Beam modulation

Abstract

A beam modulation system configured to apply a modulation to an incident linear beam of charged particles, the beam modulation system comprising a resonant cavity which comprises an electro-magnetic field generator configured to apply to the charged particle beam an electro-magnetic field that rotates in a plane perpendicular to an axis of the incident beam, such that on exiting the resonant cavity the charged particle beam travels around a circumference in a plane perpendicular to the axis; a mask comprising one or more mask apertures which intersect with the circumference travelled by the charged particle beam; and a resonant cavity which comprises an electro-magnetic field generator configured to apply to the charged particle beam an opposite electro-magnetic field such that on exiting the resonant cavity the charged particle beam is converted back to a linear beam.

Description

[0001] Beam Modulation

[0002] FIELD

[0003] The present invention relates to the modulation of a beam. The beam may be an electron beam, other charged particle beam, or a light beam.

[0004] BACKGROUND

[0005] Electron beams with a periodic pulsed time structure with repetition frequencies ranging from MHz to GHz find many applications, both in sub-relativistic electron beams used in electron microscopy and in relativistic beams used in particle accelerators.

[0006] There are two methods that are conventionally used for the generation of MHz to GHz pulsed electron beams. The first method uses ultrafast laser pulses to generate pulses of electrons, either by photoemission from a surface or by pulsed photoionization of a gas. The second method applies strong transient electromagnetic (EM) fields to chop a continuous electron beam into short pulses by sweeping it across a slit or aperture. The strong transient EM fields can be microwave fields in a resonant cavity or terahertz fields generated by rectification of femtosecond laser pulses. Alternatively, the transient EM fields can be generated by ultrafast switching of static EM fields using Auston switches.

[0007] A disadvantage of the first method is that it requires high-power, amplified femtosecond laser systems, which are expensive and cumbersome in use. It is difficult to generate high repetition-frequency bursts of light that are required for generating electrons using photogeneration methods, even more so if the required time structure is not periodic or if a very high duty cycle is required. In addition, the quality of the electron pulses in terms of energy spread and angular spread is dependent on the photogeneration process. The electron beams generated using this method do not have sufficient beam quality for some applications.

[0008] The second method allows generation of femtosecond electron pulses at much higher repetition rates, e.g. GHz, using continuous electron sources. This method can be applied to all electron sources. However, the second method does not allow more intricate time-structuring of the pulses, such as bursts at much higher repetition rates or tailored time structuring within each period. In addition, the quality of the pulses of electrons in terms of energy spread and angular spread is affected by the chopping. This is caused by the fact that the beam is chopped while the direction of the beam is changing, leading to correlations between the longitudinal position and the transverse momentum of the electrons in the beam.

[0009] It may be desirable to provide a beam modulation system which overcomes or mitigates a problem associated with the prior art.

[0010] SUMMARY

[0011] According to a first aspect of the invention there is provided a beam modulation system configured to apply a modulation to an incident linear beam of charged particles, the beam modulation system comprising: a resonant cavity which comprises an electromagnetic field generator configured to apply to the charged particle beam an electromagnetic field that rotates in a plane perpendicular to an axis of the incident beam, such that on exiting the resonant cavity the charged particle beam travels around a circumference in a plane perpendicular to the axis; a mask comprising one or more mask apertures which intersect with the circumference travelled by the charged particle beam; and a resonant cavity which comprises an electro-magnetic field generator configured to apply to the charged particle beam an opposite electro-magnetic field such that on exiting the resonant cavity the charged particle beam is converted back to a linear beam.

[0012] Advantageously, embodiments of the invention may allow:

[0013] • Generation of periodic pulsed beams with a repetition period that can be varied straightforwardly from tens of femtoseconds (repetition rates of tens of THz) to tens of nanoseconds (to repetition rates of tens of MHz).

[0014] • Intricate time-structuring of the beam within each repetition period.

[0015] • Chopping an electron beam without affecting the quality of the resulting pulsed beam in terms of energy spread and angular spread.

[0016] • Pulse repetition frequency » GHz and / or a time structure of the beam within each period which can be tailored with a high temporal resolution (~ fs).

[0017] • fs resolution pulse tailoring at significantly lower repetition frequencies (MHz range).

[0018] The beam modulation system may comprise two electro-magnetic field generators, the first electro-magnetic field generator being configured to apply the electro-magnetic field that rotates in a plane perpendicular to an axis of the incident charged particle beam, and the second electro-magnetic field generator being configured to apply the opposite electro-magnetic field.

[0019] The beam modulation system may further comprise a charged plate downstream of the electro-magnetic field generator, the charged plate being configured to direct the charged particle beam back through the electro-magnetic field generator such that the electromagnetic field generator applies the opposite electro-magnetic field to the charged particle beam.

[0020] The rotating electro-magnetic field provided by the resonant cavity may have a period which corresponds with a time taken for a charged particle to travel through the resonant cavity, so that the charged particle beam on exiting the resonant cavity is parallel with the incident charged particle beam.

[0021] The beam modulation system may further comprise a lens downstream of the resonant cavity, the lens being configured to collimate the charged particle beam.

[0022] The or each resonant cavity may be substantially cylindrical and may comprise an entrance aperture in a first face and an exit aperture in an opposite face.

[0023] The one or more mask apertures may be active apertures, the one or more mask apertures each having an associated electrode which is configured to displace the charged particle beam.

[0024] The resonant cavity may comprise a plurality of antennae connected to an RF signal generator configured to generate an RTMno mode or an RTEm mode.

[0025] The charged particle beam may be an electron beam.

[0026] According to a second aspect of the invention there is provided a method of modulating a linear beam of charged particles, the method comprising: using a resonant cavity which comprises an electro-magnetic field generator to apply to the charged particle beam an electro-magnetic field that rotates in a plane perpendicular to an axis of the incident beam, such that on exiting the resonant cavity the charged particle beam travels around a circumference in a plane perpendicular to the axis; intersecting the beam of charged particles with a mask comprising one or more mask apertures such that the beam is modulated by the mask; and using a resonant cavity which comprises an electromagnetic field generator to apply to the charged particle beam an opposite electromagnetic field such that on exiting the resonant cavity the charged particle beam is converted back to a linear beam.

[0027] According to a third aspect of the invention there is provided a beam modulation system configured to apply a modulation to a beam of light, the beam modulation system comprising: an electro-optic material inside a resonant cavity and antennae configured to apply to the beam of light an electro-magnetic field that rotates in a plane perpendicular to an axis of the beam of light, such that on exiting the electro-optic material the beam of light travels around a circumference in a plane perpendicular to the axis; and a mask comprising one or more mask apertures which intersect with the circumference travelled by the beam of light.

[0028] The beam modulation system may further comprise a first lens configured to collimate a diverging spiral beam of light output from the first device.

[0029] The beam modulation system may further comprise a an electro-optic material inside a resonant cavity and antennae configured to apply a rotating electro-magnetic field, the electro-magnetic field being opposite to the electro-magnetic field generated by the first device, such that the beam is converted back to a linear beam.

[0030] The beam modulation system may further comprise a mirror configured to reflect the beam of light back into the same electro-magnetic material and antennae, such that the same electro-magnetic material and antennae apply the opposite electro-magnetic field.

[0031] The beam modulation system may further comprise a second lens configured to focus the collimated spiral beam of light into the second device, and may further comprise a second electro-magnetic material and antennae downstream of the second lens, the second electro-magnetic material and antennae being configured to apply the opposite electro-magnetic field. The mask may be located between the first lens and the second lens.

[0032] The one or more mask apertures may be active mask apertures, electro-optic material being provided in each of the one or more mask apertures.

[0033] The mask may be provided with a single mask aperture.

[0034] The mask may be provided with a plurality of mask apertures.

[0035] The mask apertures may be periodically spaced.

