Glossary entry

Notch filter

An optical filter that blocks one narrow band of wavelengths, usually by reflection, and transmits everything else. Specified by center wavelength, blocking depth in optical density, and bandwidth. The standard way to remove a laser line from Raman or fluorescence light before it reaches the spectrometer.

Optics & beams Optics fundamentals Lab practiceUpdated October 2026

A notch filter, also called a band-stop or band-reject filter, is the complement of a bandpass: it transmits across a wide range and blocks one narrow band. In optics the blocked band is almost always a laser line. The canonical case is Raman spectroscopy, where the elastically scattered laser light is many orders of magnitude stronger than the Raman-shifted light a few nanometers away, and the notch removes the laser before the spectrometer sees it. The same part rejects the excitation in laser-induced fluorescence, strips a pump wavelength out of a fiber system, and protects a detector from one specific line.

Three numbers specify a notch. The center wavelength, which for laser-line filters is the laser wavelength (532, 633, 785 nm and so on). The blocking depth, quoted as optical density, $O D = - \log_{10} T$ , so OD 6 means a transmission of $10^{- 6}$ , or $- 60$ dB. And the bandwidth, quoted as the full width at half transmission and often also as the narrower width over which the OD exceeds a stated value. Outside the notch a good thin-film filter transmits above 90%. Two further specifications matter on the bench, the angle-of-incidence tolerance and the polarization dependence, and both follow from how the notch is made.

Nearly every reflective notch is a Bragg reflector: a periodic modulation of refractive index with period $λ / 2 n$ reflects one wavelength and passes the rest (Bragg condition). A thin-film interference notch, typically a rugate coating whose index varies continuously through a layer tens of micrometers thick, is one realization; a volume Bragg grating written in photo-thermo-refractive glass is another; a fiber Bragg grating used in transmission is the same physics inside a fiber; and an all-pass ring resonator makes a notch by resonant coupling instead of by a grating. Coupled-mode theory gives the depth of a uniform index modulation of amplitude $δ n$ and length $L$ in one line. With the coupling coefficient $κ = π δ n / λ$ , the transmission at the center of the notch is $T = {s e c h}^{2} (κ L)$ . OD 6 needs $κ L = 7.6$ , and each further unit of $κ L$ deepens the notch by another 8.7 dB. The full stopband width is $Δ λ = λ δ n / n$ . Those two relations set the design trade: depth comes from the product $δ n \cdot L$ , width from the ratio $δ n / n$ . A thin-film notch with $δ n$ of a few hundredths reaches OD 6 in a few tens of micrometers and is tens of nanometers wide; a volume Bragg grating with $δ n$ near $3 \times 10^{- 4}$ needs about 3 mm of glass for OD 4 and is correspondingly narrow, about 0.1 nm at 532 nm.

Transmission in dB against wavelength for a 532 nm notch filter, apodized and uniform designs, both reaching minus 60 dB. — **Transmission of a 532 nm notch filter.**
Computed transmission of a 532 nm reflective notch at OD 6 ( $- 60$ dB). An apodized index modulation gives a clean stop band 17.9 nm wide at $- 3$ dB; a uniform modulation with the same peak rejection ( $κ L = 7.6$ ) is narrower and has sidelobes at the band edges. Dotted lines mark the 532 nm laser line and Stokes shifts of 100 and 520 cm $^{- 1}$ .

Raman shifts are quoted in wavenumbers, and the conversion $Δ λ = λ^{2} Δ \tilde{ν}$ makes a notch's bandwidth depend on the laser wavelength in a way that matters. At 532 nm, 1 cm $^{- 1}$ is 0.028 nm; at 785 nm it is 0.062 nm. A 17.9 nm notch at 532 nm therefore blocks about 630 cm $^{- 1}$ of spectrum in total, roughly 310 cm $^{- 1}$ on the Stokes side, which is fine for the 520 cm $^{- 1}$ silicon line and hopeless for anything below 300 cm $^{- 1}$ . Low-frequency Raman, the lattice and layer-breathing modes below 100 cm $^{- 1}$ (2.8 nm at 532 nm), is what volume Bragg grating notches exist for: bandwidths of 5 to 10 cm $^{- 1}$ , OD 3 to 4 per filter, stacked two or three deep to reach OD 8 or more within a few wavenumbers of the laser.

Raman spectrum before and after a 532 nm notch filter: the laser line drops from 10⁸ to 100 counts, Raman lines remain. — **A Raman spectrum before and after the notch filter.**
Illustrative spectrum under 532 nm excitation, before (dashed) and after (solid) the apodized OD 6 notch above. The laser line falls from $10^{8}$ to 100 counts; the 520 cm $^{- 1}$ silicon line and its anti-Stokes partner pass unchanged, a line at 300 cm $^{- 1}$ , just inside the 540.9 nm band edge, keeps 33%, and a line at 100 cm $^{- 1}$ is lost.

Because the notch is an interference effect it shifts with angle of incidence. For a thin-film filter with effective index $n_{e f f}$ the center moves as $λ (θ) = λ_{0} \sqrt{1 - \sin^{2} θ / n_{e f f}^{2}}$ : with $n_{e f f} = 2$ , a 532 nm notch sits at 531.5 nm at 5° and 530.0 nm at 10°, a 2 nm shift that a 17.9 nm notch tolerates and a 0.1 nm volume-grating notch does not. Volume gratings are angle-tuned deliberately for the same reason. Away from normal incidence the s and p polarizations see different effective indices and the notch splits into two slightly offset notches, so specifications are given at normal incidence or over a stated cone half-angle. Thin-film notches are used at 0°; a reflective notch at 45° is a different design with a wider, polarization-split band, closer to a dichroic mirror.

Measuring a deep notch is harder than buying one. A grating spectrometer's stray-light floor is typically OD 3 to 4 in a single stage, so a spectrometer scan of an OD 6 filter shows the instrument's floor, not the filter's. The honest measurement is a laser and a calibrated power meter with 60 dB or more of dynamic range, or a double monochromator, with the out-of-band transmission measured separately with a broadband source; the procedure, with its error budget and the stacked-filter floor test, is in Measuring optical density beyond the stray-light floor. Two related traps: fluorescence from the filter substrate under intense laser illumination fills in the notch during the measurement, and a filter specified at OD 6 over its central band may be only OD 2 to 3 at the edges of its quoted bandwidth, which is where a laser's wavelength drift will eventually put the line.

In integrated photonics the all-pass ring is the notch. At resonance the through-port transmission is $T = {(\frac{a - t}{1 - a t})}^{2}$ for round-trip amplitude transmission $a$ and coupling $t$ , zero at critical coupling ( $a = t$ ) and only a few dB deep when the two are mismatched, with a width set by the ring's Q rather than by an index modulation. The ring resonator explorer shows the through-port notch deepen and widen as the coupling is swept through critical.

The choice between notch and edge filters for blocking the laser line in Raman spectroscopy is covered in Raman Spectroscopy Setup.

References: T. Erdogan, "Fiber grating spectra," J. Lightwave Technol. 15, 1277 (1997), for the coupled-mode results quoted here; H. A. Macleod, Thin-Film Optical Filters, 4th ed. (CRC Press, 2010), on rugate and notch designs; O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson and V. I. Smirnov, "High-efficiency Bragg gratings in photothermorefractive glass," Appl. Opt. 38, 619 (1999); manufacturer data for laser-line notch filters (thin-film and volume Bragg grating types) for the typical bandwidth and OD figures quoted.