Grating Efficiency: The efficiency of a diffraction grating at different orders varies based on its design parameters, such as groove depth and duty cycle (the ratio of the width of the grooves to the total period). Some gratings are optimized to enhance higher orders, allowing for increased intensity in those orders compared to lower ones. For instance, binary phase gratings can be designed such that their second-order efficiency peaks under specific conditions, leading to higher intensity.

In most diffraction systems, the intensity of higher-order diffraction patterns (such as the 2nd-order) is typically lower than that of the first order. However, in certain cases, the 2nd diffraction order might appear to have higher intensity due to specific conditions related to the setup or the properties of the diffracted material. Here are a few reasons why this might happen:

1. Constructive Interference: If the conditions favor constructive interference for the second-order diffraction at a particular angle or wavelength, the intensity of the second-order peak could be enhanced. This depends on how the diffracted waves overlap and interfere.

2. Grating or Crystal Properties: In diffraction gratings or crystal lattices, the shape, spacing, and quality of the grating (or lattice) can cause variations in how the diffraction orders are distributed. If the grating efficiency is higher for certain orders, the 2nd-order diffraction can be brighter.

3. Detector Sensitivity: The angle and setup of the detection system could also contribute to higher intensity in the second-order diffraction, especially if the detector is more sensitive to light at the specific angle or wavelength corresponding to that order.

4. Energy Distribution in Light Source: If the light source emits more energy or has a stronger intensity at the wavelength corresponding to the second-order diffraction, this could contribute to the observed higher intensity.

In general, this is an exception rather than a rule, as first-order diffraction is usually more intense due to the basic principles of diffraction and energy distribution across different orders.

The overall shape of the diffraction pattern of a grating is a convolution of the diffraction pattern of its singular components. For a simple grating this is 1) the diffraction pattern of the periodic structure (the grating itself), 2) the diffraction pattern of the total grating (e.g. the width of the full grating) and 3) the diffraction pattern of each individual slit. Here, 1) defines the diffraction pattern, which we typically associate with the grating and which defines the first, second, etc. diffraction order. 2) The width of the total grating typically defines the number of total slits that are illuminated, which defines the minimum line width (and with it the resolution) of the different orders. 3) The width of the individual slit defines the envoloping function of the TOTAL diffraction pattern. For the case of a simple rectangular width of a groove, this envoloping pattern is the diffraction pattern of a single slit and follows a sinc-function. This enveloping patterns als has its minima and maxima. Therefore, it is very well possible that the minimum of the envoloping function, coincides with the maximum of one of the diffraction orders of the grating. Therefore, one of the orders may "unexpectedly" be weaker than the neighboring orders, which could be the reason why your first diffraction order is weaker compared to the second or higher orders, because it sits close to the minimum of the enveloping function.

By the way, the enveloping function can be shifted and tuned as well to improve the performance of a grating, see "Blaze-grating".

I hope that helps.

Regards,

Michael