晶体,非线性晶体

1. 什么是 PPXX 技术

    PPXX is an advanced technology for high efficiency and arbitrary wavelength conversion based on making engineered microstructure on the ferroelectric materials.

2. 非线性波长转换

Nonlinear wavelength conversion means the phenomenon that input light generates new wavelength via passing through the nonlinear material. For the common 2nd order nonlinearity, photon energy of the related wavelength is defined to be conserved as the relation below:

Here are the common nonlinear process appellations and its expression of frequency relation respectively.

3. 相位匹配条件

To have high conversion efficiency, the photon momentum should be conserved as well. Otherwise, incorrect phase will lead to destructive interference causing very low efficiency.  The relation of photon momentum conservation is shown as below, which is called the phase matching condition.

4.双折射相位匹配(BPM)

Typically, due to the material feature of dispersion, phase matching condition could only be achieved in the birefringence material, which has different refractive index of its o-polarization (perpendicular to the optical axis) and e-polarization (parallel to the optical axis).

The phase matching condition could be achieved by changing temperature or the incident angle on the birefringence material with correct polarization.  Two types of phase matching condition are shown as below:  

Type I:  The polarization of the two low frequency photon is the same,

i.e.

Type II:  The polarization of the two low frequency photon is different,

i.e.

5. 准相位匹配（QPM）和周期性极化（PP）

Quasi phase matching is a technique that the photon momentum conservation is achieved through additional artificial structure.  The structure could provide an extra vector Kg which matches the momentum conservation as below.

Periodical poling is a special technique to form periodical microstructure on the ferroelectric material with a designed Kg. Not only the spatial walk-off issue in BPM material becomes eliminated through QPM technique but the phase matching temperature could also be designed.  Moreover, the  type of phase matching condition (Type 0), which is never existing in BPM (Birefringence phase matching) could be demonstrated through QPM. Type 0 is bringing about several tens of times for conversion efficiency enhancement.

6. 什么样的色散方程，我们使用的折射率计算？

We simulate the refractive index according to the reference below, which is the most appropriate function through our experience.

Gayer, O., et al, "Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3." Appl. Phys. B 91, 343-348 (2008)

7. 如何计算 QPM 期?

First you will need the information of the refractive index to calculate the wave vector mismatch of the involved wavelength.  For example (up-conversion):

Then, the QPM period equals to

Which the final wave vector mismatch is canceled

8. 如何实现转换效率?

To achieve the optimal conversion efficiency, the incident light should be focused on the center of the chip with the focusing condition L/b~2.84, where L is the chip length, b is the Gaussian beam focusing parameter.  The above condition is for SHG/SFG only and with the assumption of Gaussian beam M2=1.  For DFG, the optimal condition is more complicated and will change according to the wavelength, for further study, one can read the reference below.

T. -B. Chu and M. Broyer, "Intracavity cw difference frequency generation by mixing three photons and using Gaussian laser beams." J. Phys. (Paris) 46, 523 (1985)

9. How to know the acceptance of the chip?

The phase matching spectrum is the square of a sinc function

We know that once we design a QPM period for a target wavelength conversion, , and then we could calculate the wave vector mismatch near the designed wavelength to see when the  becomes large enough that the square of sinc function becomes smaller than 0.5. 

10.  如何实现波长调谐?

There are two ways for wavelength tuning.  One is changing the period, the other one is changing the temperature (because the refractive index is a function of  temperature).

Typically, the temperature tuning could not have wide tuning range, so we have special structures - multiple and fan-out, to achieve broadband wavelength tuning.

Multiple structure is a chip with multiple channel, each channel has different period, through the change of the incident channel and modifying the temperature, one can achieve large tuning range then a single period chip.

Fan-out structure is a chip with continuous period change in the width.  One can tune the phase matching wavelength through moving the chip without changing the temperature.