1.

Introduction

A number of applications of ultrashort laser pulses in medicine, industry, and defense require high average power and high pulse energy. However, direct amplification of ultrashort pulses can induce detrimental nonlinear effects and/or laser-induced damage in amplifiers due to the extremely high peak power of the amplified pulses. A technique called chirped pulse amplification (CPA) was proposed in Ref. 1 to mitigate these effects. In this technique, low-power ultrashort pulses are stretched (“chirped”) in time and space using dispersive optical elements. Stretched pulses having lower power density are then amplified to a power level somewhat less than the damage threshold of the amplifying system. The amplified chirped pulses are compressed by the same or similar dispersive optical elements that were used for stretching. The highest peak power that can be obtained using this technique is determined primarily by the optical damage threshold of the compressor components.

Initially, pulse stretching and compression in CPA systems were performed almost exclusively by pairs of surface diffraction gratings^2,3 that usually are called “Treacy stretchers and compressors.” Although the conventional technology that uses surface diffraction gratings provides a dramatic increase in the achievable power level, it has limitations associated with the reduced average power handling capacity of these components, which is typically in the range of tens of watts. With the availability today of fiber lasers operating at power levels easily exceeding 1 kW, this limitation has become the main obstacle to power scaling of ultrashort pulse lasers. Additionally, Treacy stretchers and compressors require highly uniform, large aperture gratings and large grating separation distances. Such stretchers and compressors are bulky, difficult to align, and susceptible to vibrations.

An important advancement in the development of CPA systems was made by the use of fiber-chirped Bragg gratings (CBGs).^4,5 This approach has dramatically increased the robustness of CPA systems enabling their use in harsh environments outside of research laboratories. However, while fiber stretching became the conventional method for CPA systems design, the limited aperture of chirped fiber Bragg gratings imposes limitations on the peak power achievable with fiber-based pulse compressors due to nonlinear effects in the fibers and laser-induced damage of the fibers. To overcome these limitations, the use of volume CBGs for pulse stretching and compression has been proposed.⁶ Initially, implementation of this proposal was slow to develop because of the absence of a suitable technology for fabrication of such optical elements. All of the photosensitive materials that were available at that time for volume hologram recording could not satisfy the requirements for high power applications in laser systems.⁷ The situation changed when the bulk holographic material—photo-thermo-refractive (PTR) glass^8,9—was developed¹⁰ which further enabled the development of the technology of high efficiency volume Bragg gratings. The creation of volume CBGs (volume Bragg gratings) with a variable period in the direction of the beam propagation) recorded in PTR glass enabled a new approach to the design of high power stretchers and compressors, and has become an important, competing CPA technique.^11–13

A conventional compressor is based on a pair of surface diffraction gratings that must be placed at some distance from each other, and occupies a volume of several liters, not including the size of large aperture telescopes, mirrors, etc. A typical CBG enables decreasing the size and weight of compressors by several orders of magnitude—to 0.005 L, for example. The most vulnerable feature of Treacy compressors is their high sensitivity to vibrations and shocks that result in misalignment between the diffraction gratings. The use of CBG stretchers and compressors enhances the robustness of CPA systems because these devices are monolithic, meaning there is nothing within the stretcher/compressor function to become misaligned (although it still must be aligned with the input beam). Thus, these devices are inherently free from the effects of vibration and shocks. The main limitation of CBG stretchers and compressors at the current level of the technology of volume Bragg gratings recorded in PTR glass is a narrow spectral width that restricts operations to pulses longer than 100 fs.

2.

Stretching and Compression of Laser Pulses by Volume CBGs

A uniform volume Bragg grating is a phase volume hologram produced by recording the interference pattern of two collimated beams [Fig. 1(a)]. This recording results in a spatial refractive index modulation (the creation of numerous planar layers having a modified refractive index) in the volume of the photosensitive optical material. These layers provide a resonant diffraction of optical beams that is described in Ref. 14 and detailed for engineering calculations in Refs. 15 and 16. The diffraction of radiation inside of this grating occurs if the Bragg conditions are satisfied

Fig. 1

Recording geometry for uniform gratings by interference of collimated beams (a) and for chirped gratings by interference of a convergent and a divergent beams (b). Arrows show the direction of the recording beam propagation. $Z$ is the axis collinear to the grating vector.