[0036] According to a fourth aspect of the invention there is provided a method of modulating a beam of light, the method comprising: using an electro-optic material and antennae to apply to the beam of light an electro-magnetic field that rotates in a plane perpendicular to an axis of the beam of light, such that on exiting the electro-optic material the beam of light travels around a circumference in a plane perpendicular to the axis; and using a mask comprising one or more mask apertures which intersect with the circumference travelled by the beam of light to modulate the beam of light.

[0037] According to a fifth aspect of the invention there is provided a beam modulation system configured to apply a modulation to an incident linear beam of charged particles, the beam modulation system comprising: a first resonant cavity which comprises a first electro-magnetic field generator configured to apply to the charged particle beam a first electro-magnetic field that rotates in a plane perpendicular to an axis of the incident beam, such that on exiting the resonant cavity the charged particle beam travels around a circumference in a plane perpendicular to the axis; a first mask comprising one or more mask apertures which intersect with the circumference travelled by the charged particle beam; a second resonant cavity which comprises a second electro-magnetic field generator configured to apply to the charged particle beam a second electro-magnetic field that rotates in a plane perpendicular to the axis of the charged particle beam, the rotation of the second electro-magnetic field having a different frequency from the first frequency; and a second mask comprising one or more mask apertures which intersect with the circumference travelled by the charged particle beam.

[0038] At least one of the apertures in the second mask may be coaxial with the incident linear beam of charged particles.

[0039] The rotating electro-magnetic field provided by the first and / or second resonant cavity may have a period which corresponds with a time taken for a charged particle to travel through that resonant cavity, so that the charged particle beam on exiting that resonant cavity is parallel with the incident charged particle beam.

[0040] A lens may be provided downstream of the first resonant cavity, the lens being configured to collimate the charged particle beam. A lens may be provided downstream of the second resonant cavity, the lens being configured to collimate the charged particle beam. According to a sixth aspect of the invention there is provided a method of modulating a linear beam of charged particles, the method comprising: using a first resonant cavity which comprises a first electro-magnetic field generator to apply to the charged particle beam a first electro-magnetic field that rotates in a plane perpendicular to an axis of the incident beam, such that on exiting the resonant cavity the charged particle beam travels around a circumference in a plane perpendicular to the axis; intersecting the beam of charged particles with a first mask comprising one or more mask apertures such that the beam is modulated by the mask; using a second resonant cavity which comprises a second electro-magnetic field generator to apply to the charged particle beam a second electro-magnetic field that rotates in a plane perpendicular to the axis of the charged particle beam, the rotation of the second electro-magnetic field having a different frequency from the first frequency; and intersecting the beam of charged particles with a second mask comprising one or more mask apertures such that the beam is further modulated by the second mask.

[0041] Features of different aspects of the invention may be combined together.

[0042] BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

[0044] Figure 1 depicts a first device used to convert a linear electron beam to a helical electron beam;

[0045] Figure 2 depicts the first device and a second device used to convert the helical electron beam to a linear electron beam;

[0046] Figure 3 depicts a beam modulation system according to an embodiment of the invention, the beam modulation system including the first and second devices of Figure 2.

[0047] Figures 4A-4C depict masks which form part of embodiments of the invention, and resulting modulated electron beams;

[0048] Figure 5 depicts an electro-magnetic field used by an embodiment of the invention;

[0049] Figure 6A-C depict electro-magnetic fields which are superpositioned to generate the an electro-magnetic field of Figure 5;

[0050] Figure 7 depicts a beam modulation system according to an alternative embodiment of the invention;

[0051] Figures 8A-C depict a resonant cavity which forms part of an embodiment of the invention;

[0052] Figure 9 depicts a beam modulation system according to an embodiment of the invention;

[0053] Figure 10 depicts a beam modulation system according to another embodiment of the invention;

[0054] Figure 11 depicts another electro-magnetic field used by an embodiment of the invention;

[0055] Figure 12A-C depict electro-magnetic fields which are superpositioned to generate the an electro-magnetic field of Figure 11 ; Figure 13 depicts an active mask which may form part of an embodiment of the invention;

[0056] Figure 14 depicts an electro-optic material which may form part of an embodiment of the invention;

[0057] Figure 15 depicts a first device used to convert a linear beam of light to a spiral beam of light;

[0058] Figure 16 depicts a beam modulation system according to an embodiment of the invention, the beam modulation system including the first device of Figure 15.

[0059] Figure 17 depicts a beam modulation system according to another embodiment of the invention, and

[0060] Figure 18 depicts a beam modulation system according to another embodiment of the invention.

[0061] DETAILED DESCRIPTION

[0062] An operational principle used by embodiments of the invention is now described in connection with Figures 1A-1 E, Figure 2, and Figure 3.

[0063] A continuous electron beam 2j is propagating along the z-axis of a Cartesian (x,y,z) coordinate system. The continuous electron beam 2j enters a device 4 schematically indicated in Figure 1 by a box of length L, centred around the origin (x,y,z)=(0,0,0). The device 4 contains EM fields which oscillate in time, giving rise to periodic radial displacement of the incoming electron trajectories. The periodic radial displacement is such that after the device the electrons trace out a spiral while still moving in the z- direction. In other words, a spiral comprising the electron beam 2Safter the device will move as a whole in the z-direction, as is schematically illustrated in Figure 1 E.

[0064] Figure 1A shows a single electron 6 that passes through the device 4. On an input side of the device 4 the electron is labelled 6j, and on an output side of the device the electron is labelled 6S. The electron 6Sexits the device 4 at a position on a circle C of radius R (not labelled) which is centred around the z-axis. The trajectory of the outgoing electron 6Sis parallel to the incoming trajectory.

[0065] Figure 1 B shows a second electron 8 of the electron beam 2j that is lagging the first electron. This electron 8 passes through the same device 4 later, undergoing radial displacement as well. Thus, the second electron 8; is coaxial with the first electron 6; when it enters the device 4. The second electron 8Sexits the device 4 at a different position on the same circle C. The trajectory of the second electron 8Swhen it exits the device 4 is parallel to its incoming trajectory (i.e. parallel to the electron beam 2j before the electron beam enters the device 4).

[0066] Analogously, Figures 1C and 2D show trajectories of electrons 10j, 12; arriving at even later times. These electrons 10s, 12sexit the device 4 at positions further around the circle C. The trajectory of the electrons 10s, 12swhen they exit the device 4 is parallel to the incoming trajectory. Figure 1 E shows an electron 14j, 14sthat is lagging the first electron by such a distance that it will exit the device 4 at the same position on the circle C as the first electron in Figure 1 A. At this point the spiralling trajectory has made one full revolution and will start a new round. The electron beam 2Shas the form of a helix that is coaxial with the incident electron beam 2j.

[0067] The length L of the device that will provide a coaxial helix electron beam is determined by the velocity v of the electron and the oscillation frequency of the EM fields inside the device:

[0068] L = vT Equation 1 where T = 2?r I o) is the oscillation period of the EM fields inside the device. Each section of length L of an incoming continuous electron beam is linearly mapped by the device 4 over the circumference of a circle C with radius R. The displacement of electrons into a helix which propagates coaxially with the incident electron beam only takes place when the electron passes the device in exactly one period of the EM fields (Equation. 1). This displacement may be referred to as radial displacement. The electron may be displaced in a radial direction, and following the radial displacement the electron may propagate in a direction which is parallel with the incident radiation beam.

[0069] The displacement of the electrons 6S, 8S, 10s, 12s, 14scan be undone by a second device 14, as is schematically illustrated in Figure 2. The second device 14 supports identical EM fields which oscillate in counterphase to the EM fields in the first device 4. Using such a second device, the original continuous electron beam 2\, travelling along the z- axis, can be restored. This is labelled in Figure 2 as 20- indicating output electron beam. Because of symmetry, the output electron beam 20has the exact same characteristics as the input electron beam 2\. The fields that the electrons experience in the first device 4 (including, e.g., stray fields at the entrance and exit apertures) have equal strengths but opposite sign compared to the fields the electrons experience in the second device 14. Hence, the second device 14 will completely cancel the effect of the first device 4.

