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Interference of Light Beams from Two Independent Lasers.

copyright (2010)  Doug Marett

    Paul Dirac in his book "The Principles of Quantum Mechanics" has claimed quite famously that the interference of two independent light beams can never occur. He stated that "the wave function gives information about the probability of one photon being in a particular place, and not the probable number of photons in that place." In  order to explain why photon interference does not lead to a violation of the conservation of energy principle when there is interference of one photon with another, he instead established a new understanding, based on the idea that a photon can only interfere with itself. And he states quite categorically that "interference between two different photons never occurs." 1

An experimental proof that two independent light beams can form an interference pattern was first demonstrated in 1963 by Mandel and Magyar. 2

Mandel and Magyar actually used very short pulses of light from two independent ruby lasers that are fired simultaneously - depending on their phase relationship they form an interference pattern that can be captured on a photographic plate much like the Young Interference experiment. It is not necessary to go to these extremes to demonstrate this kind of interference - although the two beams may not form a stable pattern that is visible to the eye, they do readily form a beat frequency between them that corresponds to the rapidly changing phase relationship of the two interfering beams - so we are essentially detecting a rapidly changing interference effect. To do this, we start with two independent, frequency-stabilized HeNe lasers that are arranged so that their beams overlap at a photodetector similar to the arrangement shown in Fig. 1 below:

Fig. 1:

The lasers emit two modes each. The mode spacing for laser 1 was experimentally determined to be ~640.5 MHz. The mode spacing for Laser 2 is ~640.0 MHz. The gain curves for the two lasers are shown below. The upper and lower mode from each laser are perpendicularly polarized (if one is horizontal, the other is vertical). 

Fig. 2:

We have essentially two modes emitted by each laser, and the two sets of beams meet at the beam splitter, where they are deflected into the photodetector as a total of four modes. Two beat signals can be seen at the photodetector by displaying the resulting signal on an oscilloscope; one is at around 500 KHz, and the other is around about 10 MHz (which will be found shortly to be two closely overlapping signals at around 10MHz, differing by around 500KHz between them). If one laser is tuned so that the modes track across the gain curve towards the modes of the other laser, one can completely null out the beats (temporarily at least, frequency shifts due to  heat make it oscillate across the null point).

Fig. 3:

However, if one now tunes away from this null point, what is found is that the lower beat remains consistently at around 500KHz (once it is visible), while the upper beat goes from say close to zero to up to 100 MHz, before it is lost out of the bandwidth of my amplifier. Included are the four screenshots from the oscilloscope to show this happening.

A polarizing filter is put in front of the photodetector and rotated to see how it changes the signal. It is found that when the polarizer is at about zero degrees, the upper beat is at a maximum and the lower beat is invisible. At 45 degrees, the lower beat is at a maximum and the upper beat is weaker. At 90 degrees, another weaker signal with a frequency of about the upper beat frequency is visible. After considering this behaviour it becomes evident that perhaps the mode spacing difference between the lasers is small, and there are three beats here, two at about the same higher frequency and one at ~500 KHz, the former one being some overlap of  two closely spaced frequencies. One of these higher frequency beats is difficult to see without the polarizer since it is being swamped by the other signal of close to the same frequency.

In order to try to explain this, an excel spreadsheet was prepared of the expected frequencies where one can adjust the difference in the cavity lengths, and it is found that at a cavity length difference of just 0.08%, the two upper beat signals will always differ by ~500 KHz, regardless of where on the gain curves they are. So what is suggested is that this lower beat signal corresponds to the difference in the mode spacings of the two lasers, which must be ~500 KHz (i.e. ~ 640MHz and 640.5 MHz). This beat is then either a sub-beat of the two upper beat signals in the RF range, or it could be the beat signal between the two UHF beat signals - in both cases they should have a maximum intensity in a plane half way between the vertical and horizontal mode alignments (i.e. at 45 degrees) which is where it is found. In figure 4 below is a graph made from an Excel spreadsheet - the test numbers are actually a number of different possible frequencies that can exist between the two sets of modes. What one finds is that regardless of where the different sets of modes are for laser 1 and laser 2, on beating together, they always result in a sub-beat frequency of around 500KHz (in our actual case, 512 KHz) which corresponds to the difference in the mode spacings between the two lasers.

Fig. 4:

 To demonstrate that the higher frequency beat signal is in fact an overlap of two beat frequencies close in frequency, it was necessary to constructed a set of active filters capable of isolating them from one another. The circuit used was the active filter in the LMH6628 data sheet. I used two sets of LMH6609 chips, as shown in Fig. 5 below: 

Fig. 5

All power supply leads (+/- 5V, except gnd) had 470 ohm resistors on them to limit oscillations.

Ra = 470 ohms, Rb = 22 ohms, R2 = 2.2K, C = 200pF, K-R = 150 ohms, R = 150 and 330 ohms.

The bandpass was sharp with a 10X drop at 500KHz either side. The center frequencies for the two filters were 2.4 and 2.9MHz. A picture of the filters in the setup is shown below:


The filters are on the breadboard. The apparatus is then adjusted so that each of the two upper beat signals from Laser 1 and Laser 2 fall each within the bandpass of one of the filters. The output of the two filters are shown one above the other on the oscilloscope trace in Fig. 6 below:

Fig. 6

The two independent beats are shown above. One is at 2.4MHz, the other at 2.9MHz. So this demonstrates that our observation is correct, and that the upper beat signal seen in the original traces of Figure 3 is actually two overlapping beats that differ in frequency by ~ 500KHz, and the frequency of these upper beats goes from close to zero to well over 100MHz, depending on how far apart the modes are between laser 1 and laser 2. This frequency can be controlled by adjusting the beam balance on one of the stabilized lasers, that then moves the two modes of that laser to a higher or lower frequency inside of the gain curve as compared to the other laser, which is held stable. Further, the lower beat signal always corresponds to the difference in the frequencies of these two upper beats, and since the two upper beats have orthogonal polarization with respect to each other, the lower beat can be isolated using a polarizer at 45  degrees to the planes of the other two. The lower beat signal always corresponds to the difference in the mode spacing between the two lasers, and as such, is a relatively constant frequency of ~ 500 KHz.


    This experiment demonstrates that the statement by Dirac that "a photon only interferes with itself" is false. It is shown herein that two independent lasers, when made to interfere at a photodetector, generate beat patterns corresponding to interference patterns changing at the difference frequency between them. These beat patterns are shown to correspond to the beating of the crossed modes of the same polarization between laser 1 and 2, and further, that a sub-beat arises which is the beating of these two beats, and corresponds to the frequency difference between them, as outlined in Fig. 2.  Looked at another way, this sub-beat at ~500 KHz corresponds to the difference between the mode spacing of the two independent lasers, and thus provides information about the difference between the two independent light sources that can only be obtained if true interference was occurring between the two independent beams. An even simpler way of verifying that the two beams interfere is to simply block one beam path - on doing so, all beat frequencies disappear from the oscilloscope screen.



1) Dirac, Paul, The Principles of Quantum Mechanics, 4th Edition, Chapter 1

2)  Magyar, G. and Mandel, L.  1963 Nature 198 255.