Multimode Fiber Output Model

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Farsang

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Jul 7, 2007, 7:14:00 PM7/7/07
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Hello:

We have a fiber with Core Dia. = 500 um and NA = 0.22 and we'd like
to model the rays coming out of this fiber in an Optics CAD (ZEMAX
here).

Can we assume that each point inside of the core area emits a cone of
light with an NA = 0.22 for this cone, and the the cones are
telecentric (i.e. axis of each cone is parallel to the optic axis).
If not, how can we model the output rays (how can we make the fiber
output as the starting object in the CAD).

thanks.

mp...@oscintl.com

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Jul 7, 2007, 9:37:55 PM7/7/07
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Are you doing imaging analysis from the output of the fiber, or are
you doing some kind of physical optics propagation (gaussian optics)
analysis?

Michael
www.oscintl.com

Farsang

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Jul 7, 2007, 11:29:02 PM7/7/07
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Hi Michael:

This is primarily for image analysis, but would like also to do
Physical Optics to simulate better the real situation.

This is the application:

We'd like to get spot size of dia = 2 Cm - 5 Cm (absolute Max) at a
minimum distance of 100 feet (ideally 250 feet) from the fiber.
Fiber output power is 200 W and wavelength = 980 nm.

I was thinking to get the required spot size using Geometric Image
Analysis of ZEMAX and then do the physical optics
for closer simulation.

Because of the optical invariance it'll be difficult to achieve the
above spot size using catalog optics.

Do you have any idea how we could get this spot size, appreciate your
suggestions and comments?

Ideally we'd like to have

Spot Size = 2 Cm - 3 Cm at 250 feet
Power in the Spot = 200 W

wadex...@provide.net

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Jul 8, 2007, 12:23:46 AM7/8/07
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On Jul 7, 11:29 pm, Farsang <youzpal...@netscape.net> wrote:

> Hi Michael:
>
> This is primarily for image analysis, but would like also to do
> Physical Optics to simulate better the real situation.
>
> This is the application:
>
> We'd like to get spot size of dia = 2 Cm - 5 Cm (absolute Max) at a
> minimum distance of 100 feet (ideally 250 feet) from the fiber.
> Fiber output power is 200 W and wavelength = 980 nm.
>
> I was thinking to get the required spot size using Geometric Image
> Analysis of ZEMAX and then do the physical optics
> for closer simulation.
>
> Because of the optical invariance it'll be difficult to achieve the
> above spot size using catalog optics.
>
> Do you have any idea how we could get this spot size, appreciate your
> suggestions and comments?
>
> Ideally we'd like to have
>
> Spot Size = 2 Cm - 3 Cm at 250 feet
> Power in the Spot = 200 W

Hi Farsang,
If you are doing imaging analysis, you can model the output of a
fiber as follows: Go to the Field Data box and click on "Object
Height". Enter enough field points to represent your fiber, perhaps
by a point in the center of the fiber, at the .7 zone, and at the
fiber's edges. Set your wavelength in the wavelength box. In the
Lens Data Editor, set the distance from your fiber face to the next
lens or point of interest. Set the fiber's numerical aperture by
setting <General> <Aperture> <Aperture Type: Object Space NA>,
<Aperture Value: 0.22>. Make the fiber's output telecentric by
clicking on "Telecentric Object Space".
If you are looking for the footprint of the light through all of
the lens surfaces (and the image plane, if there is one), you'll have
to go to <Analysis> <Geometric Image Analysis> <Settings>, set the
Field Size: to 0.500 (if your units are set to millimeters), set the
File: to CIRCLE.IMA, set the Image Size: to the size of your area of
interest at a particular surface, then set Surface: to your surface of
interest.
If you are coupling the fiber's light into another fiber, set the
NA in the <Analysis> <Geometric Image Analysis> <Settings> box to the
numerical aperture of the fiber being coupled. That will let you see
the coupling efficiency.
If you are doing physical optics propagation, you'll have to wait
for Michael's reply.
But from your last post, I think I see what you are doing.