[0070] The distance between the devices 4, 14 may be chosen arbitrarily. However, the EM fields experienced in the second device 14 should be opposite to those experienced in the first device 4. In order to achieve this, a phase adjustment of the EM fields (e.g. in the second device 14) may be needed if the distance between devices is changed.

[0071] Figure 3 schematically depicts modulation of the electron beam 2 (which may also be referred to as chopping). Between the first device 4 and the second device 14, a projection of the electron beam 2Son a plane 16 perpendicular to the z-direction has a constant azimuthal velocity. As a result, the arrival time of the electrons on this plane 16 is mapped linearly with respect to the azimuthal position of the circular projection on the plane.

[0072] A mask 18 parallel to this plane (e.g. lying on the plane) in between the first device 4 and the second device 14 has an aperture 20 at a specific position on the circular projection of the electron beam 2S. The aperture 20 is sufficiently large to let electrons pass through the aperture. At other locations the mask is sufficiently thick to stop electrons. Only electrons that are at a particular rotational position on the electron beam 2Spass through the aperture 20. Consequently, the aperture 20 allows electrons to travel between the first and second devices 4, 14 at a specific time interval.

[0073] The second device 14 shifts the resulting modulated electron beam back to the z-axis. The position of the apertures on the circular beam trajectory between the first and second devices 4, 14 is mapped linearly with respect to time in the output electron beam 20. In other words, the output electron beam 20has electrons separated with a periodic interval due to the effect of the mask 18.

[0074] In this way a desired periodic time structure can be imposed on the output electron beam 20(i.e. a periodic structure of pulses of electrons can be applied to the output electron beam 20). The pulse duration At that can be realized depends on the size of the aperture 20 (in the azimuthal direction), the width of the beam, and the transverse velocity vtof the beam in the x-y plane (e.g. plane 16). The transverse velocity vtis given by: Equation 2

[0075] As noted above, T is the oscillation period of the EM fields inside the devices 4, 14, and R is the radius of the circle C formed by the spiral electron beam 2S. Note that although the electron beam projected onto plane 16 has a transverse velocity, the electrons themselves do not have a transverse velocity. Because electrons at different times arrive at the plane 16 at different transverse positions, the beam moves across the plane while the electrons still only have a velocity component in the z-direction.

[0076] The aperture 20 may be a slit with a width w (in the azimuthal direction). For a beam with a rectangular transverse profile of width d that moves with a transverse velocity vtat right angles across the slit of width w (the width of the slit being much greater than the width of the beam), the resulting pulse duration At is given by Equation 3

[0077] A numerical example relevant for electron microscopy beams is as follows: the circle has a radius R = 1 mm, the oscillation period of the EM fields inside the devices T = 1 ns, and d « w = 1 zm. In this example At « 160 fs. In other words, an electron beam with pulses of having a duration of around 160 fs can be achieved.

[0078] The positions of apertures in the mask 18 can be tailored for any application (i.e. for any desired electron beam periodic structure). The mask 18 can be removed and replaced straightforwardly. The mask may be removed and replaced manually. Alternatively, a robot arm or other actuator may be used to remove and replace the mask. The robot arm or other actuator may be remotely controlled. The size and position of the apertures can be controlled remotely without removing and replacing the mask (as described further below).

[0079] Although one aperture is depicted in Figure 3, more than one aperture may be provided. The output electron beam 20consists of the electrons that are transmitted through the aperture(s).

[0080] In an embodiment, apertures with different properties may be provided at different radii on a single mask. For example, a pair of apertures may be provided at a first radius, and four apertures may be provided at a bigger radius. To access the four apertures, the strength of the EM field which is used to provide the displacement is increased. The strength of the EM field may be reduced to once again access the two apertures. More than two sets of apertures may be provided, at more than two radii. Each set of apertures may have any desired configuration.

[0081] Because the electrons are chopped while having no transverse velocity, no phase space correlations will be added to the beam. In other words, the energy spread and angular spread of the electron beam is unaffected by the chopping (there is no correlation between longitudinal position and transverse momentum of electrons in the beam).

[0082] The system depicted in Figure 3, comprising the first and second devices 4, 14 and the mask 18 may be referred to as an electron beam chopping system. The electron beam chopping system acts as a GHz chopping wheel for electrons. The continuous electron beam is cut into a train of pulses by a stationary mask 18 while the beam 2Sis rotating. This has the same effect as a chopping wheel consisting of the same mask, rotating with GHz frequency. The system therefore has the same functionality as chopping wheels used for laser beams. A physical chopping wheel that rotates at GHz frequencies would be technologically impossible. However, embodiments of the invention provide equivalent chopping by instead rotating the electron beam.

[0083] Figures 4A-4C show three masks with various chopping aperture configurations. The resulting pulse structures are depicted beneath each mask. These masks may be considered to be equivalent to chopper wheels that rotate at the frequency of the EM fields in the devices.

[0084] In a first example depicted in Figure 4A, a mask 22 has a single aperture 23. The mask 22 provides the equivalent effect of a 1 GHz chopper wheel (provided that the oscillation of the EM fields inside the devices 4, 14 which provide this frequency are selected).

[0085] In a second example depicted in Figure 4B, a mask 24 has eight equally spaced apertures 25. This provides the equivalent effect of an 8 GHz chopper wheel (assuming that the same oscillation frequency of the EM fields inside the devices 4, 14 is used).

[0086] In general, increasing a number of regularly spaced apertures will increase the repetition frequency of the electron beam. A mask having 1000 apertures around the circle C travelled by the electron beam 2s would provide a pulsed beam with a repetition frequency of 1 THz (for the same oscillation frequency of EM fields). For a circle with a radius of 1 mm this would imply 1000 apertures with a width of about 3 pm, which is feasible. By increasing the frequency of the EM fields and / or increasing the radius R of the circle formed by the electron beam, even higher repetition frequency beams can be generated.

[0087] Figure 4C shows how an electron beam having a desired pulse structure may be obtained. In this example, a ‘chirped’ set of six pulses per period is obtained using a mask 26 with suitably located apertures 27. Any desired pulse structure may be obtained via selection of aperture positions in a mask located between the devices 4, 14.

[0088] Rotation of the EM fields can be realized by mechanical rotation of devices producing static EM fields. Examples of such devices are capacitor plates, and magnetic coils. Alternatively, the EM fields may be produced by electrical rotation of static fields. This can be done, for example, by using two identical pairs of capacitor plates in a configuration perpendicular to the electron beam and to each other. By driving the capacitor plates with a sinusoidal voltage with a 90° phase difference, a rotating static electric field is realized (meaning that the rotating electric field is static within the frame of rotation of the electric field). Alternatively, two pairs of magnetic coils may be provided in a configuration perpendicular to the electron beam and to each other. By driving the magnetic coils with a sinusoidal current with a 90° phase difference, a rotating static magnetic field is realized.

[0089] Mechanical or electrical rotation of static EM fields works in principle. In practice, however, the mechanical or electrical rotation of static EM fields may be too slow for many applications. In most applications the electrons in a beam travel at velocities of 107-108m / s. For mechanical rotation with a kilohertz frequency this would imply a device length (see Eq. 1) of at least 104m and for electrical rotation at a megahertz frequency a device length of at least 10 m. It may be desirable to provide the effect of rotation at higher frequencies, in order to enable shorter device lengths to be used.

[0090] A shorter device length can be achieved by using an electromagnetic field which rotates at a higher frequency. An electromagnetic field which rotates with a frequency of 1 GHz may provide a device length of around 10cm. The rotating electromagnetic field may be achieved using Cylindrically symmetric Rotating Transverse Magnetic (RTM) modes.

[0091] Cylindrically symmetric Rotating Transverse Magnetic (RTM) modes, which can be excited in a resonant cavity, are now described. The devices 4, 14, 104, 114 that create the periodic radial displacement of the incoming electron beam may be cavities that support such modes. This is merely a possible embodiment. Suitable rotating EM fields can be generated in other ways (as explained further above).

