Ultrafast Fiber Technologies for Compact Laser Wake Field: History
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Contributor:
Weijian Sha
,
Jean-Christophe Chanteloup
,
Gérard Mourou
Technologies, performances and maturity of ultrafast fiber lasers and fiber delivery of ultrafast pulses are used for the medical deployment of laser-wake-field acceleration (LWFA). The compact ultrafast fiber lasers produce intense laser pulses with flexible hollow-core fiber delivery to facilitate electron acceleration in the laser-stimulated wake field near treatment site, empowering endoscopic LWFA brachytherapy. With coherent beam combination of multiple fiber amplifiers, the advantages of ultrafast fiber lasers are further extended to bring in more capabilities in compact LWFA applications.
  • fiber laser
  • LWFA
  • brachytherapy
  • coherent beam combination

1. Introduction

Progresses of laser-wake-field acceleration (LWFA) are presented in this special volume of Photonics. Over the last few decades, LWFA has advanced to become an alternative form of particle acceleration [1][2]. Energy of accelerated electrons by LWFA has reached beyond 10 GeV. LWFA produces electric field gradient at GeV/cm; acceleration length is on a scale of centimeters. Laser accelerators are seen as the space- and cost-efficient alternatives to conventional GeV accelerators such as synchrotron of large building size or linear accelerator scaled at kilometer. A typical petawatt-peak-power (1015 W) laser system that drives the LWFA occupies laboratory space of several hundred square meters in comparison, representing a large reduction in accelerator size and cost.
Electrons obtained from conventional accelerators have been used in radiation therapy. Even at the low energy levels the apparatus still occupies a very large room. The inherent advantage of LWFA, exemplified in the reduction factor above, has the potential to reduce the footprint of lower-energy accelerator proportionally or even more [3]. One promising avenue of cancer treatment is brachytherapy, in which a source of radiation is brought inside the body close to the tissues requiring treatment [4][5]. For endoscopic and intraoperative brachytherapy at the local treatment site electron radiation from few tens to few hundreds of keV are sufficient as treatment radiation needs not to traverse healthy tissues. Electron radiation is emitted from LWFA cell near the local treatment site by laser pulses from the flexible delivery system. Simulation studies in the high-density domain of LWFA have shown electron radiation at these energies can be produced using novel nanomaterials [6][7] at relatively low peak power and intensity of the drive laser. At these intensity levels laser sources can be devised in compact and reliable forms and formulated for field use.

2. Lasers for LWFA

LWFA transforms light energy from the high-peak-power laser pulses into the kinetic energy of accelerated electrons. There are excellent research on laser plasma acceleration (LPA) and the necessary lasers to drive the LPA [8][9].
Terawatt (TW, 1012 watt) lasers [10] use table-top solid-state lasers. Enabled by chirped pulse amplification [11][12], these systems attain TW peak power at various combinations of pulse energy and pulse duration (for example, 1 TW is 1 J/1 ps or 100 mJ/100 fs). Beam diameter in propagation insider the amplifier is expanded to about a centimeter [10]. TW lasers reach focused light intensity of 1018 W/cm2, at the starting point for high-field plasma physics (laser peak intensity at 1018 W/cm2 has the electric field strength that drives plasma electrons into relativistic quiver motion). Free-space optical elements (mirrors, lenses, spatial filters, stretcher and compressor, etc.) allow beam expansion for energy extraction, beam and pulse conditioning without damage. These elements need mechanics for mounting, stabilization and alignment. The laser system often has several amplification stages, stationed on top of floating optical table(s) for vibration isolation.
Petawatt (PW, 1015 watt) or tens of PW class lasers are the pinnacles of ultra-intense laser achievements [13][14]. One would only need to imagine that PW systems will have laser beams sized proportionally.
Lasers for LWFA in the lower energy regime of tens to hundreds of keV for oncology application require focused intensity from 1014 W/cm2 and up [7]. For a moderate focal diameter of 20 μm, the corresponding laser peak power is about 1 gigawatt (GW, 109 watt). LWFA laser parameters, either 1 mJ and 1 ps or 100 μJ and 100 fs, involve GW peak power from a laser system. Ultrafast solid-state lasers based on free-space optics can certainly produce the peak power and the intensity. The focus here is ultrafast fiber lasers, constructed from wave-guiding optical fibers. Bulk optics is eliminated from most parts in the system and the compactness aids or necessitates portable field application. For endoscopic LWFA, the other key element is the flexible delivery pathway for the laser pulses. Kinetic electrons are emitted in the LWFA cell at the end of the light delivery cable near the treatment site.

