Volume Bragg grating

A volume Bragg grating (VBG) is a periodic modulation of refractive index recorded through the volume of a transparent block, typically a few millimeters thick, so that light satisfying the Bragg condition is reflected or diffracted and all other wavelengths and angles pass through. Most are written holographically in photo-thermo-refractive (PTR) glass, a silicate glass that develops an index change of order $10^{-4}$ to $10^{-3}$ after UV exposure and thermal development. Reflecting gratings have bandwidths of a few tenths of a nanometer down to tens of picometers, with reflectances from a few percent for diode-laser locking to above 90% for filters. The grating is the bulk-optic counterpart of a fiber Bragg grating and is described by the same coupled-wave theory.

Bragg condition and bandwidth

For a reflecting grating with fringes normal to the beam, the reflected wavelength is

$$\lambda_B = 2n\Lambda,$$

so at 976 nm in glass with $n = 1.49$ the period is 327.5 nm. The peak reflectance of a uniform grating of length $L$ and index modulation $\delta n$ is

$$R = \tanh^2(\kappa L), \qquad \kappa = \frac{\pi\,\delta n}{\lambda}.$$

With $\delta n = 10^{-4}$ and $L = 2$ mm, $\kappa L = 0.64$ and $R = 0.32$; doubling $\delta n$ gives $\kappa L = 1.29$ and $R = 0.74$. For a weak grating the spectral width is set by the length, with the first zeros at about $\lambda^2/(2nL)$ from the peak, 0.16 nm here, and a full width at half maximum that a coupled-mode calculation also puts at 0.16 nm; for a strong grating it approaches the stop band width $\lambda\,\delta n/n$. The grating is equally selective in angle, and transmitting VBGs, with fringes tilted relative to the surface, diffract a beam into a new direction only within a narrow angular window. That angular selectivity is what distinguishes a thick volume grating from a surface relief diffraction grating, which diffracts into many orders over a wide range of angles.

Wavelength locking of diode lasers

The largest application is locking the wavelength of high-power diode lasers. A reflecting VBG with a reflectance of a few to a few tens of percent is placed after the fast-axis collimating lens, and feeds back a narrow band into the diode. The diode then operates as an external cavity laser whose wavelength follows the grating instead of the gain peak. The spectrum narrows from a few nanometers to a few tenths of a nanometer, and the temperature coefficient of the wavelength drops from about 0.3 nm/K, set by the semiconductor bandgap, to about 0.01 nm/K, set by the glass. Over a 30 K swing the free-running diode would move by 9 nm, the locked diode by 0.3 nm.

This matters wherever the pump must stay on a narrow absorption line: the 976 nm line of ytterbium, the 808 nm line of Nd:YAG in DPSS lasers, and alkali vapor lines for optical pumping. The locking range is limited: if the temperature moves the gain peak too far from the grating wavelength, the diode jumps back to free-running operation, so the gain-peak tuning range sets an operating temperature window of a few tens of kelvin.

Filters

As filters, VBGs serve where a thin-film coating cannot be made narrow enough. In Raman spectroscopy close to the laser line, VBG notch filters with bandwidths of 5 to 10 cm⁻¹ are stacked to block the laser while passing Raman lines within tens of wavenumbers of it; the corresponding laser-line cleanup filters remove the broad spontaneous background of a diode laser. Transmitting VBGs also combine lasers of slightly different wavelength into one beam.

Pitfalls

• The Bragg wavelength depends on angle: tilting a reflecting grating by $\theta$ inside the glass shifts it to $2n\Lambda\cos\theta$. Many locking assemblies tilt the grating slightly to trim the wavelength.
• Absorbed power heats the glass and shifts the Bragg wavelength; at high powers the glass absorption and the mounting set the stability.
• Locking efficiency depends on the diode's front-facet reflectance and on feedback alignment; a grating that is too strong for the facet coating can drive multimode or unstable operation.

Common questions

What is the difference between a volume Bragg grating and a fiber Bragg grating?

Both are periodic index gratings that reflect at $2n\Lambda$. A fiber grating sits in a fiber core and acts on a guided mode; a VBG acts on a free-space beam, has a clear aperture of millimeters, and handles higher powers. The fiber version is the usual choice for locking telecom pumps that are already pigtailed.

How is a volume Bragg grating made?

Two interfering UV laser beams expose a PTR glass block with a sinusoidal intensity pattern, and a heat treatment converts the exposure into a permanent index modulation. The recording angle sets the period; the exposure dose sets $\delta n$.

References: H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell System Technical Journal 48, 2909 (1969); O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson and V. I. Smirnov, "High-efficiency Bragg gratings in photothermorefractive glass," Applied Optics 38, 619 (1999); T. Erdogan, "Fiber grating spectra," Journal of Lightwave Technology 15, 1277 (1997).