# Frequency/Wavelength-Modulation Spectroscopy - how does it work?

1. Oct 23, 2009

### mikeph

Hello, I am having a little trouble getting to the fundamentals of FM (laser) spectroscopy. As I understand from some research, the frequency of the incident beam is varied with a second frequency much larger than the first:

Bjorklund 1980: "The key concept is that the modulator is driven at radio frequencies that are large compared to the width of the spectral feature of interest... As a result, the FM sidebands are widely separated and the spectral feature of interest can be probed by a single isolated sideband. Both the absorption and the dispersion associated with the spectral feature can be separately measured by monitoring the phase and amplitude of the rf heterodyne beat signal that occurs when the FM spectrum is distored by the effects of the spectral feature on the probing sideband."

I have trouble understanding what this means, not knowing what these terms mean: "sideband" (how can a continuous frequency modulation lead to 'widely separated sidebands'?), and "rf heterodyne beat signal", which has not been defined earlier in the paper. I have another source which states:

Allen 1998: "The oldest and most common approach for sensitive absorption measurements with diode lasers involves high-speed modulation of the laser injection current, introducing amplitude and frequency modulation on the output beam. These techniques are broadly termed frequency-modulating (FM) spectroscopy. Using phase-sensitive detection at some harmonic of the modulation frequency, background-equivalent absorbances of ~ 10^−7 have been demonstrated"

So I know what happens- they do this modulation and get more sensitive measurements, but I can't figure out why this works, and feel a bit restricted because I don't have a background in electrical engineering. If forced to have an educated guess, I'd say they were scanning the laser back and forth across the spectral peak, and then look at the transmission once every scan for a certain phase, the phase where the scan hits the peak? And then from this collection of results, they can work out the absorption? I don't understand why this gives you more accurate results by such a huge factor.

Thanks for any help,
Mike

2. Oct 23, 2009

### waht

Bit of a theory: The signal of the laser

$$y_{laser} = \cos(\omega_{laser}t )$$

in FM modulation, you are shifting the carrier's frequency at a rate given by the modulation frequency:

$$y_{laser} = \cos((\omega_{laser} + \sin(\omega_{mod}t )t)$$

and this will give a spectrum similar to this, the spikes are the sidebands and are related to the modulation frequency. Notice, new frequencies were generated in this process that are slighly offset from the carrier.

http://img337.imageshack.us/img337/9933/fmspec.gif [Broken]

As the $\omega_{mod}$ is swept from different values continuously, so will the sidebands from the laser sweep continuously back and forth. When a sample is subjected to the new frequencies, some will be absorbed. Once the laser reaches the detector, the laser carrier is removed, leaving you with a signal f_d which is of the same frequency as the f_lo but is different in amplitude because of absorption. So now the last step is to remove the f_lo from f_d using a device called a mixer (old school name is heterodyne) which subtracts two frequencies. The output from the mixer is the amplitude proportional to absorption and it is fed into the computer for analysis. All this is synchronized to a sweep time-base signal from the computer.

f_lo or $\omega_{mod}$ means frequency of the local oscillator.

f_d frequency coming out of the detector with laser carrier removed.

Here is a similar set up:
http://www.strath.ac.uk/Other/cpact/presentations/2004/ppts/Andrews.pdf

http://img33.imageshack.us/img33/3508/spec1r2.png [Broken]

Last edited by a moderator: May 4, 2017
3. Oct 28, 2009

### mikeph

I understand the above two equations, the second one looks interesting but I think I can understand it as just replacing w_laser by (w_laser + sin(w_mod * t)), which makes sense to me now, but further down you say "As the w_mod is swept from different values continuously", which seems to suggest that the modulation frequency itself changes?

I am having trouble working out what the "carrier" means as well. I understand the term "envelope" which multiplies two waves together to modulate the amplitude of one wave with another wave, is "carrier" like the frequency-modulation analogue of that? So you get one wave (the diode laser's operating frequency), and then have the rf oscillator changing the current of the laser with the "carrier", so the output is the original wave, frequency-modulated by the "carrier"? Is that a correct use of terminology?

