 140 m

Paraboloid mirrors

Flat mirrors

Sara Casalbuoni & Rasmus Ischebeck

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Transfer line with elliptical mirrorsfor the interferometer at 140 m

Sara Casalbuoni & Rasmus Ischebeck