Laser light vs "Regular" Light

[fog37]

Hello,
Light, laser or not, is fundamentally electromagnetic radiation with visible wavelengths. Laser light has both high spatial coherence and temporal coherence (highly monochromatic) while regular light has both very low spatial and temporal coherence. Spatial coherence is not about spectral purity but more about high correlation between different spatial points in the electromagnetic field...

Given a very high power non-laser light source (many many Watts, I am sure it exists), it is possible to make it more monochromatic by using a filter. The drawback is reducing its power.

Would it be possible,using a lens, that monochromatic, to focus and converge that monochromatic non-laser light to a small spot? Or is spatial coherence also required to produce a highly focus, high intensity ($W/m^2$) beam?

Thank you!

 

[tech99]

A concave lens can form a nearly parallel beam from a point source, or can form a point source from a parallel beam. But the limitation is how small can we create a "point source" in the first place. I suppose a point carbon arc is a good contender. Until the Laser was invented, it was not possible to obtain such parallel beams.

 

[fog37]

I see...laser cutters use lasers...is it because it would be impossible to focus any other type of light source to such a small region of space with such power?

 

[Nugatory]

Moved to Classical Physics: Lasers are quantum mechanical, but this thread seems to about trying to produce coherent light through classical interactions

 

[Nugatory]

Given a very high power non-laser light source (many many Watts, I am sure it exists), it is possible to make it more monochromatic by using a filter. The drawback is reducing its power.

Filtering will remove unwanted frequencies to make the light more monochromatic, but it won’t do anything for the phase, so we still don’t get coherent light.

A filter also reduces power as you say, but the lost energy doesn’t just disappear - it is absorbed by and heats the filter. We can’t have both a very high output and a very selective filter because we’ll vaporize our filter.

 

[fog37]

I see, so making a field more monochromatic (large center frequency and small frequency bandwidth) does not necessarily make the field temporally coherent.

To be coherent, the center frequency $\omega_{center}$ and the neighboring frequencies comprised in the bandwidth $\Delta_omega$ must keep a constant phase relationship in time. What does that really mean?
For example, consider adding (superposition) just two pure sinusoidal signals (unit amplitude) of frequencies $\omega_1$ and $\omega_2$ and constant phase terms $\theta_1$ and $\theta_2$
$$cos(\omega_1 t +\theta_1) + cos(\omega_2 t +\theta_2)$$
If we add the two sinusoids together, the resulting signal is not a pure sinusoidal signal with a single frequency and constant phase, correct?

So what does it mean when we say that two (or multiple) sinusoids of different frequency keep a constant phase relation? What we get is an oscillating signal with varying amplitude (like an envelope) and non constant phase (in the sense that the distance between the crests may vary)...

 

[Ibix]

To be coherent, the center frequency $\omega_{center}$ and the neighboring frequencies comprised in the bandwidth $\Delta_omega$ must keep a constant phase relationship in time. What does that really mean?

A useful, if slightly cartoonish, analogy is a group of people walking in the same direction. Polychromatic light is like normal people walking - all with different stride lengths and no coordination. Monochromatic light is like picking a particular stride length and removing everybody who doesn't have that stride length - but the walkers won't be synchronised. One person might be putting their left foot down while the person next to them has their right foot in the air. Finally, coherent light is like an army marching - same stride length and all left heels hitting the ground together.

In the incoherent monochromatic case, if you know the phase of a person (where in their step cycle they are) you cannot predict anything about the person next to them. With the coherent case, you know everything about the person next to them, and the person next to them, and...

We don't have electronics fast enough to directly measure the phase of vibrations as rapid as light. If we did, we could put two probes in opposite edges of a laser beam and record the electric field, and the outputs would be identical. But in the incoherent monochromatic case, the output waves would have the same frequency but random phase offsets. And if you move the probe around you will get different phase offsets.

 

[fog37]

In the incoherent monochromatic case, if you know the phase of a person (where in their step cycle they are) you cannot predict anything about the person next to them. With the coherent case, you know everything about the person next to them, and the person next to them, and...

Thank you! I have been thinking deeply about this. Let me share my view point.

Coherence is synonym of correlation which is measured by the function $<E(t) E(t+\tau)>$, to measure the temporal coherence at the same point in space, and $<E(t,r) E(t, r+\Delta r)>$ to measure the spatial coherence between any pairs of points in space, and $<E(t+r) E(t+\tau, r+\Delta r)>$ to measure both spatial and temporal coherence at the same time. The coherence length (longitudinal or transverse) indicates how far apart are spatial points that maintain a coherent relationship btw each other...

Let's consider a perfectly monochromatic field of single frequency $\omega$ (idealization) and equal amplitude $E_{max}$ at every spatial point. This means that the field oscillates in time at every arbitrary spatial point $P$ sinusoidally up and down and with a constant (maximum amplitude).