[0092] A Rotating Transverse Magnetic Mode (RTM) is an oscillating electromagnetic field, a standing wave, that can be excited in a cylindrically symmetric resonant cavity. The electric and magnetic fields in such a mode rotate in the azimuthal direction at a certain resonant frequency. The field distribution is transverse magnetic, which means that it has no magnetic field component in the longitudinal direction, i.e., Bz= 0. In a co- rotating frame, the field distribution is static.

[0093] A pillbox cavity (i.e. cylindrical in shape with entrance and exit in opposite faces) which has a given length L and radius Rc, in principle supports infinitely many different RTMmn(modes, each characterized by a set of integer index numbers (m, n, I). Here |m| indicates the number of standing wave nodes in the azimuthal direction, the sign of m indicates the direction of rotation, I the number of standing wave nodes in the z-direction, and n relates the cavity radius to the resonant frequency of the cavity:

[0094] Equation 4 with x\m\nthe n-th root of the |m|-th order Bessel function, n and I are both positive whole numbers and m can be either a positive or negative whole number.

[0095] As an example, we will now discuss a particular mode, the RTM110mode, which is the lowest order RTM mode. The RTM110mode was used to calculate the trajectories of the electrons in Figures 1 -4. The distribution of the electric and magnetic fields of the RTM110mode is given by the following equations:

[0096] Er= 0 Equation 5a

[0097] EQ = 0 Equation 5b

[0098] Ez= Eo / i(fcr) cos(0 + cot) Equation 5c

[0099] Equation 5d cot) Equation 5e

[0100] Bz= 0. Equation 5f

[0101] Here Jn(x) is the nthorder Bessel function. In Equations 5a-5e the electric and magnetic vector components are given in cylindrical coordinates (r, 0, z), with r = x2+ y2the radial distance to the z-axis and 9 = tan-1) the azimuthal angle.

[0102] Close to the z-axis the magnetic field inside the device is approximately uniform and rotating in the azimuthal direction at the resonant frequency. In this context “close” may be interpreted as meaning kr<0.1 (i.e. less than 10% of the radius of the device). For a uniform field the radius R of the circle that is traced out by the electrons is given by cocL

[0103] R = - Equation 6 co with Equation 7 the relativistic cyclotron frequency, y = (1 - v2 / c2)-1 / 2the relativistic Lorentz factor, m the mass of the particle, and Bo= the magnitude of the magnetic field in the resonant cavity and c the speed of light. To create a circle with R = 1 mm (all other parameters the same as used in section 2.1) using electrons that have an energy E = (y - l)mc2= 100 keV requires a magnetic field with a magnitude Bo« 0.25 mT. This is easily achievable in practice.

[0104] The electric and magnetic field distribution of the RTM110mode at t = 0 in the xy-plane, is depicted in Figure 5. In Figure 5, the electric field (pointing in the z-direction, indicated by shading) and magnetic field (black field lines) distribution of the RTM110mode at t = 0 are shown. Darker shading indicates a stronger electric field. The direction of the electric field is indicated by the cross and the point. The mode will rotate either clockwise or anticlockwise around the origin (x,y) = (0,0).

[0105] The magnetic field only has x and y-components, indicated by (black) field lines. The depicted field distribution will rotate in its entirety around (x,y) = (0,0). When the magnetic field points in the direction of positive electric field the mode will rotate clockwise, when it points in direction of negative electric field the mode will rotate anticlockwise. In the example depicted in Figure 6, the mode will rotate clockwise.

[0106] A difference between the RTMmn(modes and the well known TMmn(modes is their oscillatory behaviour. RTM modes have a constant but rotating field profile, i.e. , the field profile only oscillates in azimuthal angle. In contrast to this, TM modes oscillate in strength (the profile of the field amplitudes is fixed in time), with electric and magnetic fields oscillating in counter phase.

[0107] The trajectories shown in Figures 1-4 have been calculated using the RTMno field distribution given by Equation 6 and which field distribution is depicted in Figure 5.

[0108] The RTM110mode can be generated by exciting two identical TM110modes with field distributions rotated by 90° in the xy-plane with respect to each other and oscillating with a relative phase of <p = ±90°. Superposition of the fields of the two TM110modes results in a RTM110mode. This is depicted in Figure 6. The resulting field rotates either clockwise or anti-clockwise depending on the sign of the phase difference between the two TM110modes.

[0109] In Figure 6, in the left hand image A and the middle image B, two TM110field distributions are shown. The distribution in the middle image B is rotated by 90° in the xy-plane and has a relative phase of <p = 90° (TT / 2) with respect to the distribution in the left hand image A. The equipotential lines and arrows indicate the magnetic field direction and strength. The colours indicate the electric field magnitude. The sum of the two TM110results in a RTM110, which is depicted in the right hand image C.

[0110] The two individual TM110modes can be excited by two different antennae in a single resonant cavity at the same resonant frequency. This is merely an example of how an RTM110mode can be excited. It is also possible to excite the RTM mode directly using a specially designed antenna. P.H. Ceperley et. al., Rev Sci Instrum, 66 (1), 256-260 (1995) describes how to build and excite a RTM110mode in a resonant cavity. A practically implementation of an RTM110mode in a resonant cavity is described further below.

[0111] It may be desirable to provide an electron beam with a modulation frequency which is of the order of MHz or kHz, whilst using an electromagnetic field which rotates with a frequency of 1 GHz or more (thus avoiding an excessively long device). This may be achieved for example by using two devices that have different repetition frequencies. One way to explain this is via analogy with chopping wheels. The combination of the two devices and two masks can be regarded as two chopper wheels (each with a single hole) that rotate at different frequencies. The first chopper wheel will cut the continuous beam into a pulsed beam at the first frequency. Two chopper wheels in succession will only let pulses through at the difference frequency, i.e. , the holes align only once during the period corresponding to the difference frequency.

[0112] Both frequencies may lie in the GHz range, but the difference frequency may be in the MHz range. Figure 7 shows an embodiment which uses this principle. A first device 104 is followed by a first mask 118 having a single aperture 120. This arrangement creates a pulsed beam 2Pat the oscillation frequency of the first device 104. A second device 114 then follows. The second device 114 has a different length L2 to the length Li of the first device 104 (in this example the second device 114 is shorter) and thus provides a different oscillation frequency. The second device does not return the electron beam to the initial axis of the electron beam 2i (as occurs in Figure 3). Instead, a new azimuthal velocity is applied to the electron beam 2S2. The circle formed by the electron beam 2s2 intersects with the initial axis of the electron beam (which may be referred to as the z- axis). A second mask 130 is provided. The second mask 130 has an aperture 132 on the z-axis. Consequently, when the electron beam passes over the z-axis the electron beam is transmitted by the aperture 132.

[0113] The electron pulse is shifted back to the z-axis at the difference frequency of the first and second devices 104, 114. Electron pulses formed by the first mask 118 will be blocked by the second mask 130, except for electron pulses that are on the z-axis. The second device 114 and second mask 130 select pulses at the difference frequency from the pulse train generated by first device and first mask. In this way the device length can be reduced while it is still possible to create very short pulses at a MHz (and lower) repetition frequency. For example, the first device can have a frequency of 1 GHz while the second device has a frequency of 1 .1 GHz. This provides a difference frequency of 100 MHz. The first device 104 and first mask 120 modulate the beam. The second device 114 and second mask 130 further modulate the beam. In the depicted embodiment the output beam 20is coaxial with the incident beam 2j. However, this is not essential and the output beam may lie on a different axis from the incident beam. An advantage of the output beam 20being coaxial with the incident beam 2j is that when the devices are switched off the beam will not be blocked by the apparatus. This may for example facilitate alignment with downstream apparatus.

[0114] Figure 8 schematically depicts various views of a resonant cavity 201 which is an example of the beam modulation devices referred to further above. Figure 8A is a lateral cross-sectional view of the resonant cavity 201 , observed along the z axis. When located in an electron beamline, the cavity 201 will be placed / aligned so that the electron beam axis 202 extends along this z-axis. Figure 8B is a longitudinal cross-sectional view of the same resonant cavity 201 , in which the z-axis and the y-axis are in the plane of the figure, now horizontal. Figure 8C is a longitudinal cross-sectional view of the same resonant cavity 201 , in which the z-axis and the x-axis are in the plane of the figure.

