coherence length

I thought most lasers have much wider bandwidths than 100kHz -- isn't it more like in the GHz?

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com 

I'm looking for work -- see my website!

(I'm likely to say something wrong... but anyway) GHz would be a coherence length of ~10 cm. I think that some cheap diode laser pointers are that bad. (Only hear say.) Maybe even worse. I should measure some (someday). This is a Sanyo (DL7140-201) used in CD players. From what I hear right out of the box it has a BW of ~6 MHz. We put it in an ECDL. (External Cavity) which is a grating on the output that reflects light back into the diode... making a second cavity. This reduces the BW. My 100 kHz number is mostly a best guess. That's the width I saw on the 'scope FFT*. Not the most accurate spectrum analyzer. :^)

It would be nice to have a second way to measure the number. Laser jocks are always asking about the line width.

George H.

*beating two lasers together into a fast photodiode

The coherence length L is the round-trip equivalent width of the envelope of the fringes of a Michelson interferometer.

It's also given by

L = c / delta nu

where delta nu is the equivalent width of the laser line.

I got most of this from Goodman, iirc, but FWIW it's in my Section 2.5.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Your average run-of-the-mill HeNe will have a coherence length of 300 metres or so, as long as you drive it gently so it's single longitudinal mode (SLM). (There are other ways of making this happen, but that's the simplest one.)

Diode lasers vary all over the map, from ~10 MHz for a good SLM one if you stand on one leg a bit, out to about a terahertz for DVD lasers run with strong UHF modulation, as is often done to eliminate mode hopping.

ECDLs like George's typically start at 1 MHz and go down from there. Sam Goldwasser will have lots more detail if he chimes in.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Thanks Phil, (I was mostly asking so there would be something science/ electronics related on SED.)

I'm not sure I'm thinking about this the right way. But could you measure the BW by measuring the coherence length?

I picturing (say) a kilometer of fiber, I split the beam sending 1/2 into the fiber and then recombining the output (with some attenuator to match the intensity in both beams.) and then looking at the fringe contrast. Thinking (perhaps naively) that if the contrast is then

1/2 (or 1/e) then the coherence length is ~ 1 km.

George H.

That's one approach that can be useful for long coherent lengths, but there are a lot of devils in the details. For instance, you have to make sure you don't get snookered by polarization shifts making the contrast anomalously low.

My fave is to use a delay discriminator followed by a spectrum analyzer. That way you don't need such a long length of fibre, and can measure a wide range of coherence lengths. To recover the line shape, you have to multiply the spectrum by 1/omega. (That's not exact, but it's close for short delays.)

As long as the delay is at least 1% of the coherence length, you can do a good job with few worries. If you need to get down to 0.01%, you have to apply a lot of low frequency gain to the discriminator output, which hurts the SNR, but you can always integrate for longer.

The super-duper keen method is *closure*: build three lasers, beat them together in pairs, and (via a minor blizzard of math) get the AM and PM noise spectrum of all of them at once. That takes a lot more apparatus though. Martin Brown and his radio astronomy folks use that method a lot, as well as more complicated variations based on overdetermined systems. (Overdetermined systems are nice because they supply a built-in error estimate.)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

This video is worthwhile. My principal mentor in optics was one of Dr. Shaoul Ezekiel's students. Keep in mind, in the Helium Neon Laser adjacent longitudinal modes have orthogonal polarizations. This is not always the case in other lasers.

Steve

Another relevant video..

Steve

That's interesting--I didn't know that. Is it on account of the He-Ne's very low round trip gain?

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

Steve reaches for his copy of Silfvast and the chapter on effects in cavities without internal polarizing optics in a discrete, uniform magnetic field. Then mutters this might take a while.

Steve

There are, in the liturature, at least four effects that cause the subtle flip in polarization. I'll type a quick summary in the morning.

Steve

We've got little HeNe's (for Mells groit I think) I've seen the loss of coherence due to the two (or three) competing modes. I don't think there is any polarization change... brewster windows on the output of the plasma tube.

George H.

Yup, it would just be the randomly-polarized ones where the effect exists.

Brewster windows change the round-trip gain by a lot--four quartz/air surfaces at Brewster's angle cost almost 40% loss per pass, which is a lot more than the gain of a He-Ne.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

I just requested this on interlibrary loan:

1.html

From the FAQ,

Quoting Tony Siegman:

(From: A. E. Siegman ( snipped-for-privacy@stanford.edu).)

