Speaking* of green laser diodes.

On Apr 12, 2019, Phil Hobbs wrote
(in article<a8KdnfNtO80RSi3BnZ2dnUU7-fXNnZ2d@supernews.com>):

On 4/12/19 12:25 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<J_-dndTKptWxHi3BnZ2dnUU7-b2dnZ2d@supernews.com>):

On 4/11/19 9:43 PM, George Herold wrote:

On Thursday, April 11, 2019 at 9:04:55 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 5:08 PM, George Herold wrote:
On Thursday, April 11, 2019 at 4:40:35 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 3:51 PM, Lasse Langwadt Christensen wrote:
torsdag den 11. april 2019 kl. 20.24.56 UTC+2 skrev Phil Hobbs:
On 4/11/19 1:26 PM, George Herold wrote:
On Thursday, April 11, 2019 at 11:39:57 AM UTC-4, Phil Hobbs
wrote:
On 4/10/19 12:15 PM, George Herold wrote:
On Wednesday, April 10, 2019 at 7:21:53 AM UTC-4, Phil
Hobbs wrote:
On 4/9/19 8:05 PM, George Herold wrote:
*I think it was speff and a new 3-D laser theater
system. These seem to be the only good green laser
diodes
https://www.digikey.com/product-detail/en/osram-opto-semiconduct
or
s-inc/PL-520_B1/PL520_B1-ND/5719264
DK link provided.
The output spectrum is terrible! 1-2 nm wide! wtf?
data sheet here?
https://www.osram.com/apps/product_selector/#!/?query=*&sortField=
&sortOrder=&start=0&filters=producttype,Visible%20Laser%20Diodes&f
ilters=color,True%20Green%20(513-545%20nm)&deeplink=
There's a deeplink at the end so be careful.

George H.

Most short-wavelength diode lasers have multiple
longitudinal modes. That's not necessarily a bad
thing--it makes them much less sensitive to mode
hopping due to backreflections. You sure don't want to
use them for tunable-diode spectroscopy, though.

Cheers

Phil Hobbs
Say Phil, did you mean multiple transverse modes in the
above? It's just because I'm having a hard time
understanding how one can get lasing in different
longitudinal modes. (My simple model is that the
longitudinal mode with the highest gain 'wins' and sucks
all the gain out of the other modes... The single mode
DL's I use have many longitudinal modes.)

Whereas if there were different transverse modes, then
those would occupy different areas in the gain medium,
and I can then picture the thing lasing in different
modes, (using different portions of the gain medium, and
not 'sucking' the gain away from each other... Though it
does get a little complicated looking... and I can
imagine that the modes interact with each other some, as
you said in your later post.

George H.

Nope, longitudinal. In a Fabry-Perot laser, there are
nodes and antinodes of the standing wave, leading to
spatial hole burning, where the carriers are locally
depleted near the antinodes. Different modes have
different antinode positions, but they do overlap quite a
lot, which makes the longitudinal modes strongly coupled.
OK, Thanks. Lets see if the cavity was ~1mm (1000um) I'd get
2000 wavelengths in the thing and the longitudinal modes are
separated by 500nm/2000 ~0.25 nm (plus or minus a factor of
2) Can I see the modes with a spectrometer? That would be
fun.


You can see them by using a DVD as a grating. Use a reasonably
broad beam and come out of the DVD near grazing.

the DVD trick is neat, https://youtu.be/EoAZ-u6hn6g?t=1m19s

It's a little tougher with laser modes, but perfectly doable. It's
very instructive to put a photodiode where it measures just one
mode and see just how noisy it is. Typically the fluctuations are
of order unity.

I've also used it to measure the tuning range of single-frequency
diodes between mode jumps. You just tune till the spot suddenly
changes position, and voila.
Right, I've done that with a spectrometer and single mode diodes.

Can I ask a question about these multiple longitudinal modes? How the
Heck does That happen!? It implies multiple optical path lengths.

No. As you noted upthread, you can have 2000, 2001, 2002, etc cycles
per round trip. OPL is very nearly the same for all, but they're at
different frequencies.


I know the carrier density (how much current you are pushing through
the diode) can change the optical length*... but still at one time it
seems like there should be one optical length.

OPL is measured in metres. The eigenmodes of a given cavity form a comb
in 1/lambda. In the absence of dispersion, that's an equally spaced
frequency comb.


Is it lasing at many modes at once.. or jumping around between modes
all the time?

Generally it's lasing in many modes at once, though I suppose it's
possible to make a system that has one mode at a time. A nominally
single-frequency laser can hop between modes, as we both know very well.
;)


I think if it's the later, there's some chance you could do some
external feedback and make it single mode at low currents, (above
threshold)

A lot of lasers are single-mode near threshold. At any given
temperature, there will be one mode that crosses threshold first, and if
the gain delta between modes is big enough, it'll maintain itself stably.

I recommend Wolfgang's pages,<https://hololaser.wordpress.com> and
http://hololaser.kwaoo.me>, for a lot more about diode laser behaviour.

It's somewhat rambling and poorly organized, but his plots of laser
noise vs. temperature and frequency are super illuminating.
Specifically, he evaluates a lot of diodes for ECDL operation at
http://hololaser.kwaoo.me/laser/ECDL-test.html

Huh.. I'll have to read a bunch of that. My experience with one
diode laser is that the position of the coupling lens is the most
tweaky adjustment. And putting a layer of teflon tape on the
threads of the Thor labs lens helps a bunch in removing
hysteresis in the threads. (and other wobbles)

George H.

George H. *Besides the heating effects of current.

