SYMPTOM.

Failure of C619

Sharp Television Models

DV5932H,DV5935H, DV5937H DV6635H

CAUSE.

R632 mounted too close to C619

ACTION.

Replace C619 as necessary and move R632 as shown in the diagram.
PLEASE CARRY OUT THIS CIRCUIT IMPROVEMENT TO ALL SETS THAT REQUIRE SERVICE
Ref No C619 Description Capacitor 0.56nF 250v Order Code SH1010

Figure 1.1: Historical brightness of X-ray devices (adapted from Winick [91]). The lack of innovation in conventional source technology has left a large gap in performance between local sources and those of large light sources. Conventional sources not only take more integrated time to perform an experiment, but they are also not tunable, and hence functionally handicapped. Even a moderate brightness synchrotron radiation source, such as the one under study, can be eectively utilized by researchers if it could be made available as a home-lab source.
Wider application of synchrotron radiation would naturally follow if compact and more aordable sources become available. For structural biologists, the centralization of research at a handful of national synchrotron radiation laboratories has led to the proposed paradigm of high-throughput protein crystallography in which a few synchrotron beamlines will be factories for biology research. Many life science researchers, however, would benet from a local, on demand, synchrotron radiation
1.1. BACKGROUND AND MOTIVATION
source which would be better matched to the pace and scale of existing biological laboratory research. Local sources would likely open more avenues of exploration and opportunities for experimentation to a wider set of scientists. There are also a number of medical and industrial applications that have been developed using synchrotron radiation but are impractical because no local sources yet exist with the necessary intensity and spectral properties. In particular, several groups are working on enhanced medical imaging techniques that will become clinically feasible only when a more powerful local X-ray source is available [3, 45].
Compact Hard X-Ray Devices
Currently only a handful of physics research ideas are candidates to develop compact and powerful X-ray sources, especially those that retain the advantageous characteristics of synchrotron radiation such as tunability and high monochromatic intensity. The compact storage rings utilized by industry for lithography have electron energies which are too low to produce X-rays needed for most material and biological applications [50]. Storage rings could be made compact, for instance with superconducting magnets, but the cost and complexity of these proposals still require more resources than most users are willing to expend [16,93]. Of possible alternative techniques, such as channeling radiation [51] or uorescence [52], the leading candidate for producing hard X-rays is laser-electron scattering, rst investigated over a decade ago [75]. Early proposals, however, encountered diculties, mainly from fundamental intensity limitations or designs that produce X-rays in very high-energy ranges which, again, are not suitable for the majority of current synchrotron applications. These laser-electron researchers have been historically from one of two camps: accelerator physicists, who leverage their existing storage rings to produce high-energy X-rays or gamma rays, and laser physicists, who use advances in high peak-energy pulsed lasers. Much of the research published in the literature today comes from the latter group where table-top terawatt lasers collide with electron beams produced from pulsed linear accelerators [55, 61, 79]. These devices generate ashes of subpicosecond X-ray pulses that have very attractive peak brightness, but are orders