[0115] As depicted in Figure 8, the cavity 201 has a substantially cylindrical transverse crosssection, with a first axis parallel to the x-axis (first direction) and a second axis parallel to the y-axis (second direction). As is evident from Figure 8, the cavity 201 is cylindrical in shape, and its cylindrical axis is substantially collinear with the depicted electron beam axis 202. An entrance aperture 203a and exit aperture 203b allow an electron beam propagating along the optical axis 202 to enter and leave the interior of the cavity 201 , respectively. A cavity of such form is sometimes referred to as a “pillbox cavity”.

[0116] The entrance aperture 203a and exit aperture 203b may for example be of the order of about a millimetre wide (although other sizes may be used). The exit aperture 203b may be somewhat wider than the entrance aperture 203a, to allow for a larger diameter of the electron beam (the electron beam is helical at the exit aperture). In this respect, it should be noted that apertures 203a and 203b are not drawn to scale.

[0117] Cavity wall 204 is made of conducting material, e.g., copper. The conducting material may have a thickness of a few mm. Provided in the cavity wall 204 at successive angular intervals of 90° about the z-axis and in a common plane perpendicular to the z-axis are bores 205a, 205b, 205c, 205d. A pair of bores 205a, 205c oppose one another along the y-axis, and a pair of bores 205b, 205d oppose one another along the x-axis. Out of these bores 205a, 205b, 205c, 205d protrude respective rods 206a, 206b, 206c, 206d. Two of these rods 206a, 206b are respective excitement antennae, whereas the other two rods 206c, 206d are respective pickup antennae. Additionally, provided in wall 204 at an angular spacing of 90° about the z-axis and in a common plane normal to the z- axis are bores 207a, 207b. Out of these bores 207a, 207b protrude respective rods 208a, 208b which carry respective tuning elements 209 and 210.

[0118] The tuning elements 209, 210 take the form of plungers (rods) that can be moved into and out of the cavity 201. This allows adjustment of the effective internal width of the cavity 201 along the y- and x-axes, respectively (or serves to alter the net dielectric constant of the cavity interior). This allows tuning of the resonant frequency of the cavity 201. The excitement antennae 206a, 206b are located adjacent to a radial wall 204 of the cavity 201. The excitement antennae 206, 206b may be closer to the radial wall 204 than to the electron beam axis 202. The excitement antennae 206a, 206b are connected via coaxial cables to respective (RF) gigahertz oscillating power supplies (not shown). In one possible embodiment, the antennae 206a, 206b simply takes the form of the inner conductor (core) of a coaxial cable. The output of said power supplies is adjusted to produce the desired simultaneous resonances of the cavity 201 . In the current example, two TM resonance modes that are mutually perpendicular and have the same frequency are excited. The phases of the oscillating power supplies are tuned such that the two modes oscillate with a desired phase difference.

[0119] Because of the circular cross-section of the cavity 201 in combination with non-perfect manufacturing, with the attendant difference in its internal width along the x- and y-axes, these the two TM resonances will have nearly identical resonant frequencies. The resonance frequency values can be tuned to be exactly the same by sliding either or both of the tuning elements 209, 210 into or out of the cavity 201 .

[0120] In a specific example, it may be elected to have the resonant frequency of the cavity 201 at or close to a value of a few GHz. This is not a limiting value: it is merely conveniently achievable and has an additional advantage that the length of the cavity will stay manageable, see Equation 1.

[0121] It is also straightforward to tune the two resonant frequencies of the cavity 201 by moving the tuning elements 207b, 208b into and out of the cavity. The resonant frequencies may a tuned to, for example, 3 GHz along the cylindrical cavity's first axis (x-axis) and 3 GHz along its second axis (y-axis) — leading to a net zero frequency difference. For the frequency value in question, the lateral dimensions of the cavity 201 will depend inter alia on the dielectric medium present within the wall 203.

[0122] The cavity 201 may be held at a vacuum. In an alternative case, the cavity 201 may be substantially filled with a ceramic dielectric (or other dielectric). The ceramic dielectric may be formed as a cylinder. Dashed lines 211 indicate the form of the ceramic dielectric. A bore through the ceramic dielectric may be provided to allow passage of the electron beam. The frequency of a resonant cavity may be selected via selection of the diameter of the cavity, and selection of a type and diameter of dielectric provided in the cavity.

[0123] The cavity is configured such that an electron beam travels through the cavity in exactly one period. This ensures that the electron gains no net transverse momentum and is merely displaced. The length of cavity 201 is dependent on the resonant frequency of the modes excited in the cavity and the velocity of the charged particle and is matched accordingly (see further above).

[0124] Additionally, to produce a circle of the electron beam on the mask the amplitudes of the EM fields in the two orthogonal RF cavity modes should match. This can be achieved by measuring the actual field amplitudes per mode using pickup antennae 206c and 206d. The results of these measurements can be used to stabilize the field amplitudes by changing the amplitude of the RF signal sent to the excitement antennae 206a and 206b. Additionally the pickup antennae can also be used to stabilize the phase difference between both modes.

[0125] Figure 9 shows a practical example of pulsed beam generation using a beam modulation system 301 according to an embodiment of the invention. An electron beam travels from left to right along a central axis 308 of the depicted system. A first resonant cavity 201a is as depicted in Figure 8. The first resonant cavity supports an RTM110mode which applies a periodic radial displacement to the incoming electron beam. The resulting helical electron beam passes through apertures (not depicted) provided in a mask 309. A second resonant cavity 201 b is also as depicted in Figure 8. The second resonant cavity 201b will restore the modulated beam back to the central axis 308.

[0126] Each cavity mode is driven by an RF signal that originates from a shared RF source 302. The signal from this source is split in four by an RF splitter 303. The signal is adjusted by control electronics 307a-d provided for each mode. The control electronics 307a for one mode is depicted and comprises a phase shifter 304, attenuator 305 and amplifier 306 (only one set of these is depicted). The control electronics 307b-d is the same for the other modes. The control electronics 307a-d can be used to control the phase and amplitude of the fields in each mode.

[0127] The fields experienced by the electrons in the second resonant cavity 201b are exactly opposite to those experienced in the first resonant cavity 201a. To achieve this the control electronics 307a-d can be tuned so that the phase and the amplitude of the fields in the four cavity modes are matched.

[0128] Figure 10 shows a practical example of pulsed beam generation using a beam modulation system 401 according to another embodiment of the invention. In this embodiment, two resonant cavities 201 a, 201 b are operated at different frequencies. For example, the first resonant cavity 201a may be operated at 1 GHz and the second resonant cavity may be operated at 1.1 GHz, providing a difference frequency of 100 MHz. Operation of this embodiment is as described further above in connection with Figure 7.

[0129] An electron beam travels from left to right along a central axis 408 of the depicted system. The first resonant cavity 201a is as depicted in Figure 8. The first resonant cavity supports an RTM110mode which applies a periodic radial displacement to the incoming electron beam. The resulting helical electron beam passes through apertures (not depicted) provided in a mask 409. A second resonant cavity 201 b is also as depicted in Figure 8. The second resonant cavity 201b operates at a different frequency than the first resonant cavity 201a. The second resonant cavity does not restore the electron beam to the central axis 408, but instead applies a new periodic radial displacement to the electron beam (see Figure 7). A second mask 410 has an aperture (not depicted) on the central axis 408 through which electrons pass. The electrons which pass through the second mask 410 have a frequency which is the difference between the frequencies of the first and second resonant cavities 201a, 201 b.

[0130] The first cavity 201a has a mode driven by an RF signal that originates from a first RF source 402a. The signal from this source is split in two by an RF splitter 403a. The signal is adjusted by control electronics 407a, b provided for each mode. The control electronics 407a for one mode is depicted and comprises a phase shifter 404, attenuator 405 and amplifier 406 (only one set of these is depicted). The control electronics 407b is the same for the other mode. The control electronics 407a, b can be used to control the phase and amplitude of the fields in each mode.

