Fourier Series question

Hi All,

I have a fundamental confusion. This relates to Fourier series.

Suppose I take a dirac pulse. It will have all the frequencies of the
world in equal magnitude.
Now suppose I pass it through an optical fibre. Assume that fibre
allows all frequency to pass through it. In fibre the velocity of each
sinusodial component of dirac will be different. This means each
component reaches the fibre output at diferent time. This is pulse
broadening.

Can we "intutively" predict what will be shape of the pulse at the
fibre output ? notice, I want the shape, not the fact it will be broad
(which I know it will be).

regs
ashu

On 24 Jun, 12:25, ashu <ashutosh.ghildi...@gmail.com> wrote:
> Hi All,
>
> I have a fundamental confusion. This relates to Fourier series.
>
> Suppose I take a dirac pulse. It will have all the frequencies of the
> world in equal magnitude.
> Now suppose I pass it through an optical fibre. Assume that fibre
> allows all frequency to pass through it. In fibre the velocity of each
> sinusodial component of dirac will be different. This means each
> component reaches the fibre output at diferent time. This is pulse
> broadening.
>
> Can we "intutively" predict what will be shape of the pulse at the
> fibre output ? notice, I want the shape, not the fact it will be broad
> (which I know it will be).

You are talking about the impulse response of the fibre.

I don't know if it qualifies as 'intuitive', but you can
predict how it will look if you know the physical dimensions
of the fibre, the material composition, the optical properties
of the materials, and the governing differential equations.

Rune

On Wed, 24 Jun 2009 03:25:27 -0700, ashu wrote:

> Hi All,
> 
> I have a fundamental confusion. This relates to Fourier series.
> 
> Suppose I take a dirac pulse. It will have all the frequencies of the
> world in equal magnitude.
> Now suppose I pass it through an optical fibre. Assume that fibre allows
> all frequency to pass through it. In fibre the velocity of each
> sinusodial component of dirac will be different. This means each
> component reaches the fibre output at diferent time. This is pulse
> broadening.
> 
> Can we "intutively" predict what will be shape of the pulse at the fibre
> output ? notice, I want the shape, not the fact it will be broad (which
> I know it will be).
> 
> regs
> ashu

Blue, then green, then yellow, then orange, then red, then IR (if I have 
my spectrum right).

Etc.

-- 
www.wescottdesign.com

ashu wrote:
> Hi All,
>
> I have a fundamental confusion. This relates to Fourier series.
>
> Suppose I take a dirac pulse. It will have all the frequencies of the
> world in equal magnitude.
> Now suppose I pass it through an optical fibre. Assume that fibre
> allows all frequency to pass through it. In fibre the velocity of each
> sinusodial component of dirac will be different. This means each
> component reaches the fibre output at diferent time. This is pulse
> broadening.
>
> Can we "intutively" predict what will be shape of the pulse at the
> fibre output ? notice, I want the shape, not the fact it will be broad
> (which I know it will be).
>
> regs
> ashu

"Intuitively" it will be flat as long as the dispersion is flat.  If the 
dispersion isn't flat but is some other function of frequency then the pulse 
will be bunched up where the delays are smaller and smaller where the delays 
are larger.

Fred 

Tim Wescott wrote:
> On Wed, 24 Jun 2009 03:25:27 -0700, ashu wrote:
> 
>> Hi All,
>>
>> I have a fundamental confusion. This relates to Fourier series.
>>
>> Suppose I take a dirac pulse. It will have all the frequencies of the
>> world in equal magnitude.
>> Now suppose I pass it through an optical fibre. Assume that fibre allows
>> all frequency to pass through it. In fibre the velocity of each
>> sinusodial component of dirac will be different. This means each
>> component reaches the fibre output at diferent time. This is pulse
>> broadening.
>>
>> Can we "intutively" predict what will be shape of the pulse at the fibre
>> output ? notice, I want the shape, not the fact it will be broad (which
>> I know it will be).
>>
>> regs
>> ashu
> 
> Blue, then green, then yellow, then orange, then red, then IR (if I have 
> my spectrum right).

That depends on the medium. Anomalous dispersion is likely somewhere.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Hey Ashu,

> >> Can we "intutively" predict what will be shape of the pulse at the fibre
> >> output ? notice, I want the shape, not the fact it will be broad (which
> >> I know it will be).

There's a lot of research out there on this topic...
http://www.google.com/search?client=safari&rls=en&q=impulse+response+optical+fibres&ie=UTF-8&oe=UTF-8

Ken

On Wed, 24 Jun 2009 21:46:22 -0400, Jerry Avins wrote:

> Tim Wescott wrote:
>> On Wed, 24 Jun 2009 03:25:27 -0700, ashu wrote:
>> 
>>> Hi All,
>>>
>>> I have a fundamental confusion. This relates to Fourier series.
>>>
>>> Suppose I take a dirac pulse. It will have all the frequencies of the
>>> world in equal magnitude.
>>> Now suppose I pass it through an optical fibre. Assume that fibre
>>> allows all frequency to pass through it. In fibre the velocity of each
>>> sinusodial component of dirac will be different. This means each
>>> component reaches the fibre output at diferent time. This is pulse
>>> broadening.
>>>
>>> Can we "intutively" predict what will be shape of the pulse at the
>>> fibre output ? notice, I want the shape, not the fact it will be broad
>>> (which I know it will be).
>>>
>>> regs
>>> ashu
>> 
>> Blue, then green, then yellow, then orange, then red, then IR (if I
>> have my spectrum right).
> 
> That depends on the medium. Anomalous dispersion is likely somewhere.