Yup, backreflections from the lens (and even the window in the package)
are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a trick
from photography to cause reflections to fall in harmless places. Basically,
if one displaces object to one side the image will migrate the other way, and
back reflections will no longer re-enter the lens. This is an application of
the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn
Sort of. In a laser collimator, light reflected back down the beam axis
hits the laser exactly, regardless of minor lens misalignment.

I’m not visualizing this. In my mental picture, the reflection misses the
lens, and so cannot get to the hapless laser diode.

..
It can help a bit with the first-surface reflection from the collimator,
especially if the first surface is concave.

I think we have different optical systems in mind. .
Problem is, in a LD collimator the coma builds up pretty fast as you go off
axis.

What if one has two collimators, one expanding the beam, the other
compressing the beam, squinting at one another from the same side, but facing
one another. Would not the coma cancel out?

Joe Gwinn
 
On Friday, April 12, 2019 at 6:08:29 PM UTC-4, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<a8KdnfNtO80RSi3BnZ2dnUU7-fXNnZ2d@supernews.com>):

On 4/12/19 12:25 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<J_-dndTKptWxHi3BnZ2dnUU7-b2dnZ2d@supernews.com>):

On 4/11/19 9:43 PM, George Herold wrote:

On Thursday, April 11, 2019 at 9:04:55 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 5:08 PM, George Herold wrote:
On Thursday, April 11, 2019 at 4:40:35 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 3:51 PM, Lasse Langwadt Christensen wrote:
torsdag den 11. april 2019 kl. 20.24.56 UTC+2 skrev Phil Hobbs:
On 4/11/19 1:26 PM, George Herold wrote:
On Thursday, April 11, 2019 at 11:39:57 AM UTC-4, Phil Hobbs
wrote:
On 4/10/19 12:15 PM, George Herold wrote:
On Wednesday, April 10, 2019 at 7:21:53 AM UTC-4, Phil
Hobbs wrote:
On 4/9/19 8:05 PM, George Herold wrote:
*I think it was speff and a new 3-D laser theater
system. These seem to be the only good green laser
diodes
https://www.digikey.com/product-detail/en/osram-opto-semiconduct
or
s-inc/PL-520_B1/PL520_B1-ND/5719264
DK link provided.
The output spectrum is terrible! 1-2 nm wide! wtf?
data sheet here?
https://www.osram.com/apps/product_selector/#!/?query=*&sortField> > > &sortOrder=&start=0&filters=producttype,Visible%20Laser%20Diodes&f
ilters=color,True%20Green%20(513-545%20nm)&deeplink> > > > > > There's a deeplink at the end so be careful.

George H.

Most short-wavelength diode lasers have multiple
longitudinal modes. That's not necessarily a bad
thing--it makes them much less sensitive to mode
hopping due to backreflections. You sure don't want to
use them for tunable-diode spectroscopy, though..

Cheers

Phil Hobbs
Say Phil, did you mean multiple transverse modes in the
above? It's just because I'm having a hard time
understanding how one can get lasing in different
longitudinal modes. (My simple model is that the
longitudinal mode with the highest gain 'wins' and sucks
all the gain out of the other modes... The single mode
DL's I use have many longitudinal modes.)

Whereas if there were different transverse modes, then
those would occupy different areas in the gain medium,
and I can then picture the thing lasing in different
modes, (using different portions of the gain medium, and
not 'sucking' the gain away from each other... Though it
does get a little complicated looking... and I can
imagine that the modes interact with each other some, as
you said in your later post.

George H.

Nope, longitudinal. In a Fabry-Perot laser, there are
nodes and antinodes of the standing wave, leading to
spatial hole burning, where the carriers are locally
depleted near the antinodes. Different modes have
different antinode positions, but they do overlap quite a
lot, which makes the longitudinal modes strongly coupled.
OK, Thanks. Lets see if the cavity was ~1mm (1000um) I'd get
2000 wavelengths in the thing and the longitudinal modes are
separated by 500nm/2000 ~0.25 nm (plus or minus a factor of
2) Can I see the modes with a spectrometer? That would be
fun.


You can see them by using a DVD as a grating. Use a reasonably
broad beam and come out of the DVD near grazing.

the DVD trick is neat, https://youtu.be/EoAZ-u6hn6g?t=1m19s

It's a little tougher with laser modes, but perfectly doable. It's
very instructive to put a photodiode where it measures just one
mode and see just how noisy it is. Typically the fluctuations are
of order unity.

I've also used it to measure the tuning range of single-frequency
diodes between mode jumps. You just tune till the spot suddenly
changes position, and voila.
Right, I've done that with a spectrometer and single mode diodes.

Can I ask a question about these multiple longitudinal modes? How the
Heck does That happen!? It implies multiple optical path lengths.

No. As you noted upthread, you can have 2000, 2001, 2002, etc cycles
per round trip. OPL is very nearly the same for all, but they're at
different frequencies.


I know the carrier density (how much current you are pushing through
the diode) can change the optical length*... but still at one time it
seems like there should be one optical length.

OPL is measured in metres. The eigenmodes of a given cavity form a comb
in 1/lambda. In the absence of dispersion, that's an equally spaced
frequency comb.


Is it lasing at many modes at once.. or jumping around between modes
all the time?

Generally it's lasing in many modes at once, though I suppose it's
possible to make a system that has one mode at a time. A nominally
single-frequency laser can hop between modes, as we both know very well.
;)


I think if it's the later, there's some chance you could do some
external feedback and make it single mode at low currents, (above
threshold)

A lot of lasers are single-mode near threshold. At any given
temperature, there will be one mode that crosses threshold first, and if
the gain delta between modes is big enough, it'll maintain itself stably.

I recommend Wolfgang's pages,<https://hololaser.wordpress.com> and
http://hololaser.kwaoo.me>, for a lot more about diode laser behaviour.

