A fiber Bragg grating (FBG) is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by creating a periodic variation in the refractive index of the fiber core, which generates a wavelength-specific dielectric mirror. Hence a fiber Bragg grating can be used as an inline optical filter to block certain wavelengths, can be used for sensing applications, or it can be used as wavelength-specific reflector.
History The first in-fiber Bragg grating was demonstrated by Ken Hill in 1978. Initially, the gratings were fabricated using a visible laser propagating along the fiber core. In 1989, Gerald Meltz and colleagues demonstrated the much more flexible transverse holographic inscription technique where the laser illumination came from the side of the fiber. This technique uses the interference pattern of ultraviolet laser light to create the periodic structure of the fiber Bragg grating.
Theory
The fundamental principle behind the operation of an FBG is Fresnel reflection, where light traveling between media of different refractive indices may both reflect and refract at the interface.
The refractive index will typically alternate over a defined length. The reflected wavelength (), called the Bragg wavelength, is defined by the relationship,
where is the effective refractive index of the fiber core and is the grating period. The effective refractive index quantifies the velocity of propagating light as compared to its velocity in vacuum. depends not only on the wavelength but also (for multimode waveguides) on the mode in which the light propagates. For this reason, it is also called modal index.
The wavelength spacing between the first minima (nulls, see Fig. 2), or the bandwidth (), is (in the strong grating limit) given by,
where is the variation in the refractive index (), and is the fraction of power in the core. Note that this approximation does not apply to weak gratings where the grating length, , is not large compared to \ .
The peak reflection () is approximately given by,
where is the number of periodic variations. The full equation for the reflected power (), is given by,
where,
Types of gratings The term type in this context refers to the underlying photosensitivity mechanism by which grating fringes are produced in the fiber. The different methods of creating these fringes have a significant effect on physical attributes of the produced grating, particularly the temperature response and ability to withstand elevated temperatures. Thus far, five (or six) types of FBG have been reported with different underlying photosensitivity mechanisms.J. Canning, Fiber Gratings and Devices for Sensors and Lasers, Laser and Photonics Reviews, 2 (4), 275-289, Wiley, USA (2008) These are summarized below:
Standard, or type I, gratings Written in both hydrogenated and non-hydrogenated fiber of all types, type I gratings are usually known as standard gratings and are manufactured in fibers of all types under all hydrogenation conditions. Typically, the reflection spectra of a type I grating is equal to 1-T where T is the transmission spectra. This means that the reflection and transmission spectra are complementary and there is negligible loss of light by reflection into the cladding or by absorption. Type I gratings are the most commonly used of all grating types, and the only types of grating available off-the-shelf at the time of writing.
Type IA gratings Regenerated grating written after erasure of a type I grating in hydrogenated germanosilicate fiber of all types
Type IA gratings were first observed in 2001 during experiments designed to determine the effects of hydrogen loading on the formation of IIA gratings in germanosilicate fiber. In contrast to the anticipated decrease (or 'blue shift') of the gratings' Bragg wavelength, a large increase (or 'red shift') was observed.
Later work showed that the increase in Bragg wavelength began once an initial type I grating had reached peak reflectivity and begun to weaken. For this reason, it was labeled as a regenerated grating.
Determination of the type IA gratings' temperature coefficient showed that it was lower than a standard grating written under similar conditions.
The key difference between the inscription of type IA and IIA gratings is that IA gratings are written in hydrogenated fibers, whereas type IIA gratings are written in non-hydrogenated fibers.
Type IIA, or type In, gratings These are gratings that form as the negative part of the induced index change overtakes the positive part. It is usually associated with gradual relaxation of induced stress along the axis and/or at the interface. It has been proposed that these gratings could be relabeled type In (for type 1 gratings with a negative index change; type II label could be reserved for those that are distinctly made above the damage threshold of the glass).For a contemporary review, see
Later research by Xie et al. showed the existence of another type of grating with similar thermal stability properties to the type II grating. This grating exhibited a negative change in the mean index of the fiber and was termed type IIA. The gratings were formed in germanosilicate fibers with pulses from a frequency doubled XeCl pumped dye laser. It was shown that initial exposure formed a standard (type I) grating within the fiber which underwent a small red shift before being erased. Further exposure showed that a grating reformed which underwent a steady blue shift whilst growing in strength.
