Note: Descriptions are shown in the official language in which they were submitted.
1
APPARATUS AND METHOD FOR TUNABLE GENERATION OF COHERENT
RADIATION
[0001]
Field of the Invention
[0002] The
present invention relates to non-linear light-matter interaction in solids.
More
specifically, the present invention is directed to controlled generation of
high-order harmonics
in solid-state media and applications of this control.
Related Art
[0003]
Extracting information from fast-evolving phenomena requires probe signals
that
are shorter in duration than the time scale of the physical phenomena under
study. As in
stroboscopic photography, wherein the fastest motion that can be captured is
defined by the
camera shutter speed or the duration of the flash, accurate measurement of
ultrafast phenomena
are generally bound by the duration of the probe pulse. A laser pulse, for
example, may be used
as an optical probe for measurement of ultra-fast processes unraveling at
molecular and atomic
scales. The minimum achievable duration for an optical pulse is the time
period of a single
optical cycle. For standard lasers in infrared spectral ranges, this period
corresponds to a few
femtoseconds. A few femtoseconds are therefore the limit for the shortest
pulse that can be
generated with standard lasers. Breaching the attosecond atomic time scale
barrier necessarily
requires pushing the spectral region of operation from near-infrared (NIR)
regime of standard
lasers into the ultraviolet regime (VUV or XUV) and beyond.
[0004]
Converting NIR photons (e.g. 1.6 eV) to much higher photon energies (e.g., 100
eV)
requires a significant generation-energy boost. The necessary frequency up-
conversion,
Date Recue/Date Received 2022-02-28
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2
required for generating ultraviolet range radiation from infrared range
lasers, may occur when
the optical response of a generating medium is driven into the non-linear
regime. This may be
accomplished, for example, through exposure to a very high intensity laser
pulse. Any
nonlinear system that is driven by an intense monochromatic field will respond
at harmonic
frequencies of the driving electromagnetic field. The harmonic response may
stabilize over
an extended range of harmonic-orders before it eventually drops off. Such a
harmonic
response profile, is characteristic of neutral atoms subjected to an intense
electromagnetic
field. When such an atomic medium is driven, for example, by an intense NIR
laser pulse of
central frequency mo, it may exhibit a broadband emission profile consisting
of several
harmonics of the fundamental frequency wo. The broadband emission profile may
span a
spectral range up to, for example, XUV and soft x-ray regime. This nonlinear
strong-field
optical process wherein a laser pulse of standard wavelength, such as infrared
laser beam, is
converted into coherent radiation in a much shorter wavelength regime, such as
XUV or soft
X-ray frequency regime, is known as high-order harmonic generation (HHG)
process.
[0005] In the
context of HHG, a laser pulse is considered strong when its electromagnetic
field intensity approaches the characteristic atomic binding field strength,
i.e., field strength
or force experienced by electrons in the coulomb field of an atom in the
generation medium.
The strong electric field present at a laser focus will suppress the coulomb
potential that holds
the electron to the nucleus. The suppression of the coulomb potential
facilitates a valence
electron to tunnel through the potential barrier by a process known as strong
Held ionization.
Following the ionization process the freed electron is accelerated in a
trajectory away from its
parent ion by the same electric field. When the oscillating electric field
changes direction,
during the negative half of the oscillation cycle, the electron trajectory is
reversed. The
electron is now accelerated back towards the parent ion by the electric field.
On its way back
the electron acquires a large amount of kinetic energy due to the strong
acceleration imparted
by the laser electric field. Upon re-collision and recombination with the
parent ion the stored
ionization energy and the kinetic energy of the electron, gained by its
interaction with the
laser field, is released as a radiation pulse.1 This radiation pulse will have
a frequency related
to the harmonics of the driving laser field.2 Since many electrons take part
in this process,
during each half-cycle of the laser field, there will be a broad distribution
of possible
trajectories and kinetic energies at recombination. This will correspond to
multiple frequency
components in the emission spectrum. The result is a broadband XUV emission
with a typical
3 4 5
spectrum of high-order harmonics.' ' If the radiation is continuous and phase
locked, the
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corresponding temporal profile will be that of an attosecond pulse whose
duration decreases
as the number of combined harmonics increases. The attosecond time-scale of
the pulse
emerges as a result of coherent superposition of harmonic orders of the
fundamental
frequency (Qno). Since this coherent process occurs at every half cycle of the
periodic drive
laser, the XUV emissions will be characterized by a series of attosecond-scale
bursts
separated in the time domain by half the laser period, i.e., ¨2 T. The
corresponding frequency
domain representation is that of a harmonics frequency comb consisting of
frequency peaks
(harmonics) separated by twice the fundamental frequency, i.e., 2(Do. The
consecutive bursts
correspond to respective electron-ion collisions emanating from opposite
directions (due to
being driven by opposite polarity half cycles of the oscillating laser field.)