It's somewhat rambling and poorly organized, but his plots of laser
noise vs. temperature and frequency are super illuminating.
Specifically, he evaluates a lot of diodes for ECDL operation at
http://hololaser.kwaoo.me/laser/ECDL-test.html

Huh.. I'll have to read a bunch of that. My experience with one
diode laser is that the position of the coupling lens is the most
tweaky adjustment. And putting a layer of teflon tape on the
threads of the Thor labs lens helps a bunch in removing
hysteresis in the threads. (and other wobbles)

George H.

George H. *Besides the heating effects of current.

Yup, backreflections from the lens (and even the window in the package)
are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a trick
from photography to cause reflections to fall in harmless places. Basically,
if one displaces object to one side the image will migrate the other way, and
back reflections will no longer re-enter the lens. This is an application of
the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn
Sort of. In a laser collimator, light reflected back down the beam axis
hits the laser exactly, regardless of minor lens misalignment.

I’m not visualizing this. In my mental picture, the reflection misses the
lens, and so cannot get to the hapless laser diode.
Hi Joe, if I may interrupt. I think you are talking about two different
reflections. In photography (which I don't know so well) the light source
is off axis from the detector (well, most of the time, with a flash they are
close.)
In the laser diode case the diode is source and detector.
People pay ~$1k for Faraday opto-isolators.

George H.
.
It can help a bit with the first-surface reflection from the collimator,
especially if the first surface is concave.

I think we have different optical systems in mind. .
Problem is, in a LD collimator the coma builds up pretty fast as you go off
axis.

What if one has two collimators, one expanding the beam, the other
compressing the beam, squinting at one another from the same side, but facing
one another. Would not the coma cancel out?

Joe Gwinn
 
On Friday, April 12, 2019 at 2:23:17 PM UTC-4, Phil Hobbs wrote:
On 4/12/19 12:25 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<J_-dndTKptWxHi3BnZ2dnUU7-b2dnZ2d@supernews.com>):

On 4/11/19 9:43 PM, George Herold wrote:

On Thursday, April 11, 2019 at 9:04:55 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 5:08 PM, George Herold wrote:
On Thursday, April 11, 2019 at 4:40:35 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 3:51 PM, Lasse Langwadt Christensen wrote:
torsdag den 11. april 2019 kl. 20.24.56 UTC+2 skrev Phil Hobbs:
On 4/11/19 1:26 PM, George Herold wrote:
On Thursday, April 11, 2019 at 11:39:57 AM UTC-4, Phil Hobbs
wrote:
On 4/10/19 12:15 PM, George Herold wrote:
On Wednesday, April 10, 2019 at 7:21:53 AM UTC-4, Phil
Hobbs wrote:
On 4/9/19 8:05 PM, George Herold wrote:
*I think it was speff and a new 3-D laser theater
system. These seem to be the only good green laser
diodes
https://www.digikey.com/product-detail/en/osram-opto-semiconductor
s-inc/PL-520_B1/PL520_B1-ND/5719264
DK link provided.
The output spectrum is terrible! 1-2 nm wide! wtf?
data sheet here?

https://www.osram.com/apps/product_selector/#!/?query=*&sortField=

&sortOrder=&start=0&filters=producttype,Visible%20Laser%20Diodes&f
ilters=color,True%20Green%20(513-545%20nm)&deeplink=
There's a deeplink at the end so be careful.

George H.

Most short-wavelength diode lasers have multiple
longitudinal modes. That's not necessarily a bad
thing--it makes them much less sensitive to mode
hopping due to backreflections. You sure don't want to
use them for tunable-diode spectroscopy, though.

Cheers

Phil Hobbs
Say Phil, did you mean multiple transverse modes in the
above? It's just because I'm having a hard time
understanding how one can get lasing in different
longitudinal modes. (My simple model is that the
longitudinal mode with the highest gain 'wins' and sucks
all the gain out of the other modes... The single mode
DL's I use have many longitudinal modes.)

Whereas if there were different transverse modes, then
those would occupy different areas in the gain medium,
and I can then picture the thing lasing in different
modes, (using different portions of the gain medium, and
not 'sucking' the gain away from each other... Though it
does get a little complicated looking... and I can
imagine that the modes interact with each other some, as
you said in your later post.

George H.

Nope, longitudinal. In a Fabry-Perot laser, there are
nodes and antinodes of the standing wave, leading to
spatial hole burning, where the carriers are locally
depleted near the antinodes. Different modes have
different antinode positions, but they do overlap quite a
lot, which makes the longitudinal modes strongly coupled.
OK, Thanks. Lets see if the cavity was ~1mm (1000um) I'd get
2000 wavelengths in the thing and the longitudinal modes are
separated by 500nm/2000 ~0.25 nm (plus or minus a factor of
2) Can I see the modes with a spectrometer? That would be
fun.


You can see them by using a DVD as a grating. Use a reasonably
broad beam and come out of the DVD near grazing.

the DVD trick is neat, https://youtu.be/EoAZ-u6hn6g?t=1m19s

It's a little tougher with laser modes, but perfectly doable. It's
very instructive to put a photodiode where it measures just one
mode and see just how noisy it is. Typically the fluctuations are
of order unity.

I've also used it to measure the tuning range of single-frequency
diodes between mode jumps. You just tune till the spot suddenly
changes position, and voila.
Right, I've done that with a spectrometer and single mode diodes.

Can I ask a question about these multiple longitudinal modes? How the
Heck does That happen!? It implies multiple optical path lengths.

No. As you noted upthread, you can have 2000, 2001, 2002, etc cycles
per round trip. OPL is very nearly the same for all, but they're at
different frequencies.


I know the carrier density (how much current you are pushing through
the diode) can change the optical length*... but still at one time it
seems like there should be one optical length.