[0131] The second cavity 201a has a mode driven by an RF signal that originates from a second RF source 402b. The second RF source 402b operates at a different frequency than the first RF source 402a. The difference between the frequencies provided by the first and second RF sources 402a, b is fixed. This is schematically depicted by a padlock symbol. The signal from the second source 402b is split in two by an RF splitter 403b. The signal is adjusted by control electronics 407c, d provided for each mode. The control electronics 407c, d correspond with those depicted for the first source 402a and are not described again. The control electronics 407c, d can be used to control the phase and amplitude of the fields in each mode.

[0132] Above described embodiments of the invention use a Rotating Transverse Magnetic Mode (RTM). However, a Rotating Transverse Electric Mode (RTE) can alternatively be used. An RTE is an oscillating electromagnetic field, a standing wave, that can be excited in a cylindrically symmetric resonant cavity. The electric and magnetic fields in such a mode rotate in the azimuthal direction at a resonant frequency. The field distribution is transverse electric, which means that it has no electric field component in the longitudinal direction, i.e., Ez= 0. In a co-rotating frame, the field distribution is static.

[0133] A pillbox cavity with a given length L and radius Rc, in principle supports infinitely many different RTEmn(modes, each characterized by a set of integer index numbers (m, n, I). Here |m| indicates the number of standing wave nodes in the azimuthal direction, the sign of m indicates the direction of rotation, I the number of standing wave nodes in the z-direction, and n relates the cavity radius to the resonant frequency of the cavity:

[0134] Equation 8 with x'\m\nthe n-th root of the derivative of the |m|-th order Bessel function, n and I are both positive whole numbers and m can be either a positive or negative whole number. In contrast to a transverse magnetic mode the index I should be non-zero.

[0135] As an example, we will now discuss a particular mode, the RTE, , , mode, which is the lowest order RTE mode. The distribution of the electric and magnetic fields of the RTE, , , mode is given by the following set of equations:

[0136] With k = — . Here Jn(x) is the nthorder Bessel function. In Equations 9a-f the electric Rc and magnetic vector components are given in cylindrical coordinates (r, 0, z), with r =jx2+ y2the radial distance to the z-axis and 9 = tan-1) the azimuthal angle.

[0137] Close to the z-axis the electric field inside the device is approximately uniform and rotating in the azimuthal direction at the resonant frequency. The electric and magnetic field distribution of the RTE, , , mode at t = 0 in the xy-plane at the centre of the cavity, is depicted in Figure 11. In Figure 11 , the magnetic field is indicated by shading, with darker shading indicating a stronger field. The direction of the magnetic field is indicated by the cross and the point. The electric field is indicated by field lines, and has a distribution of the RTE, , , mode at t = 0 in the centre of the cavity. The mode will rotate either clockwise or anti-clockwise around the origin (x,y) = (0,0).

[0138] The magnetic field is pointing in the z-direction. The electric field only has x and y- components, indicated by field lines. The depicted field distribution will rotate in its entirety around (x,y) = (0,0). When the electric field points in the direction of positive magnetic field (right hand side of Figure 11) the mode will rotate in the clockwise direction, when it points in direction of negative magnetic field (left hand side of Figure 11) the mode will rotate in the anti-clockwise direction.

[0139] A difference between the RTEmn(modes and the well known TEmn(modes is their oscillatory behaviour. RTE modes have a constant but rotating field profile, i.e. , the field profile only oscillates in azimuthal angle. TE modes oscillate in strength (the profile of the field amplitudes is fixed in time), with electric and magnetic fields oscillating in counter phase. The RTEmmode can be generated by exciting two identical TEU1modes with field distributions rotated by 90° in the xy-plane with respect to each other and oscillating with a relative phase of <p = ±90°. Superposition of the fields of the two TEU1modes results in a RTEmmode. This is depicted in Figure 12. The resulting field is rotating either clockwise or anti-clockwise depending on the sign of the phase difference between the two TEU1modes.

[0140] In a left hand image 12A a first TEU1field distribution is shown. A second TEU1field distribution is shown in a middle image 12B. The TEU1field distribution in the middle image 12B is rotated by 90° in the xy-plane and has a relative phase of <p = 90° (TT / 2) with respect to the TEU1field distribution in the left image 12A. The equipotential lines and arrows indicate the electric field direction and strength. The colours indicate the magnetic field magnitude. The sum of the two TEU1results in an RTEmmode. This is the field distribution depicted in the right hand image 12C.

[0141] The two individual TEU1modes can be excited by two different antennae in a single resonant cavity at the same resonant frequency. This is merely an example of how an RTEm mode can be excited. It is also possible to excite the RTE mode directly using a specially designed antenna. An RTEm mode may be excited in the resonant cavity described above in connection with Figure 8.

[0142] The RTE mode can exist in the exact same cavity as discussed earlier but merely at a different resonant frequency because of the difference in longitudinal index, l=0 for the RTM110 mode and 1=1 for the RTE111 mode. The position of the antennas is different because the antennas for the RTM 110 mode couple to the electric field. The TE mode can best be coupled via the magnetic field. The skilled person working in the field of electromagnetic cavities knows how to couple such a mode and therefore the coupling is not described further here.

[0143] Above described embodiments have used a passive mask that generates a constant pulse structure. However, it is also possible to implement an active mask. Figure 13 shows an example of an active mask 404 with eight actuators. The electron beam travels around the circle 405, and electron pulses are transmitted through apertures 450 (only some of which are labelled). Electrodes V1-V8 are provided at each aperture 450. Electrical pulses may be applied to the electrodes. The electric pulses act as a switch (actuator) that determines whether the electron pulse passes through an aperture 450. Each electrode applies an electric field across the circular area. This field pushes the electron beam out of its trajectory. The electron beam passes through a respective aperture 450 but is deflected such that it does not form part of the beam that is output from the beam modulation system.

[0144] The beam moves around the circle 405 and across the apertures 450 with a rotation frequency determined by the fields in the modulation device (see further above). In the absence of any electrical pulses applied to the electrodes, a periodic electron beam is output as depicted at the bottom of Figure 13. However, electrical pulses provided to the electrodes V1-V8 can be used to remove pulses from the periodic electron beam. The electrical pulses can thus be used to imprint information on the electron beam. The amount of information that can be added to the electron beam is determined by the number of apertures with electrodes. This may be considered to be multiplexing of information on the electron beam since every aperture can be controlled at the same frequency as the rotation frequency.

[0145] For example, a beam rotates across 100 active apertures with a rotation frequency of 1 GHz. 100 active apertures (i.e. apertures with associated electrodes) are provided that can imprint information at a rate of 1 GHz. However, because of the multiplexing in time a total information rate of 100 GHz is provided on the final beam. This is achieved without having to increase the information rate of the individual active apertures.

[0146] Embodiments of the invention have been described above in connection with a beam of electrons. However, embodiments of the invention may be used for beams of other charged particles.

[0147] Embodiments of the invention may be used to generate light pulses. Physical chopper wheels used to generate optical pulses generally work in the kHz range, and cannot operate at higher frequencies. In embodiments of the invention, instead of rotating a chopper wheel, a light beam can be rotated across a stationary mask. One way to implement this is to excite a rotating electric field in a resonant cavity that is filled with an electro-optic material.

[0148] Applying an electric field across an electro-optic material with a specific crystal orientation will result in a refractive index that increases linearly along the direction of the applied electric field. When a suitable crystal is used one can deflect light in the direction of the applied electric field. This is schematically illustrated in Figure 14, which shows electro-optical deflection of a light ray 502 passing through an electro-optic material 560 placed in an external electric field (indicated by arrows E). In Figure 14 the light ray 502 is bent in the direction of the applied electric field E, which is the direction in which the refractive index increases, and exits at an angle a.