3. Ultrafast Fiber Lasers and Amplifiers

3.1. Ultrafast Fiber Laser Oscillator

Nature has offered mechanisms of organizing broad spectral bandwidth in laser media into ultrashort pulses in time. In the early 1980s, colliding pulse mode-locking was discovered in dye lasers [15][16] using saturable absorbers. The first-ever femtosecond pulses were generated, opening the ultrafast time scale. Kerr-lens mode-locking in Ti:Sapphire lasers were later revealed and developed [17]. Around the same time, mode-locked femtosecond fiber lasers were reported [18]. Mode-lock mechanisms shaping laser light into ultrashort pulses are based on one type or another of nonlinear optical processes.
Advances in ultrafast fibers are reviewed by a number of excellent papers for example [19][20][21]. Many ultrafast fiber oscillators are mode-locked or aided (start action and stabilization) by saturable absorption and the mechanisms alike. Saturable absorption is a nonlinear process in which the lower intensity of a pulse’s pedestals or wings is absorbed to a greater extent than the peak. Repetitive laser action shapes random waveform into pulse of short duration supported by laser gain bandwidth. Semiconductor, carbon nanotube [22] and other materials can be made of this function. Semiconductor saturable absorber mirror (SESAM) [23] is often used in mode-locking ultrafast lasers. Other effective saturable mechanisms—such as nonlinear polarization evolution (NPE) and nonlinear amplifying loop mirror (NALM) [18][24]—also function very well.
Ultrafast fiber lasers also have to deal with large amounts in nonlinearity and group velocity dispersion (GVD) due to small mode area and long propagation length. These factors can either benefit pulse shaping or have detrimental effects. Silica fiber has normal GVD at 1 μm (Yb gain region) and is anomalous at 1.5 μm (Er region). A laser cavity can be configured in a net dispersion of either way. Soliton lasers take advantage of the soliton mechanism in balancing self-phase modulation (SPM) and anomalous dispersion [25][26]. Pulse energy in soliton fiber lasers is typically low. In the normal dispersion regime, similariton is effective in producing higher energy pulses, where the interplay of dispersion, SPM, and gain renders an input pulse of arbitrary shape evolving asymptotically into an amplified, linearly chirped pulse. The pulse grows in duration, spectral width, and peak power in a self-similar manner to that the temporal profile and the chirp rate remains unchanged [19][27][28]. Chirp can be externally compressed. Additional techniques—such as spectral filtering and polarization control—can also be useful to assist the mode-locking [29].
Robustness of well-designed femtosecond fiber lasers has been established. For example, in the SLAC National Accelerator Laboratory’s Linac Coherent Light Source, the injector ultrafast laser system has an Yb ultrafast fiber laser as its source. Up-converted UV pulses from this femtosecond laser system emit photoelectrons in the injector photocathode. Synchronized electrons are accelerated by the linear accelerator to generate femtosecond X-rays in the free-electron laser section [30].

3.2. Ultrafast Fiber Amplifiers

Packing a gigawatt laser into a fiber laser system has many challenges. Intensity of short pulses in fiber is inherently high. Nonlinear (non-recoverable) phase accumulation can quickly deteriorate the spectral and temporal profiles as the pulse propagates. When the pulse gains intensity above the material damage threshold, it damages or vaporizes the fiber.
Two major technologies are the key enablers to overcome the obstacles: chirped-pulse amplification (CPA) helps to boost amplifier output peak power by 3 to 4 orders, while large mode area (LMA) fibers increase by another 2 to 3 orders.

3.2.1. Chirped-Pulse Amplification

CPA proceeds in three steps: (1) an ultra-short laser pulse is stretched in time by several orders of magnitude, so that its peak power is correspondingly reduced, (2) it is amplified in a laser material without damaging it, (3) it is compressed in time back to its original duration, resulting in very high peak power [11].
Light amplification by stimulated emission preserves the optical phase. Pulse stretched into a linear chirp prior to amplifier is a reservable process by the corresponding compression after amplification.