To model the optical system, if you need a 3 cm spot at 250 feet,
from a 0.5 mm diameter source, your optical system's focal length
needs to be about (250/30)* 0.5 (sorry about the mixed units) = 4.16
feet. At a numerical aperture of 0.22, your system's aperture needs
to be about 23 inches in diameter. It might be hard to come up with a
23" diameter f/2.27 diffraction-limited lens. It's not impossible,
but it would be expensive. Even the military might want to see a
better solution.
The problem arises from the size of your source. You'll get a lot
further if you use the output of the diode directly (whose source is
effectively the size of a bacterium), without passing it through a
fiber, if that is possible.

Wade Kelman

mopa

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Jul 8, 2007, 7:34:13 AM7/8/07
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> Wade Kelman-

hi, Wade,

Your reply is really helpful for me also. Do you have any idea
about modeling a high power laser diode as a source in Zemax? It has
a 200micron*1micron aperture and different divergence angles in the
two orthogonal direction. I have studied the Zemax manual and looked
for solutions on Internet for several days, but no proper answers were
founded. Who can help me? Thank you very much.

Laurence Zhu

wadex...@provide.net

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Jul 8, 2007, 11:25:30 AM7/8/07
to
>
> hi, Wade,
>
> Your reply is really helpful for me also. Do you have any idea
> about modeling a high power laser diode as a source in Zemax? It has
> a 200micron*1micron aperture and different divergence angles in the
> two orthogonal direction. I have studied the Zemax manual and looked
> for solutions on Internet for several days, but no proper answers were
> founded. Who can help me? Thank you very much.
>
> Laurence Zhu

Hi Laurence,
Zemax provides an example of how to model a diode source. You can
find it at Zemax \Samples \Sequential \Miscellaneous \Diode source
simulation.zmx. Just open it and see how it was done. You'll have to
modify the file to correspond to your own situation.
Also, Zemax Support can often point you in the right direction. If
you use Zemax often (or for profit), their support is worth having.
They don't always give you the answer you need, and they've only
admitted (to me) that their program was doing something wrong once,
but about 85 to 90% of the time, they will help you get to the
answer. And that's pretty good for a work in process.

Wade Kelman

Farsang

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Jul 8, 2007, 5:41:11 PM7/8/07
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> Wade Kelman- Hide quoted text -
>
> - Show quoted text -

Hello Wade:

1- With " Object Space NA = 0.22 " and " Telecentric Object Space "
checked on if we selectec CIRCLE.MA for
the object does that mean that every point inside of the circle emits
a cone of light with cone having NA = 0.22 and all these cones are
telecentric (i.e. thier axes are parallel to the Optics Axis)?


2-We'd like to see the footprint of the beam coming out of the fiber
on a surface 250 feet away (after going through some optics). To use
CIRCLE.MA as an object for this purpose correctly requires that every
point on CIRCLE.MA emits a cone of light as stated in (1) above. I am
not sure if this is the case.


3- Instead of a single lense to image fiber output face (its core) to
a surface 250 feet away (which requires a large lense as you noted) we
could use two lenses. This would help to reduce the size of the
lenses, fiber is at the focal point of the first lens so the beam out
of the first lens has lower divergence (idealy zeo divergence for the
on axis point i.e. center of the fiber core), the seocond lens images
the beam spot on the first lens to the required size on the image
surface (surface 250 feet away). However, even in this scheme the
second lens still turns out to be large and there is no catalog lens
with required focal length and diameter.

Originally we thought we could use a simple comercial Newtonian
Telescope to do this, but again because of the 400 um rather large
size of the core and limitation imposed by the Optical Invariance this
is not achivevable (i.e. to get 2Cm - 5Cm spot 250 feet away and
having most of the 200 W fiber output power).


4-Your diode sugestion would work if there were a diode that has 200 W
output power .
There are diode arrays on a chip that hav a total output of 100 W, but
it require a micro lens array to collimate individual
diodes.