The reason that HeNe lasers can run - more accurately, like to run - in mul tiple axial modes is associated with inhomogeneous line broadening (See sec tion 3.7, pp. 157-175 of my book) and "hole burning" effects (Section 12.2, pp. 462-465 and in more detail in Chapter 30) in the Doppler-broadened las er transitions commonly found in gas lasers (though not so strongly in CO2) and not in solid-state lasers.

The tendency for alternate modes to run in crossed polarizations is a bit m ore complex and has to do with the fact that most simple gas laser transiti ons actually have multiple upper and lower levels which are slightly split by small Zeeman splitting effects. Each transition is thus a superposition of several slightly shifted transitions between upper and lower Zeeman leve ls, with these individual transitions having different polarization selecti on rules (Section 3.3, pp. 135-142, including a very simple example in Fig. 3.7). All the modes basically share or compete for gain from all the trans itions.

The analytical description of laser action then becomes a bit complex - eac h axial mode is trying to extract the most gain from all the subtransitions , while doing its best to suppress all the other modes - but the bottom lin e is that each mode usually comes out best, or suffers the least competitio n with adjacent modes, if adjacent modes are orthogonally polarized.

There were a lot of complex papers on these phenomena in the early days of gas lasers; the laser systems studied were commonly referred to as "Zeeman lasers". I have a note that says a paper by D. Lenstra in Phys. Reports, 19

80, pp. 289-373 provides a lengthy and detailed report on Zeeman lasers. I didn't attempt to cover this in my book because it gets too complex and len gthy and a bit too esoteric for available space and reader interest. The ea rly (and good) book by Sargent, Scully and Lamb has a chapter on the subjec t. You're probably aware that Hewlett Packard developed an in-house HeNe la ser short enough that it oscillated in just two such orthogonally polarized modes, and used (probably still uses) the two frequencies as the base freq uencies for their precision metrology interferometer system for machine too ls, aligning airliner and ship frames, and stuff like that.

From the FAQ,

I still miss Tony. He narrowly missed being on my thesis committee (his excuse was that it was the summer and he wanted to get some research done), but he was a mentor and friend for years, and helped me get started in my consulting business.

Interesting references, Steve. Thanks.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

H41.html

ultiple axial modes is associated with inhomogeneous line broadening (See s ection 3.7, pp. 157-175 of my book) and "hole burning" effects (Section 12.

2, pp. 462-465 and in more detail in Chapter 30) in the Doppler-broadened l aser transitions commonly found in gas lasers (though not so strongly in CO 2) and not in solid-state lasers.

more complex and has to do with the fact that most simple gas laser transi tions actually have multiple upper and lower levels which are slightly spli t by small Zeeman splitting effects. Each transition is thus a superpositio n of several slightly shifted transitions between upper and lower Zeeman le vels, with these individual transitions having different polarization selec tion rules (Section 3.3, pp. 135-142, including a very simple example in Fi g. 3.7). All the modes basically share or compete for gain from all the tra nsitions.

ach axial mode is trying to extract the most gain from all the subtransitio ns, while doing its best to suppress all the other modes - but the bottom l ine is that each mode usually comes out best, or suffers the least competit ion with adjacent modes, if adjacent modes are orthogonally polarized.

f gas lasers; the laser systems studied were commonly referred to as "Zeema n lasers". I have a note that says a paper by D. Lenstra in Phys. Reports,

1980, pp. 289-373 provides a lengthy and detailed report on Zeeman lasers. I didn't attempt to cover this in my book because it gets too complex and l engthy and a bit too esoteric for available space and reader interest. The early (and good) book by Sargent, Scully and Lamb has a chapter on the subj ect. You're probably aware that Hewlett Packard developed an in-house HeNe laser short enough that it oscillated in just two such orthogonally polariz ed modes, and used (probably still uses) the two frequencies as the base fr equencies for their precision metrology interferometer system for machine t ools, aligning airliner and ship frames, and stuff like that.

Fun! Thanks Steve.

George H.

There have been a number of days and weeks that I have wanted to talk to Tony again, and not always for work.

Keep in mind the Zeeman effect is only ONE of about four reasons you can get Orthogonal Polarization.

A few other lasers exhibit this property, including ND:YAG under certain circumstances. Which is why I ordered the book.

Steve