Optical fiber has dispersion, and I'm 99.44% sure that longer wavelengths 
go slower (and there's multiple modes, of course).

-- 
www.wescottdesign.com

Tim Wescott wrote:
> On Wed, 24 Jun 2009 21:46:22 -0400, Jerry Avins wrote:
> 
>> Tim Wescott wrote:
>>> On Wed, 24 Jun 2009 03:25:27 -0700, ashu wrote:
>>>
>>>> Hi All,
>>>>
>>>> I have a fundamental confusion. This relates to Fourier series.
>>>>
>>>> Suppose I take a dirac pulse. It will have all the frequencies of the
>>>> world in equal magnitude.
>>>> Now suppose I pass it through an optical fibre. Assume that fibre
>>>> allows all frequency to pass through it. In fibre the velocity of each
>>>> sinusodial component of dirac will be different. This means each
>>>> component reaches the fibre output at diferent time. This is pulse
>>>> broadening.
>>>>
>>>> Can we "intutively" predict what will be shape of the pulse at the
>>>> fibre output ? notice, I want the shape, not the fact it will be broad
>>>> (which I know it will be).
>>>>
>>>> regs
>>>> ashu
>>> Blue, then green, then yellow, then orange, then red, then IR (if I
>>> have my spectrum right).
>> That depends on the medium. Anomalous dispersion is likely somewhere.
> 
> Optical fiber has dispersion, and I'm 99.44% sure that longer wavelengths 
> go slower (and there's multiple modes, of course).

Most of tht spectrum, yes. but anomalous dispersion dies exist in fibers 
and is sometimes exploited. See, for example, 
http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-9-13-681

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On 25 Jun, 17:43, Tim Wescott <t...@seemywebsite.com> wrote:
> On Wed, 24 Jun 2009 21:46:22 -0400, Jerry Avins wrote:

> > That depends on the medium. Anomalous dispersion is likely somewhere.
>
> Optical fiber has dispersion, and I'm 99.44% sure that longer wavelengths
> go slower (and there's multiple modes, of course).

Well, that's a topic that can be debated till the cows
come home.

First of all, the term 'velocity' becomes diffuse in
dispersive media: The group velocity is slower than
the free-field speed in the medium; the phase velocity
is faster. Johan Leander wrote a piece about this in
'95 or '96, in the Journal of the Acoustical Society
of America. He found that in certain types of media,
some of the 'familiar' velocity concepts become very
weird.

Second, depending on the point of view, the dispersion
can be viewed as an interference pattern of waves criss-
crossing the interior of the waveguide (which explains
intuitively what disperion is and why energy travels
slower through a waveguide), or as a property of the
steady-state solution to a wave propagation problem with
geometric scales similar to the free-field wavelength.

And no, this is not mere semantics. I've done stuff in
the past that no one else had done before me, because
I very carefully selected what terminology and POV to
base the analysis of a waveguide system on. Everybody
who had attempted the same before me, had chosen the
'physical' (= intuitive) interpretation of the system
representations.

Rune

On Jun 25, 12:07&#4294967295;pm, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 25 Jun, 17:43, Tim Wescott <t...@seemywebsite.com> wrote:
>
> > On Wed, 24 Jun 2009 21:46:22 -0400, Jerry Avins wrote:
> > > That depends on the medium. Anomalous dispersion is likely somewhere.
>
> > Optical fiber has dispersion, and I'm 99.44% sure that longer wavelengths
> > go slower (and there's multiple modes, of course).
>
> Well, that's a topic that can be debated till the cows
> come home.
>
> First of all, the term 'velocity' becomes diffuse in
> dispersive media: The group velocity is slower than
> the free-field speed in the medium; the phase velocity
> is faster. Johan Leander wrote a piece about this in
> '95 or '96, in the Journal of the Acoustical Society
> of America. He found that in certain types of media,
> some of the 'familiar' velocity concepts become very
> weird.
>
> Second, depending on the point of view, the dispersion
> can be viewed as an interference pattern of waves criss-
> crossing the interior of the waveguide (which explains
> intuitively what disperion is and why energy travels
> slower through a waveguide), or as a property of the
> steady-state solution to a wave propagation problem with
> geometric scales similar to the free-field wavelength.
>
> And no, this is not mere semantics. I've done stuff in
> the past that no one else had done before me, because
> I very carefully selected what terminology and POV to
> base the analysis of a waveguide system on. Everybody
> who had attempted the same before me, had chosen the
> 'physical' (= intuitive) interpretation of the system
> representations.
>
> Rune

Actually quite a bit of fiber optic communications is done in the 1300
to 1550 nm wavelength (to use existing IR laser repeater technology)
range. Also by using "loud" pulses on the erbium doped (allows
transparency in the infared) fibers and with existing laser fiber
repeaters, the anomalgous dispersion is actually counted on to keep
the pulses focused in time. Yes these are solitons and they have some
really cool properties. For example the speed of a soliton is
dependant on its total energy. You can launch a high energy soliton
after a low energy one so that the latter actually catches up with a
passes through the low energy pulse. I recall 10 years ago where the
state of the art was for simple on-off signalling with dispersion
maxed out in the 2-4 GBS range, but solitons over existing fiber
networks were achieving over 10 times that! The amount of existing
ocean floor fiber optic cable is tremendous. So there has been a great
deal of work with improving the capacity of existing infrastructure.

Clay