Fig. 2

Schematics of beam diffraction by volume Bragg gratings. (a) Transmitting grating, (b) uniform reflecting grating (Bragg mirror), and (c) chirped reflecting grating, ${\lambda }_1>{\lambda }_2>{\lambda }_3$. Spatial modulation is not in scale—the typical period for a Bragg mirror at 1 μm is about 0.3 μm.

Fig. 3

Modeled spectra of diffraction efficiency of lossless reflective gratings with different spectral chirp rates (SCRs). Parameters of modeling: central wavelength ${\lambda }_0=1550\mathrm{nm}$, spatial refractive index modulation $\delta n=700\mathrm{ppm}$, and thickness $T=5\mathrm{mm}$. SCR $\mathrm{d}\lambda /\mathrm{d}z$, $\mathrm{nm}/\mathrm{cm}$: 1–0; 2–0.5; and 3–5, respectively.

Although uniform volume gratings are recorded using an interference pattern produced by two collimated beams [Fig. 1(a)], it is possible to interfere a divergent beam with a convergent one [Fig. 1(b)]. In this case, the interference pattern consists of dark and bright planes with a period ($\mathrm{\Lambda }$) gradually changing in the $Z$-direction perpendicular to a bisector of the recorded beams. If the convergence and divergence angles are equal, the resulting volume reflecting Bragg grating would have a period linearly varying in the $Z$-direction. If the period variation is directed along the beam propagation direction ($Z$) of such an element, it is a longitudinal chirped reflecting volume Bragg grating depicted in Figs. 1(b) and 2(c). A detailed model of beam propagation in CBGs is described in Ref. 17. Thus, in this paper, we will use a simplified description for the specification of the basic parameters of CBGs. It is clear that a CBG can be considered as the sum of a great number of uniform gratings with different periods which provide an increased spectral width compared to that of a uniform grating.

The reflection spectrum of a CBG depends on the chirp rate of the grating period, $\mathrm{d}\mathrm{\Lambda }/\mathrm{d}z$. For normal incidence, Eq. (1) gives a resonant wavelength $\lambda =2n\mathrm{\Lambda }$. Therefore, a spectral chirp rate (SCR), which is the basic parameter of a CBG working close to the retroreflecting geometry, is determined as

Such a grating can work as a wide band filter with a spectral width extending up to tens of nanometers depending on the SCR and the grating thickness as shown in Fig. 3 (curves 2 and 3). The total spectral width of a CBG is the product of the SCR and its thickness ($T$)

The capability of CBGs for stretching pulses is illustrated in Fig. 2(c). One can see that different spectral components of a laser pulse would be reflected from different sections of the CBG. The total delay time (the maximum stretching) $t_{\mathrm{s}}$ between spectral components corresponding to the front and back ends of a CBG with not very high diffraction efficiency 17 is determined by

This parameter (TDD or SF) is in common use for CPA system design with dimensionality ($\mathrm{ps}/\mathrm{nm}$). For a given SCR, a simple way to estimate SF for CBGs recorded in PTR glass with a refractive index close to $n=1.5$ is

For an ideal CBG with a linear chirp, the delay of the different spectral components is a linear function of wavelength (a straight line in Fig. 4). In reality, the material dispersion of the photosensitive material, along with imperfections of a photosensitive material and within a hologram recording system, cause deviations from such a linear function. This distorted dispersion curve is often modeled by polynomial functions where the linear term is equal to the SF [Eq. (5)] and higher-order terms are called third-order dispersion (TOD), etc.

Fig. 4

Dependence of time delay on wavelength (time delay dispersion) of a 50-mm thick CBG centered at 1555 nm with a SCR of $3.2\mathrm{nm}/\mathrm{cm}$. Straight line—linear dispersion and squares—experimental data.