[0149] The light ray that passes through the electro-optic material 560 is deflected in the direction of the electric field, because in that direction the refractive index induced by the electric field is increasing. To maximise the deflection angle a for a given field strength a crystal with a relatively large electro-optic coefficient may be selected. As an example, KTN (Potassium Tantalate Niobate) may be used. KTN is a well-known material with a relatively large electro-optic coefficient, widely used in electro-optical beam deflection devices.

[0150] Figure 15 illustrates how a device 562 comprising an electro-optic material in a rotating electric field can be used to provide a periodic deflection of an incident light beam 502. The rotating electric field is provided by placing the electro-optic material inside a cavity (e.g. the cavity described further above in connection with other embodiments). With reference to Figures 8A-C, the dashed line 211 represents the electro-optic material rather than dielectric. When dielectric is used in connection with an electron beam a hole is provided through the centre of the dielectric to allow electrons to pass through the dielectric. However, when electro-optic material is used, photons pass through the electro-optic material (a hole is not provided). The light beam 502 is initially propagating along the z-axis of a Cartesian (x,y,z) coordinate system, and then enters the device 562. The device 562 is schematically indicated in Figure 15 by a box of length Lc, centred around the origin (x,y,z)=(0,0,0). The device 562 comprises an electro-optic material and an electric field which rotates around the z-axis with a desired frequency. The electric field has an electric field distribution that is constant in the co-rotating frame. The electro-optic material and rotating electric field gives rise to periodic deflection of the incoming light beam.

[0151] The light beam can be manipulated in the same way as described further above for the electron beam. For the electron beam a device has been described in which the electron beam undergoes periodic radial displacement by a rotating magnetic field. This is accomplished by having the electrons pass through the device in one period of the rotating EM field. For the light beam 502 a shorter interaction length (shorter device 562) may be used. As a result, as depicted in Figure 15A, after deflection by the device 562 the light beam 502sis not parallel to the z-axis but instead is diverging away from the z- axis.

[0152] Deflection of the light beam 502 to a diverging beam is more practical than displacement to be parallel with the z-axis. To achieve displacement to a light beam parallel to the z- axis the length of the electro-optic material would become large (e.g. 0.3m for 1GHz rotation frequency). It may be difficult to configure a sufficiently large electro-optic material. In addition, absorption of the light beam 502 by the electro-optic material will start to become significant for large device lengths (e.g. 0.3m). Finally, a deflection angle that can be achieved using a conventional length of electro-optic material is sufficient for embodiments of the invention (as explained below). A conventional length of electro- optical material may be between 10 mm and a few cm, and may provide a deflection angle of between 10 mrad and a few 100 mrad.

[0153] Figure 15A shows a light ray 506; that passes through the device 562 such that the ray passes the device in much less time than one period. Inside the device there exists an electric field pointing in the y-direction. The light ray is deflected by the device such that the light ray 506smakes an angle in the y-z plane. This is analogous to what is depicted in Figure 14.

[0154] Figure 15B shows a second light ray 508; that is lagging the first light ray 506;. This second light ray 508; passes through the same device 562 when the EM field has rotated by 90 degrees around the z-axis. The second light ray 508i undergoes deflection. This ray 508; exits the device with a same angle but now in the x-z plane.

[0155] In Figure 15C, an incident third light ray 510; has been rotated. The rotated light ray 510shas the same angle as the first light ray 506sbut is on an opposite side of the z-axis.

[0156] In Figure 15D, an incident fourth light ray 512; has been rotated. The rotated light ray 512shas the same angle as the second light ray 508sbut is on an opposite side of the z-axis.

[0157] Figure 15E shows fifth light ray 514, that is lagging the first light ray 506; by such a distance that it will exit the device 562 at the same angle as the first light ray 506s(i.e. as depicted in Figure 15A). At this point the spiralling trajectory of the light ray has made one full revolution and will start a new round.

[0158] As noted above, the length of device 562 needed to displace the light beam such that it runs parallel to the z-axis may be around 0.3m for a frequency of 1GHz. This is calculated using the equation below, in which the length L is determined by the speed of light c and the oscillation frequency o) of the EM fields inside the device 562:

[0159] L = cT, Equation 10 where T = 2?r I o) is the oscillation period of the EM fields inside the device. Each section of length L of an incoming continuous light beam is linearly mapped over the circumference of a radially growing spiral. For a frequency <u = 2n • 1 GHz this results in a length L = 0.3 m. As noted above, this length may be difficult to provide in practice. In practice the device length Lcmay be much smaller than L (e.g. 1 mm, up to a few cm). Advantageously, when this is the case there is negligible change of the EM field whilst a given photon passes through the device. When a shorter device 562 (i.e. shorter than 0.3m) is used, this results in a diverging spiral light ray.

[0160] Figure 16 depicts a beam modulation system 501 according to an embodiment of the invention. A light beam 502; passes through a device 562 comprising an electro-optic material in a rotating electric field. The device changes the light beam to a diverging spiral 502s. A positive lens 564 is located downstream of the device 562. The focal length of the lens 564 is equal to the distance between the lens and the device 562. The lens 564 therefore converts the diverging spiral 502s to a collimated spiral 502c When the collimated spiral is incident on a mask provided with one or more apertures, the continuous light beam is modulated in time in the same way as described further above in connection with an electron beam.

[0161] The modulated light beam can be restored back to the optical axis (z-axis) by using a second lens and second device (not depicted). The second lens and second device provide the same operations as the first lens and first device, but operating in reverse order (equivalent to the electron beam as described further above). Thus, the second lens is also a positive lens, and focuses the modulated spiral light beam into the second device. The second device then deflects the light beam back onto the optical axis (z- axis).

[0162] In one example, a first device comprises a rotating electric field having a field strength of 1 MV / m applied across a KTN crystal with a length Lc= 1 mm. This results in a beam angle of 10 mrad. A lens with a focal length of 10 cm is placed 10 cm behind the first device. This provides a collimated spiral light beam having a radius of 1 mm. Using a mask that has 1 um holes (with a 50 / 50 duty cycle) placed around the circumference of the collimated spiral, pulses on the order of 3 fs can be made. On such a circle about 3000 holes can be placed which results in an optical beam that is modulated at 3 THz. A second lens with a focal length of 10 cm is placed 10 cm in front of a second device which has the same properties as the first device. The second lens and second device deflect the light beam back onto the optical axis.

[0163] Figure 17 depicts a beam modulation system 601 according to another embodiment of the invention. This embodiment is similar to the embodiment of Figure 16, but includes a mirror 670 and uses polarization selectivity. A linearly polarized light beam 602; is incident upon a polarizing beam splitter cube 670. The light beam is reflected by the polarizing beam splitter cube 670 and passes through a device 662 comprising an electro-optic material in a rotating electric field. The device changes the light beam to a diverging spiral 602s. A positive lens 664 is located downstream of the device 662. The focal length of the lens 664 is equal to the distance between the lens and the device 662. The lens 664 therefore converts the diverging spiral 602s to a collimated spiral 602c

[0164] A quarter wave plate 674 is located after the positive lens 664. The quarter wave plate changes the polarization of the collimated spiral beam 602c from linear polarization to circular polarization.

[0165] The collimated spiral 602c is incident on a mask 675 provided with one or more apertures. The collimated spiral 602c applies a modulation in time in the same way as described further above in connection with an electron beam. The mask may be an active or a passive mask. In the case of an active mask, the distance between the mask and the mirror may be minimised such that the light ray passes through the mask, is reflected and returns through the mask in less time than one period of the RF field in device 662. A mirror 676 reflects the collimated spiral beam 602c. The reflected beam has the same form as the incident beam but has an opposite circular polarization.

[0166] The reflected beam passes back through the mask 675 and the quarter wave plate 674, which changes the polarization of the beam to linear polarization. The linear polarization is now orthogonal to the linear polarization of the incident beam.

[0167] The reflected beam then passes back through the lens 664, which focuses the beam into the device 662. The device 662 converts the beam back into a linear beam. The polarization of the linear beam is orthogonal to the incident beam 602; and as a result the linear beam passes through the polarizing beam splitter cube 670, providing a modulated output beam 602o.