Description of a Laser-Electron Storage Ring Source
A conceptual picture of the X-ray source is shown in Fig. 1.2. The ring is injected with a short linear accelerator that accelerates the electron beam to the full energy desired in the ring. The electron energy necessary for 1 radiation is 25 MeV. The electron A source produces a single electron bunch using an rf gun with a laser photocathode. The injector periodically refreshes the electron bunch in the storage ring to maintain high beam quality. The storage ring is designed to allow the bunch to circulate in a stable fashion for about one million turns. The beam is kept tightly bunched by an rf cavity. On one side of the ring is a straight section in which the electron beam is transversely focused to a small spot. This straight section also serves as the optical gain enhancement cavity for the laser pulse. The electron bunch and the laser pulse collide each turn at the interaction point producing a burst of X-rays.
from the Structural Biology Synchrotron Users Organization (BioSync) compilation of beamlines in the U.S. at http://biosync.sdsc.edu/.
Figure 1.2: Concept drawing of a compact X-ray source. Major components are the injector (electron gun and accelerator section), the electron storage ring (shown with focusing quadrupole and bending dipole magnets), and the integrated optical cavity (between mirrors). Electron-photon scattering at the interaction point produces naturally collimated, narrow bandwidth X-rays.
Table 1.1: Target output X-ray performance. Total Average Flux Avg. Monochromatic Flux Source Spot Size Source Divergence Source Brightness X-ray Energy Range
1013 ph/s 1010 ph/s 30 m radius 3 mrad keV 6 keV
matched beam waists ph/s/mm2 /mrad2 /0.1% BW 1 = 12.4 keV A
Typical value for a beamline monochromator bandwidth. Spot size and divergence correspond to n 1 x 107. Peak energy of X-rays scales as square of (tunable) electron beam energy.
A 1 m wavelength mode-locked laser resonantly drives the enhancement cavity to build-up a high power laser pulse. The high nesse (low loss) cavity is possible due to improvements of high-reectivity, multi-layer optics. High reliability, solid-state, mode-locked laser systems that can supply the needed laser power are also currently available. Matched 1 cm long laser pulses and electron bunches collide to produce an X-ray spectrum equivalent to a 20,000 period undulator magnet. The X-rays are directed in a narrow cone in the direction of the electron beam as shown graphically in Fig. 1.2. They can be focused using conventional X-ray optics down to the source image size of 60 m diameter, or slightly smaller if a larger divergence is acceptable. The target brightness and ux are shown in Table 1.1. The narrow band ux is the same magnitude as PX bend beamlines at 2nd generation storage ring sources like NSLS. Gross X-ray energy can be tuned by adjusting the electron beam energy (where ne-tuning can be accomplished by monochromator or lter adjustments). Note that the X-ray phase space follows the guidelines from the previous section: a transverse emittance of 1 x 107 implies a normalized transverse emittance of 5 x 106 for a 25 MeV beam. The conguration as described above operates with a similar photon ux up to X-ray energies of many tens of kV, and can be scaled in principle to gamma ray energies as well.

Figure 1.3: Electron-photon beam-beam interaction. The waists are shown matched, i.e. equivalent waist size and focus depth. For electrons, 2 = where 1 x 107 and 1 cm determines the focus depth (and bunch length). For photons 2 = zR (0 /4), so the diraction limited emittance yields a similar focus depth zR 1 cm, where zR is the Rayleigh range.
How To Optimize X-Ray Flux
Beam-Beam Interaction: Luminosity Fig. 1.3 illustrates the bunch collision at the interaction point where the waists are shown matched. From an accelerator physics view, Thomson scattering can be expressed as a particle beam-beam interaction [89]. The total intensity of scattered photons can be described as a luminosity multiplied by the cross section of the event, N = L0 Th. The Thomson cross section is given by Th = where re = e2 /m0 c2 ( is L0 = r = 6.65 x 1029 m2 , 3 e (1.1)
2.82 x 1015 m) is the classical electron radius. The
luminosity for two round beams with identical Gaussian distributions and waist size Ne NL fc 2 4r (1.2)
where Ne is the number of electrons, NL is the number of laser photons, fc is the collision repetition rate, and r is the transverse spot size. The eect of bunch lengths and crossing angles are discussed later in Sect. 2.4. Besides large numbers of particles, a high luminosity requires tight focusing and high collision rates. The benet of a small storage ring over linac-based sources is the very high repetition rate: 100 MHz compared to 100 Hz. This 106 increase in ux from the high
collision rate relaxes both the energy per pulse of the beams as well as the focusing requirements. The main diculty with Thomson scattering sourcesthe low cross sectioncan in fact be used to an advantage with this kind of source. The weak interaction between the laser photons and electrons allows for a design of virtually independent storage systems: a storage ring for the electron bunches, and a resonantly driven optical enhancement cavity for the photons. In each case, the details of the storage system design, not the electron-photon interaction, are responsible for the loss mechanisms and dynamics. The eciency for this device is dominated by the separate eciencies of the particle storage systems rather than the scattering cross section. Parameter Trade-os Parameters related to luminosity are listed in Table 1.2 along with their likely limiting factors. Of course, changing one parameter can aect others, so the task of optimizing the overall luminosity is a compromise between more ux vs. stability or power handling. A brief discussion follows for each parameter to qualitatively justify the nominal values. The design choices are examined in more detail in subsequent chapters. Table 1.2: Nominal values of parameters aecting luminosity. Parameter Number of electrons/bunch Ne Laser pulse energy Focus spot size Interaction rate Injection rate U0 r frep finj Value 1 nC 1 mJ 30 m 90 MHz 60 Hz Limits beam dynamics; injector optical cavity mirrors; input power stability; focusing depth ring geometry; size emittance growth; avg. power

