A zero-order waveplate is a high-precision optical component with parameters covering various aspects. Here is a detailed analysis: 

I. Focal Length

Explanation: Focal length is usually used to describe the ability of optical components such as lenses to converge or diverge light. A zero-order waveplate mainly functions to change the polarization state of light and does not have a specific focal length itself. However, it can be applied in different optical systems and used in conjunction with elements that have a focal length, such as lenses. 

II. Reflectance

Explanation: Reflectance refers to the ratio of the intensity of energy reflected by the coated surface to the incident energy. To reduce the energy loss caused by reflection, zero-order waveplates are usually coated to lower the reflectance. For example, some zero-order waveplates require the coating transmittance to be less than 0.2% per surface (R < 0.2%). 

III. Transmittance

Explanation: Transmittance is the ratio of the intensity of energy passing through the waveplate to the incident light energy. For a zero-order waveplate, there exists a relationship of T + R + A = 1 among transmittance, reflectance, and absorptance, that is, after the light beam passes through the waveplate, part of it is transmitted, part is reflected, and the rest is absorbed. High-quality zero-order waveplates usually have a high transmittance to ensure that more light can pass through the waveplate. 

IV. Length

Explanation: The parameter of “length” is generally not mentioned for zero-order waveplates. Instead, more attention may be paid to their thickness. For example, the air gap thickness of a zero-order waveplate composed of two pieces of quartz is between 1.5 - 2 mm, while the thickness of a true zero-order quarter-wave quartz plate in the visible light range may only be 15 um. 

V. Diameter Tolerance

Explanation: Diameter tolerance refers to the allowable difference between the actual diameter and the designed diameter of the waveplate. The common diameter tolerance for zero-order waveplates is +0.0, -0.1 mm. The diameter tolerance may vary among different manufacturers and specifications of waveplates.

 VI. Surface Finish

Explanation: Surface finish reflects the smoothness of the waveplate surface, which can affect the optical performance of the waveplate. The common surface finish standard for zero-order waveplates is 20/10, which means the waveplate surface has a high quality and can reduce the impact of surface defects on light scattering and other effects. 

VII. Substrate Material

Explanation: Zero-order waveplates often use crystalline quartz materials with birefringence effects. In addition, other birefringent crystal materials may also be used. These materials can make light with different polarization directions propagate at different speeds, thereby achieving a phase shift.

VIII. Coating

Explanation: In order to improve the transmittance of zero-order waveplates, reduce reflectance, and enhance their durability, the waveplates are usually coated. The common coating requirement is to achieve a low reflectance at specific wavelengths, such as r < 0.2% on the s1&s2 surfaces at specific wavelengths, and the coating can be customized according to specific usage requirements and the requirements of the optical system.