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 with high index $n_H$ and low index $n_L$ on a substrate of index $n_s$, the peak reflectivity is:

$$R \;=\; \left[ \frac{1 - (n_H/n_L)^{2N} (n_H^2/n_s)}{1 + (n_H/n_L)^{2N} (n_H^2/n_s)} \right]^2.$$

For $n_H = 2.3$ (TiO₂), $n_L = 1.46$ (SiO₂), $N = 10$ pairs, $n_s = 1.46$: $R > 99.99$%.

Standard configurations.

Configuration	Description	Application
Short-pass dichroic	Transmits wavelengths shorter than cutoff, reflects longer	Fluorescence excitation filter
Long-pass dichroic	Transmits wavelengths longer than cutoff, reflects shorter	Fluorescence emission separation
Bandpass dichroic	Transmits a narrow band, reflects on both sides	Multi-color laser combining
Notch dichroic	Reflects a narrow band, transmits elsewhere	Raman scattering filter, laser blocking

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 shifts the transition wavelength by approximately:

$$\Delta \lambda_\text{cutoff} \;\approx\; \lambda_0 \left[ 1 - \sqrt{1 - \frac{\sin^2\theta}{n_\text{eff}^2}} \right],$$

where $n_\text{eff} \approx 1.7 - 2.0$ for typical dichroic stacks. For a 500 nm cutoff at 45°, the cutoff shifts by $\sim 20$ nm if operated at 50° instead.

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.

Parameter	Standard value
Transmission in pass band	90 – 99%
Reflection in stop band	95 – 99.9%
Transition (10% to 90%) width	10 – 50 nm
Surface flatness	$\lambda/4$ to $\lambda/10$ at 633 nm
Damage threshold (CW)	1 – 10 kW/cm²
Damage threshold (pulsed)	0.5 – 5 J/cm² (10 ns pulses)
Substrate thickness	1 – 6 mm
Useful temperature range	$-20$ to $+80$°C

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: 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
• OCT and confocal microscopy: separates illumination from collected backscattered light
• 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 — 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.