(2.13)

The above relation gives the power in a given energy bandwidth accepted over all angles per electron, i.e.

dP 0 d

= P. The angular spread for a small bandwidth,
however, is naturally collimated much better than the full 1/ opening angle. For a relative bandwidth (/ ) around the peak energy, all the power falls within an angle max = with a total integrated power

(2.14)

(2.15)
which shows there is a factor 3 peak in forward intensity for small bandwidths when calculating the power compared to simply multiplying the bandwidth by P. For example, given a desired 1% relative bandwidth around and a 25 MeV electron ( 50), the total power is 0.03P and is conned within a forward cone of 2 mrad.
Electron Beam Energy Spread and Emittance
A real electron beam has a distribution of angular spread and energies which must be folded in to the power spectrum (Eq. 2.12). To qualitatively understand these eects, the consequence of beam energy spread and emittance can be examined separately. First, if the beam energy spread is included, the spectral width broadens (/ ) = 2(E /Ee ). From Eq. 2.14, the natural angular spread increases as well. For the nominal design, an energy spread of 0.3% would lead to an intrinsic angular spread of 1 mrad, which is still relatively small. Next, the angular spread can be folded in. The average angular beam divergence, e is a related to the normalized emittance n = r e. For a spot size of 30 m, n = 5 m, and 50, the natural beam divergence is 3.3 mrad. The beam 2.7%. angular spread then dominates the character of the resulting X-ray beam. The full energy spread of the X-rays, calculated from Eq. 2.9, is then
From this analysis, the X-ray beam inherits the same emittance as the electron beam. The eective use of this spectrum will require a lter or optics designed to take advantage of this particular X-ray phase space distribution. For instance, for a xed angular acceptance, the ux is optimized in a given energy band when the center of the band is slightly o the peak frequency . This source also naturally matches the requirements of large-area imaging applications [45] which need locally small divergences, i.e. radiation emanating from small spots. For focusing applications like protein crystallography, the 60 m x 60 m spot size can be imaged or slightly magnied through appropriate X-ray optics.
Laser Cooling and Quantum Excitation
The radiative damping of the electron beam by the laser can be calculated by treating the photon emission as weak undulator radiation. If the laser pulse length is short compared to the depth of focus zR (Eq. 4.8), P can be integrated to calculate the
2.3. LASER COOLING AND QUANTUM EXCITATION
average energy loss per electron [43], (E) = where the laser pulse energy U0 = P 2 U0 dz = r , 2c 3 e zR 0 (2.16)

Luminosity

Luminosity is one of the most important parameters to optimize in the entire design. Since the laser intensity is too low to cause any non-linear electron motion, there is no ponderomotive or other beam-beam eects besides that of radiation damping as discussed in Sect. 2.3. The simple luminosity formula (Eq. 1.2) can then be modied by two major geometrical eects: one from a nite crossing angle, and the other from the bunch length to focal depth ratio (the hourglass eect).

2.4. LUMINOSITY

Crossing Angle
Thomson scattering experiments are usually congured either at crossing angles of 90 to generate short (sub-picosecond) X-ray pulses, or close to 180 to optimize both the luminosity and energy transfer. The particle model predicts the energy transfer to the scattered photon as well as the relativistic 1/ opening angle eect, but it does not address any geometrical aspects of the beams, which must be accounted for separately. In practice, there is often some small crossing angle c to avoid the back-scattered X-rays from impinging on an optical mirror surface. For linac-based sources, where the bunch lengths are short, this angle may not be a concern. Also, for cavities driven by CW sources, a slight crossing angle is often designed [14] or experimentally implemented [27]. For long laser pulses, however, the timing and geometrical overlap of the bunches becomes important for luminosity, which is well understood for particle colliding machines [31]. An estimate of the crossing angle sensitivity on luminosity can be evaluated by considering the angle at which the projected spot size x in the crossing dimension becomes dominated by the angle instead of the focused waist x. Using the projection, x =

