It all depends on their in phase or out of phase interference i.e constructive or destructive interference.

But in actual practice, No, there  will not be an interference pattern. You can find interference patterns at the point where two lasers meet. After the laser beams crossed, you will not observe any effects of the crossing since there are no elemental photon-photon interactions.

But according to optical heterodyning, two light beams with different frequencies must interfere and give a signal at the difference frequency.

Whenever there is a frequency difference in two waves, in principle, hetrodyning will takes place but the frequency difference of 50 kHz in optical frequency lasers of frequency TerraHz range will be significant for any experimental observation of beats formed.

Sorry for the typing error. Will not be significant for any experimental observation.

There will be an interference but at 50 KHz. If you take a spectrum analyser and tune the frequency to 50 KHz to look for activity at that frequency you will notice beats. this is indeed the principle of optical heterodyning. What I would suggest you do it to take a photodiode and put the interfered output on that. Then take the photodiode output and put onto a spectrum analyser.  You will see activity at 50 KHz. Removing any of the two input laser will remove the 50 Khz interference. Then zoom into the 50 Khz to see activity. I should also add that you will only see the effect if you take one single laser beam and form the two 50 KHz offset beams from that. If you are going to see two different sources, you wont see any beats because the phase relationship would constantly drift. 

Some slightly confusing answers.

As Basudev points out, there will be interference which can be detected.  Where the beams overlap, the local intensity will oscillate at the difference frequency of 50 kHz, unless the signals have precisely orthogonal polarisation states.  If the beams differ in polarisation, the local polarisation state will rotate at 50 kHz where the beams overlap.

To observe the beats, the width of the detector should be less than the interference fringe spacing.  The fringe spacing will depend on the difference in wavefront slope where the beams overlap.

A slow drift in the relative phases of the beams will change the phase of the 50 kHz beat, but not the beat intensity.  In practice, sufficiently narrow line width and acceptable frequency stability can be difficult to achieve from two independent lasers.  As Basudev suggests, an alternative is to use a single laser which is split into two beams, each modulated by a different acousto-optic modulator to produce beams whose frequencies differ by 50 kHz.

With sufficient laser power, it may be more convenient to observe the interference with a photodiode connected to an oscilloscope, rather than a spectrum analyser.

The photodiode converts optical signal to electrical signal. But in this case, the signal at 50 kHz cannot be an optical signal (its a RF signal). It won't contain any photons.

How will then photodiode convert this signal to electrical signal that will be input to spectrum analyzer?

Had the photodiode had enough bandwidth to detect 10^15 Hz, it would have even detected the optical signal but since there is a bandwidth,typically at best about 2 GHz, it will automatically filter out the 50 KHz signal and not show the optical. The photodiode is merely a transducer, it converts optical energy to electrons.

By the way, who said RF cannot be electromagnetic radiation.

Note that heterodyning and interference are not the same.

When electromagnetic waves overlap the fields can combine constructively and destructively, so the local intensity changes.  This can occur in a vacuum and is a linear process.  As Vinay points out, there are no photon-photon interactions.  No new optical frequencies are created.  If the beam directions differ, then after separating, each will continue to propagate as if the other beam did not exist.

To detect the interference fringes we must convert optical energy into some other signal.  Basudev suggested a photodiode.  A high speed camera would record the instantaneous intensity distribution across its sensor.  A sufficiently high speed video or cine camera could record how the interference fringes evolve as the phase difference between the two beams changes.  With visible lasers and a much smaller frequency difference, we might simply use our own eyes.

In contrast, heterodyning is a non-linear process which creates new electromagnetic frequencies.  A photodiode can be treated as a square law detector.  The output current is proportional to the square of the input electric field.  As an optical detector it responds to the optical intensity, which oscillates at the laser difference frequency in our interferometer.  Fed instead with two RF electrical signals, it will generate new electrical signals at both sum and difference frequencies.

Returning to Arpit's original question.  If two lasers beams, differing in frequency by 50 kHz, are made to interfere, then the output is the same two laser beams unchanged in frequency or intensity.  There is interference where they overlap, but if the propagation medium is linear, transparent and free of scattering or absorption, then the interference does not perturb the propagation of either beam.

If the beams cross and then separate, Vinay is correct, and it will be difficult to detect any change in the output beams.

If the spatial overlap is more complete, as would be the case if both are coupled into the same single mode waveguide, then the composite output will oscillate at 50 kHz.

http://en.wikipedia.org/wiki/Heterodyne

You will have the usual fringe pattern, but travelling in the direction orthogonal to the fringes. The travelling speed is related to the frequency difference and is called doppler shift. As an example, this kind of interference is used in Laser Doppler Anemometry (LDA). In this technique, a Bragg cell is used to split a laser beam into two beams with a frequency difference in the range of the MHz. This provides a pattern travelling at a speed of the order of 1-10 m/s and permits to determine whether a tracer particle is moving towards left or right.

But the photodiode in general has its peak response in visible or infrared region.

Will it be possible to get measureable output from photo diode at 50 kHz frequency?

My friend the 50 Khz is a sideband on the visible radiation that is incident on the photodiode. The photodiode detects the visible and also the sideband. 

You are dealing with two coherent plane waves I assume. The output consists in oscillations of the current with frequency of 50 kHz, when both beams are directed on the photodiode. Be careful to achieve the spatial period (D = wavelength/sin(theta) ) more than photodiode dimensions, other way the current will have a constant value ! Theta is the angle between beams.

For example, if the photodiode have 1 mm diameter, the angle may be less then 2'. Such small values can be obtained by using a cube beam splitter or 60 Degree prism.

Hello,

There is a document on my ResearchGate page titled "MOM (Metal-Oxide-Metal) Devices", which discusses the history of laser heterodyning using the MOM 'diode' as the mixer/detector.

Regards,

Tom Cuff