OPL is measured in metres. The eigenmodes of a given cavity form a comb
in 1/lambda. In the absence of dispersion, that's an equally spaced
frequency comb.


Is it lasing at many modes at once.. or jumping around between modes
all the time?

Generally it's lasing in many modes at once, though I suppose it's
possible to make a system that has one mode at a time. A nominally
single-frequency laser can hop between modes, as we both know very well. ;)


I think if it's the later, there's some chance you could do some
external feedback and make it single mode at low currents, (above
threshold)

A lot of lasers are single-mode near threshold. At any given
temperature, there will be one mode that crosses threshold first, and if
the gain delta between modes is big enough, it'll maintain itself stably.

I recommend Wolfgang's pages,<https://hololaser.wordpress.com> and
http://hololaser.kwaoo.me>, for a lot more about diode laser behaviour.

It's somewhat rambling and poorly organized, but his plots of laser
noise vs. temperature and frequency are super illuminating.
Specifically, he evaluates a lot of diodes for ECDL operation at
http://hololaser.kwaoo.me/laser/ECDL-test.html

Huh.. I'll have to read a bunch of that. My experience with one
diode laser is that the position of the coupling lens is the most
tweaky adjustment. And putting a layer of teflon tape on the
threads of the Thor labs lens helps a bunch in removing
hysteresis in the threads. (and other wobbles)

George H.

George H. *Besides the heating effects of current.

Yup, backreflections from the lens (and even the window in the package)
are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a trick
from photography to cause reflections to fall in harmless places. Basically,
if one displaces object to one side the image will migrate the other way, and
back reflections will no longer re-enter the lens. This is an application of
the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn

Sort of. In a laser collimator, light reflected back down the beam axis
hits the laser exactly, regardless of minor lens misalignment.

It can help a bit with the first-surface reflection from the collimator,
especially if the first surface is concave.

Problem is, in a LD collimator the coma builds up pretty fast as you go
off axis.
Fiber couplers too. (or is that what you mean by a collimator?)
When I measure LD's in the wavemeter Jr. I always
have to add a 'poor mans' isolator; linear polarizer and 1/4 wave plate.
Best is if it's the first element before reflection, (as you know.)

George H.
Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com
 
On 4/12/19 6:54 PM, George Herold wrote:
On Friday, April 12, 2019 at 2:23:17 PM UTC-4, Phil Hobbs wrote:
On 4/12/19 12:25 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<J_-dndTKptWxHi3BnZ2dnUU7-b2dnZ2d@supernews.com>):

On 4/11/19 9:43 PM, George Herold wrote:

On Thursday, April 11, 2019 at 9:04:55 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 5:08 PM, George Herold wrote:
On Thursday, April 11, 2019 at 4:40:35 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 3:51 PM, Lasse Langwadt Christensen wrote:
torsdag den 11. april 2019 kl. 20.24.56 UTC+2 skrev Phil Hobbs:
On 4/11/19 1:26 PM, George Herold wrote:
On Thursday, April 11, 2019 at 11:39:57 AM UTC-4, Phil Hobbs
wrote:
On 4/10/19 12:15 PM, George Herold wrote:
On Wednesday, April 10, 2019 at 7:21:53 AM UTC-4, Phil
Hobbs wrote:
On 4/9/19 8:05 PM, George Herold wrote:
*I think it was speff and a new 3-D laser theater
system. These seem to be the only good green laser
diodes
https://www.digikey.com/product-detail/en/osram-opto-semiconductor
s-inc/PL-520_B1/PL520_B1-ND/5719264
DK link provided.
The output spectrum is terrible! 1-2 nm wide! wtf?
data sheet here?

https://www.osram.com/apps/product_selector/#!/?query=*&sortField=

&sortOrder=&start=0&filters=producttype,Visible%20Laser%20Diodes&f
ilters=color,True%20Green%20(513-545%20nm)&deeplink=
There's a deeplink at the end so be careful.

George H.

Most short-wavelength diode lasers have multiple
longitudinal modes. That's not necessarily a bad
thing--it makes them much less sensitive to mode
hopping due to backreflections. You sure don't want to
use them for tunable-diode spectroscopy, though.

Cheers

Phil Hobbs
Say Phil, did you mean multiple transverse modes in the
above? It's just because I'm having a hard time
understanding how one can get lasing in different
longitudinal modes. (My simple model is that the
longitudinal mode with the highest gain 'wins' and sucks
all the gain out of the other modes... The single mode
DL's I use have many longitudinal modes.)

Whereas if there were different transverse modes, then
those would occupy different areas in the gain medium,
and I can then picture the thing lasing in different
modes, (using different portions of the gain medium, and
not 'sucking' the gain away from each other... Though it
does get a little complicated looking... and I can
imagine that the modes interact with each other some, as
you said in your later post.

George H.

Nope, longitudinal. In a Fabry-Perot laser, there are
nodes and antinodes of the standing wave, leading to
spatial hole burning, where the carriers are locally
depleted near the antinodes. Different modes have
different antinode positions, but they do overlap quite a
lot, which makes the longitudinal modes strongly coupled.
OK, Thanks. Lets see if the cavity was ~1mm (1000um) I'd get
2000 wavelengths in the thing and the longitudinal modes are
separated by 500nm/2000 ~0.25 nm (plus or minus a factor of
2) Can I see the modes with a spectrometer? That would be
fun.


You can see them by using a DVD as a grating. Use a reasonably
broad beam and come out of the DVD near grazing.

the DVD trick is neat, https://youtu.be/EoAZ-u6hn6g?t=1m19s

It's a little tougher with laser modes, but perfectly doable. It's
very instructive to put a photodiode where it measures just one
mode and see just how noisy it is. Typically the fluctuations are
of order unity.