2 x + (z c )2 ,

(2.22)
the angle becomes important when c x /z. For the device parameters, c = 30 m/1 cm = 3 mrad. If a crossing angle is chosen to avoid scattered photons hitting the laser optics, this angle should be some factor larger than the far eld divergence of the laser envelope, 0 = 0 , 2r (2.23)
where r = w0 /2 is the equivalent RMS spot size for the Gaussian laser waist w0. For a matching laser waist r = 30 m, the divergence mrad. If the mirrors contain several 0 to avoid diraction losses in the optical cavity, the required crossing angle would dominate the projected beam size in Eq. 2.22, which further degrades the luminosity when the time structure is accounted for as well. To avoid the crossing angle eect, some researchers propose more complicated optical systems. For instance, Tsunemi [79] built an interaction chamber in which
high-powered CO2 laser pulses reect o a focusing mirror with a hole for electron beam and radiation passage; the laser uses a hybrid mode pattern where the modes interfere to produce a donut shaped pattern at the mirror (to avoid losing photons through the central hole), yet interfere at the focal point as a nearly-Gaussian peak. Such systems are elaborate and generally unworkable for very high nesse cavities, however. The most straightforward solution, and the one adopted for this design, is to have no crossing angle whatsoever, and let the X-rays simply pass through the optical mirror. Very high reectivity multi-layer dielectric mirrors need /4 optical thickness layers, which for = 1 m and typical materials results in a physical thickness of 5 m. In theory, then, a very good reector for IR may be a good window for hard X-rays. More about this X-ray-window/IR-mirror is discussed in Sect. 2.5.

layers often contain dense, high-Z metallic oxides, like Tantalum (Ta2 O5 ) or Hafnium (HaO2 ). Most of these high-Z materials have X-ray K-edge absorptions within the desired working range of hard X-ray applications (618 keV). One promising combination of materials, however, is Titania/Silica (TiO2 /SiO2 ), developed as ultra-low loss mirrors for ring-laser gyroscopes [13]. The K-edge is at 5 keV, which makes the X-ray transmission reasonable over most of the desired X-ray energy range. Fig. 2.3 illustrates the X-ray transmission losses for a typical thickness high-reectivity stack.
Figure 2.3: TiO2 /SiO2 mirror X-ray transmission for a 32 quarter-wave layer stack. The physical thickness of each layer is 40 /n, where for Silica, nL = 1.35, for Titania, nH = 2.20, and 0 = 1.06 m. Data and plots available from the LBL Center for X-ray Optics (www-cxro.lbl.gov/optical constants/). Another possible solution is to use two alternating low-Z materials that exhibit some index of refraction dierence, like Alumina/Silica layers. The diculty with such a scheme is that losses in the mirror are intrinsically higher since the optical elds must penetrate into more layers (in order to retain the high reectivity) where power can be absorbed. The scaling for the limiting losses (for R 1) in a quarterwave stack is described by Koppelmans equation [5], L0 = 2 n0 (|kH | + |kL |) n H 2 nL 2 (2.26)
where n0 , nH , and nL are the refraction indexes of the media, high-index layer, and low-index layer, while the ks are the extinction coecients (imaginary part of the total index of refraction). The coating technique is often more important than the material in determining the eective k value, so for a given coating technology, one wants to maximize the dierence in the layer indexes. A possible hybrid solution1 is to coat the very top layers (which contribute to the most loss) with a standard high-Z thin lm and then use the low-Z materials for the remainder of the stack. The other necessary ingredient for optical high reectivity is to coat the multilayers on a superpolished substrate, like Si, SiC, or even sapphire (Al2 O3 ). These examples are chosen because they are also very mechanically rigid and can be made thin over the 1 cm diameter. The usual X-ray window material, Beryllium, is typically more dicult to polish and has limited use because of regulatory safety concerns. The detailed engineering design of this mirror will likely need a close collaboration with commercial coating experts, but the overall requirements should be within technical reach. The issue of radiation damage degrading long-term optical performance is discussed in Ch. 4, Sect. 4.1.4.

