hi i am a computer science student writing a computer program to
calculate the radar cross section using ray tracing. I'm simulating
the plane waves by using a set of parallel rays and i need to
calculate electric field. According to the thesis that i am following,
the electric field along a ray is given as:
E(s) = E(0) * exp(-jks)
where E(0) is the electric field at a reference point, k is wave
number(2 * pi / wavelength and s is the distance travelled in the
dierction of propogation. It says exp(-jks) represents the phase
change along the ray.
I have a few questions with regards to above as my thesis does not
expand on them:
1. What in your opinion are E(s) and E(0) ? Shouldn't be they 3d
vectors. But it seems multplying E(0) with exp(-jks) will result in a
complex vector i.e. a vector whose components are complex number and i
am not sure what is the physical significance behind this. I mean why
introduce a complex phase notation ? How do I specify E(0) ? can I
simply specify a magnitude(v/m) and the direction ?
2. The ray undergoes specular reflection when it hits a body. The
formula given in my thesis is:
E(s) = R * Eincident(Qr) * ( 1/s )* exp(-jks)
where E(s) is the reflected field at distance s, Qr is point of
reflection Eincident(qr) is the incident electric field at Qr , 1/s
represents the attenuation, exp(-jks) is phase variation. R is the
reflection matrix given as:
[ - 1 0]
[ 0 1]
according to my thesis, this means the tangential component(the one
will be affected with the coefficient -1 and the parallel component
with 1. I read somewhere that the electric field can be broken up into
3 components, one is along the ray and its zero but seems like this is
different from the global x, y, z system. more like a ray based
coordinate system ?
Ian Parker
Jun18-08, 05:00 AM
On 15 Jun, 20:01, pereges <Brol...@gmail.com> wrote:
> hi i am a computer science student writing a computer program to
> calculate the radar cross section using ray tracing. I'm simulating
> the plane waves by using a set of parallel rays and i need to
> calculate electric field. According to the thesis that i am following,
> the electric field along a ray is given as:
>
> E(s) = E(0) * exp(-jks)
>
> where E(0) is the electric field at a reference point, k is wave
> number(2 * pi / wavelength and s is the distance travelled in the
> dierction of propogation. It says exp(-jks) represents the phase
> change along the ray.
>
> I have a few questions with regards to above as my thesis does not
> expand on them:
>
> 1. What in your opinion are E(s) and E(0) ? Shouldn't be they 3d
> vectors. But it seems multplying E(0) with exp(-jks) will result in a
> complex vector i.e. a vector whose components are complex number and i
> am not sure what is the physical significance behind this. I mean why
> introduce a complex phase notation ? How do I specify E(0) ? can I
> simply specify a magnitude(v/m) and the direction ?
>
> 2. The ray undergoes specular reflection when it hits a body. The
> formula given in my thesis is:
>
> E(s) = R * Eincident(Qr) * ( 1/s )* =A0exp(-jks)
>
> where E(s) is the reflected field at distance s, Qr is point of
> reflection Eincident(qr) is the incident electric field at Qr , 1/s
> represents the attenuation, exp(-jks) is phase variation. R is the
> reflection matrix given as:
> [ - 1 0]
> [ =A0 0 =A01]
>
> according to my thesis, this =A0means the tangential component(the one
> will be affected with the coefficient -1 and the parallel component
> with 1. I read somewhere that the electric field can be broken up into
> 3 components, one is along the ray and its zero but seems like this is
> different from the global x, y, z system. more like a ray based
> coordinate system ?
I think part of the source of your confusion may be due to the fact
that an EM wave has got two planes of polarization. exp(-jks) is
perfectly correct but it describes only a wave with no polarization.
You mention reflection. I think it might be useful if you looked up
"Brewster Angle" in Google. This tells you about reflection from a
dielectric. This is different for the different planes of
polarization. You will also get an explanation of how reflection and
refraction take place. You have to add up the incident, reflected and
refracted ray. References will tell you how to do this.
You need to treat the two planes of polarization separately.