I've also used it to measure the tuning range of single-frequency
diodes between mode jumps. You just tune till the spot suddenly
changes position, and voila.
Right, I've done that with a spectrometer and single mode diodes.

Can I ask a question about these multiple longitudinal modes? How the
Heck does That happen!? It implies multiple optical path lengths.

No. As you noted upthread, you can have 2000, 2001, 2002, etc cycles
per round trip. OPL is very nearly the same for all, but they're at
different frequencies.


I know the carrier density (how much current you are pushing through
the diode) can change the optical length*... but still at one time it
seems like there should be one optical length.

OPL is measured in metres. The eigenmodes of a given cavity form a comb
in 1/lambda. In the absence of dispersion, that's an equally spaced
frequency comb.


Is it lasing at many modes at once.. or jumping around between modes
all the time?

Generally it's lasing in many modes at once, though I suppose it's
possible to make a system that has one mode at a time. A nominally
single-frequency laser can hop between modes, as we both know very well. ;)


I think if it's the later, there's some chance you could do some
external feedback and make it single mode at low currents, (above
threshold)

A lot of lasers are single-mode near threshold. At any given
temperature, there will be one mode that crosses threshold first, and if
the gain delta between modes is big enough, it'll maintain itself stably.

I recommend Wolfgang's pages,<https://hololaser.wordpress.com> and
http://hololaser.kwaoo.me>, for a lot more about diode laser behaviour.

It's somewhat rambling and poorly organized, but his plots of laser
noise vs. temperature and frequency are super illuminating.
Specifically, he evaluates a lot of diodes for ECDL operation at
http://hololaser.kwaoo.me/laser/ECDL-test.html

Huh.. I'll have to read a bunch of that. My experience with one
diode laser is that the position of the coupling lens is the most
tweaky adjustment. And putting a layer of teflon tape on the
threads of the Thor labs lens helps a bunch in removing
hysteresis in the threads. (and other wobbles)

George H.

George H. *Besides the heating effects of current.

Yup, backreflections from the lens (and even the window in the package)
are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a trick
from photography to cause reflections to fall in harmless places. Basically,
if one displaces object to one side the image will migrate the other way, and
back reflections will no longer re-enter the lens. This is an application of
the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn

Sort of. In a laser collimator, light reflected back down the beam axis
hits the laser exactly, regardless of minor lens misalignment.

It can help a bit with the first-surface reflection from the collimator,
especially if the first surface is concave.

Problem is, in a LD collimator the coma builds up pretty fast as you go
off axis.

Fiber couplers too. (or is that what you mean by a collimator?)
When I measure LD's in the wavemeter Jr. I always
have to add a 'poor mans' isolator; linear polarizer and 1/4 wave plate.
Best is if it's the first element before reflection, (as you know.)

The circular polarization trick is always worth a try--it generally gets
you about 40 dB (optical) isolation. Problem is, you need >60 dB for
real insurance against mode hopping due to back-reflections. That needs
a two-stage Faraday isolator.

RF modulation of the diode laser bias current can make that a lot easier.

Cheers

Phil Hobbs


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com
 
On 4/12/19 6:08 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<a8KdnfNtO80RSi3BnZ2dnUU7-fXNnZ2d@supernews.com>):

On 4/12/19 12:25 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<J_-dndTKptWxHi3BnZ2dnUU7-b2dnZ2d@supernews.com>):

On 4/11/19 9:43 PM, George Herold wrote:

On Thursday, April 11, 2019 at 9:04:55 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 5:08 PM, George Herold wrote:
On Thursday, April 11, 2019 at 4:40:35 PM UTC-4, Phil Hobbs wrote:
On 4/11/19 3:51 PM, Lasse Langwadt Christensen wrote:
torsdag den 11. april 2019 kl. 20.24.56 UTC+2 skrev Phil Hobbs:
On 4/11/19 1:26 PM, George Herold wrote:
On Thursday, April 11, 2019 at 11:39:57 AM UTC-4, Phil Hobbs
wrote:
On 4/10/19 12:15 PM, George Herold wrote:
On Wednesday, April 10, 2019 at 7:21:53 AM UTC-4, Phil
Hobbs wrote:
On 4/9/19 8:05 PM, George Herold wrote:
*I think it was speff and a new 3-D laser theater
system. These seem to be the only good green laser
diodes
https://www.digikey.com/product-detail/en/osram-opto-semiconduct
or
s-inc/PL-520_B1/PL520_B1-ND/5719264
DK link provided.
The output spectrum is terrible! 1-2 nm wide! wtf?
data sheet here?
https://www.osram.com/apps/product_selector/#!/?query=*&sortField=
&sortOrder=&start=0&filters=producttype,Visible%20Laser%20Diodes&f
ilters=color,True%20Green%20(513-545%20nm)&deeplink=
There's a deeplink at the end so be careful.

George H.

Most short-wavelength diode lasers have multiple
longitudinal modes. That's not necessarily a bad
thing--it makes them much less sensitive to mode
hopping due to backreflections. You sure don't want to
use them for tunable-diode spectroscopy, though.

Cheers

Phil Hobbs
Say Phil, did you mean multiple transverse modes in the
above? It's just because I'm having a hard time
understanding how one can get lasing in different
longitudinal modes. (My simple model is that the
longitudinal mode with the highest gain 'wins' and sucks
all the gain out of the other modes... The single mode
DL's I use have many longitudinal modes.)

Whereas if there were different transverse modes, then
those would occupy different areas in the gain medium,
and I can then picture the thing lasing in different
modes, (using different portions of the gain medium, and
not 'sucking' the gain away from each other... Though it
does get a little complicated looking... and I can
imagine that the modes interact with each other some, as
you said in your later post.

George H.