Chapter 4 The Optical Storage System
The optical storage system would consist of an external enhancement cavity resonantly driven by a CW mode-locked laser. There are three major performance demands on the optical enhancement cavity: low internal losses, a narrow transverse waist at the interaction point (IP), and optical/mechanical stability. The drive laser has two major requirements: ecient coupling to the cavity eigenmode by transverse mode-matching and alignment, and tracking the central frequency of the cavity by maintaining an overall frequency stability within the cavity bandwidth. One mutual requirement is to match the laser pulse repetition rate to the free spectral range of the cavity, where both also match the electron storage ring circulation frequency. An examination of these criteria is explored in this chapter, with emphasis on the technical requirements needed to fulll the nominal laser-electron storage ring design.
The Power Enhancement Cavity
The issues of accumulating a large circulating power in an external cavity are well known for single-mode CW lasers. The added complication with a mode-locked laser is that the mode structure of the laser must match the mode structure of the cavity, or in time domain, the round-trip time in the cavity must very closely match the 41
CHAPTER 4. THE OPTICAL STORAGE SYSTEM
repetition rate of the laser.1 The following section describes a basic, two-mirror FabryPerot cavity in order to illustrate the various longitudinal and transverse issues, some of which are directly relevant to the experiments performed in Ch. 5.

The Fabry-Perot Cavity

The simplest optical cavity conguration is a two-mirror Fabry-Perot interferometer in which power is coupled through the backside of one partially transmissive mirror (Fig. 4.1). The mirrors have a spherical radius of curvature to provide stability for the fundamental transverse eigenmode of the cavity (TEM00 ). The mirror radii, together with the cavity length, fully determine the waist size and position, the mirror spot sizes, and the inherent stability, i.e. sensitivity to alignment and transverse modematching errors. The mirrors reectivity, combined with transmission and other losses, determine the external coupling and cavity nesseor expected gain. Higher nesse cavities mean longer ll times (lower cavity bandwidths) and correspondingly more stringent frequency stability of the driving source (discussed in Sect. 4.3.1).
Figure 4.1: A basic pulse-stacking cavity geometry is a symmetric, standing-wave Fabry-Perot interferometer that has a round-trip circulation time equal to the inverse of the laser pulse repetition frequency and a central waist determined by the cavity eigenmode. Under steady-state, matched conditions, the power of the drive laser matches the losses of the cavity and results in an amplied circulating laser pulse with a gain losses1.
or more generally they should be related by a harmonic, either for storing multiple pulses in a longer cavity, or having one pulse undergo multiple bounces in a folded cavity.

Iteration of pulse waveforms: Bn = Ar Cn t Dn = Cn r + At Cn+1 = Dn p ; z z Figure 4.4: Field relations for dynamic evaluation of power build-up in a resonator at the coupling interface. Input A represents a train of Gaussian shaped pulse elds. The values r and t are the reection and transmission (eld) coecients of the coupling mirror, i.e. t2 = T1 and r2 = 1 T1. For the two-mirror cavity case, the reection coecient of the output mirror is added to all other path losses so that p2 = 1 T2 L1 L2. The algorithm is conveniently implemented in LabVIEW where the eld relations are evaluated point-by-point on waveforms that are viewable dynamically as the simulation runs. To avoid waveform sampling eects, the calculation of arbitrary small displacements, , is accomplished by adding a scaled numerical derivative of the circulating pulse to itself. Gaussian functions slightly oset in time subtracted from each other). Another interesting feature is that the ll-time of the cavity changes character. On the peak mode, the ll-time behaves exponentially just as CW source, but o this mode, the peak gain abruptly saturates and reaches steady-state at a time much sooner than at peak (Fig. 4.5). By resonating at further axial mode slips, not only does the power coupling eciency decrease but the eective cavity bandwidth changes as well (see Fig. 4.6). Looking ahead to Ch. 5, this feature was advantageous experimentally since it provides a means to vary the cavity bandwidth in small steps. In terms of the intended source design, the results of these models suggest that operation is optimal at the peak axial mode, which is well dened but will undoubtedly require some slow feedback mechanism to track it. The peak circulating eld, although easy to measure, is not as good a measure of performance as the power coupling eciency since the value of interest is the circulating pulse energy. For the case of a 10,000 cavity gain, the results of Fig. 4.3 show a drop of 25% in coupling power for a slip of one axial mode o peak. Although only discrete envelope shifts associated with axial modes have so far been addressed, the tools developed in this section allow for arbitrary envelope phase slips, which is the topic of the next section.
Figure 4.5: Dynamic peak power buildup in a resonator for a few axial mode slips. Although this example uses parameters relevant for experimental cavities described in Ch. 5, the dynamics illustrate the character of how power reaches steady-state in the resonator. These results are for a matched cavity with T = 300 ppm, FSR = 80 MHz, = 1 m, and = 0.6 cm. Peak gain is 3300 and the nominal cavity bandwidth, cav = 7.6 kHz.
Figure 4.6: Power coupling eciency and eective bandwidth vs. axial mode slip. The gure on the left contrasts the actual power coupling vs. peak power measurement for a series of integer envelope slips using the cavity parameters from Fig. 4.5. If either the pulse length or cavity nesse is known, the other can be solved. (Such a measurement of the laser pulse length was experimentally conrmed in Fig. 5.15, pg. 90.) The gure on the right measures the eective bandwidth of the cavity by taking curves like those in Fig. 4.5 and dening the ll-time ( 6 ) as the time to achieve 90% of steady-state power. This tunability of the cavity bandwidth was an important experimental tool in measuring tracking stability of the laser center frequency to that of the cavity (see Sect. 5.3.3).

