To illustrate how effective transmission gratings can be, we will consider two common spectrometer applications: a Raman spectrometer
with a laser wavelength of 785 nm and a UV spectrometer.
High-Dispersion Raman grating for 785 nm
The first example is a high-dispersion grating well suited for Raman spectroscopy at a laser wavelength of 785 nm. The groove
density of the grating is 1765 lines/mm (with a 566-nm period) and the angle of incidence in air is 50°. Ideally, the grating
should provide polarization-independent high efficiency from 785 nm to 1000 nm. We used a finite element method (4) to solve
Maxwell's equations combined with topological optimization (5) to find the best VPH and SRTG grating structures for this problem.
Figure 6 shows the resulting theoretical efficiencies for the SRTG and the VPH. The efficiencies are very high for both gratings
and both polarizations at the center wavelength. As expected, the VPH displays a smaller bandwidth than the SRTG. Also plotted
on Figure 6 are real measurements on realized SRTG and VPH gratings, which confirms that an efficiency of >90% can be obtained
at the peak wavelength and >80% efficiency is obtained over a 200-nm bandwidth around the peak.
Figure 6: Diffraction efficiencies for SRTG and VPH gratings. The solid lines are theoretical curves and the colored squares
are actual measurements on realized gratings.
The second example is a broadband UV grating for the 190–435 nm wavelength range. This grating has a groove density of 2420
lines/mm (period of 413 nm). Since this is a UV grating we have only considered a SRTG. Figure 7 shows the theoretical grating
efficiency as well as the efficiency measured at three different wavelengths. The error bars indicate the total spread of
efficiency over more than 60 individual gratings. As can be seen, the efficiency is high for both polarizatons and fairly
flat across the complete range from 190 nm to 435 nm.
Figure 7: Diffraction efficiencies for an SRTG UV grating in pure fused silica. The solid lines are theoretical curves and
the marks with error bars are actual measurements on realized gratings.
In summary, we have shown how near 100% efficiency, polarization-independent gratings can be designed by choosing the average
refractive index, index modulation, and grating thickness appropriately. Furthermore, we have described two types of transmission
gratings — the surface relief transmission grating (SRTG) and the volume phase hologram (VPH) — and shown that both types
can provide the average index, index modulation, and grating thickness required for producing gratings with near 100% efficiency.
VPHs generally have weak index modulation and SRTGs have strong index modulation. As a result, VPHs generally have thick gratings
and a smaller bandwidth compared to SRTGs, which have thin gratings with a larger bandwidth. SRTGs based on fused silica can
be made for any wavelength range from UV through NIR and VPH can be made for any range from ~350 nm through NIR.
(1) M.G. Moharam and T.K. Gaylord, J. Opt. Soc. Am.
71, 811–818 (1981).
(2) K. Baldry et al., Publ. Astron. Soc. Pac.
116, 403–414 (2004).
(3) H. Kogelnik, The Bell System Technical Journal
48, 2909–2947 (1969).
(4) J. Jin, The Finite Element Method in Electromagnetics (Wiley, Hoboken, New Jersey, 2002).
(5) J. Jensen and O. Sigmund, Laser Photonics Rev.
5, 308–321 (2011).
Thomas Rasmussen is VP Business Development for Sales and Marketing at Ibsen Photonics in Farum, Denmark. Direct correspondence to: Thomas.Rasmussen@ibsen.dk