Dichroic mirror

A dichroic mirror is an interference-based optical filter that reflects light in one spectral band while transmitting another, with the transition between bands typically occurring over a wavelength range of 10 – 50 nm. The mirror consists of a stack of alternating thin films of high- and low-refractive-index dielectric materials deposited on a transparent substrate (usually fused silica or BK7).

Operating principle. Each interface between high- and low-index layers produces a partial reflection. By choosing each layer thickness to be a quarter-wavelength at the design center, all reflections from the high-to-low interfaces interfere constructively, producing high reflectivity over a stopband centered at the design wavelength. Outside the stopband, the layer thicknesses no longer satisfy the constructive-interference condition, and the stack becomes transparent.

For a stack of $N$ quarter-wave pairs plus a final high-index layer, $(HL{)}^{N}H$, with high index $n_H$ and low index $n_L$ on a substrate of index $n_s$, the peak reflectivity is:

$$R={\left[\frac{1-(n_H\mathrm{/}{n}_L{)}^{2N}(n_H^2\mathrm{/}{n}_s)}{1+(n_H\mathrm{/}{n}_L{)}^{2N}(n_H^2\mathrm{/}{n}_s)}\right]}^2\mathrm{.}$$

For $n_H=2.3$ (TiO₂), $n_L=1.46$ (SiO₂), $N=10$ (21 layers), $n_s=1.46$: $R\approx 99.99$%; exactly 10 pairs, 20 layers, give 99.97%.

Standard configurations.

Use at non-normal incidence. Most dichroic mirrors are designed for 45° angle of incidence (AOI), separating beams into perpendicular paths. The thin-film stack must be designed for the specific AOI. Operating at a different angle moves the transition wavelength, approximately as

$${\lambda }_c(\theta )\approx {\lambda }_c(0)\sqrt{1-\frac{{\sin }^2\theta }{n_{\text{eff}}^2}},$$

where ${\lambda }_c(0)$ is the cutoff at normal incidence and $n_{\text{eff}}\approx 1.7-2.0$ for typical dichroic stacks. A mirror with its cutoff at 500 nm at 45° has ${\lambda }_c(0)\approx$ 535 – 550 nm, and at 50° its cutoff moves about 6 – 9 nm to shorter wavelength.

Polarization dependence. At non-normal incidence, the stack's response differs for s-polarization (TE, electric field perpendicular to plane of incidence) and p-polarization (TM, electric field in plane of incidence). Standard dichroic mirrors show 5 – 20 nm shift in cutoff wavelength between s and p at 45° AOI. Polarization-insensitive dichroics are available but more expensive and use compensated multilayer designs.

Typical specifications.

Common applications.

• Fluorescence microscopy: separates excitation laser (reflected from sample) from longer-wavelength fluorescence (transmitted to detector)
• Multi-wavelength laser combining: combines red, green, blue laser beams into a single collinear output for projectors and display systems
• Raman spectroscopy: a notch filter or notch dichroic blocks the elastically-scattered laser line while transmitting Stokes-shifted Raman signal
• Pump-probe spectroscopy: separates pump and probe wavelengths on a common path
• Confocal fluorescence microscopy: separates the excitation beam from the fluorescence collected back through the same objective
• WDM in free-space optical communications: separates uplink and downlink wavelengths on the same telescope

Comparison to neutral beam splitters. A 50:50 beam splitter divides input intensity wavelength-independently, losing half the light into the unused port. A dichroic mirror, when used at its design wavelengths, redirects nearly 100% of input light to the desired port. That is substantially more efficient when wavelength separation is sufficient.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 7 (multilayer interference filters); Macleod, Thin-Film Optical Filters (5th ed., 2017) for the comprehensive thin-film design treatment.