Regenerated gratings These are gratings that are reborn at higher temperatures after erasure of gratings, usually type I gratings and usually, though not always, in the presence of hydrogen. They have been interpreted in different ways including dopant diffusion (oxygen being the most popular current interpretation) and glass structural change. Recent work has shown that there exists a regeneration regime beyond diffusion where gratings can be made to operate at temperatures in excess of 1,295 °C, outperforming even type II femtosecond gratings. These are extremely attractive for ultra high temperature applications.
Type II gratings Damage written gratings inscribed by multiphoton excitation with higher intensity lasers that exceed the damage threshold of the glass. Lasers employed are usually pulsed in order to reach these intensities. They include recent developments in multiphoton excitation using femtosecond pulses where the short timescales (commensurate on a timescale similar to local relaxation times) offer unprecedented spatial localization of the induced change. The amorphous network of the glass is usually transformed via a different ionization and melting pathway to give either higher index changes or create, through micro-explosions, voids surrounded by more dense glass.
Archambault et al. showed that it was possible to inscribe gratings of ~100% (>99.8%) reflectance with a single UV pulse in fibers on the draw tower. The resulting gratings were shown to be stable at temperatures as high as 800 °C (up to 1,000 °C in some cases, and higher with femtosecond laser inscription). The gratings were inscribed using a single 40 mJ pulse from an excimer laser at 248 nm. It was further shown that a sharp threshold was evident at ~30 mJ; above this level the index modulation increased by more than two orders of magnitude, whereas below 30 mJ the index modulation grew linearly with pulse energy. For ease of identification, and in recognition of the distinct differences in thermal stability, they labeled gratings fabricated below the threshold as type I gratings and above the threshold as type II gratings. Microscopic examination of these gratings showed a periodic damage track at the grating's site within the fiber ; hence type II gratings are also known as damage gratings. However, these cracks can be very localized so as to not play a major role in scattering loss if properly prepared.
Grating structure
The structure of the FBG can vary via the refractive index, or the grating period. The grating period can be uniform or graded, and either localised or distributed in a superstructure. The refractive index has two primary characteristics, the refractive index profile, and the offset. Typically, the refractive index profile can be uniform or apodized, and the refractive index offset is positive or zero.
There are six common structures for FBGs; uniform positive-only index change, Gaussian apodized, raised-cosine apodized, chirped, discrete phase shift, and superstructure. The first complex grating was made by J. Canning in 1994.J. Canning, M. G. Sceats, "p-phase-shifted periodic distributed structures in germanosilicate fiber by UV post-processing", Electron. Lett., 30, (16), 1344-1345, (1994) This supported the development of the first distributed feedback (DFB) fiber lasers, and also laid the groundwork for most complex gratings that followed, including the sampled gratings first made by Peter Hill and colleagues in Australia.
Apodized gratings There are basically two quantities that control the properties of the FBG. These are the grating length, , given as
and the grating strength, . There are, however, three properties that need to be controlled in a FBG. These are the reflectivity, the bandwidth, and the side-lobe strength. As shown above, in the strong grating limit (i.e., for large ) the bandwidth depends on the grating strength, and not the grating length. This means the grating strength can be used to set the bandwidth. The grating length, effectively , can then be used to set the peak reflectivity, which depends on both the grating strength and the grating length. The result of this is that the side-lobe strength cannot be controlled, and this simple optimisation results in significant side-lobes. A third quantity can be varied to help with side-lobe suppression. This is apodization of the refractive index change. The term apodization refers to the grading of the refractive index to approach zero at the end of the grating. Apodized gratings offer significant improvement in side-lobe suppression while maintaining reflectivity and a narrow bandwidth. The two functions typically used to apodize a FBG are Gaussian and raised-cosine.
Chirped fiber Bragg gratings The refractive index profile of the grating may be modified to add other features, such as a linear variation in the grating period, called a chirp. The reflected wavelength changes with the grating period, broadening the reflected spectrum. A grating possessing a chirp has the property of adding dispersion—namely, different wavelengths reflected from the grating will be subject to different delays. This property has been used in the development of phased-array antenna systems and polarization mode dispersion compensation, as well.
Tilted fiber Bragg gratings In standard FBGs, the grading or variation of the refractive index is along the length of the fiber (the optical axis), and is typically uniform across the width of the fiber. In a tilted FBG (TFBG), the variation of the refractive index is at an angle to the optical axis. The angle of tilt in a TFBG has an effect on the reflected wavelength, and bandwidth.
Long-period gratings