Beam splitter

A beam splitter divides an incident beam into two output beams, one transmitted and one reflected, with a specified ratio of their powers. Common ratios are 50:50, 70:30 and 90:10 (the order, reflected or transmitted first, varies between catalogs), and a split may be defined by power, by polarization or by wavelength. An uncoated glass surface of index 1.5 is already a weak splitter, reflecting 4% at normal incidence. Coated splitters use a partially reflecting thin-film stack or a thin metal layer to set the ratio over a design band, typically at 45° incidence so that the two outputs leave at right angles.

Types

Four geometries cover most laboratory use.

• Plate splitters are a flat glass substrate, typically 1–6 mm thick, with the splitting coating on the front face and an anti-reflection coating on the back.
• Cube beamsplitters embed the coating at the cemented hypotenuse of two right-angle prisms, so both outputs leave normal to a face with no lateral offset.
• Pellicle beamsplitters are a membrane a few micrometers thick, which removes the ghost reflection and beam offset of a plate at the cost of fragility and sensitivity to acoustic vibration.
• Dichroic mirrors split by wavelength, reflecting one band and transmitting another, for example to separate fluorescence from excitation light.

A fifth class, the polarizing beam splitter, reflects s-polarized light and transmits p-polarized light. It is made as a coated cube or plate or as a birefringent crystal prism, and serves as a polarizer or, with a waveplate, as a variable splitter. In coated cubes the transmitted port usually has much higher polarization purity than the reflected port; datasheet extinction ratios differ widely by design and should be read port by port.

Splitting ratio and polarization

Energy conservation gives $R + T + A = 1$, where $A$ is the absorbed fraction. Dielectric coatings absorb almost nothing, so the two ports of a dielectric splitter together carry nearly all the input. Metallic splitters (thin films of nickel-chromium alloys or aluminum) absorb a substantial fraction of the light, but their ratio varies slowly with wavelength and angle.

At oblique incidence every coating is polarization dependent, because the Fresnel equations treat s and p differently. The effect is visible even on bare glass: for N-BK7 ($n = 1.517$) at 45°,

$$R_s = 9.6\%, \qquad R_p = 0.92\%.$$

A "non-polarizing" 50:50 splitter is designed to bring $R_s$ and $R_p$ close together over its band, and the residual difference, often several percent, is quoted as a separate specification.

Offset and ghost reflections in a plate

A plate at 45° shifts the transmitted beam sideways by

$$d = t\sin\theta\left(1-\frac{\cos\theta}{\sqrt{n^2-\sin^2\theta}}\right).$$

For a 3 mm plate of $n = 1.517$ at $\theta = 45°$, the internal angle is 27.8° and $d = 1.00$ mm. The back surface also produces a second reflected beam, parallel to the first and displaced from it by $2t\tan\theta_t\cos\theta = 2.24$ mm. With a 50:50 front coating and a back surface reflecting 0.5%, this ghost carries about 0.5 × 0.005 × 0.5 = 0.125% of the input power, 0.25% of the main reflection. Because it is coherent with the main beam, it produces fringes in interferometers and double images in imaging. Wedged plates (typically 30 arcminutes to a few degrees) send the ghost off at a different angle so that it can be blocked.

Measurement and use

The ratio is checked by placing an optical power meter in the input beam and then in each output, at the wavelength, angle and polarization of the application; the sum of the outputs against the input gives the loss. Catalogue tolerances of a few percent are usual.

Beam splitters form the arms of Michelson and Mach-Zehnder interferometers, pick off a small sample of a laser beam for power monitoring (a 99:1 or uncoated wedge is common), combine a reference beam with a signal in balanced detection and couple illumination into microscopes. In a Michelson interferometer each arm's light meets the splitter twice, so the light reaching the detector port from each arm is 0.5 × 0.5 = 25% of the input; the two contributions interfere, so the detector port receives between 0 and 100% and on average half the light returns toward the source, one reason to protect feedback-sensitive lasers with an optical isolator.

Pitfalls

Ratios are specified at one angle of incidence, and tilting a coated splitter by a few degrees changes them. Cemented cubes add glass path and dispersion, which matters for ultrashort pulses, and their cement can fail at high power before the coating does. A plate used back to front can have a different ratio.

Common questions

What is the difference between a beam splitter and a partially reflecting mirror?

Both are partially reflecting coatings. "Beam splitter" usually means a part designed for oblique incidence with both outputs used; a partial reflector at normal incidence inside a laser is an output coupler.

Does a 50:50 beam splitter lose half the light?

No light is lost in an ideal dielectric splitter; it is divided between two ports. When only one output is used, half the input goes unused, and a metallic splitter additionally absorbs a fraction.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 4 and 9; M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Ch. 1; H. A. Macleod, Thin-Film Optical Filters, 4th ed. (CRC Press, 2010).