This article provides a basic overview of the capabilities of transmission gratings optimized for molecular spectroscopy.
These gratings offer near 100%, polarizationinsensitive efficiency over a broad wavelength range and are ideal for applications
such as Raman spectroscopy where the available light intensity from the sample is very low. The design, manufacturing, and
performance of the two most commonly used types of transmission gratings — the surface relief transmission grating (SRTG)
and the volume phase hologram (VPH) — are described and examples of the two grating types are discussed.
Most diode array–based diffractive spectrometers for the ultraviolet (UV), visible (vis), and nearinfrared (NIR) spectral
ranges use reflectiontype diffraction gratings and are generally optimized for high resolution rather than high optical throughput.
During the past 5–10 years, transmissiontype gratings have been developed that provide near 100% efficiency for any polarization.
These gratings have found widespread use for Raman spectroscopy and astronomy, where very little light is available, but elsewhere
the awareness of the distinct benefits provided by transmission gratings seems quite limited. The purpose of this article
is to provide a basic overview of the capabilities of transmission gratings optimized for molecular spectroscopy. Specifically,
we will describe the two most commonly used types of gratings: the surface relief transmission grating (SRTG) and the volume
phase hologram (VPH).
Transmission Grating Basics
Figure 1: Transmission grating structure. Key grating parameters: Λ = grating period; t = grating thickness; n_{AVE} = average refractive index; and Δn = refractive index modulation.

This section describes the three key performance parameters of a transmission diffraction grating: the angular dispersion,
the diffraction efficiency, and the bandwidth of the grating.
Angular Dispersion: The Grating Equation
A transmission (or phase) grating consists of a region with a periodic modulation of the refractive index as shown in Figure
1. The period of the index modulation is on the same order of magnitude as the wavelength, and the form of the modulation
can be sinusoidal, rectangular, triangular, or even more complex. From the plane wave ray tracing drawn on Figure 1 it can
be seen that the plane waves add up in phase for exit angles β that fulfill the following criteria:
Equation 1 is the general grating equation that is valid for any grating structure. The term m is the order of diffraction, and in the remainder of this article we will consider firstorder diffraction (m = 1) only.
For a certain spectrometer design, the center wavelength as well as the period Λ (or groove density G = 1/Λ) for the grating are often given parameters that cannot be freely chosen. Furthermore, a spectrometer is used in a
range of wavelengths around the center wavelength and equation 1 determines the angular dispersion of this wavelength range.
Diffraction Efficiency
Although the grating equation determines the angular direction (β) of the diffracted light as a function of wavelength (λ),
it does not say anything about the diffraction efficiency. The calculation of the diffraction efficiency for a transmission
grating geometry generally requires complicated numerical methods such as rigorous coupled wave theory (1) for solving Maxwell's
equations. However, Baldry and colleagues (2) approximated analytical equations based on Kogelnik's original work from 1969
(3) to provide a basic relationship between the physical parameters of the gratings and the diffraction efficiency and bandwidth
of the grating. This analysis is based on a pure sinusoidal index modulation and is surprisingly accurate for a certain range
of gratings. Based on this analysis, it can be shown that a grating's diffraction efficiency, for a fixed grating period and
center wavelength, depends on three factors:
 the average refractive index (n
_{AVE})
 the thickness of the grating (t)
 the index modulation (Δn)