Re: [Phys-L] two-slit interference for non-laser sources

[John Denker <jsd@av8n.com>]

On 10/07/2016 07:21 AM, Carl Mungan wrote:

> what determines the temporal coherence of a filtered blackbody 
> source? (I assume the bandwidth of the filter should play into the 
> answer.

Sure.

You can guess the right answer, within a factor of 2 or a factor
of π, just using dimensional analysis:

          c Q
    L = -------                                [1a]
          π f

or equivalently

          2 c Q
    L = ---------                             [1b]
            ω

The next step after guessing is /check the work/.  It is cheap to
check against a reference such as
   https://www.rp-photonics.com/coherence_length.html
which asserts the formula without proof.  It mentions that it is
a common mistake to overlook the factor of π in equation 1a.

At the next level of detail:  The coherence time is defined by
looking at the shape of the time-time correlation function.  You
can write down the definition, feed it with white noise, and do
the integrals.  See any optics book or perhaps
  https://en.wikipedia.org/wiki/Degree_of_coherence

> the high Q due to the long effective pathlength inside a HeNe laser
> cavity

Yes.  The laser cavity is essentially an etalon.

> acting in concert with stimulated emission must dramatically increase
> the longitudinal coherence length L

Well, the stimulated emission can work for you or against you.
There is such a thing as "mode locking".  Much depends on which
mode gets locked.  By convention, when people talk about mode
locking it refers to a mode consisting of a very short pulse.
As such, it necessarily has a very broad frequency distribution.

At the opposite extreme you can have a "single mode" CW laser,
with a super-narrow frequency distribution.

   In between, there are the generic messy multi-mode lasers.

To my way of looking at it, "mode locked" and "single mode" both
depend on stimulated emission.  So at the most fundamental level,
they involve the same physics, but the engineering is different,
with spectacularly different results.

Some (but not all) HeNe lasers are of the stabilized single-mode
narrow-band variety:
  https://www.thorlabs.de/newgrouppage9.cfm?objectgroup_id=5281

You can get single-mode /diode/ lasers, too:
  http://www.cnilaser.com/SLM_laser.htm