The (electric) field time behavior at two different arbitrary points $P$ and $Q$ could be represented as $$E_P (t) = E_{max} cos (\omega t +\theta_P)$$ and $$ E_Q (t) = E_{max} cos (\omega t +\theta_Q)$$

Calculating the linear correlation $<E(t)_P E(t+\tau)_Q>$ between the fields at these two different spatial points, we would obtain a constant value due to the time average. In reality, the fields and the correlation would be all oscillating in time but their time average would be constant.

The correlation function is truly the sum of three terms. The first two terms are constants and the third term, the product term, also being constant regardless of the phase difference between $\theta_P$ and $\theta_Q$. The third term is constant because the frequency is the same at both points and the phase terms $\theta_P$ and $\theta_Q$ are both constant.

If

a) the frequency of the oscillating fields was different for points $P$ and $Q$
and/or if
b) if the two phase constant $\theta_P$ and $\theta_Q$ were not actually constant but random functions of time,

the fields'correlation would not be constant and the fields at the two spatial points or at the same point would not be coherent .

Is my understanding correct?

 

[fog37]

Additionally, a way to explore the coherence of a field, is the phenomenon of interference: a stable interference pattern (dark and bright areas that don't change in time in location and intensity) indicates both temporal and spatial coherence...

 

[sophiecentaur]

Filtering will remove unwanted frequencies to make the light more monochromatic, but it won’t do anything for the phase, so we still don’t get coherent light.

Consider the RF equivalent process. If you take a very narrow band conventional (resonance) filter and pass a noise signal through it, what will be left is a narrow band signal that 'fills' the passband of the filter. That can be regarded (quite validly) as a single carrier wave with sidebands which will be the equivalent to a 'perfect' coherence component with additional phase and amplitude variations. The length over which the coherence is high will then be about c Δf , where Δf is the range of frequencies passed by the filter. For an optical filter with a (wavelength) bandwidth of 0.07nm (like the Hydrogen Alpha Etalon filters used in Astronomy), the coherence length will be about this value, which is much less than you get with a laser (typical multimode laser is tens of cm).

So my guess is that even a power laser would likely be much better than any passive filter. Reason is that the laser has effectively an active filter (with feedback), giving preposterously high Q, ( by magnifying the Q of its internal etalon filter)

Hα filters of astronomical quality are several $k to buy - you may do better but . . . . .

 

[Andy Resnick]

Would it be possible,using a lens, that monochromatic, to focus and converge that monochromatic non-laser light to a small spot? Or is spatial coherence also required to produce a highly focus, high intensity ($W/m^2$) beam?

Thank you!

There are some persistent misconceptions in this thread- for example, laser light can have very poor spatial coherence. The short answer is 'yes', but it depends on what you mean by 'small' - you are somewhat correct that the focused spot size relates to the degree of spatial coherence. Beams can be parameterized by both spatial and temporal coherence, these can be independently changed.

Spectral filtering will increase the temporal coherence of a beam; I don't think there's a converse operation. Increasing temporal coherence does not result in an altered spot size (excepting chromatic aberration by the lens) but does increase the allowed path difference in, for example, a Mach-Zender interferometer. This is the essence of Post #8.

Spatial filtering will increase the spatial coherence of a beam; the converse operation is frequently performed by using a piece of rotating ground glass in the optical system. Increasing the spatial coherence will generally decrease the spot size, perhaps the best explanation is that spatial filtering acts to reduce the angular spectrum of the beam.

Given any source, there are relationships between the size of the source and the angular spread of the emitted light, with how efficiently that emitted light can be converted into a 'collimated beam' or focused down to a 'diffraction-limited Airy disc'. A good primer on coherence is Wolf's "Introduction to the Theory of Coherence and Polarization of light". Note the title- fully coherent light is also fully polarized light.

 

[sophiecentaur]

Spatial filtering will increase the spatial coherence of a beam;

For instance reducing the aperture - as we used to do with a gas discharge tube?

 

[Andy Resnick]

For instance reducing the aperture - as we used to do with a gas discharge tube?

In a sense- spatial filtering usually involves < 0.1 mm diameter pinholes (I typically use 5 or 10 um diameter) in order to get the spatial coherence high enough.

 

[sophiecentaur]

In a sense- spatial filtering usually involves < 0.1 mm diameter pinholes (I typically use 5 or 10 um diameter) in order to get the spatial coherence high enough.

That Laser invention was pretty useful then.

 

[fog37]

So the "focusability", how small the focused spot size can be, depends primarily on the spatial coherence and on the center wavelength (the smallest the laser center wavelength the smaller spot).

the maser was the first "laser". Being microwaves, I assume it very highly coherence both spatially and spectrally but the sport size may not be as small as with a laser...