- Ian Parker
pereges
Jun21-08, 05:00 AM
On Jun 18, 11:41 am, Ian Parker <ianpark...@gmail.com> wrote:
> On 15 Jun, 20:01, pereges <Brol...@gmail.com> wrote:
>
>
>
> > hi i am a computer science student writing a computer program to
> > calculate the radar cross section using ray tracing. I'm simulating
> > the plane waves by using a set of parallel rays and i need to
> > calculate electric field. According to the thesis that i am following,
> > the electric field along a ray is given as:
>
> > E(s) = E(0) * exp(-jks)
>
> > where E(0) is the electric field at a reference point, k is wave
> > number(2 * pi / wavelength and s is the distance travelled in the
> > dierction of propogation. It says exp(-jks) represents the phase
> > change along the ray.
>
> > I have a few questions with regards to above as my thesis does not
> > expand on them:
>
> > 1. What in your opinion are E(s) and E(0) ? Shouldn't be they 3d
> > vectors. But it seems multplying E(0) with exp(-jks) will result in a
> > complex vector i.e. a vector whose components are complex number and i
> > am not sure what is the physical significance behind this. I mean why
> > introduce a complex phase notation ? How do I specify E(0) ? can I
> > simply specify a magnitude(v/m) and the direction ?
>
> > 2. The ray undergoes specular reflection when it hits a body. The
> > formula given in my thesis is:
>
> > E(s) = R * Eincident(Qr) * ( 1/s )* exp(-jks)
>
> > where E(s) is the reflected field at distance s, Qr is point of
> > reflection Eincident(qr) is the incident electric field at Qr , 1/s
> > represents the attenuation, exp(-jks) is phase variation. R is the
> > reflection matrix given as:
> > [ - 1 0]
> > [ 0 1]
>
> > according to my thesis, this means the tangential component(the one
> > will be affected with the coefficient -1 and the parallel component
> > with 1. I read somewhere that the electric field can be broken up into
> > 3 components, one is along the ray and its zero but seems like this is
> > different from the global x, y, z system. more like a ray based
> > coordinate system ?
>
> I think part of the source of your confusion may be due to the fact
> that an EM wave has got two planes of polarization. exp(-jks) is
> perfectly correct but it describes only a wave with no polarization.
> You mention reflection. I think it might be useful if you looked up
> "Brewster Angle" in Google. This tells you about reflection from a
> dielectric. This is different for the different planes of
> polarization. You will also get an explanation of how reflection and
> refraction take place. You have to add up the incident, reflected and
> refracted ray. References will tell you how to do this.
>
> You need to treat the two planes of polarization separately.
Hi, by two planes of polarizations are you talking about the
transverse electric and magnetic polarisation ? Let's consider only
one ray. Using (theta, phi) notation where theta is the azimuth and
phi is zenith, we can define the unit direction vector of the ray
(towards the origin) as:
if you take thetahat X phihat it gives the direction of the ray. that,
phihat and direction of ray are all mutually perpendicular. So while
writing my program, I thought of considering the thetahat as direction
of electric field vector and phihat as the direction of the magnetic
field vector. Is this what you call polarization ? I really don't know
what it means. I tried looking up on wikipeda but the explanation is
very verbose and not to the point or lucid.
Btw, I have had many people tell me that I should take only the real
part of E0 * exp(-jks) which is as good as E0*cos(ks)
..Then I ask what is point in such complex notation ?
also, in my program, there is only specular reflection when ray hits
the surface and refraction must not be taken into account.
p.kinsler@ic.ac.uk
Jun21-08, 05:00 AM
pereges <Broli00@gmail.com> wrote:
> hi i am a computer science student writing a computer program to
> calculate the radar cross section using ray tracing. I'm simulating
> the plane waves by using a set of parallel rays and i need to
> calculate electric field. According to the thesis that i am following,
> the electric field along a ray is given as:
> E(s) = E(0) * exp(-jks)
> where E(0) is the electric field at a reference point, k is wave
> number(2 * pi / wavelength and s is the distance travelled in the
> dierction of propogation. It says exp(-jks) represents the phase
> change along the ray.
> E(s) = E(0) * exp(-jks)
> [...] a vector whose components are complex number and i
> am not sure what is the physical significance behind this.
... admittedly, many authors neglect this point, and indeed
in many problems it makes little difference (as long as you
remember to take the real part of your complex E at the end).
It's worth thinking about when it matters though -- e.g.
what about nonlinear processes?