AES

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Jul 8, 2007, 6:53:11 PM7/8/07
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In article <1183930871.6...@g4g2000hsf.googlegroups.com>,
Farsang <youzp...@netscape.net> wrote:

> 1- With " Object Space NA = 0.22 " and " Telecentric Object Space "
> checked on if we selectec CIRCLE.MA for
> the object does that mean that every point inside of the circle emits
> a cone of light with cone having NA = 0.22 and all these cones are
> telecentric (i.e. thier axes are parallel to the Optics Axis)?

No expertise on optical design here, and only limited experience with
fibers; but I think the *physical thinking* you have to use to approach
this problem is roughly the following:

* The large-core fiber you use can propagate a *huge* number of
independent transverse mode patterns -- the number is some constant
times the V number of the fiber, and will be given in a standard text
(like Saleh and Teich, for example).

* If you couple into the fiber in some random way at the input end,
you'll excite some random mixture of a large number of those modes; and
if you then propagate any significant distance down that fiber random
scattering and bending will ensure that the light gets divided up among
more or less *all* of them ("random mode conversion"), with random (and
time-varying, and motion-sensitive) amplitudes for each mode.

* In this situation, one way to view the output is to picture the
output face as being divided up into the *same* total number of small
spots or patches ("coherence areas"), each of them acting like a
separately emitting patch and radiating a totally independent and
randomly phased tiny plane wave across that patch, with this cone of
diffraction-limited radiation (diffraction-limited by the patch size)
being in fact telecentric with the fiber (unless the fiber end face is
cut skewed, in which case you have to take that into account).

* So, calculate roughly what sort of spot pattern each of those little
coherence areas will be imaged to at the target plane, taking into
account the size of the patch and how far off axis each spot is at the
input plane; and then just add up the *intensities* (i.e., powers, not
field amplitudes) of those target plane spots.

That's my off-the-cuff input on how this problem can be thought about;
others may want to correct or modify this.

Farsang

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Jul 8, 2007, 10:15:12 PM7/8/07
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> * In this situation, one way to view the output is to picture the
> output face as being divided up into the *same* total number of small
> spots or patches ("coherence areas"), each of them acting like a
> separately emitting patch and radiating a totally independent and
> randomly phased tiny plane wave across that patch, with this cone of
> diffraction-limited radiation (diffraction-limited by the patch size)
> being in fact telecentric with the fiber (unless the fiber end face is
> cut skewed, in which case you have to take that into account).
>


Thank you AES for the feedback.

1- Does " *same* total number " refer to the total number of
modes?


2- Does " spots or pathes " refer to the individual modes and by "
the sizes of these spots" you mean the size of
each mode at the fiber output face?


AES

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Jul 8, 2007, 11:43:37 PM7/8/07
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In article <1183947312....@g4g2000hsf.googlegroups.com>,
Farsang <youzp...@netscape.net> wrote:

> > * In this situation, one way to view the output is to picture the
> > output face as being divided up into the *same* total number of small
> > spots or patches ("coherence areas"), each of them acting like a
> > separately emitting patch and radiating a totally independent and
> > randomly phased tiny plane wave across that patch, with this cone of
> > diffraction-limited radiation (diffraction-limited by the patch size)
> > being in fact telecentric with the fiber (unless the fiber end face is
> > cut skewed, in which case you have to take that into account).
> >
>
>
> Thank you AES for the feedback.
>
> 1- Does " *same* total number " refer to the total number of
> modes?

Yes. It's a matter of "degrees of freedom" of the system. To fully
characterize the radiation in the fiber (just before the output end of
the fiber, say) you need 2N numbers to gives the amplitudes and phases
of each of the N individual modes -- which translates into 2N numbers to
give the amplitudes and phases of each of the N coherence areas.

(Give or take an additional factor of 2 to account for the polarization
of the fields in each individual mode.)