This results in the
emission of spectral components with opposite phases (but the same amplitude
due to the
inversion-symmetric property of the generating medium.) The upshot is inherent
destructive
interference of the even-order harmonics (interchangeably referred to as even
harmonics) and
constructive interference of the odd-order harmonics (interchangeably referred
to as odd
harmonics.) Consequently, even-order harmonics are erased and only odd-order
harmonics
are observed in the standard HHG spectrum.
[0006] In principle
a broad spectral width enables the formation of attosecond pulses.
Following the identification of electron-ion re-collision as the primary
interaction underlying
HHG from atomic gas-based medium, experimental techniques have been developed
to
modulate the interaction to thereby tune and enhance the harmonic response of
the atomic
gas-based medium. These techniques are typically based on shaping the
intensity profile of a
driving field to thereby influence and modify the spectral phase of the
resulting high
harmonic emissions (i.e., enhance the harmonic bandwidth generated through the
laser-driven
electron-ion re-collision process).'' 75.
9'10'11
[00071 Since the
first observation of high-order harmonics about two decades ago, much
of the relevant effort has been directed toward the theoretical study,
analysis and
experimental realization of the HHG technology in gas-phase medium.12' 13'
HHG
implementation in gaseous medium has been the domain of primary progress in
the field.
Consequently, relative to solid-state domain, HHG in gases is far more
developed and in
widespread application today. Motivated, in part, by the deficiency in
understanding of the
HHG process in solid-state medium, one aspect realized by the present
invention cultivates a
detailed insight into the emission mechanism underlying HHG in solids and
solid-state
CA 02912310 2015-11-19
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medium by building upon the established similarity in the strong-field
ionization response of
solids and gases. Furthermore, disclosed embodiments seek to identify,
characterize and
experimentally verify the dominant interaction underlying high-order harmonic
generation in
solids and solid-state medium. Other embodiments of the present invention
disclose an
operational platform and methodology for in-situ generation, measurement and
manipulation
of broadband emission of coherent XUV radiation and tunable attosecond pulse
formation in
solid-state medium (i.e., semiconductor substrate). Accordingly, it is a goal
of the present
invention to expand the scope and extend the commercial relevance and
applicability range of
the HHG technology.
[0008] Disclosed
embodiments of the present invention provide novel methods, systems
and applications enabled by a solid-state based (i.e., semiconductor-based)
implementation of
broadband coherent XUV radiation and tunable attosecond pulse formation,
accomplished via
controlled high harmonic generation from solid-state matter (i.e.,
semiconductor generation
medium.)
SUMMARY
[0009] According to
first broad aspect, the present invention provides a method
comprising applying a driving electromagnetic field having a first frequency
and a first
intensity to a solid-state medium to thereby trigger a high harmonic
generation process in the
solid-state medium. The high harmonic generation may process results in a
generation of a
harmonic beam from the solid-state medium. The harmonic beam may comprise a
plurality
of high-order harmonics of the first frequency. The method may apply a control
field having
a second frequency, a second intensity and a relative phase with respect to
the driving
electromagnetic field to an interaction region of the electromagnetic field
and the solid-state
medium to thereby control one or more spectral, temporal and spatial
properties of the
harmonic beam generated from the solid-state medium.
[0010] According to
a second broad aspect, the present invention provides an apparatus
comprising a semiconductor generation medium comprising a semiconductor-laser
interaction region; a first input configured to focus a drive laser field onto
the semiconductor-
laser interaction region to thereby initiate a high harmonic generation
process in the
semiconductor-laser interaction region; a second adjustable input for
introducing a control
field onto the semiconductor-laser interaction region to thereby control the
high harmonic
generation process, wherein the control field spatially and temporally
overlaps the drive laser
CA 02912310 2015-11-19
field. The apparatus may also comprise an output for directing a signal
generated from the
semiconductor-laser interaction region onto one or more terminals, wherein the
signal
comprises one or more high harmonics.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] The accompanying drawings, which are incorporated herein and
constitute part of
this specification, illustrate exemplary embodiments of the invention, and,
together with the
general description given above and the detailed description given below,
serve to explain the
features of the instant invention.
[0012] FIG. 1 is a pictorial representation of an electron's trajectories
and field profiles for
two successive half-cycles of a fundamental field in presence of a second-
harmonic control
field, according to one embodiment of the present invention.