Recording of phase volume Bragg gratings in PTR glass is a result of the refractive index change caused by photoinduced precipitation of sodium fluoride nanocrystals.¹⁸ The refractive index modulation is proportional to the volume fraction of crystals precipitated in the volume of the PTR glass matrix.¹⁹ Although PTR glass is a highly transparent material, hologram recording causes some additional scattering and absorption.²⁰ This induced absorption is caused by silver and silver halides in the short wavelength spectral region ($\lambda <800\mathrm{nm}$) and by a valence change of different impurities in the longer wavelength range.²¹ Induced scattering is the result of the precipitation of nanocrystals of sodium fluoride¹⁸ and it is proportional to the concentration of those crystals.²² The level of scattering in PTR glass containing a certain volume fraction of the crystalline phase is determined by the size of the crystals. The current technology results in a minimum size of crystals of about 15 nm; a further decrease of the crystal size would require the development of a new photosensitive material.

The spectral dependence of the scattering coefficient (the internal optical density divided by the thickness in centimeters) ${\alpha }_{\mathrm{s}}(\lambda )$ produced by particles with sizes far below visible or IR wavelengths is described by the Rayleigh formula

An experimental diffraction spectrum of a CBG centered at 1555 nm is shown in Fig. 5 (curve 1). One can see that the absolute diffraction efficiency (a combination of relative diffraction efficiencies and losses) at short wavelengths is lower than at longer wavelengths. It was confirmed that the relative diffraction efficiency, which is determined by the spatial refractive index modulation, is identical for all spectral components and the asymmetry in the diffraction spectrum is caused by losses. However, this asymmetry is not caused by the corresponding asymmetry of absorption or scattering spectra (which are flat in this narrow spectral region) but is a result of illuminating the CBG from the end with the larger grating period [from the left side in Fig. 2(c)] which is called the “red end”. In this case, the spectral components with shorter wavelengths propagate longer distances and accumulate higher losses. Illumination of the same CBG from the “blue end” results in higher losses and a lower absolute diffraction efficiency for the long wavelength spectral components. Therefore, measurements of the different parameters of CBGs should refer to a direction of the exciting radiation from “red” or “blue” ends. Sequential stretching and compression provide a symmetric spectrum because this CBG is sequentially illuminated from both ends.

Fig. 5

The spectrum of the absolute diffraction efficiency of a CBG illuminated from the “red end” (1) and the spectra of the input (2) and diffracted beams: single pass (3) and double pass (4).

It is important to note that the reflection spectrum of a CBG is close to a tabletop profile while the emission spectra of pulsed lasers are close to Gaussian in shape (Fig. 5). This means that for efficient reflection of the whole spectrum of a laser system, which is determined by the full width at half maximum (FWHM) for a Gaussian function, a CBG should have about two times the spectral width of the FWHM for a tabletop function.

One can see from Eq. (4) that for stretching a laser pulse to 1 ns, a CBG with a thickness of 100 mm is necessary. This means that for stretching to this pulse length and further recompression of a laser pulse in the vicinity of 1 μm, each spectral component propagates for 200 mm inside of a volume hologram recorded in PTR glass and crosses about 600,000 layers having a modified refractive index. This feature of the CBG technology necessitates strict requirements on the quality of the optical material (the optical homogeneity of PTR glass) and the quality of the holographic recording (the uniformity of the recorded interference pattern). This is why one of the most important parameters of a CBG is the divergence of the stretched and compressed ultrashort pulse laser beams. The most commonly used laser beam quality metric is the $M^2$ method accepted by the International Standardization Organization.²³ The $M^2$ factor of a beam is calculated by measuring the dependence of the beam radius on the distance from a plane where the beam is focused by an aberration-free lens and compared to this dependence for a diffraction-limited Gaussian beam. $M^2$ is usually determined by the single diffraction of a beam with its spectral width adjusted to match the reflection spectrum of the CBG; this will be the metric for certification of CBGs.