[0168] A beam modulation system 701 according to a further alternative embodiment is depicted in Figure 18. This embodiment is similar to the embodiment of Figure 3, but includes a mirror 770.

[0169] An input electron beam 702; is guided by a bending magnet 772 such that it is directed to a device 762 which provides a rotating electromagnetic field. The device 762 changes the electron beam to a collimated spiral 702s. The collimated spiral 702s passes through a mask 763 provided with an aperture. A reflector 770, which comprises a positively charged plate reflects the electron beam

[0170] The reflected electron beam passes back through the mask 763 and device 762. The reflected beam then passes back through the bending magnet 772, providing a modulated output beam 702o. The mask may be a passive or an active mask. When using an active mask the mask may be close to the mirror, such that the time it takes to pass the mask and back is shorter than the period of the oscillating field in device 762.

[0171] Embodiments of the invention which modulate a light beam may comprise a passive mask or an active mask. The passive mask may have features which correspond with those described further above in connection with electron beam modulation. For example, the passive mask may have a single aperture or multiple apertures. The passive mask may have periodically spaced apertures, or apertures with a non-periodic spacing (e.g. to provide a chirp or other form of pulse structure).

[0172] The active mask may comprise apertures within which electro-optic material is provided. An electrical field applied to the electro-optic material may be used to alter the trajectory of the light beam as it passes through the electro-optic material. The electrical field may for example be used to deflect the light beam out of a path that will result in it being in an output beam, so that light only passes into the output beam when the electric field is not applied. An opposite arrangement may be used such that light only passes into the output beam when the electric field is being applied.

[0173] Features of embodiments of the invention which modulate an electron beam may also apply to embodiments of the invention which modulate a light beam.

Claims

CLAIMS:1 . A beam modulation system configured to apply a modulation to an incident linear beam of charged particles, the beam modulation system comprising: a resonant cavity which comprises an electro-magnetic field generator configured to apply to the charged particle beam an electro-magnetic field that rotates in a plane perpendicular to an axis of the incident beam, such that on exiting the resonant cavity the charged particle beam travels around a circumference in a plane perpendicular to the axis; a mask comprising one or more mask apertures which intersect with the circumference travelled by the charged particle beam; and a resonant cavity which comprises an electro-magnetic field generator configured to apply to the charged particle beam an opposite electro-magnetic field such that on exiting the resonant cavity the charged particle beam is converted back to a linear beam.

2. The beam modulation system of claim 1 , wherein the beam modulation system comprises two electro-magnetic field generators, the first electro-magnetic field generator being configured to apply the electro-magnetic field that rotates in a plane perpendicular to an axis of the incident charged particle beam, and the second electromagnetic field generator being configured to apply the opposite electro-magnetic field.

3. The beam modulation system of claim 1 , wherein the beam modulation system further comprises a charged plate downstream of the electro-magnetic field generator, the charged plate being configured to direct the charged particle beam back through the electro-magnetic field generator such that the electro-magnetic field generator applies the opposite electro-magnetic field to the charged particle beam.

4. The beam modulation system of any preceding claim, wherein the rotating electro-magnetic field provided by the resonant cavity has a period which corresponds with a time taken for a charged particle to travel through the resonant cavity, so that the charged particle beam on exiting the resonant cavity is parallel with the incident charged particle beam.

5. The beam modulation system of any of claims 1 to 3, wherein the beam modulation system further comprises a lens downstream of the resonant cavity, the lens being configured to collimate the charged particle beam.

6. The beam modulation system of any preceding claim, wherein the or each resonant cavity is substantially cylindrical and comprises an entrance aperture in a first face and an exit aperture in an opposite face.

7. The beam modulation system of any preceding claim, wherein the one or more mask apertures are active apertures, the one or more mask apertures each having an associated electrode which is configured to displace the charged particle beam.

8. The beam modulation system of any preceding claim, wherein the resonant cavity comprises a plurality of antennae connected to an RF signal generator configured to generate an RTMno mode or an RTEm mode.

9. The beam modulation system of any of any preceding claim, wherein the charged particle beam is an electron beam.

10. A method of modulating a linear beam of charged particles, the method comprising: using a resonant cavity which comprises an electro-magnetic field generator to apply to the charged particle beam an electro-magnetic field that rotates in a plane perpendicular to an axis of the incident beam, such that on exiting the resonant cavity the charged particle beam travels around a circumference in a plane perpendicular to the axis; intersecting the beam of charged particles with a mask comprising one or more mask apertures such that the beam is modulated by the mask; and using a resonant cavity which comprises an electro-magnetic field generator to apply to the charged particle beam an opposite electro-magnetic field such that on exiting the resonant cavity the charged particle beam is converted back to a linear beam.

11. A beam modulation system configured to apply a modulation to a beam of light, the beam modulation system comprising: an electro-optic material inside a resonant cavity and antennae configured to apply to the beam of light an electro-magnetic field that rotates in a plane perpendicular to an axis of the beam of light, such that on exiting the electro-optic material the beam of light travels around a circumference in a plane perpendicular to the axis; and a mask comprising one or more mask apertures which intersect with the circumference travelled by the beam of light.

12. The beam modulation system of claim 11 , wherein the beam modulation system further comprises a first lens configured to collimate a diverging spiral beam of light output from the first device.

13. The beam modulation system of any of claim 11 or clam 12, further comprising a an electro-optic material inside a resonant cavity and antennae configured to apply a rotating electro-magnetic field, the electro-magnetic field being opposite to the electromagnetic field generated by the first device, such that the beam is converted back to a linear beam.

14. The beam modulation system of any of claim 13, wherein the beam modulation system further comprises a mirror configured to reflect the beam of light back into the same electro-magnetic material and antennae, such that the same electro-magnetic material and antennae apply the opposite electro-magnetic field.

15. The beam modulation system of claim 13, wherein the beam modulation system further comprises a second lens configured to focus the collimated spiral beam of lightinto the second device, and further comprises a second electro-magnetic material and antennae downstream of the second lens, the second electro-magnetic material and antennae being configured to apply the opposite electro-magnetic field.

16. The beam modulation system of claim 15, wherein the mask is located between the first lens and the second lens.

17. The beam modulation system of any of claims 11 to 16, wherein the one or more mask apertures are active mask apertures, electro-optic material being provided in each of the one or more mask apertures.

18. The beam modulation system of any preceding claim, wherein the mask is provided with a single mask aperture.

19. The beam modulation system of any of claims 1 to 16, wherein the mask is provided with a plurality of mask apertures.

20. The beam modulation system of claim 19, wherein the mask apertures are periodically spaced.21 . A method of modulating a beam of light, the method comprising: using an electro-optic material and antennae to apply to the beam of light an electro-magnetic field that rotates in a plane perpendicular to an axis of the beam of light, such that on exiting the electro-optic material the beam of light travels around a circumference in a plane perpendicular to the axis; and using a mask comprising one or more mask apertures which intersect with the circumference travelled by the beam of light to modulate the beam of light.

22. A beam modulation system configured to apply a modulation to an incident linear beam of charged particles, the beam modulation system comprising: a first resonant cavity which comprises a first electro-magnetic field generator configured to apply to the charged particle beam a first electro-magnetic field that rotates in a plane perpendicular to an axis of the incident beam, such that on exiting the resonant cavity the charged particle beam travels around a circumference in a plane perpendicular to the axis; a first mask comprising one or more mask apertures which intersect with the circumference travelled by the charged particle beam; a second resonant cavity which comprises a second electro-magnetic field generator configured to apply to the charged particle beam a second electro-magnetic field that rotates in a plane perpendicular to the axis of the charged particle beam, the rotation of the second electro-magnetic field having a different frequency from the first frequency; and a second mask comprising one or more mask apertures which intersect with the circumference travelled by the charged particle beam.

23. The beam modulation system of claim 22, wherein at least one of the apertures in the second mask is coaxial with the incident linear beam of charged particles.

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