4.3. LASER FREQUENCY STABILIZATION
Characteristics of CW Mode-Locked Lasers
Diode-pumped, solid-state lasers provide very stable and reliable sources for highpower, near-IR, picosecond optical pulses. CW, passively mode-locked Nd:YAG or Nd:YVO4 (vanadate) lasers are commercially available that produce more than 10 watts of average power at 1064 nm with pulse widths as small as 7 ps in the TEM00 mode. To avoid some dispersion eects due to the short pulse (see 4.2.3) an internal lter may be added to reduce the laser cavity bandwidth in order to produce long pulse widths without sacricing beam quality. The mode-locked repetition frequency typically operates between 70200 MHz and matches the expected design range for the electron storage ring circulation frequency. In frequency domain, the number of CW modes contributing to the pulse train is given by the gain bandwidthwhich is inversely proportional to the pulse width divided by the repetition rate of the laser. For laser pulse widths in the 10s of picoseconds operating at repetition rates near 100 MHz, there are typically several hundred modes within the bandwidth of the laser. The modes are uniformly spaced across this band (down to a part 1017 [80]), but may have a comb oset given by the dispersion within the laser (see Sect. 4.2.3). The lowest achievable linewidth, or spectral bandwidth, of each mode is usually described by the Schawlow-Townes limit and is a measure of the spectral broadening due to quantum noise uctuations (spontaneous emission). This limit is noticeable in only extremely stable lasers that have sub-Hz linewidths. In practice, the free-running frequency noise of solid-state lasers is dominated rather by technical noiseacoustic-mechanical environmental noise coupling to the laser cavity optics or gain media. The optical path length changes induced by this noise is manifested as frequency jitter on the entire mode spectrum. In order to implement a frequency stabilization feedback, there must be a mechanism to adjust the laser cavity optical path in response to the measured noise. One common technique is adding a piezo driven mirror or other high-bandwidth actuator like an electro-optic crystal in the laser cavity itself.

linear bounds. A commonly used estimate for peak-to-peak frequency is to multiply the measured RMS frequency noise by 5. This scaling is consistent with the required frequency stability necessary for eciently coupling power (Eq. 4.24). Conversely, if the residual laser noise is a signicant fraction of the external cavity bandwidth, both the tracking performance and coupling eciency are expected to degrade. Another interesting result of Eq. 4.29 is that the intrinsic sensor gain scales inversely to the cavity bandwidth, or proportional to the cavity nesse. Therefore, it is not surprising that high performance, low noise, control loops prefer to use very high nesse cavities, as Eq. 4.22 predicts.
Chapter 5 Optical Cavity Experiments
Little work has been done previously to determine the performance and limitations of amplifying mode-locked laser pulses in high-nesse, passive optical cavities. The most relevant experiments in the literature report either modest cavity gain enhancements (gains 100), or describe the use of optical cavities as interferometers for implementing laser frequency stabilization. In the rst group are studies of optical pulse stacking, such as at the Stanford mid-IR FEL [17, 37, 74], or the use of external cavities to drive more ecient harmonic conversion with mode-locked lasers [59, 64]. On the other hand, frequency stabilization [72] by itself does not require cavity enhancement, but it is a prerequisite for stable, high gain operation. Therefore, demonstrating pulse-stacking with a high-power mode-locked laser is one of the most important experimental verications necessary to validate the basic design of the laser-electron ring X-ray source. There are two primary cavity tests that can be independently performedachieving high gain, requiring longitudinal stability, and achieving a small waist, requiring transverse stability. Of course, both conditions must be met in a practical design, but separating these issues makes them experimentally more convenient. Near-concentric cavities with small waists are best studied using stable, single-mode CW lasers. CW lasers have the freedom of driving any axial mode for a cavity resonator, so adjusting the cavity waist given a set of mirror radii is straightforward. However, for pulse 66
5.1. EXPERIMENTAL APPARATUS
Figure 5.1: Experimental layout shown roughly to scale on 4x8 ft optical table. Beam propagates clockwise from laser to Fabry-Perot cavity (enclosed in Plexiglas cover).

