f9417584   
   From: noreply@invalid.invalid   
      
   "dsb"  wrote in message   
   news:fe888799-059f-4967-96d2-74583ae51368@g17g2000yqo.googlegroups.com...   
   On Oct 11, 2:49 pm, Phil Hobbs   
    wrote:   
   > dsb wrote:   
   > > On Oct 10, 5:43 pm, AES wrote:   
   > >> In article   
   > >> <10343961-1082-45db-9a56-6366044f6...@c13g2000vbr.googlegroups.com>,   
   >   
   > >> dsb wrote:   
   > >>> Anyone have experience trying to mode match a laser into a confocal   
   > >>> etalon? I'm setting up a NICE-OHMS apparatus, and trying to inject   
   > >>> light from a single mode, PM fiber coupled DFB laser (1530 nm) into a   
   > >>> home built, 300 MHz FSR etalon. The cavity Q is 600 and the laser   
   > >>> linewidth is 500 MHz, implying an "exact" match between the cavity and   
   > >>> laser bandwidths. But, I can only get 20 to 25% of the light into the   
   > >>> cavity. I expect to do a factor of two better. I've gotten some   
   > >>> improvement by focusing the beam into the cavity, but that is what got   
   > >>> me to the 20 to 25% point. Changing the input beam diameter doesn't   
   > >>> make any difference. Any suggestions?   
   >   
   > >> Is your objective to get 100% of the light **transmitted through** the   
   > >> cavity at resonance? -- i.e., all input light emerges at the output   
   > >> end,   
   > >> and there is no light reflected back at the input end?   
   >   
   > >> Or is it to get all the light delivered into **and dissipated inside**   
   > >> the cavity at resonance?   
   >   
   > >> These need very different mirror reflectivities at the input and output   
   > >> ends.   
   >   
   > > I am not so much concerned with throughput as I am with needing to   
   > > lock the cavity to the laser as the laser wavelength is scanned. (15   
   > > GHz scan in 0.01 to 0.1 s.) I want to implement the Pound-Hall-Drever   
   > > method using the back-reflected beam. The cavity is constructed with   
   > > two mirrors of equal reflectivity (99.5%). I assume that the best   
   > > case -- 100% coupling into the cavity -- will reduce the back   
   > > reflected beam intensity by 50%. Once a photon gets into the cavity,   
   > > it has almost an equal probability of exiting through the front or   
   > > rear mirrors. If "all" the light gets in, half exits through the   
   > > entrance mirror, and the reflected beam will show that 50% intensity   
   > > dip. But, with only 20 to 25% getting in, the back-reflected beam   
   > > intensity dips by only 10 to 12%, and that isn't a strong enough   
   > > signal to provide good locking while scanning the laser wavelength.   
   >   
   > You can do a lot better than Pound-Drever by detecting both the R and T   
   > signals, and taking a linear combination, L = T-aR, and servoing where   
   > L=0. The parameter a is chosen so that dR/df = - dT/df at the point   
   > where L=0.   
   >   
   > This decouples the AM and FM noise completely, so that you can get   
   > shot-noise limited locking with a simple DC servo, without being limited   
   > by the nasty tendency of diode lasers to turn FM noise into AM when you   
   > lock them. (I patented this about 20 years ago, but it's out of   
   > maintenance IIRC.)   
   >   
   > It does require that the short-term natural linewidth of the laser is   
   > narrow enough that the loop can cope with it and the etalon doesn't cut   
   > the noise sidebands, but on the other hand getting to the shot noise   
   > means you don't need nearly as much cavity finesse to get the same line   
   > width when you're done.   
   >   
   > Cheers   
   >   
   > Phil Hobbs   
      
   Wow!   
   Phil,  Do you have the full reference to the patent?  Also, in dR/df =   
   - dT/df, what is "f"?   
      
   thanks,   
   DSB   
      
   Are you sure that your mirror absorption and scattering losses are much   
   smaller than the transmission losses of the mirrors?  If not, then the non   
   transmission losses will limit your maximum transmission.  While it is   
   possible to get mirrors for this wavelength with losses of a few   
   parts-per-million, this isn't the typical performance of mirrors from most   
   suppliers.   
      
   If the laser linewidth is 500 MHz and the cavity FSR is 300 MHz with a   
   finesse of 600, then the laser linewidth is a factor of 1000 broader than   
   the cavity linewidth.  Did you mean a laser linewidth of 500 kHz?  This   
   would match the two linewidths, but you would only see 100% transmission if   
   the laser linewidth were much less than the cavity linewidth.   
      
   You say you are wanting to servo the cavity to the laser, but the loop   
   bandwidth will be quite small if you are using a mechanical motion to close   
   the servo loop.  Why not lock the laser to the cavity and have use the fast   
   current tuning of the laser phase/frequency to close the servo loop.  Then   
   to tune the laser you tune the cavity and the laser will follow.  You might   
   want to add feed forward to the diode laser current to increase the tuning   
   width.   
      
   Have you chosen your mirror spacing so that the higher order transverse   
   modes are all well separated from the 00 transverse mode?  Near confocal is   
   about the worst place to be.  If any of the first few higher order   
   transverse modes overlap the fundamental transverse mode to within a few   
   times the cavity linewidth, this can lead to unstable locking as the laser   
   frequency jumps between different zero crossings in the in the PDH error   
   signal.   
      
   Bret Cannon   
      
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