Basic of basics of polarization and reflection.

Once upon a time these were taught in college; but I need to refresh them in my mind every once in a while.

p and s polarization: (forget about their Greek/German/? equivalent) Here p means "plunge", s means "stick". Because p light is easier to penetrate (plunge into water) whereas s light is easier to be reflected (a stick bounced from water).

At Brewster angle, the reflected beam is purely s-polarized, meaning the p-polarized light has zero reflectance. Wikipedia [1] has an excellent image to show this effect:



Reflectance vs incident angle is below (for 532nm and fused silica):

At Brewster angle (~56^o), reflectance of s-polarization is about 14%.

References and notes
[1] http://en.wikipedia.org/wiki/Polarizer

Using Zemax as a calculator to calculate for Gaussian beam

Using Zemax to calculate for Gaussian beam propagation is handy and precise.

First set up your optical system in sequential mode. For example, a lens comprised of two surfaces. Here I have a diode window and a collimating lens:



Go to Analysis -> Physical Optics -> Paraxial Gaussian Beam, or simply Ctrl-B. A "Paraxial Gaussian Beam Data" window appears. Click Settings, or right click mouse, the setting menu appears.

Zemax asks for 4 initial values to define the input Gaussian beam:
(1)Wavelength: defined in "Wav" tab.
(2)Waist size: this is 1/e² radius value. Note that this is for the embedded ideal Gaussian beam.^{Note 1}
(3)M² factor: the true Gaussian beam has Mx beam radius and Mx divergence compared to the embedded ideal Gaussian beam.
(4)Waist location.



After hitting OK, the "Paraxial Gaussian Beam Data" window gives Gaussian beam characteristics on all surfaces^{Note 2}. Both embedded and true Gaussian modes will be given. This is better than calculating by hand or by Matlab code that I used to do.

What would be better: I wish Zemax can creat a drawing showing Gaussian beam's marginal ray.

Notes:
1. To convert your real beam's waist size to its embedded Gaussian beam's waist, divided it by M.
2. This is ideal paraxial result without considering any aberrations on the optics. To see how aberration changes the Gaussian beam size, use "Skew Gaussian Beam" function.

Abbe number and glass code

Abbe number:

V =

nD - 1 nF-nC

(1)

where n_D, n_F and n_C are the refractive indices of the material at the wavelengths of the Fraunhofer D-, F- and C- spectral lines (589.2 nm, 486.1 nm and 656.3 nm respectively). Low dispersion (low chromatic aberration) materials have high values of V [1].

Glass code:
Example of BK7:
517642
n = 1.517
V = 64.2
(both at 587.56 nm) [2]

References:
[1] http://en.wikipedia.org/wiki/Abbe_number
[2] http://en.wikipedia.org/wiki/Glass_code

ZEMAX un-organized tips

I have to do extensive ZEMAX work to start my semi-new job. Had some non-sequential mode experience but now I really have to use sequential mode, and optimization and tolerancing functions. The first two tasks are aspheric collimating lens for diode and fiber-coupling. Now let me start to accumulate the little rules/tips of ZEMAX:

1. When defining a sequential system, the first parameter to set is aperture. Some aperture types are:
a. Float by stop size: defined by the radius of the stop surface. This type of aperture is used when the stop surface is a real, unchangeable aperture buried in the system, for example, fiber coupling.
b. Object cone angle: defined by the half-angle in degrees of the marginal ray in object space. This can be used when designing a collimating lens for a diode laser.
(Ref[1], page 63)

2. Afocal system [2]. The strict definition of an afocal system is a system in which both object and image conjugates are at infinity. For example, a laser beam expander in which both input and output beams are collimated. In Zemax, as long as the image conjugate is at infinity, the system is afocal. For example, when designing a diode collimating lens, one will choose "Afocal image space" in Aperture settings:


3. Apodization type. This describes amplitude variation of the pupil illumination. Gaussian apodization is what a laserist often uses:

A(ρ) = exp(-Gρ2)

Here ρ is the normalized pupil coordinate, i.e., ρ = 0~1 from the center to the edge of the pupil. G is the apodization factor. If G = 1, the amplitude at the edge of the entrance pupil falls to 1/e of the center value (intensity falls to 1/e²). So the marginal ray represents the 1/e² ray.
(Ref[1] page 64)

Marginal ray: is the ray that travels from the center of the object, to the edge of the entrance pupil, and onto the image plane.
(Ref[1] page 30)


References:
[1] ZEMAX user's guide Jan 2003
[2] Mark Nicholson, ZEMAX users' knowledge base - How to design afocal systems. http://www.zemax.com/kb/articles/36/1/How-to-Design-Afocal-Systems/Page1.html

LED and photodiode

LED

LED physics: as shown in Fig. 1, current flows from the p-side (anode) to the n-side (cathode) when the diode is forward biased. When an electron meets a hole (electron-hole combination), it falls into a lower energy level, and releases energy in the form of a photon.