[0013] FIG. 2 illustrates the measured high harmonic spectra versus the
relative delay
between the two color fields (fundamental or drive field and second-harmonic
control field),
according to one embodiment of the present invention.
[0014] FIG. 3 is a graphic illustration of the extracted data from FIG. 2
showing the
modulation phase that maximizes the intensity of a respective harmonic order,
as a function of
the harmonic order, according to one embodiment of the present invention.
[0015] FIG. 4 illustrates an out of phase modulation of the even and odd
harmonics when
the intensity of the second-harmonic control field is 1*10-4 of the
fundamental field,
according to one embodiment of the present invention.
[0016] FIG. 5 illustrates the in phase modulation of all harmonics when the
intensity of
the second-harmonic control field is increased to 3*10-3 of the fundamental
field, according
to one embodiment of the present invention.
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DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Definitions
[0017] Where the definition of terms departs from the commonly used meaning
of the
term, applicant intends to utilize the definitions provided below, unless
specifically indicated.
[0018] For purposes of the present invention, it should be noted that the
singular forms,
"a," "an" and "the," include reference to the plural unless the context as
herein presented
clearly indicates otherwise.
[0019] For purposes of the present invention, directional terms such as
"top," "bottom,"
"upper," "lower," "above," "below," "left," "right," "horizontal," "vertical,"
"up," "down,"
etc., are used merely for convenience in describing the various embodiments of
the present
invention. The embodiments of the present invention may be oriented in various
ways. For
example, the diagrams, apparatuses, etc., shown in the drawing figures may be
flipped over,
rotated by 90" in any direction, reversed, etc.
[0020] For purposes of the present invention, a value or property is
"based" on a particular
value, property, the satisfaction of a condition or other factor if that value
is derived by
performing a mathematical calculation or logical operation using that value,
property or other
factor.
[0021] For purposes of the present invention, the term "AC field" refers to
a periodically
or non-periodically varying electric field.
[0022] For purposes of the present invention, the term "characteristic
atomic binding field
strength" refers to the atomic field strength keeping outer most electrons
bound to the parent
atom. In order for an impinging electromagnetic field to ionize the atom it
must have a field
strength equal to or in excess of the characteristic atomic binding field
strength.
[0023] For purposes of the present invention, the term "DC field" refers to
a constant
electric field.
[0024] For purposes of the present invention, the term "drive laser" may be
used
interchangeably with the term "driving laser".
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[0025] For purposes of the present invention, the term "driving field" or
"drive field"
refers to the electric field associated with a driving laser and may be used
interchangeably
with the terms "driving laser field" or "drive laser field".
[0026] For purposes of the present invention, the term "driving laser"
refers to the
fundamental signal, if the fundamental signal is a laser pulse.
[0027] For purposes of the present invention, the term "fundamental field"
refers to the
electric field associated with a fundamental signal.
[0028] For purposes of the present invention, the term "fundamental
frequency" refers to
the frequency of the fundamental signal.
[0029] For purposes of the present invention, the term "fundamental signal"
refers to a
signal that non-linearly interacts with a medium in order to produce high-
order harmonics of
the fundamental signal frequency from the medium.
[0030] For purposes of the present invention, the term "high-order
harmonic" refers to the
high integer multiples of the fundamental signal.
[0031] For purposes of the present invention, the term "interaction region"
refers to the
region where a fundamental signal interacts with a medium in order to generate
high-order
harmonics of the fundamental signal from the medium.
[0032] For purposes of the present invention, the term "laser-driven
electron-ion re-
collision process" refers to the electron re-collision process underlying the
high harmonic
generation process when such a process is driven by a laser signal.
[0033] For purposes of the present invention, the term "modulated" refers
to the act,
effect, outcome or condition of modulation upon a signal.
[0034] For purposes of the present invention, the term "modulation" refers
to any type of
modification or alteration brought upon or imposed onto the spatial, temporal
or spectral
properties of a signal.
[0035] For purposes of the present invention, the term "nano-plasmonic
features" refers to
any feature that produces/controls/modifies or is subjected to one or more
plasmonic events
at the nano scale.
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[0036] For purposes of the present invention, the term "nano-plasmonic"
refers to the
plasmonic effect that occurs at the nano scale.
[0037] For purposes of the present invention, the term "optical signal"
refers to an
electromagnetic signal with a wavelength range extending from Infra-red to X-
ray regime.
[0038] For purposes of the present invention, the term "plasmonie" refers
to an effect or
condition that involves or is related to the collective oscillation of
conduction-band electrons
in a medium in response to an electromagnetic field.