3.2.2. Large Mode Area Fiber

Increasing the mode-field diameter (MFD) in the amplifying fiber is another key to mitigate the peak power problem [28][31]. In doing so, single mode must be maintained. Modal dispersion in multi-mode propagation obliterates temporal profile of the pulses. Furthermore, the fundamental mode allows diffraction-limited focusing for the targeted intensity. SM fiber designs with step-index or graded-index profiles are limited due to the small index contrast and the simple spatial profile. Breakthrough in photonic crystal fibers (PCF) makes large-mode-area single-mode fiber design possible and enables much higher peak power in ultrafast fiber amplifiers, in conjunction with CPA.
PCF guiding employs periodic index modulation with air holes to achieve high index contrast. Preferential design in the cladding discriminates high-order modes allowing single mode with larger core sizes. Commercial PCF fibers with MFD over 30 μm are now available. As evident in Figure 1, fiber amplifier output peak power level goes hand-in-hand with mode-field area. In the fiber system producing 4 GW, the final amplifier stage employed a PCF Yb gain fiber with 105 μm MFD [32].

3.3. Towards Gigawatt

In Figure 1, a survey of high-power ultrafast fiber laser research in last 15 years is presented. Even with this limited survey it can be seen the extraordinary advances in laser peak power from tens or hundreds of megawatts to gigawatts. As remarked earlier, the first CPA gigawatt system was based on table-top solid-state lasers with free-space optics. Now gigawatt can be condensed to a fiber laser system. Gigawatt fiber lasers enable compact, portable LWFA medical applications.
/media/item_content/202207/62c6390a93559photonics-09-00423-g003.png
Figure 1. Survey of research work in CPA ultrafast fiber amplifiers from a number of publications in this limited survey. Triangle data points mark reduced peak power of stretched pulse (stretch ratio up to 4000) in fiber amplifiers. Blue notations are the resulted output pulse energy and pulse width after compression and the corresponding output peak power is marked in red. Output peak power up to 4 GW is seen increasing with fiber effective area. The ratio of instantaneous power (stretched) in the vertical axis over fiber area in horizontal axis is light intensity in fiber. Blue triangle data points are seen following along the intensity line of 10 GW/cm2, indicative of the limit imposed by nonlinear phase accumulation.

3.3.1. Limitation due to Fiber Nonlinearity

Over the length L in fiber, nonlinear phase φnl is accumulated from the small but existent nonlinearity index n2 (3 × 10−16 m2/W in silica),
where A is effective mode-field-area. P is the peak power of the pulse averaged over the fiber length, already reduced by the stretch ratio from CPA. L is typically of meters. φnl can be also viewed as proportional to the light intensity P/A in fiber.
As a rule-of-thumb estimate, acceptable φnl (or B integral) is about 2π. Above this level, non-correctable detrimental effects are seen on temporal and spectral quality of the pulse. This obstacle is seen at lower intensity levels in fiber amplifiers, compared to solid-state lasers.
Note that the blue triangle data points in Figure 1 are “pushed” along the intensity line of 10 GW/cm2, indicative of the limit imposed by nonlinear phase accumulation. Further increasing the fiber mode area is becoming more difficult. MFD of 100 μm is already 100 times that of the laser wavelength. With large core diameters, single-mode guiding becomes highly sensitive to fiber bending. In fact, some of the large-core fibers are the rod-type fibers.

4. Coherent Beam Combining (CBC) Lasers

Coherent beam combining (CBC) introduces a paradigm shift in laser architecture offering major opportunities for laser design and consequently for applications. CBC can be seen as the space domain equivalent to what CPA allows in time domain: spreading the energy prior to amplification to mitigate limitations such as B integral. CBC consists indeed in the spatial splitting of an initial laser beam into N small aperture sub-beams followed by subsequent recombination of the amplified beams. The above-mentioned limitations remain valid at each individual fiber level but are overcome at a global scale if the N amplifying channels are ultimately successfully coherently combined. Gigawatt ultrafast fiber systems can then be empowered by a third key technology:
CBC improves amplification by a factor η N (η being the combining efficiency).

Figure 2 illustrates Ecole Polytechnique/Thales N = 61 channel XCAN CBC prototype (with η experimentally ranging from 40% to 50%).

