Diffractive Optics (1)
Transcript of Diffractive Optics (1)
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Phase angle ()= (2/) (path difference)
= 2/ (1/2*D*Sin )
= D*Sin
I = I0(Sin /)2
Sin Sin I
0 0 0
/D 0 0
2/D 0 0
I0
3/2D 3/2 -1 [4/9 2] I0
Diffraction by Single Slit
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Interference by Multi Slits
I = I0 [Sin (N/2) / Sin /2]2
= 2/ (d*Sin )
Long distanced
N= number of slits
For N=4
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Long distanceD d
Single slit diffraction and multi slit interference
I = I0(Sin /)2 [Sin (N/2) / Sin /2]2
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Ex: Fresnel Lens
Difference between classical optical elements and diffractive elements
Fresnel lens will do the same action as classical Plano-convex lens will do.
Remove the slabs of glass that do not contribute
to the bending of light rays to a focal point
The surface profile of the lens that is responsible
for the optical power of the element is preserved
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Diffraction grating diffracts light in a preferred direction
Preferred direction depends on wavelength of the light and characteristics of grooves
Various types of diffractive optical elements
Discrete number of phase controlling surface
Smooth phase controlling surfaces
Calculated interference pattern is
reduced to a series of phase masks
Interference pattern is recorded on
a hologram recording plate
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Propagation of light through a classical optical system (lens) can be understood by tracing
rays bundles following the Snell’s law.
DOE can be understood in terms of wavefronts: the surface of constant phase perpendicular
to the path of light rays
Planar elements consisting of zones which retard the incident wave by a modulation of
the refractive index or by a modulation of the surface profile
Diffractive optics has emerged from holography
DOEs have comparable optical properties with those of refractive elements
Diffractive optics operates on the basis of interference and diffraction.
Focal length of a diffractive lens depends on the surface-relief profile
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Advantages:
Flexibility in complex wavefront construction
Aberration correction
Thin and Light weight chromatic systems made of only one material
Multiple optical elements can be written on a single substrate
Drawbacks
Require advanced fabrication technologies
Incorporate fabrication (writing) errors and substrate errors
Produce multiple diffraction orders and may lead to confusion if not
separated and understood correctly
Expensive than those for conventional optics
Generally less efficient than refractive optics
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Novel characteristics of diffractive optics
Large negative dispersion
No contribution to petzval sum
General aspheric fuction
Unique optothermal coefficient
Diffractive optics operates on the basis of interference and diffraction.
Spectral characteristics are very different that that of conventional lens
Diffractive optics are typically blazed to maximise the amount of light thatpropagates in a particular diffraction order
Diffraction efficiency is a measure of the energy in a given order relative to the energy
Contained in the incident illumination
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Diffractive optical element with complementary dispersion
properties to that of glass can be used to correct for color aberration
Gratings inherently diffract shorter wavelength light through smaller angles
Hybrid lens
Correction of chromatic aberration
Classical arrangement
Applications of diffractive optics
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The amount of dispersion of a material is characterized by Abbe V-number
The expression is based on the refractive indices at three wavelengths of visible region
Crown glass is weak dispersive glass while flint glass is strongly dipersive.
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Lensmaker’s formula to express the power of a lens at each of three wavelengths
Measure of chromatic aberration
* Refractive index is larger than at shorter wavelengths,
* the power of the lens is greater
* Focal length is shorter than at longer wavelengths
Cauchy’s formula
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Correction of chromatic aberration
Combine two lenses whose total power is equal to the required power but total dispersion is zero
Total power of the lens
Refractive indices and powers are so chosen that the sum of the individual chromatic aberration of lenses get cancelled
Condition for chromatic correction
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Power of a diffracting lens
=grating period at a distance r from the axis
(r) r represents the profile and therefore is a constant of the lens.
Power of the lens changes linearly with wavelength.
