Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures  Transmission grating spectrometer: Measuring and calculating the angular dispersion. Understanding resolving power.  Reflection grating spectrometer: Using a machinist scale to measure the laser wavelength.  The far-field (Fraunhofer) diffraction pattern of randomly placed identical particles: Measuring the particle size from the diffraction pattern. Topics

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Transmission Grating – Normal Incidence mm mm a A B What determines whether m=positive is above the dashed line or below the dashed line?

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Transmission Grating – Oblique Incidence mm mm a A B Our convention: ccw angles are positive; cw angles are negative. In the example above: both  i and  m are positive. ii C D ii

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Angular Dispersion Different colors (wavelengths) of light have their maxima at slightly different transmitted angles given a particular transmission grating and incident angle. (White light gets “broken up” into rainbow colors at the maxima for m  0. The m = 0 maximum remains white.) Angular dispersion quantifies the change in the (transmitted) angle at which the maxima occur per unit wavelength change:

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Calculating the Angular Dispersion

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Resolving Power Under which conditions can you resolve the sodium doublet? Hint: You are given and . You can make a (numerical) statement involving N, a,  m and  i.

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures White Light Source Lens (138mm) Screen Diffraction Grating VIII.A Measurement of Angular Dispersion with White Light Source  138mm Lens (48mm)  48mm  Look at “green” light to get some average wavelength.  Measure  from red to blue (  400nm).  Calculate the angular dispersion.

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures VIII.A Measurements with the Helium-Neon Laser Laser View from top Screen m=0 m=1 m=-1 m=2 m=-2 What happens as the grating is rotated? How do the maxima move? Do they? Laser Screen ?

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures VIII.A Wavelength Measurements using  i =0  and  i =30  View from top Know what you measure when doing the 30  incident angle measurement! An example: Laser Screen ii m=0 m=+1 m=-1 ii  m=-1  m=+1  m=+1  m=-1

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Once you have figure out what  m=-1 and  m=-1 are, you can calculate the wavelength as follows: (Subtract the first equation from the second on each side)

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Reflection Grating Normal Incidence Laser mm mm A B Convention: ccw angles are positive; cw angles are negative. In this example:  m is negative  m negative

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Reflection Grating Normal Incidence Laser m=0 m=1 m=-1 m=2 m=-2

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Reflection Grating Oblique Incidence mm A C ii Laser B D Convention: ccw angles are positive; cw angles are negative. In this example:  i is positive  m is negative.

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Reflection Grating Oblique Incidence Laser m=0 ii mm

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Reflection Grating Oblique Incidence Laser m=0 m=-1 m=1 m=-2 m=2

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Let’s rotate the picture to see what we do in VIII.B m=0 m=1 m=2 Laser Machinist Scale d L Screen xoxo xoxo xmxm 

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Evaluation of Wavelength Get wavelength from slope

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Machinist Scale: The “grid” spacing d depends on where the laser hits the scale! Example: d

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Another example: d An example of how not to do it: d=?

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures VIII.C Measuring the Size and Shape of Randomly Distributed Small Particles Look at single slit pattern first. What effect does moving the slit left or right have on the far-field diffraction pattern?

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures Imagine randomly placed slits of the same width: Just as we found with the double slit pattern: We would see an intensity variation in the far field diffraction pattern due to each slit (a single slit pattern). What about the diffraction pattern due to the interaction between the slits (like the double slit pattern for a double slit, or the diffraction grating pattern with regularly placed slits)?

Modern Optics Lab Lab 8: Diffraction by Periodic and Non-Periodic Structures VIII.C Measuring the Size and Shape of Randomly Distributed Small Particles For identical particles,the diffraction pattern from each individual object will look the same in the far field. How about the pattern due to the interaction between the objects? What if the objects were regularly spaced in a pattern?