/media/item_content/202207/62c639196f561photonics-09-00423-g004.png

Figure 2. XCAN 61 channel CBC laser. The bundle of 61 YB doped 30 µm MFD amplifying fiber can be seen fluorescing. The fibers are arranged in the laser head in a honeycomb distribution and subsequently collectively collimated through a lenslet array (far right of the left image). Collective phase delays recording through interference pattern (right).

XCAN relies on far field CBC (also described as tiled-aperture CBC), a combining approach inherently limiting the efficiency to η = 65% theoretical value but offering two experimental key advantages: absence of a final optic dealing with the full combined peak and average power and near field access to individual control of phase, amplitude and polarization for digital laser applications [33][34].
Alternative architectures falling into the near field combining category (also described as filled-aperture CBC) does not face such an efficiency limit with experimental η only limited by optics quality (generally above 90%). Recently, 81 beams have recently been combined with a diffractive combiner [35] whereas 16 amplifying channels were combined with beam splitters [36]. More recently, the same group achieved a similar channel number coherent addition within a single multicore fiber [37], paving the way for even more compact (even though the involved fiber was not flexible) laser system. Each core has a diameter of 19 μm with a pitch of 55 μm between the core centers.

5. Photonic Bandgap Fiber (Hollow-Core Fiber) for Pulse Delivery

5.1. High-Index Guiding PCFs

Conventional step-index fibers utilize total internal reflection (TIR) to guide light rays, having higher optical index in the core than in the cladding. This index contrasts (with converging power) shapes collective wave-guiding by balancing natural light diffraction in the fiber. Proper single-mode fiber design is to have only the fundamental mode. PCFs greatly broaden the limited design capabilities with step-index fiber design.
PCFs have a sophisticated microstructure of different refractive indexes [38][39]. They are typically glass fibers fabricated by pulling from a preform in a furnace—like conventional fibers—and they maintain bending flexibility. The background material is often undoped silica and low index regions are typically air voids. Air has the lowest optical index, thus producing very high index contrasts. Stronger guiding results from this modified total internal reflection (M-TIR) [39]. Locations of air-hole networks can be arranged according to desired function, such as mode-guiding differentiation, dispersion, and cut-off wavelength (or the absence of it).
PCFs allow a new range of novel properties. The large-mode-area (LMA) PCF is an essential element in ultrafast fiber amplifiers for reducing intensity. In a commercial offering of an Yb-doped fiber, for example, using precise control of airhole diameter and spacing and induced birefringence yields a single mode polarizing fiber with diffraction-limited beam quality at 40 μm diameter core size.
Another example of PCF having the opposite function of large-mode-area fibers is the highly nonlinear fiber for supercontinuum generation. The small-core (1 or 2 μm) fiber sharply increases the light intensity, and the near-zero-dispersion design allows long interaction length without dispersing the femtosecond pulses. The resultant supercontinuum spans over an octave wide in frequency, allowing f-to-2f interferometry for carrier-envelop-phase stabilization in the laser oscillator. The accomplished system generates phase-synchronized frequency comb in high-precision metrology applications [40].

5.2. Hollow-Core Fiber (Low-Index Guiding) for Ultrafast Pulse Delivery

Low-index-guiding PCFs uses photonic bandgap (PBG) effect to guide light. The guiding mechanism in PBG fiber is fundamentally different from high-index guiding in M-TIR. The light is typically confined to the empty core such as air while the surrounding microstructure region as the cladding displays a photonic bandgap [41]. Much like electron waves in a crystal where a band of electron wavevectors is forbidden, optical waves of certain wavelengths in the photonic bandgap cannot propagate. Therefore, light is trapped and propagates only in the hollow core surrounded by the anti-resonant (being reflective) microstructure. Only the edge of the transverse profile (less than a few percent of the light power) sees the glass material.
PBG fiber is a new paradigm in fiber design. Nature has existing examples of the PBG effect; for example, the color of a butterfly is the result of anti-resonant nano-cavities at the reflecting wavelength. Dispersion of PBG fibers can be tailored as it is mostly determined by the microstructure. PBG fiber design is sophisticated, which requires full vectorial calculation from Maxwell Equations. Mechanically PBG fibers are also flexible.
With light being guided in the hollow core of air, vacuum, or gas, the high-intensity ultrafast laser pulses do not experience nonlinearity (and damage) as in the solid core fibers—facilitating fiber delivery applications with ultrafast pulses. For example, high-harmonics generation (UV) from laser pulses can be generated at the end of the delivery fiber as UV light darkens fiber. Ophthalmology surgery can be performed with the laser delivered by the hollow-core fiber. This is also what is needed in endoscopic LWFA.
Capabilities of hollow-core fibers are given in a couple of demonstrated results. In the first result [42], 70 W of average power of picosecond pulses are transmitted over the hollow-core fibers with only a few percent power loss after 5-10 meters. Diffraction-limited beams in MFD of 8 μm, 13 μm, and 22 μm fibers are delivered while bending radii are kept at 8 cm. Another demonstrated result [43] is the hollow-core fiber with a MFD of 40 μm. It has the capacity to carry 500 fs pulses of 500 μJ energy. This amounts to 1 GW of peak power. The bending radius of the fiber is about 25 cm. Ultimately, hollow-core fibers are limited due to damage of the glass structure at the edge of the laser intensity profile.