Nope, longitudinal. In a Fabry-Perot laser, there are
nodes and antinodes of the standing wave, leading to
spatial hole burning, where the carriers are locally
depleted near the antinodes. Different modes have
different antinode positions, but they do overlap quite a
lot, which makes the longitudinal modes strongly coupled.
OK, Thanks. Lets see if the cavity was ~1mm (1000um) I'd get
2000 wavelengths in the thing and the longitudinal modes are
separated by 500nm/2000 ~0.25 nm (plus or minus a factor of
2) Can I see the modes with a spectrometer? That would be
fun.


You can see them by using a DVD as a grating. Use a reasonably
broad beam and come out of the DVD near grazing.

the DVD trick is neat, https://youtu.be/EoAZ-u6hn6g?t=1m19s

It's a little tougher with laser modes, but perfectly doable. It's
very instructive to put a photodiode where it measures just one
mode and see just how noisy it is. Typically the fluctuations are
of order unity.

I've also used it to measure the tuning range of single-frequency
diodes between mode jumps. You just tune till the spot suddenly
changes position, and voila.
Right, I've done that with a spectrometer and single mode diodes.

Can I ask a question about these multiple longitudinal modes? How the
Heck does That happen!? It implies multiple optical path lengths.

No. As you noted upthread, you can have 2000, 2001, 2002, etc cycles
per round trip. OPL is very nearly the same for all, but they're at
different frequencies.


I know the carrier density (how much current you are pushing through
the diode) can change the optical length*... but still at one time it
seems like there should be one optical length.

OPL is measured in metres. The eigenmodes of a given cavity form a comb
in 1/lambda. In the absence of dispersion, that's an equally spaced
frequency comb.


Is it lasing at many modes at once.. or jumping around between modes
all the time?

Generally it's lasing in many modes at once, though I suppose it's
possible to make a system that has one mode at a time. A nominally
single-frequency laser can hop between modes, as we both know very well.
;)


I think if it's the later, there's some chance you could do some
external feedback and make it single mode at low currents, (above
threshold)

A lot of lasers are single-mode near threshold. At any given
temperature, there will be one mode that crosses threshold first, and if
the gain delta between modes is big enough, it'll maintain itself stably.

I recommend Wolfgang's pages,<https://hololaser.wordpress.com> and
http://hololaser.kwaoo.me>, for a lot more about diode laser behaviour.

It's somewhat rambling and poorly organized, but his plots of laser
noise vs. temperature and frequency are super illuminating.
Specifically, he evaluates a lot of diodes for ECDL operation at
http://hololaser.kwaoo.me/laser/ECDL-test.html

Huh.. I'll have to read a bunch of that. My experience with one
diode laser is that the position of the coupling lens is the most
tweaky adjustment. And putting a layer of teflon tape on the
threads of the Thor labs lens helps a bunch in removing
hysteresis in the threads. (and other wobbles)

George H.

George H. *Besides the heating effects of current.

Yup, backreflections from the lens (and even the window in the package)
are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a trick
from photography to cause reflections to fall in harmless places. Basically,
if one displaces object to one side the image will migrate the other way, and
back reflections will no longer re-enter the lens. This is an application of
the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn
Sort of. In a laser collimator, light reflected back down the beam axis
hits the laser exactly, regardless of minor lens misalignment.

I’m not visualizing this. In my mental picture, the reflection misses the
lens, and so cannot get to the hapless laser diode.

Light propagation is time-reversal symmetric. If you send it back the
way it came, it winds up where it began.

It can help a bit with the first-surface reflection from the collimator,
especially if the first surface is concave.

I think we have different optical systems in mind. .
Problem is, in a LD collimator the coma builds up pretty fast as you go off
axis.

What if one has two collimators, one expanding the beam, the other
compressing the beam, squinting at one another from the same side, but facing
one another. Would not the coma cancel out?

Two collimators? Are you talking about anamorphic prisms? A collimator
is a lens.

Cheers

Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com
 
On Apr 12, 2019, Phil Hobbs wrote
(in article<Psadnaf9IIXWpCzBnZ2dnUU7-KGdnZ2d@supernews.com>):

On 4/12/19 6:08 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<a8KdnfNtO80RSi3BnZ2dnUU7-fXNnZ2d@supernews.com>):
[big snip]

Yup, backreflections from the lens (and even the window in the package

are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a tric

from photography to cause reflections to fall in harmless places. Basica
ly,
if one displaces object to one side the image will migrate the other way

and back reflections will no longer re-enter the lens. This is an applic
tion
of the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn
Sort of. In a laser collimator, light reflected back down the beam axis
hits the laser exactly, regardless of minor lens misalignment.

I'm not visualizing this. In my mental picture, the reflection
misses the lens, and so cannot get to the hapless laser diode.


Light propagation is time-reversal symmetric. If you send it back the
way it came, it winds up where it began.

It can help a bit with the first-surface reflection from the collimator,
especially if the first surface is concave.

I think we have different optical systems in mind. .
Problem is, in a LD collimator the coma builds up pretty fast as you go of

axis.

What if one has two collimators, one expanding the beam, the other
compressing the beam, squinting at one another from the same side, but
facing
one another. Would not the coma cancel out?

Two collimators? Are you talking about anamorphic prisms? A collimator
is a lens.

I´m thinking of two fiber-optic collimators facing one another, with a 2mm
diameter free-space light beam connecting them. The free-space beams traverse
various interesting optical components, some of which have annoying
reflections. The intent is to misdirect the various reflections such that
they miss the collimator apertures and so are lost.

Joe Gwinn
 
Worth a read, I had this open and reading it about four months ago...