However, a number of applications based on threshold processes, e.g., ablation, require reliable data for the power density at the central spot of a laser beam on a target. This value has a good correlation with $M^2$ if it is below 1.1. To provide reliable power density data for CBGs providing higher $M^2$, such a parameter as “power-in-the-bucket”^24,25 is used. To enable a direct correlation of this parameter with $M^2$ measured by means of commercial devices, a cylindrical “bucket” can be substituted having two orthogonal slits enabling an easy comparison of “power-in-the-bucket” with $M^2$ in the corresponding directions.

As it was mentioned in Sec. 1, the main limitation in power scaling of ultrashort pulse lasers is the instantaneous peak power density that triggers a number of detrimental nonlinear effects. A CPA reduces this power density in an amplified laser pulse inversely with the stretching time and, therefore, enables a corresponding increase in pulse energy after amplification. This is why an increase in stretching time is usually considered as a promising method for peak power/pulse energy scaling. Increasing the stretching time requires a proportional increase in the CBG thickness [Eq. (4)]. This is limited by the current technology for fabricating large size PTR glass wafers and for recording large aperture holograms. However, it is possible to increase the stretching time (and further decrease power density) by providing multiple passes of the laser pulse through the CBG (Ref. 26) or by designing multisectional devices consisting of several CBGs (Ref. 27) (Fig. 6). The multiple pass geometry for stretching and compression is produced by the use of mirrors and beam steering optical components that provide an increase in the time delay between the different spectral components. One can see in Fig. 4 that a double pass through the same grating provides doubling of the SF. Of course, this additional propagation length causes additional losses (about 8% in Fig. 5) but it enables a doubling of the stretching time and, therefore, almost double the pulse energy with the use of the same CPA device. It was shown in Ref. 27 that placing a sequence of several CBGs having adjacent reflection spectra and with proper spacing between them provides the same stretching and compression as a monolithic volume Bragg grating (VBG) with the same reflection spectrum and thickness. This approach enables the design of stretchers and compressors having an equivalent thickness that exceeds the current technological capability.

Fig. 6

Schematics of beam diffraction by multipass (a) and multisectional (b) CBGs. M—mirror, PM—phase mask. ${\lambda }_1>{\lambda }_2>{\lambda }_3$. Spatial modulation is not in scale—the typical period for a Bragg mirror at 1 μm is about 0.3 μm.

It should be noted that the use of multipass CBGs enables a new opportunity for pulse shape control.²⁸ One can see in Fig. 6(a) that after the first diffraction in the multipass geometry, different spectral components are dispersed in a direction perpendicular to the direction of the beam propagation. Placing a phase mask between a CBG and a mirror [Fig. 6(a)] provides a phase shift between the different spectral components. This shift results in pulse distortions in the time domain. An example from modeling is shown in Fig. 7. One can see that placing a binary phase mask that provides a phase shift of $\lambda /2$ for half of the beam (this means half of the pulse spectrum) causes a dramatic deformation in the pulse shape. It was found that the use of different phase masks could enable complex transformations in the pulse shape. Similarly, fine tuning of the spacing between sections of a multisectional compressor [Fig. 6(b)] provides a temporal shaping of the compressed pulse.²⁷

Fig. 7

The temporal profiles of a pulse stretched and recompressed by a double pass CBG without (a) and with a phase mask (b) placed before the retroreflector. This binary phase mask provides a phase shift $k=\lambda /2$ for half of the beam.

3.

CBGs Recorded in PTR Glass

As it was mentioned above, practical CBGs that can be installed in CPA ultrashort pulse laser systems became a reality when the technology of extremely high optical homogeneity PTR glass and the technology of extremely uniform large aperture hologram recording was demonstrated and made commercially available by the OptiGrate Corp, (Oviedo, Florida) ( www.optigrate.com). Currently, these technologies enable fabrication of CBGs for the spectral region from 0.8 to 2.5 μm with low absorption and high laser-induced damage threshold that ensures compression of pulses with an energy exceeding 1 mJ and an average power exceeding 250 W. The aperture for commercially available CBGs is up to $10\times 10{\mathrm{mm}}^2$ with a thickness up to 50 mm. The level of diffracted beam quality that has been achieved for such CBGs is currently $M^2<1.4$. A further extension of the aperture and thickness will be dependent upon achieving improvements in the PTR glass technology and large aperture hologram recording techniques.

