# C through fiber optics

1. Apr 9, 2004

### Glenn

Is C less than 300,000 kph when traveling through fiber optic cable?

Would a pulse of light travel any faster through a straight fiber optic than through a tightly coiled fiber of the same length?

Thanks,
Glenn

2. Apr 9, 2004

### Chen

c is constant throughout the universe. The speed of light does change, depending on the medium through which the light travels. The general formula is:
$$V = \frac{c}{n}$$
That is, the speed of light through any medium is the speed of light in vacuum (c) divided by the refraction index of the medium (n).

Yes, light would travel faster through a straight fiber optic than it would in a bent one. If the fiber is bent, light will refract as it hits the sides of the fiber, therefore it will take more time to travel the same horizontal distance:
https://www.physicsforums.com/attachment.php?attachmentid=813
The red line represents a ray of light that does not refract, whereas the blue line is a ray of light that does refract off the sides of the fiber.

(Nice avatar, by the way.)

3. Apr 9, 2004

### da_willem

c, the velocity of light in vacuum, is a constant of nature. So it does not depend on the medium you are looking at. What you probably mean is: does light move with a speed lower than c in a fiber optic cable?

The answer is a bit ambiguous: although the photons making up the ligh rays still (always!) move with c, the so called phase velocity of light in a different medium than vacuum can differ from c.

This is because of the repetative process of scattering with he atoms making up the material, which introduces a phase shift in the scattered light. When this scattered light recombines with the transmitted light it interferes and shifts the phase of the combined wave. This happens continuously, and because the speed of the wave is the rate of advance of the condition of constant phase, a change in the phase should correspond to a change in the speed. For a fiber optic cable this speed is slightly below c.

The proces described above can in some circumstances even yield a phase speed higher than c. This does not contradict special relativity because the speed at which information is transported depends on the speed of the photons, wich is still c.

4. Apr 9, 2004

### Glenn

Thanks for the help!

-Glenn

5. Apr 9, 2004

### Staff: Mentor

Fiber optics works on total internal reflection - so it shouldn't matter if the cable is coiled.

6. Apr 9, 2004

### Chen

Yes, and? Do you not agree with what I said?

7. Apr 9, 2004

### Integral

Staff Emeritus
I am with Russ on this one. I do not think propagation time in a fiber optic depends on the bends in the cable. Most fiber optics have a minimum allowed radius of curvature, you cannot coil them into an arbitrarily small radius and maintain the signal. It would not surprise me if the coiled fiber had higher losses then the straight one, but I do not think it would change the propagation time,Signifinatly.... (gotta throw that qualifier in there!)

8. Apr 9, 2004

### Chen

Well now, there's a large difference between changing the time and changing it "significantly". I still believe the propagation time would change. In a straight fiber, light is free to take the shortest possible path - a straight line, which would have the same length as the length of the fiber. However, with a bent fiber of the same length, this is not possible. For the light to go through the fiber while traversing a distance of L, it would have to go directly through the center (of the cross section) of the fiber, and do so throughout the whole journey. Obviously this cannot happen, as the light is bound to hit the boundaries of the fiber and reflect. By doing so it is no longer going through the center and the distance it has to pass grows. I think the difference in the propagation times would depend on the radius of the fiber, among other factors. The thinner the fiber, the less noticeable the difference would be.

(I agree, by the way, that the difference would not be that significant, but I still believe there is a difference, small as it may be.)

Last edited: Apr 9, 2004
9. Apr 9, 2004

### turin

I'm pretty sure that you don't measure the speed of a light pulse based on the very first photon that you register at the end. Since the aggregate pulse travels down the fiber by total internal reflection, then the aggregate will always be slower than the front runner. In a bent fiber, the bending actually decreases the pulse spead. I wish I still worked in a fiber lab. Does anyone have access to some equipment and a good length of fiber and is willing to try the experiment?

10. Apr 9, 2004

### Njorl

If you introduce loss, you are changing the imaginary part of the effective index, and usually, this means you are changing the real part as well. However, I believe it depends on several factors whether the real part will increase or decrease. It is possible that the speed will increase.

Njorl

11. Apr 10, 2004

### Nacho

Then why would long distance cables require repeaters/amplifiers for attenuation?

12. Apr 10, 2004

### Staff: Mentor

Total internal reflection means no absorption loss during the reflection - but has nothing to do with absorption loss during transmission. Any medium will absorb a little while transmitting - no medium is perfectly transparent.

Chen, its a minor quibble: the light does go more or less straight down the cable, but obviously no cable is going to be perfectly straight, so there will be a lot of bouncing off the walls, especially since the cable is pretty thin. Yeah, the word "significant" is vague, so how about this: the diameter of the cable is so thin compared to the minimum radius at which you can bend the cable that any change in transmission time will be negligible.

HERE is a good explanation of both the total internal reflection and the absorption loss in fiber optics.

Last edited: Apr 10, 2004
13. Apr 10, 2004

### Chen

Negligible it is then. Extant, but negligible.

14. Apr 10, 2004

### swansont

But because the fiber already depends on total internal reflection, the path length is greater than the linear distance of the cable - the light doesn't go straight through.

15. Apr 11, 2004

### Chen

But if the fiber was originally straight there would be the possibility that the light would go straight through. That's the point.

16. Apr 10, 2006

### Aries-in-physics

I have recently performed this experiment several times. I have found out that if it is coiled, there is a fast speed of light, then if it propagates through a straight fiber optic cable. Further experiments are underway as I am typing this to see if its a function of intesity, radius, number of coils etc. But as i see it now, with 101 number of coils, a 20.036 meter long cable, a radius of .5 meters, the speed of light is .1 times more through the coiled cable. We think its due to the internale stresses of the cable, one end being in compression and the other in tension, and due to the reflection through the cable, there might be more tension then compression per unit delta length.