They have a blue version in another journal:


High-power broadly tunable grating-coupled external cavity laser in green region

Review of Scientific Instruments 89, 125106 (2018); https://doi.org/10.1063/1.5048977

Steve
 
On 4/13/19 10:52 AM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<Psadnaf9IIXWpCzBnZ2dnUU7-KGdnZ2d@supernews.com>):

On 4/12/19 6:08 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<a8KdnfNtO80RSi3BnZ2dnUU7-fXNnZ2d@supernews.com>):
[big snip]

Yup, backreflections from the lens (and even the window in the package

are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a tric

from photography to cause reflections to fall in harmless places. Basica
ly,
if one displaces object to one side the image will migrate the other way

and back reflections will no longer re-enter the lens. This is an applic
tion
of the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn
Sort of. In a laser collimator, light reflected back down the beam axis
hits the laser exactly, regardless of minor lens misalignment.

I'm not visualizing this. In my mental picture, the reflection
misses the lens, and so cannot get to the hapless laser diode.


Light propagation is time-reversal symmetric. If you send it back the
way it came, it winds up where it began.

It can help a bit with the first-surface reflection from the collimator,
especially if the first surface is concave.

I think we have different optical systems in mind. .
Problem is, in a LD collimator the coma builds up pretty fast as you go of

axis.

What if one has two collimators, one expanding the beam, the other
compressing the beam, squinting at one another from the same side, but
facing
one another. Would not the coma cancel out?

Two collimators? Are you talking about anamorphic prisms? A collimator
is a lens.

I´m thinking of two fiber-optic collimators facing one another, with a 2mm
diameter free-space light beam connecting them. The free-space beams traverse
various interesting optical components, some of which have annoying
reflections. The intent is to misdirect the various reflections such that
they miss the collimator apertures and so are lost.

Joe Gwinn

Minor misalignment of the free-space optics is a win, because the
available etendue (area-solid angle product) is so large compared with a
fibre that you can misalign them without losing signal.

The collimators themselves don't have that luxury.

Cheers

Phil Hobbs



--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com
 
Just returned from two weeks away.

On Apr 14, 2019, Phil Hobbs wrote
(in article<JdqdnVCDIseDRC7BnZ2dnUU7-SOdnZ2d@supernews.com>):

On 4/13/19 10:52 AM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<Psadnaf9IIXWpCzBnZ2dnUU7-KGdnZ2d@supernews.com>):

On 4/12/19 6:08 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<a8KdnfNtO80RSi3BnZ2dnUU7-fXNnZ2d@supernews.com>):
[big snip]

Yup, backreflections from the lens (and even the window in the pac
age

are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a
ric

from photography to cause reflections to fall in harmless places. Ba
ica
ly,
if one displaces object to one side the image will migrate the other
way

and back reflections will no longer re-enter the lens. This is an ap
lic
tion
of the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn
Sort of. In a laser collimator, light reflected back down the beam axi

hits the laser exactly, regardless of minor lens misalignment.

I'm not visualizing this. In my mental picture, the reflection
misses the lens, and so cannot get to the hapless laser diode.


Light propagation is time-reversal symmetric. If you send it back the
way it came, it winds up where it began.

It can help a bit with the first-surface reflection from the collimato
,
especially if the first surface is concave.

I think we have different optical systems in mind. .
Problem is, in a LD collimator the coma builds up pretty fast as you g

off axis.

What if one has two collimators, one expanding the beam, the other
compressing the beam, squinting at one another from the same side, but
facing one another. Would not the coma cancel out?

Two collimators? Are you talking about anamorphic prisms? A collimator
is a lens.

I´m thinking of two fiber-optic collimators facing one another, with a 2mm
diameter free-space light beam connecting them. The free-space beams
traverse various interesting optical components, some of which have annoying
reflections. The intent is to misdirect the various reflections such that
they miss the collimator apertures and so are lost.

Joe Gwinn

Minor misalignment of the free-space optics is a win, because the
available etendue (area-solid angle product) is so large compared with a
fibre that you can misalign them without losing signal.

It´s the free-space reflections that mainly bedevil us.

The lenses typically have (or can be required to have) a larger NA than the
fiber, so there should be some wiggle room before light is lost.

.
The collimators themselves don't have that luxury.

Unless some loss of light is acceptable?

With single-mode graded-index fiber, there would be no reason not to point
the light cone directly at the lens aperture, as both "object" and
"image" are ~ diffraction-limited spots.

I may be missing something critical. Is there an article I should read?

Hmm. I do know of conservation of etendue, but in a cookbook way. I´ve
always wondered what physics entity (like energy or momentum) is being
conserved by etendue.

Joe Gwinn
 
On 4/27/19 10:03 AM, Joseph Gwinn wrote:
Just returned from two weeks away.

On Apr 14, 2019, Phil Hobbs wrote
(in article<JdqdnVCDIseDRC7BnZ2dnUU7-SOdnZ2d@supernews.com>):

On 4/13/19 10:52 AM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<Psadnaf9IIXWpCzBnZ2dnUU7-KGdnZ2d@supernews.com>):

On 4/12/19 6:08 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<a8KdnfNtO80RSi3BnZ2dnUU7-fXNnZ2d@supernews.com>):
[big snip]

Yup, backreflections from the lens (and even the window in the pac
age

are a problem. Stick-slip in the threads is a nuisance, though I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there is a
ric

from photography to cause reflections to fall in harmless places. Ba
ica
ly,
if one displaces object to one side the image will migrate the other
way

and back reflections will no longer re-enter the lens. This is an ap
lic
tion
of the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn
Sort of. In a laser collimator, light reflected back down the beam axi

hits the laser exactly, regardless of minor lens misalignment.

I'm not visualizing this. In my mental picture, the reflection
misses the lens, and so cannot get to the hapless laser diode.


Light propagation is time-reversal symmetric. If you send it back the
way it came, it winds up where it began.