The characteristics of the CBGs recorded in PTR glass are a strong function of the spectral range where they are intended to be used because of the dramatic difference in the feasible SF (or SCR) and scattering loss for different spectral regions. There are four main spectral regions and CBG product types where commercially available laser sources may utilize CPA technology: type I CBGs for 0.8 μm Ti:Sapphire lasers; type II for 1 μm Yb and Nd doped fiber and solid state lasers, type III for 1.5 μm lasers based on Er-doped fiber and solid state lasers, and type IV for 2 μm novel laser sources that are currently under development.

3.1.

Type I CBGs for 0.8 μm

The uses of CBGs in high power Ti:Sapphire laser systems have both positive and negative aspects. On the one hand, the use of CBGs is very beneficial since they can handle high peak powers. However, the use of CBGs in this short wavelength spectral region is limited due to the limited spectral bandwidth and high scattering losses that affect the diffraction efficiency. Figure 8(a) shows the dependence of the maximum achievable diffraction efficiency and the minimum achievable scattering losses on the spectral bandwidth of CBGs operating at 800 nm. It is known¹² that an increase in the CBG spectral bandwidth requires a higher spatial refractive index modulation in the PTR glass. The maximum refractive index modulation in PTR glass of $\sim {10}^{-3}$ limits the achievable spectral width to about 20 nm for 800 nm operation. One can see that the diffraction efficiency decreases while the losses increase when the spectral width is increased. CBGs with a spectral bandwidth of 20 nm at 800 nm have diffraction efficiencies barely exceeding 50%. The main factor that restricts the diffraction efficiency of a CBG in this spectral range is the material losses caused by the light scattering in the bulk of the CBG material. As it was shown in the previous section, a decrease in the spectral width of CBGs in this region requires a smaller refractive index modulation and, therefore, smaller scattering losses [Fig. 8(a)]. CBGs designed for this spectral range can have SFs ranging from 15 to $300\mathrm{ps}/\mathrm{nm}$ (Table 1). One can see that the maximum achievable SF is inversely proportional to the spectral bandwidth. From this table, one can calculate the maximum dispersion that can be provided by CBGs. For gratings having a spectral bandwidth from 2 to 20 nm, the achievable stretching time is 500 ps.

Fig. 8

Diffraction efficiency and losses achieved in chirped Bragg gratings versus spectral bandwidth for different wavelengths.

Table 1

The parameters of chirped Bragg gratings used in the different spectral regions.

Wavelength (nm)	Bandwidth (nm)	Stretching factor ($\mathrm{ps}/\mathrm{nm}$)
		Max	Min
800	1	300	15
	2	250	15
	5	100	15
	10	30	15
	20	15	15
1000	1	500	7
	2.5	170	7
	5	80	12
	10	30	12
	25	18	12
1500	2	150	20
	5	100	10
	10	50	10
	20	25	10
	50	10	10
2000	1	90	40
	5	90	20
	10	50	7
	50	10	7
	100	7	7

4.

Conclusions

Reflecting volume Bragg gratings recorded with the grating period gradually varying along the beam propagation direction provide effective stretching and recompression of short laser pulses. CBGs are monolithic devices that have three orders of magnitude smaller usage volumes compared to the conventional Treacy compressors. CBGs recorded in photo-thermo-refractive glass can be used in the spectral range from 0.8 to 2.5 μm with diffraction efficiencies exceeding 90%, and provide pulse stretching up to 1 ns and compression down to 200 fs for laser pulses with energies and average powers exceeding 1 mJ and 250 W, respectively, while keeping the recompressed beam quality $M^2<1.4$.