Add laser envelope of “supersine” form with exact zero boundaries

[lyqyq6]

Background

Currently, ABACUS supports a Gaussian laser envelope, which requires numerical truncation at the beginning and end of the pulse. This may introduce artifacts in strong-field simulations.
In many studies, laser envelopes that are strictly zero at the pulse boundaries are preferred, as they provide cleaner numerical behavior. For example, in Neufeld et al. (PNAS 2022, 119(25): e2204219119), a “supersine” envelope is used (Eq. 7), which smoothly goes to zero at both ends of the pulse.

Describe the solution you'd like

We would like to request the implementation of a laser envelope in the “supersine” form as defined in Eq. 7 of the above paper. The corresponding vector potential should follow Eq. 1 in the same paper.
This improvement would enhance the robustness of time-dependent simulations and reduce boundary-induced artifacts in strong-field calculations.

Task list only for developers

• Notice possible changes of behavior
• Explain the changes of codes in core modules of ESolver, HSolver, ElecState, Hamilt, Operator or Psi

Notice Possible Changes of Behavior (Reminder only for developers)

No response

Notice any changes of core modules (Reminder only for developers)

No response

Notice Possible Changes of Core Modules (Reminder only for developers)

No response

Additional Context

No response

Task list for Issue attackers (only for developers)

• Review and understand the proposed feature and its importance.
• Research on the existing solutions and relevant research articles/resources.
• Discuss with the team to evaluate the feasibility of implementing the feature.
• Create a design document outlining the proposed solution and implementation details.
• Get feedback from the team on the design document.
• Develop the feature following the agreed design.
• Write unit tests and integration tests for the feature.
• Update the documentation to include the new feature.
• Perform code review and address any issues.
• Merge the feature into the main branch.
• Monitor for any issues or bugs reported by users after the feature is released.
• Address any issues or bugs reported by users and continuously improve the feature.

[AsTonyshment]

We will implement this feature in the near future.