>
>
> 2- Does " spots or pathes " refer to the individual modes and by "
> the sizes of these spots" you mean the size of
> each mode at the fiber output face?

No, not at all. As per paragraph above, you can describe the field by
giving the individual amplitudes of N modes -- or by giving the
amplitudes at N points (or in N individual coherence areas, aka
"patches") across the output end of the fiber. Each individual mode
more or less fills the whole fiber.

It's a "sampling theorem" sort of thing: you can describe a time signal
of specified duration and bandwidth by giving the amplitudes of N
equally spaced spectral (frequency) components -- or the amplitudes at N
equally spaced instants in time during the duration of the signal. Same
thing here, except it's 2D position instead of 1D time.

Farsang

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Jul 9, 2007, 3:47:21 AM7/9/07
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On Jul 8, 7:43 pm, AES <sieg...@stanford.edu> wrote:
> In article <1183947312.166175.51...@g4g2000hsf.googlegroups.com>,

Please check see if I am correct:

1-At the output face of the fiber all N individual modes add up and
form a Complex Amplitude (amplitude + its phase)
across the face.
2-We then divide this complex amplitude distribution into N areas
(patches).
3-Each patch is considered as a single plane wave with its amplitude
and phase as obtained in (1) above.
4-Each patch radiates into a cone (which is telecentric with the
fiber) with the same NA as given in the fiber
specifications.
5- Knowing the area of the fiber core we know how large ( the area
of ) each patch is.


Questions:

a- If as in (3) each patch is a single plane wave how that telecentric
cone into which it radiates comes about?
I thought this cone is the due to the plane waves of the
individual modes that pass through the patch, the plane
waves come at different angles lying within this cone.

b- Even though the patches have random phases, don't they cause
interference at the image plane (the number
of patches are finite).

c- Is there a reference (books, etc.) that goes through all these in
the same line of explanation as yours?


thank you again


AES

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Jul 9, 2007, 11:25:39 AM7/9/07
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In article <1183967241.0...@j4g2000prf.googlegroups.com>,
Farsang <youzp...@netscape.net> wrote:

The description I've given is an essentially statistical one, that
assumes you have a very large number of modes (so many that you can't
possible actually keep track of the exact amplitudes of all of them),
and sufficient randomness in the parameters of the system that the
energy in the beam gets more or less randomly distributed among them
(random scattering the central limit theorem at work). So, you just
assume all mode amplitudes (and patch amplitudes) are random numbers,
with mean square values equal to the fractional power per mode (which is
also the fractional power per match). Interference effects are then
irrelevant -- they average out, you just add powers.

For fiber physics (number of modes, etc), Saleh and Teich, "Photonics".
For statistical aspects, I don't know -- that's something one learns
from repeated encounters with noise and statistics; maybe Mandel and
Wolf, "Optical Coherence and Quantum Optics", except that's a massive
tome. For how an input wave into a fiber gets spatially randomized over
distance, the fiber optics literature; I don't know of a specific
reference, I just know it happens.

philip.m...@gmail.com

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Jul 9, 2007, 6:57:00 PM7/9/07
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I believe that in most cases, assuming that some finite point within a
multimode fiber will emit with equal intensity and at a cone whose NA
matches the fiber is perfectly valid for determining light path and
size. I would set the NA of the system at 0.22, since this is likely
a laser source, apodization as Gaussian and a value of 1.0. This
should give you a source with the NA and intensity profile. Recall
the limitations of sequential raytracing though, you will be modelling
where they rays of light from this source go, and not their
interference with one-another.

-philip m.

Himansu Pattanaik

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Nov 16, 2021, 4:23:41 PM11/16/21
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Hi Wade,
I am working on something similar. I can do the geometric image analysis with CIRCLE.IMA. But what you described will give me the beam profile at the image plane for one field. If I have to get superposition of all the field points so that I can have the geometric image of the fiber core at the image plane, what do I have to do in Zemax?

Thanks
Himansu
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