Signals and Systems

SNR

https://en.wikipedia.org/wiki/Signal-to-noise_ratio

Laser

Laser Cooling

Coherent light property

Coherence is one of the most important concepts in optics and is strongly related to the ability of light to exhibit interference effects. A light field is called coherent when there is a fixed phase relationship between the electric field values at different locations or at different times.

Quantum

Coherent State in Quamtum

In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state that has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator.

Squeezed states

In quantum physics, light is in a squeezed state if its electric field strength Ԑ for some phases ϑ has a quantum uncertainty smaller than that of a coherent state.

To obey Heisenberg's uncertainty relation, a squeezed state must also have phases at which the electric field uncertainty is anti-squeezed, i.e. larger than that of a coherent state.

Squeezed light is used to reduce the photon counting noise (shot noise) in optical high-precision measurements, most notably in laser interferometers.

Nonlinear Optics

Second-harmonic generation(SHG)

Phase Match

Many phase-sensitive nonlinear processes require phase match to be efficient. Essentially, this means ensuring that a proper phase relationship between the interacting waves is maintained along the propagation direction.

The fundamental wave can be expressed as

E_\omega = E \cos(\omega t- k_1 z), k_1 = \frac{n_1\omega}{c}

Through SHG, the second-harmonic wave should be

P_{2\omega} = \frac{1}{2}\chi^2(\omega, \omega)E^2\cos(2\omega t- 2k_1 z)

The wave vector of SHG is $2k_1$ , but not the corresponding one to the wave $k_2 = \frac{2n_2\omega}{c}$ .

Since chromatic dispersion, usually $\Delta k = 2k_1-k_2 \neq0$ or $n1 \neq n2$ , so the nonlinear processes are not phash matched, and therefore, the SHG wave is hard to increase during propagating.

Birefringence Phase Match(BPM)

In Birefringence material, we can let the fundamental and SHG wave to be o-light and e-light respectively. Since birefringence effect, there are some possible angles to realize $n_o$ and $n_e$ is the same for $\omega$ and $2\omega$ .

For example, in KDP, a kind of negative uniaxial crystal, we can choose a proper angle to make $n_o^\omega$ between $n_o^{2\omega}$ and $n_e^{2\omega}$ .

Quasi Phase Match(QPM)

A nonlinear material with spatially modulated nonlinear properties; the crystal axis is flipped at a regular interval $\Lambda = 2l_c$ . The material is always a ferroelectric material.

For example, Periodically-poled lithium niobate (PPLN) is a domain-engineered crystal with alternating ferroelectric domains (+c/-c direction) at periods of 5-35 µm. Shorter periods enable second harmonic generation, longer ones support optical parametric oscillation. The domains are reversed through electrical poling.

(a) phase match, (b) quasi phase match, (c) phase mismatch

Spatical Optics

Numerical aperture

In most areas of optics, and especially in microscopy, the numerical aperture of an optical system such as an objective lens is defined by

NA = n\sin\theta

The size of the finest detail that can be resolved (the resolution) is proportional to $\lambda/2NA$

The NA of a fiber is $\sqrt{n^2_{core} - n^2_{clad}}$

Field Theory

Lagrangian 拉氏量

$L = T -V$ , is a function of position and first derivative of position

T for Kinetic energy, V for Potential energy

Action = \int dt L(t_1 \rightarrow t_2)

S =\int dt L(\phi, \partial\phi)

Others

homodyne detection

❌ Unsupported block ($column_list)

Photodiodes

power detector

They are semiconductor devices which contain a p–n junction, and often an intrinsic (undoped) layer between n and p layers. The photocurrent can be quite precisely proportional to the absorbed (or incident) light intensity over a wide range of optical powers.

The resulting photocurrent is proportional to the total optical intensity, thus to the square of the total electric field amplitude. If the signal and local oscillator powers and frequencies are constant, the photocurrent has two different frequency components:

The constant (zero-frequency) part is proportional to the sum of local oscillator and signal power.
The part oscillating with the difference frequency (the beat note) has an amplitude proportional to the product of the electric field amplitudes (not the optical powers) of signal and local oscillator.

Explanation for Terms in Optics