--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (PHOT) (ph) +44-20-759-47734 (fax) 47714
Imperial College London, Dr.Paul.Kinsler@physics.org
SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/
John C. Polasek
Jun21-08, 05:00 AM
On Wed, 18 Jun 2008 06:41:49 +0000 (UTC), Ian Parker
<ianparker2@gmail.com> wrote:
>On 15 Jun, 20:01, pereges <Brol...@gmail.com> wrote:
>> hi i am a computer science student writing a computer program to
>> calculate the radar cross section using ray tracing. I'm simulating
>> the plane waves by using a set of parallel rays and i need to
>> calculate electric field. According to the thesis that i am following,
>> the electric field along a ray is given as:
>>
>> E(s) = E(0) * exp(-jks)
>>
>> where E(0) is the electric field at a reference point, k is wave
>> number(2 * pi / wavelength and s is the distance travelled in the
>> dierction of propogation. It says exp(-jks) represents the phase
>> change along the ray.
This is a representation of a sine wave with amplitude E0.
de Moivre's theorem IIRC has
exp(-jks) = cos(ks) + jsin(ks)
ks here is the number of cycles: k cy/m x s meters.
Think of the two projections on x and jy of phasor of length E(0)
rotating through the angle ks, screwing itself through space with a
pitch of 1/k.
The angle should be in radians for sin, cos.
>> I have a few questions with regards to above as my thesis does not
>> expand on them:
>>
>> 1. What in your opinion are E(s) and E(0) ? Shouldn't be they 3d
>> vectors. But it seems multplying E(0) with exp(-jks) will result in a
>> complex vector i.e. a vector whose components are complex number and i
>> am not sure what is the physical significance behind this. I mean why
>> introduce a complex phase notation ? How do I specify E(0) ? can I
>> simply specify a magnitude(v/m) and the direction ?
>>
>> 2. The ray undergoes specular reflection when it hits a body. The
>> formula given in my thesis is:
>>
>> E(s) = R * Eincident(Qr) * ( 1/s )* =A0exp(-jks)
>>
>> where E(s) is the reflected field at distance s, Qr is point of
>> reflection Eincident(qr) is the incident electric field at Qr , 1/s
>> represents the attenuation, exp(-jks) is phase variation. R is the
>> reflection matrix given as:
>> [ - 1 0]
>> [ =A0 0 =A01]
>>
>> according to my thesis, this =A0means the tangential component(the one
>> will be affected with the coefficient -1 and the parallel component
>> with 1. I read somewhere that the electric field can be broken up into
>> 3 components, one is along the ray and its zero but seems like this is
>> different from the global x, y, z system. more like a ray based
>> coordinate system ?
>
>I think part of the source of your confusion may be due to the fact
>that an EM wave has got two planes of polarization. exp(-jks) is
>perfectly correct but it describes only a wave with no polarization.
>You mention reflection. I think it might be useful if you looked up
>"Brewster Angle" in Google. This tells you about reflection from a
>dielectric. This is different for the different planes of
>polarization. You will also get an explanation of how reflection and
>refraction take place. You have to add up the incident, reflected and
>refracted ray. References will tell you how to do this.
>
>You need to treat the two planes of polarization separately.
>
> - Ian Parker
Ian Parker
Jun24-08, 05:00 AM
On 21 Jun, 10:59, pereges <Brol...@gmail.com> wrote:
> On Jun 18, 11:41 am, Ian Parker <ianpark...@gmail.com> wrote:
>
>
>
>
>
> > On 15 Jun, 20:01, pereges <Brol...@gmail.com> wrote:
>
> > > hi i am a computer science student writing a computer program to
> > > calculate the radar cross section using ray tracing. I'm simulating
> > > the plane waves by using a set of parallel rays and i need to
> > > calculate electric field. According to the thesis that i am following,
> > > the electric field along a ray is given as:
>
> > > E(s) = E(0) * exp(-jks)
>
> > > where E(0) is the electric field at a reference point, k is wave
> > > number(2 * pi / wavelength and s is the distance travelled in the
> > > dierction of propogation. It says exp(-jks) represents the phase
> > > change along the ray.