Thanks very much,

Oh, I have one more question, another paper I am reading states that wavelength and frequency modulation are different things?! I thought they were dependant on one another (chosing one fixes the other for light?):

Arroyo & Hanson (1993):

"The emphasis in previous water-vapor papers has been mostly on frequency-modulation detection strategies suited for very low absorption (< 0.1%) in connection with trace gas detection applications. In that case the feature of central interest is the magnitude of the line-center absorption over a fixed path length. However, accurate characterization of the shape of the absorption features is more complex, with frequency-modulation detection strategies, because of the mathematical transform that relates the actual line shape to the wave form observed. This problem is particularly acute for doublets, triplets, and other cases of overlapping lines, which are common features in the water-vapor spectrum. Since our interest is focused on quantitatively measuring concentrations, temperature, pressure, and even velocity, of water vapor at high temperatures, a wavelength- modulation technique with direct absorption detection is used."

4. Oct 28, 2009

### waht

I thought the f_lo must be swept like in an actual spectrum analyzer, however there is a much neater trick. The laser frequency is swept by the scan controller, and at the same time it is modulated by a constant frequency f_lo. The trick is when absorption occurs, the FM modulation is converted to an AM modulation. The resultant AM modulation is picked by the a detector which removes the laser signal leaving you with an f_lo but amplitude modulated which is related to absorption.

here is a nice paper on fm spectroscopy:
http://www.newfocus.com/products/documents/literature/apnote7.pdf

I should wave used the term CW (continuous wave) instead of a carrier. The carrier is a CW modulated to sent data. There is no data sending in this experiment.

5. Nov 11, 2009

### MeChaState

Hi Wahl,
Would you be able to describe Wavelength Modulation too as you did very nice for FM?

PS:
FM: How can we in practice modulate the frequency of a LASER?

Thanks
David

6. Nov 26, 2009

### mikeph

Hello

sorry I have not replied, I have focused on a few other things due to confusion over this. I'll work through that link, but for the time being I can try to answer MeChaState's question.

As I have learnt, WM is like FM except the modulation is a lot slower, so in WMS the laser is modulated with a frequency of say 50kHz, whereas in FMS it is modulated on the scale of MHz or even GHz, so the analysis is different.

I found a neat explanation from a PhD thesis by Zhou(2005) who did his work at Stanford,CA:

For diode lasers you modulate the frequency by modulating the injection current. For large amplitude modulations you have the side-effect that the actual laser output intensity changes, but if you modulate over a small amplitude you can approximate the amplitude to be constant. I think this was first done by Reid(1981) experimentally, and he gives a neat introduction to it in that paper, if you have access,

7. Dec 2, 2009

### mikeph

In fact, I have found the best explanation yet:

"The temporal point of view for the description of the modulation is that the laser optical frequency varies as a sinusoidal function of time, between two extrema separated by twice the modulation depth. A complementary analysis is obtained by adopting the spectral point of view: the modulation creates a broadening of the laser spectrum, with the creation of sidebands around the time-averaged value, equally spaced in frequency by the modulation frequency... The temporal description suitably describes the interaction of the modulated light with an absorption feature as long as the laser instantaneous optical frequency can be considered as constant on a time scale characteristic of the molecular (atomic) transition. This limit is reached when the modulation frequency approaches the width of the absorption line (in frequency units), and it marks the transition between wavelength-modulation spectroscopy and FM spectroscopy. In the latter case, one has to adopt the spectral viewpoint by considering the absorption of each of the individual sidebands and their heterodyne mixing on a square-law photodetector."

Phillipe & Hanson (1993)

I have a single question remaining: to understand exactly how these sidebands arise, how can I simulate this modulated wave in MATLAB? Can I just try to find the Fourier transform of a modulated wave? I don't know a lot about Fourier transforms so I don't think I'd learn a lot without a little pointing in the right direction.

Thanks,