(Image is from: http://en.wikipedia.org/wiki/Light-emitting_diode)

The wavelength of the light emitted, and therefore its color, depends on the band gap energy of the materials forming the p-n junction.

Photodiodes

Photodiodes are one type of photo detectors (other types includes thermal detectors, photoresistors, photomultipliers, etc.).

Same as LED, a photodiode is a semiconductor p–n junction device. But opposite to LED, in a photodiode light is absorbed in a depletion region and generates a photocurrent. There are two operation modes for a photodiode:

Photovoltaic mode: operated in zero bias. The illuminated photodiode generates a voltage which can be measured. This is photovoltaic effect, which is the basis for solar cells—in fact, a solar cell is just an array of large area photodiodes.

Photoconductive mode: operated in reverse bias (opposite to LED). The resulting photocurrent can be measured. Detectors operated in this mode have high linearity and dynamic range.

Material	Spectrum range
Silicon (Si)	400-1000 nm
Germanium (Ge)	900-1600 nm
Indium gallium arsenide phosphide (InGaAsP)	1000-1350 nm
Indium gallium arsenide (InGaAs)	900-1700 nm

References:
[1] http://en.wikipedia.org/wiki/Light-emitting_diode
[2] http://www.rp-photonics.com/photodiodes.html

Luminescence - photoluminescence - phosphorescence

Luminescence refers to light emission caused by electron transition from excited state to ground state; not by a rise in temperature (light emission from pure heat source is incandescence).

By different excitation(pumping) mechanism, luminescence has various types, for example:

• Photoluminescence: material is pumped by absorption of photons (e.g., fluorescent lamp).


• Cathodoluminescence: pumped by electron beam (e.g., CRT monitor).


• Electroluminescence: pumped by electric current or field (e.g., LED).

Photoluminescence:
From the transition speed, photoluminescence is divided into two types:

• Fluorescence: an almost instantaneous effect; the emission ends within ~10^-8 second after excitation.


• Phosphorescence: this term describes the persistent luminescence (afterglow) of phosphors (the "glow-in-the-dark" phenomenon). The upper state is either metastable with long lifetime or is transition forbidden to the ground state.

Phosphorescence:
Materials exihibiting phosphorescence are known as phosphors. Phosphors are usually some microcystalline materials. In these crystals, there are impurity ions called activators, which replaces some host ions in the crystal lattice. These activators form luminescing centers and are where the excitation-emission process occurs.

References
[1] John Wilson and John Hawkes, Optoelectronics, an introduction, 3rd ed., Prentice Hall Eruope, 1998. Chapter 4.
[2] Luminescence article at www.britannica.com
[3] Other sites that explain the phosphorescence physics:
http://math.ucr.edu/home/baez/spin/node17.html
http://en.wikipedia.org/wiki/Phosphorescence

Photometric meters

1. Goniophotometer [1]
The Greek word "gonio" means angle. A goniophotometer measures spatial distribution (xyz and angular) of a radiation source. It has a built-in photopic [2] filter so all measured radiometric quantities automatically convert to photometric ones after calibration. A goniophotometer is able to measure:

• Luminous power (flux) in lm.


• Luminous intensity in cd = lm/Sr.


• Illuminance in lux = lm/m².


• Luminance in cd/m² = lm/m²-Sr.


• Color coordinates and correlated color temperature.


• Sample's retro-reflection as function of angle in cd/lx.

2. Colorimeter [3]
There are also filters in a colorimeter to mimic the human cone response. A colorimeter produces numerical results in one of the CIE color models.

References and notes:
[1] X-Rite GmbH - Optronik catalog.
[2] The word "photopic" refers to vision by cone receptors in the human eye (while "scotopic" refers to rod receptors).
[3] Bruce Fraser, Chris Murphy, and Fred Bunting, Real World Color Management, 2nd ed. Peachpit Press 2005. Page 43.