Key: ES = Electronic Shutter, M = Mirror, OI = Optical Isolator, /2 = Half-Wave Plate, PBS = Polarizing Beam Splitter, F = Lens, FC = Cylindrical Lens, EOM = Electro-Optic Modulator, /4 = Quarter-Wave Plate, S = Linear Stage, C = Cavity Mirror, BS = Beam Splitter, PD = Photodiode, OSC = Oscillator, PS = Phase Shifter, BPF = Band-Pass Filter, AMP = Amplier, DBM = Double-Balanced Mixer, PZT = Piezo-Electric Mirror Mount.
stacking, the condition of matching the passive cavity length to that of the modelocked laser cavity dictates that the mirror radii eectively determine the cavity waist. Because of the limited repetition-rate frequency tuning of the laser and limited choice of mirror curvatures commercially available, near-concentric, very small-waist geometries were not tested in the experiments reported here. The pulse-stacking amplication requirements, though, are identical for any stable cavity; larger-waist cavities are simply less sensitive to alignment and mode-matching errors but more sensitive to high-power handling since the spot sizes on the mirrors are reduced.
CHAPTER 5. OPTICAL CAVITY EXPERIMENTS

Experimental Apparatus

The optics layout, viewed schematically in Fig. 5.1, consists of the laser, the transport optics, and the FP cavity. The entire setup ts on one isolated optical table (Newport RS4000/I-2000) which is located in a class 10,000 cleanroom lab.

Mode-Locked Laser

The laser used in these experiments is a High-Q IC-10000 a 10 W, diode-pumped, Nd:YVO4 CW passively (SESAM) mode-locked laser operating at a wavelength of 1064 nm. The laser is packaged in a compact, OEM-style housing and includes two factory modications, one for timing synchronization and the other for lengthening the pulse. The timing stabilization option allows a small tuning (< 100 kHz) of the nominal 79.33 MHz pulse repetition rate and is intended to phase-lock an external rf signal to the pulse train in order to reduce pulse-to-pulse timing jitter ( 0.5 ps). In practice, this system does little to improve the free-running frequency noise of the laser, and was quickly abandoned. However, one part of the systemthe piezo-mirror mount in the laser cavityeventually proved useful as part of the frequency stabilization feedback. The worst deciency of the installed piezo is that it is not optimized for high-bandwidth applications since the timing synchronization electronics do not need much more than 1 kHz bandwidth. Even so, it is fortunate that the rst serious mechanical resonance of the piezo measures out at nearly 20 kHz. The other modication to the laser cavity is an added etalon lter. Since shorter pulses are more sensitive to dispersion eects (Sect. 4.2.3), the natural 7 ps pulse width was stretched to 2530 ps. The etalon limits the available gain bandwidth, thereby reducing the number of axial modes forming the pulse envelope while still maintaining stable transform limited pulses. The predicted eects of dispersion for 30 ps pulses is quite small even for the highest nesse cavities tested (see Sect. 4.2.3).

Experimental Procedure

Cavity Mode-Matching
With a xed cavity length, L = 1.89 m, and chosen mirror radii, R = 1.0 m, the TEM00 eigenmode of the cavity is fully determined. For our symmetric FP cavities, the axial waist location, z0 , is centered between the mirrors and has a size (Eq. 4.7), L R 2 L

280 m.