It can help a bit with the first-surface reflection from the collimato
,
especially if the first surface is concave.

I think we have different optical systems in mind. .
Problem is, in a LD collimator the coma builds up pretty fast as you g

off axis.

What if one has two collimators, one expanding the beam, the other
compressing the beam, squinting at one another from the same side, but
facing one another. Would not the coma cancel out?

Two collimators? Are you talking about anamorphic prisms? A collimator
is a lens.

I´m thinking of two fiber-optic collimators facing one another, with a 2mm
diameter free-space light beam connecting them. The free-space beams
traverse various interesting optical components, some of which have annoying
reflections. The intent is to misdirect the various reflections such that
they miss the collimator apertures and so are lost.

Joe Gwinn

Minor misalignment of the free-space optics is a win, because the
available etendue (area-solid angle product) is so large compared with a
fibre that you can misalign them without losing signal.

It´s the free-space reflections that mainly bedevil us.

The lenses typically have (or can be required to have) a larger NA than the
fiber, so there should be some wiggle room before light is lost.

Nope. Light propagation is time-reversal symmetric, so in a single
mode, if misalignment reduces the reverse coupling by N dB, it reduces
the forward coupling by the same factor.

.
The collimators themselves don't have that luxury.

Unless some loss of light is acceptable?

A whole lot of loss.

With single-mode graded-index fiber, there would be no reason not to point
the light cone directly at the lens aperture, as both "object" and
"image" are ~ diffraction-limited spots.

I may be missing something critical. Is there an article I should read?

Hmm. I do know of conservation of etendue, but in a cookbook way. I´ve
always wondered what physics entity (like energy or momentum) is being
conserved by etendue.

Conservation of etendue, at bottom, is the same physics as the
Heisenberg uncertainty--you can't localize both the real-space and
k-space wave function simultaneously to better than a certain bound.

Cheers

Phil Hobbs


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com
 
On Apr 27, 2019, Phil Hobbs wrote
(in article<cIGdnQscvI2Sd1nBnZ2dnUU7-LXNnZ2d@supernews.com>):

On 4/27/19 10:03 AM, Joseph Gwinn wrote:
Just returned from two weeks away.

On Apr 14, 2019, Phil Hobbs wrote
(in article<JdqdnVCDIseDRC7BnZ2dnUU7-SOdnZ2d@supernews.com>):

On 4/13/19 10:52 AM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<Psadnaf9IIXWpCzBnZ2dnUU7-KGdnZ2d@supernews.com>):

On 4/12/19 6:08 PM, Joseph Gwinn wrote:
On Apr 12, 2019, Phil Hobbs wrote
(in article<a8KdnfNtO80RSi3BnZ2dnUU7-fXNnZ2d@supernews.com>):
[big snip]

Yup, backreflections from the lens (and even the window in the
pac
age

are a problem. Stick-slip in the threads is a nuisance, though
I
haven't tried your teflon tape trick.
As for back reflections from windows (and maybe lenses), there i
a
ric

from photography to cause reflections to fall in harmless places
Ba
ica
ly,
if one displaces object to one side the image will migrate the o
her
way

and back reflections will no longer re-enter the lens. This is a
ap
lic
tion
of the Scheimpflug
principle:<https://en.wikipedia.org/wiki/Scheimpflug_principle

Joe Gwinn
Sort of. In a laser collimator, light reflected back down the beam
axi

hits the laser exactly, regardless of minor lens misalignment.

I'm not visualizing this. In my mental picture, the reflection
misses the lens, and so cannot get to the hapless laser diode.


Light propagation is time-reversal symmetric. If you send it back the
way it came, it winds up where it began.

It can help a bit with the first-surface reflection from the colli
ato
,
especially if the first surface is concave.

I think we have different optical systems in mind. .
Problem is, in a LD collimator the coma builds up pretty fast as y
u g

off axis.

What if one has two collimators, one expanding the beam, the other
compressing the beam, squinting at one another from the same side, b
t
facing one another. Would not the coma cancel out?

Two collimators? Are you talking about anamorphic prisms? A collimator
is a lens.

I´m thinking of two fiber-optic collimators facing one another, with a
2mm
diameter free-space light beam connecting them. The free-space beams
traverse various interesting optical components, some of which have
annoying
reflections. The intent is to misdirect the various reflections such tha

they miss the collimator apertures and so are lost.

Joe Gwinn

Minor misalignment of the free-space optics is a win, because the
available etendue (area-solid angle product) is so large compared with a
fibre that you can misalign them without losing signal.

It´s the free-space reflections that mainly bedevil us.

The lenses typically have (or can be required to have) a larger NA than the
fiber, so there should be some wiggle room before light is lost.

Nope. Light propagation is time-reversal symmetric, so in a single
mode, if misalignment reduces the reverse coupling by N dB, it reduces
the forward coupling by the same factor.

I do see that, now.

.

.
The collimators themselves don't have that luxury.

Unless some loss of light is acceptable?

A whole lot of loss.


With single-mode graded-index fiber, there would be no reason not to point
the light cone directly at the lens aperture, as both "object" and
"image" are ~ diffraction-limited spots.

I may be missing something critical. Is there an article I should read?

Hmm. I do know of conservation of etendue, but in a cookbook way. I´ve
always wondered what physics entity (like energy or momentum) is being
conserved by etendue.

Conservation of etendue, at bottom, is the same physics as the
Heisenberg uncertainty--you can't localize both the real-space and
k-space wave function simultaneously to better than a certain bound.

Conservation of uncertainty, because both concern waves. I do recall this
being mentioned somewhere, but how they got there was not explained. Again,
is there an article or book chapter that I should read?

Joe Gwinn
 

Welcome to EDABoard.com

Sponsor

Back
Top