Diffraction problem in DMD

Hello Marco,

 Please find answers in blue:

1) in reference to the Littrow configuration (alpha=beta=blazed angle) and having fixed grating pitch and mirror tilt, should I be choosing laser wavelength that is best for this mirror since the blaze angle is the mirror tilt angle? and will this do the job?

If you use Littrow, you are correct that you will have to choose a laser wavelength tha is near a blaze for the Littrow condition for the pixel pitch and tilt of the device.

2) It was written in the earlier note that "it is possible to move the incident angle to arrange a blaze for a given (n,n) order." How is this optimal incident angle found (say for 1st order) knowing that mirrors tilts 12 degrees, given a particular wavelength ?

This is only within a limited range.  There is a 2 dimensional blazed grating equation that will predict where or if a blaze is possible for a given wavelenth, (n,n) order, pixel pitch and tilt angle. 

3) (cont in Q2) if incident light is at this particular angle where it's blaze is for a given order, will the diffraction at other oder not be seen at a close distance to the mirror OR will it be seen at close distance the mirror but not at further distance?

Diffraction is a far field effect, not a near field effect.  If you mean will the nearby orders be suppressed, the answer is yes.  All orders not blazed will be reduced significantly.  This is because the power is conserved.  If the blaze order receives let say 80% of the energy the other 20% must be in all the other orders combined.

I hope this helps.

Fizix

Helloo DC,

You are correct that this is a result of the DMD acting as a 2D grating.

Merging the beams depends on the application.  If you are planning to re-image the DMD surface, then use ordinary optics that capture the multiple orders.  The beams will reconverge correctly at the image plane.  This is saying that diffraction does not make the beams extra-ordinary, it only restricts the energy to particular directions, but the orders still behave according to standard geometric optics with respect to lenses. 

If you do not plan to re-image the DMD surface, then you will likel need to adjust the incident angle.  I cannot think of any other way short of polarizers and ciruclators.  Note:  In some cases it is not possible to reach a blaze condition even moving the incident angle.

Fizix

DC,

Such a solution would be prohibitively expensive.  Actually it would be a component of a circulator, a Faraday rotator. 

for each secondary beam (order) you would use a Faraday rotator to rotate the polarization 90 degrees and then use a polarization beam combiner to combine the orders.  This would need to be repeated for each order to be added back.  This is not a realistic solution.

From your description it sounds like you may want to use a lens that makes all the orders parallel (i.e. collimated space) then use a final lens to reimage them from "infinity".  This is equivalent to cutting a lens in half and separating the two halves by whatever distance you need. 

Fizix

Hello Marco,

It is not possible to extinguish all but one order, even for a blaze condition.  You can get about 75 - 80 % of the overall energy there, but the remaining 20 -25 % will go into the other orders.  You could use a stop that only allows one order to exit the system.

1.  Your understanding of 1. is basically correct.  For a given pixel pitch and mirror tilt, there are only certain wavelengths that will have a Littrow blaze.  So if say there is a first order Littrow blaze at X nm, then there will also be a second order Littrow blaze at X/2 nm, . . . and an nth order Littrow blaze at X/n nm.

2.  The equation is basically as follows: Theta_inc(Theta_tilt, n) = Theta_tilt - acos[ (n*wavelength) / (d*sqrt(2)*sin(Theta_tilt))] where d is the pixel pitch and n is the blaze order.

3. if the light is a collimated laser, the orders will have the same divergence as the original beam.  So the orders will not spread in area quickly if it incident beam is collimated.

I hope this is helpful,

Fizix