Amount of chromatic aberration
Powers of the lens at three wavelengths
V-number of a diffractive lens is
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Diffractive optics as converging lens
Diffractive optics as wavefront corrector
Diffractive optics as Null element for optical testing
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Diffractive optics as beam sampler
Diffractive optics as lenslet array
Diffractive optics as Laser beam splitter
Spot array generator
Fan-out elements
Multiple beam gratings
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Optical communications
Laser machining
Biomedical sensor optics
Projection display systems
Head-up-displays
Historical application: Spectroscopy (analysis of fine spectrum by ruled gratings )
Imaging applications (broadband illumination):
Reduction of chromatic and thermal aberrations
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Fresnel zones
Fresnel zone plate
Block the even zones
Fresnel phase plate
/2
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Two level Fresnel phase plate
Four level Fresnel phase plate
Eight level Fresnel phase plate
Multi-level (smooth)
Physical Optics: Blazed Grating
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Physical Optics: Blazed Grating
Prism Blazed Grating
Prism is sliced in to one-wavelength-high pieces
Will direct all the light in to the first order
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Almost any wavefront can be generated using diffractive optics
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1871 Lord Rayleigh Fresnel zone plate Acts as a lens Low efficiency 10%
1898 Wood Fresnel phase plate 40% efficiency
1950s Blazed zone plates
1960s Development of fabrication techniques
1972 Surface profile creation by photolithography
1980s MIT Lincoln Laboratory ……Binary optics Program
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Fabrication of Diffractive Optical Elements
Created as spatially varying surface relief profiles in or on an optical substrate
Simple binary phase diffractive element
=period
b=groove size
d=depth of the structure
b/=duty cycle
If duty cycle is half then the grating is a square-wave yep grating
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Lithography techniques
Developed for microelectronics industry
Uses light sensitive polymers
Controlled etching or deposition methods
Direct writing
Controlled Material removal process
Two steps
Replication of photomasks pattern into photresist
Subsequent transfer of the pattern into the substrate material to a precise depth
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Photolithography
Mask makers can achieve a minimum feature size of 0.8 microns quite easily.
However it can go down to 0.3 microns with e-beam lithography
Alignment of mask to the substrate features are very critical
Material (Substrate) for Diffractive optics
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Material (Substrate) for Diffractive optics
Spectral transmission properties
Refractive index of the material
For reflective elements:High reflectivity and coating
Coefficient of thermal expansion
Selection of substrate depends on optical
and mechanical properties
Fused silica is suitable choice for UV to IRregion due to its transmission properties and
low coefficient of thermal expansion
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Photoresist: to protect the underlying substrate during subsequent processing steps
Positive photoresist: when exposed resist dissolves upon development
Negative photoresist: when exposed polymerizes and remains after development
a. Photoactive compound
b. Solvent carrier
c. Matrix material
Light sensitive component optimum for a specific wavelength
Steps involved in application of photoresist
Clean Substrate
Application of adhesion
Spin coating
Soft baking
Exposure and development
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Exposure and development
Patterns are formed in the photoresist layer
Spatially varying pattern of light energy created with a lithographic mask
Mostly binary lithographic masks with clear and opaque regions (chrome on a glass)
are prepared
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Uniform ultraviolet light is used for exposure
After exposure the Substrate is subjected to a development step
Washing away of exposed photoresist layer
Contact printing : Mask is placed in intimate contact with the photoresist
[1:1 transfer of the image]
Deteriorates the mask
Proximity printing: To mask at proximity to the photoresist by 5 to 50 microns
Projection lithography: Mask is imaged onto photresist with a demagnification upto 20X
- Using high quality projection lenses, Photoreduction of mask is possible
- Small features ~ 0.5 microns can be achieved
- Becomes expensive
- Suitable for volume manufacturing
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Etching
Dry etching
Wet etching
During etching process, the areas not covered by the photoresist are removed
Highly controlled
Repeatable
Anisotropic in nature: it etches preferentially perpendicular to the substrate’s surface
Isotropic in nature
Chemical process
Reactive ion beam etching (RIBE)
Important aspects
Etching rate
Quality of etched area
Multi-level diffractive optics
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A diffractive element with many levels is fabricated by using multiple masks
and repeating the lithography process
Multi level diffractive optics
Lithography errors j
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t og ap y e o s
Lithographic
error
doe j
Substrate
error
p
p
p Lithographic positioning error (constant)
p Periods
p is large ~ lithographic errors are not critical
p is small ~ lithographic errors are becoming critical
(High frequency DOE)
Alignment errors
Over/underexposure of photoresist
Etching error
Other sources of error Rule of thumb
Lithographic errors should be less than
5 percent of the minimum feature size
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The system is based on water cooled Ar-ion laser working at a wavelength of 363 nm.
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Dual wavefront encoded DOE : Striped
Sliced Combo-DOE
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Combo-DOE, sliced in stripes of 50 m, alternatively
assigned to the spherical and aspheric waves
Sliced Combo-DOE
Off-axis spherical
wavefront
On-axis asphericalwavefront
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Dual wavefront encoded DOE : Superposed
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Fabrication Techniques for Diffractive Optical Elements
1. Lithographic methods
2. Direct machining
3. Replication methods
4. Dynamic methods
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1. Lithographic methods
Photolithography
Direct lithographic writing
Interferometric exposure
Gray scale lithography
Near field holography
Di li h hi i i
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Direct lithographic writing
Writing the exposure pattern directly into the photoresist.