The laser input must match this waist size and position to best couple power. For a real laser, the beam is not ideally a pure Gaussian but a superposition of LaguerreGauss resonator modes and is characterized by the M 2 value (M 2 1) where w0 = W0 /M, (5.2)
Table 5.3: Measure of laser mode-matching t to cavity. Parameter z0 (mm) W0 (mm) zR (mm) M

x 958 0.1.13

y 1.16

Error 1 4

Cavity 944.8 0.2781 228.4 1.00

0.301 0.002

measured from input mirror. axes dened relative to ellipticity of beam.
such that the measured waist W0 is M times larger than the embedded Gaussian in both x and y [48]. The appropriate parameter to match is then the Rayleigh range, zR , related to the focusing depth and common to all the modes, zR = wW= M 2 (5.3)
Therefore, the general strategy is to characterize the laser, including its M 2 , and place the optics necessary to focus the waist at the proper location and focus depth. Transverse Mode-Matching Results The laser was rst corrected for astigmatism (z0x = z0y ) and slight asymmetry (w0x = w0y ) by adding a cylindrical lens, fc , upstream of the mode-matching lenses f2 and f3 (Fig. 5.1, pg. 67). The two mode-matching lenses formed a telescope such that moving their relative separation changed the focus depth while moving them together changed the waist location. After placing the optics in their calculated positionsincluding an input mirror which acts a slight defocusing lensthe cavity waist was measured in situ and positioned as close as possible to the geometric cavity center. Using a simple 4-cuts method [48] to t the waist parameters, several small iterations in lens placement yielded the nal matching values shown in Table 5.3. Small mode-matching errors of the input beam excite some of the next radial higher-order cavity modes. However, near resonance of the fundamental mode, the

Figure 5.5: Reected and transmitted photodiode signals for a broad-band cavity using a free-running laser scanning through resonance. This cavity was formed from a 99.5 99.5 pair where T1 = 0.438%, T2 = 0.306%, and the calculated parameters are b = 94.7 and c0 = 0.84. The added losses are therefore 0.31%, the cavity bandwidth cav = 133 kHz, and the gain 160. The coupling is near the expected maximum considering the M 2 of the beam (Sect. 5.2.1).
excursions. However, at some servo gain the piezo mechanical resonances turn on and begin to frequency modulate the laser. As long as these resonances fall within the cavity bandwidth, some fraction of that power still enters the cavity and the reduction in coupling is minimized. In fact, the best stability often occurred while purposely overdriving the systemthe improved low frequency noise allowed the laser to track the cavity more eectively while the piezo resonances acted as sideband modulations that still coupled power well inside the cavity bandwidth (Fig. 5.6). Once the laser is stabilized well enough to lock to a cavity, the spectral noise of the closed-loop error signal, , measures the level of residual frequency noise (see Sect. 4.3.2). Also, by knowing the servo transfer function, this data gives a good estimate of the free-running laser noise spectrum (where the noise introduced by the discriminator is still considered small compared to the remaining laser noise). The overall magnitude of the free-running noise spectrum eectively determines the required servo bandwidth necessary to suppress the residual noise to a target RMS level. The RMS laser frequency noise as a function of Fourier frequency is calculated from the amplitude noise spectrum Slaser (f ) as flaser =

|Slaser (f )|2 df ,

(5.12)
Figure 5.6: Reected and transmitted photodiode signals for a laser locked to a 126 kHz BW cavity. The reected signal shows the remaining frequency uctuations while the transmission signal is ltered by the cavity. The servo gain was increased to the point of just starting a sharp 38 kHz piezo resonance. The measured coupling ratio dropped 1015% from the predicted case, but the residual RMS noise improved (below).
Figure 5.7: Spectral noise, Slaser (f ), of the closed-loop error signal for the 126 kHz BW cavity shown in Fig. 5.6. The 20 kHz piezo resonance could sometimes remain suppressed at gains where a strong resonance near 38 kHz dominated (not shown). Note that integrated noise is on a linear scale and that the major contributions over this range come in at low frequencies.
which is plotted on the right axis in Fig. 5.7 (where fu is the upper frequency limit of the measurement). The value integrated over all frequencies denes the residual laser noise which is ideally suppressed to less than the external cavity bandwidth for ecient coupling and feedback stability.