5.3. Additional Delivery Capability

The limit of hollow-core fiber transmission is affected by damage at the edge of the intense laser mode profile. To further increase delivery capability, researchers may anticipate the coming of a multi-hollow-core fiber. There are multi-core fibers existent today based on step-index solid materials. This type of design has multiple cores with a common outer wall, protection coating, enforcement, etc. It has been developed as a compact form for space-division multiplexing in optical communication to multiply the data-carrying bandwidth. Similarly, researchers may boost throughput of laser pulses with multiple hollow cores in a common fiber structure. Laser channels in the close spatial vicinity help to facilitate a common focal point with the use of a lenslet array for collimation prior to a common focusing lens. It is similar to CBC lasers in spatially combining beams, but without phase locking. Power addition is not coherent thus intensity distribution varies from shot-to-shot within the focal boundary. Effectiveness of such a laser field in LWFA requires further study.

6. Applying Ultrafast Fiber Technologies to Endoscopic LWFA

One promising avenue of cancer treatment is brachytherapy, in which a source of radiation is brought inside the body close to the tissues requiring treatment. For endoscopic and intraoperative brachytherapy at the local treatment site, electron radiation from few tens to few hundreds of keV can be effective (see brief introductions in see Sections 1 and 6). Laser intensity for electron acceleration in the high-density LWFA regime for endoscopic applications needs to be 1014 W/cm2 and higher. Researchers have brought forth ultrafast fiber technologies for this application: ultrafast fiber lasers (single-fiber system or coherent-beam-combining lasers) which are capable of generating gigawatts and above as the light source, and hollow-core fibers for delivering these intense laser pulses endoscopically.

Laser pulses are delivered flexibly to the LWFA cell and ready to focus on to the target material to generate and accelerate electrons. Engineering design must be mindful of damage in the delivery optics due to the nature of the intense laser pulses. For such the laser beam after exiting the hollow-core fiber should be expanded to encounter optics based on solid material. Furthermore, the expanded beam is necessary for the proper beam size to optimize diffraction-limited focusing to the target. The choice of focusing design also depends on the Rayleigh range needed for LWFA. At a modest 20 μm focal diameter, Rayleigh range is about 300 μm for laser wavelength of 1 μm; 1 gigawatt peak power will yield  W/cm2, in range for target LWFA laser intensity.

An effective scheme of LWFA utilizing the relatively low laser intensity of  W/cm2 is the plasma beat-wave accelerator (PBWA) [[7],[44]]. The scheme uses two co-propagating laser pulses with two optical frequencies—  and —and the beat gives a modulated laser amplitude for the resonant excitation of a plasma wave at where  is the plasma frequency. The modulated laser intensity profile which is resonant with plasma wave gives in-phase pondermotive kicks to accelerate the electrons. The advantage of PBWA is that lower peak power and longer laser pulses from the fiber lasers can be used. Researchers may choose two common fiber laser wavelengths of 1.03 μm and 1.56 μm respectively for the two laser frequencies of and . Reference [[7]] has more discussion and data about electron energy spectrum, plasma frequency related to this setup and application.

Since hollow-core fiber is anti-resonant design to specific wavelength (or to the specific photonic bandgap), a single hollow-core may not support the transmission of both wavelengths for the generation of the plasma beat wave. In that case, two hollow-core fibers for the respective wavelengths can be employed and are brought together at a common focus for the PBWA.

This entry is adapted from the peer-reviewed paper 10.3390/photonics9060423

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