It can be performed by either laser beam Or electron beam
Laser beam lithographyelectron beam lithography
There is no need to establish a pattern through a series of mask exposures
Intensity of the beam is varied so that the local exposure is proportional to the
required depth of the resist
(He-Cd) laser or Ar-ion laser
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Laser beam writing machine
E-beam lithography
Can write feature down to 0.7 microns
E-beam spot size can be down to 0.0125 microns
However, physiochemistry of the resist does not
Allow accurate exposure and development below
0.2 to 0.3 microns
Direct lithographic writing
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Advantages
Eliminate the need of lithographic masks
Time effective
Cost effective
Large number of phase levels can be generated
Limitations
Direct writing is a serial process. Each element must be written one at a timeby the scanning beam
Finite writing-spot sizes cause non-vertical side walls.
Interferometric exposure
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Optical Interference patterns can be used to expose a photoresist layer
Provide a patterning of very small feature sizes over a large area in one shot
limitation Profile is limited to binary or sinusoidal variations.
Gray scale lithography
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Photoresist is exposed to varying exposures
Multi-level DOE can be fabricated with a single lithographic masking and etching step
Mask with spatially varying transmission is used
Local surface relief depth in photoresist is proportional to the energy transmitted through
that area of the gray-scale mask
Advantages
Any arbitrary number of phase
levels can achieved
Eliminates the need of multi mask alignments
Limitations
High cost for mask
More sensitive to the
Substrate material
Near field holography
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Bragg grating fabrication
It uses near field diffraction patterns from diffractive phase mask
A phase grating is used that minimises the zeroth order and the irradiance pattern id
Generated from the interference of -1 and +1 order of transmitted diffraction orders
Direct machining methods
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Mechanical ruling
Diamond turning
Laser ablation
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Laser ablation
A focussed beam from an excimer laser is used to directly machine the surface
No need of photoresist and etching process
Local depth of the diffractive structure is proportional to the length of time that
beams dwells on a specific location
Laser ablation describes the interaction of intense optical fields with matter, in which
atoms are selectively driven off by thermal or nonthermal mechanisms.
Focused ion beam
Focused beam of ions sputters the atoms in the material off the surface
Replication methods
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High cost and time in lithography and direct machining
Make a master and replicate it
Solution
PolyCarbonate (PC)
Polymethyle methacrylate (PMMA)
Compact Disks (CD)
Solid plastic heated above transition temp
Embossed on thermoplastic foils
Security holograms on credits cards
Liquid polymer layer is
sandwiched between the blank
and the mold
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Photorefractive materials as Dynamic DOEs
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y
Photorefractive materials exhibit internal refractive index changes when illuminated by
a laser beam or interference pattern
The resulting fringe pattern transferred into the crystal as refractive fringe pattern and
Act as a diffractive element
Refractive pattern can be erased by the use of a powerful laser beam and another
pattern can be transferred into the same crystal
Liquid crystal spatial light modulators as DOEs
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Testing of Diffractive Optical Elements
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Testing of Diffractive Optical Elements
Measurement of dimensions and geometry of the surface structures
Measurement of optical performance of the component
Feature size
Locations of the features (transition points)
Grating depth
Verticality of the grating side wall
Edge quality
Surface roughness
Capabilities of the
Fabrication process
Measurement of dimensions and geometry of the surface structures
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Optical microscopy
Mechanical profilometry
Form Talysurf Profilometer
Contact Profilometer
Form Talysurf Series 2 PGI Diamond Conical Tip
Tip radius 2 m
Vertical Range 10 mm
Stylus Movement speed .5mm/min
Stylus Force 2mgF
Limitations:
1 Destroy the surface
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Avd:- 1. good sensitivity in Z-direction (depth accuracies upto 10 Angstroms)
2. Reflectivity of the surface/object is
not a prerequisite
1. Destroy the surface
2. Delivers only 1D profile
3. Only rotationally symmetric profiles can be measured
4. profile is the path traversed by the center of curvature of the stylus tip
(not the actual surface)
Phase Shifting Interferometry Developed in 1970s
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For high precision measurements
Three unknowns
White light interferometry for roughness measurement
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A typical optical profilometer based on the Mirau interferometry principle.
For Roughness measurement
White light interferometry for roughness measurement
Adv. Provides a 3D data set with high speed without destroying the surface
Atomic force microscopy Developed in 1986
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AFMs probe the sample and make measurements in three dimensions, x, y, and z (normal
to the sample surface), thus enabling the presentation of three-dimensional images of a
sample surface.
Resolution in the x-y plane ranges from 0.1 to 1.0 nm and in the z direction is 0.01 nm
Tip never comes in contact with sample. It measures small forces with a small tip on a
cantilevered arm with a feed mechanism
Scanning electron microscopy
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Scans the surface with high energy beam of electrons in a raster scan pattern
Interaction of surface atoms with electrons gives the information about the surface features