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





Interference by Multi Slits

I = I0 [Sin (N/2) / Sin /2]2

= 2/ (d*Sin )

Long distanced

N= number of slits

For N=4



Long distanceD d

Single slit diffraction and multi slit interference

I = I0(Sin /)2 [Sin (N/2) / Sin /2]2



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



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



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



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



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



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

http://upload.wikimedia.org/wikipedia/commons/e/e4/Diffractive.png

http://upload.wikimedia.org/wikipedia/commons/1/15/Lens6b-en.svg

http://upload.wikimedia.org/wikipedia/en/4/47/Lens6a.svg



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.



http://upload.wikimedia.org/wikipedia/commons/b/bd/Abbe-diagram_2.svg



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



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



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



Diffractive optics as converging lens

Diffractive optics as wavefront corrector

Diffractive optics as Null element for optical testing



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



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



Fresnel zones

Fresnel zone plate

Block the even zones

Fresnel phase plate

/2



Two level Fresnel phase plate

Four level Fresnel phase plate

Eight level Fresnel phase plate

Multi-level (smooth)

Physical Optics: Blazed Grating



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



Almost any wavefront can be generated using diffractive optics



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



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



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



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



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



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



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



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



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



A diffractive element with many levels is fabricated by using multiple masks

and repeating the lithography process

Multi level diffractive optics

Lithography errors j



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



The system is based on water cooled Ar-ion laser working at a wavelength of 363 nm.



Dual wavefront encoded DOE : Striped

Sliced Combo-DOE



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



Dual wavefront encoded DOE : Superposed





Fabrication Techniques for Diffractive Optical Elements

1. Lithographic methods

2. Direct machining

3. Replication methods

4. Dynamic methods



1. Lithographic methods

Photolithography

Direct lithographic writing

Interferometric exposure

Gray scale lithography

Near field holography

Di li h hi i i




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



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




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



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



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



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



Mechanical ruling

Diamond turning

Laser ablation



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



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



Photorefractive materials as Dynamic DOEs



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



Testing of Diffractive Optical Elements



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



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



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



For high precision measurements

Three unknowns

White light interferometry for roughness measurement



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



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



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

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Diffractive Optics (1)