>
> > > I have a few questions with regards to above as my thesis does not
> > > expand on them:
>
> > > 1. What in your opinion are E(s) and E(0) ? Shouldn't be they 3d
> > > vectors. But it seems multplying E(0) with exp(-jks) will result in a
> > > complex vector i.e. a vector whose components are complex number and i
> > > am not sure what is the physical significance behind this. I mean why
> > > introduce a complex phase notation ? How do I specify E(0) ? can I
> > > simply specify a magnitude(v/m) and the direction ?
>
> > > 2. The ray undergoes specular reflection when it hits a body. The
> > > formula given in my thesis is:
>
> > > E(s) = R * Eincident(Qr) * ( 1/s )* exp(-jks)
>
> > > where E(s) is the reflected field at distance s, Qr is point of
> > > reflection Eincident(qr) is the incident electric field at Qr , 1/s
> > > represents the attenuation, exp(-jks) is phase variation. R is the
> > > reflection matrix given as:
> > > [ - 1 0]
> > > [ =9A0 1]
>
> > > according to my thesis, this means the tangential component(the one
> > > will be affected with the coefficient -1 and the parallel component
> > > with 1. I read somewhere that the electric field can be broken up into
> > > 3 components, one is along the ray and its zero but seems like this is
> > > different from the global x, y, z system. more like a ray based
> > > coordinate system ?
>
> > I think part of the source of your confusion may be due to the fact
> > that an EM wave has got two planes of polarization. exp(-jks) is
> > perfectly correct but it describes only a wave with no polarization.
> > You mention reflection. I think it might be useful if you looked up
> > "Brewster Angle" in Google. This tells you about reflection from a
> > dielectric. This is different for the different planes of
> > polarization. You will also get an explanation of how reflection and
> > refraction take place. You have to add up the incident, reflected and
> > refracted ray. References will tell you how to do this.
>
> > You need to treat the two planes of polarization separately.
>
> Hi, by two planes of polarizations are you talking about the
> transverse electric and magnetic polarisation ? Let's consider only
> one ray. Using (theta, phi) notation where theta is the azimuth and
> phi is zenith, we can define the unit direction vector of the ray
> (towards the origin) as:
>
> ( =9A-cos(theta) * sin(phi) , sin(theta) * sin(phi) , cos(phi) )
>
> thetahat(unit vector) is given as:
>
> (-sin(theta) , cos(theta) , 0)
>
> phihat(unit vector) is given as:
>
> (cos(theta) * cos(phi) , sin(theta) * cos(phi), -sin(phi) )
>
> if you take thetahat X phihat it gives the direction of the ray. that,
> phihat and direction of ray are all mutually perpendicular. So while
> writing my program, I thought of considering the thetahat as direction
> of electric field vector and phihat as the direction of the magnetic
> field vector. Is this what you call polarization ? I really don't know
> what it means. I tried looking up on wikipeda but the explanation is
> very verbose and not to the point or lucid.
>
> Btw, I have had many people tell me that I should take only the real
> part of E0 * exp(-jks) which is as good as E0*cos(ks)
> .Then I ask what is point in such complex notation ?
>
> also, in my program, there is only specular reflection when ray hits
> the surface and refraction must not be taken into account.- Hide quoted text -
>
In an EM wave travelling forwards the electric field, the magnetic
field and the direction of propagation are all mutually at right
angles. We can take an arbitary direction and say the one plane of
polatization has its electric field in this direction, another has its
electric field at right algles. If an electric field is at an angle
theta we cabn resolve into the two planes.
Meaning of a complex number :- EM radiation has a time variation of
exp(jwt) The electric field is Sin(wt) the magnetic Cos(wt). Cos^2 +
Sin^2 = 1 so the wave does have an energy. Complex numbers are the
basis of Physical Optics. To get the light intensity at any point we
need to sum COMPLEX numbers.
To take a simple example, if we have a disc and the light intensity (+
phase) of exp(jk=96(y^2+r^2) it is clear from Pythagoras that at a point
distance y at right angles to the disc we will get all the phase from
the disc summed. This is the "Physical" as opposed to the
"Geometrical" approach to optics.
This is an important point. I was looking at NASA's ideas for Space
Solar Power. Theyy talk about superconducting transmission of
electrical power to a central point. They seem to have completely
missed that with phase control they can generate light/microwaves
where the solar power is gathered. So this is very important.