Description
[0039] While the present invention is disclosed with references to certain
embodiments,
numerous modification, alterations, and changes to the described embodiments
are possible
without departing from the sphere and scope of the present invention, as
defined in the
appended claims. Accordingly, it is intended that the present invention not be
limited to the
described embodiments, but that it has the full scope defined by the language
of the following
claims, and equivalents thereof. It is understood that other embodiments may
he utilized and
structural changes may be made without departing from the scope of the
invention.
[0040] Electron-hole pair creation by high order multiphoton transitions
(often
approximated as tunnelling), followed by the motion of the electrons and holes
within and
between their respective bands is the fundamental .mechanism underlying strong-
field light
matter interactions and harmonic generation. In atoms, the motion of the
electron can be
characterized by two different dynamics. In one, known as intra-hand
transition, the newly
freed electron undergoes oscillatory motion in the presence of the applied
electric field:7 In
the other, illustrated in FIG. 1, the freed electron undergoes a boomerang
type trajectory that
results in re-collision and recombination of the electron with its associated
hole (parent ion)
and emission of a high energy photon as a consequence of the process. Since
both dynamics
involve the formation of an oscillating dipole, they are both potential
sources of harmonic
radiation. In gaseous medium the former dominates low-order harmonics
generation while
the latter dominates high-order harmonics generation. In the case of high-
order harmonic
generation (HHG) in solids, contributions from both dynamics must be
considered.
9
[0041] Intra-band transition in solids deviates from the free electron
model in gases. Due to
the interaction of the electron with the lattice, the electron motion does not
follow the sinusoidal
motion of the electric field.", 16' 17 HHG model in solids must, therefore,
include both
mechanisms18, 19, namely the non-sinusoidal electron dynamics, and the
electron-ion re-
collision dynamics following a high-field ionization process. HHG processes in
solid-state
medium may be used as a diagnostic tool for studying, for example, the
ultrashort temporal and
spatial dynamics and probing attosecond time-scale phenomena associated with
solid-state
electronics. In order to understand, control and ultimately exploit the
potential of the HHG
process as a solid-state based diagnostic tool, the primary physical mechanism
for high-order
harmonics generation in solids such as, for example, a semiconductor
generation medium must
be identified.
[0042] In accordance with one aspect of the present invention a mid-
infrared (MIR) laser
pulse is used to study a response of a Zinc oxide (ZnO) based semiconductor
medium to an
incident high-intensity field. Short emission bursts corresponding to odd-
ordered harmonics of
the fundamental frequency of the MIR laser are recorded. This observation
demonstrates
successful generation of high-order harmonics from a semiconductor medium.
Emissions
corresponding to even-order harmonics of a driving field are observed when a
driving field,
introduced, for example, via a first input is perturbed with a weak secondary
control field
introduced, for example, via a second adjustable input. The secondary control
filed may have
a frequency equal to the second harmonic of the fundamental frequency
(frequency of the
driving field.) Further control over the high-order harmonic generation
process is demonstrated
by utilizing the adjustable input to variably delay the second-harmonic
control field relative to
the fundamental field. Modulation of the relative delay between second-
harmonic control field
and fundamental field results in modulation in the strength of the observed
even harmonics
emitted from the semiconductor medium. It is experimentally observed that the
phase of the
modulation as a function of harmonic order determines the spectral phase
(emission time) of
the emitted harmonic beam. This observation facilitates the characterization
of physical
mechanism underlying the HHG process in the semiconductor-based medium such
as, for
example, ZnO. Similar results, namely controlled generation of high harmonics
and
characterization of the underlying generation mechanism, are demonstrated for
a silicon-based
semiconductor medium, for example, as described in U.S. Provisional Patent
Application No.
62/248,372, entitled "GENERATION OF HIGH HARMONICS FROM SILICON," filed
October 30, 2015. It should be noted that the second-harmonic control field
may have an
Date Recue/Date Received 2022-02-28
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internal or an external source, i.e., it may be applied through one or more
internal terminals
fashioned on the surface or within the bulk of the semiconductor medium, or
applied through
one or more external terminals coupled to one or more external sources.
[0043] As stated earlier, strong-field assisted electron tunneling" and
the subsequent
motion of the electron in the continuum, followed by a possible re-combination
of the electron-
hole pair is the fundamental mechanisms underlying HHG process. Due to its
quantum nature,
the interaction is governed by the phase of the released electron wave-packet.
Therefore
tracking the dynamics of the electron wave packet (from ionization to field-
driven acceleration
to radiative recombination with the parent ion) by way of treating HHG as a
balanced electron
interferometer, may help to elucidate the above-stated experimental
observations.
[0044] Initially, an intense laser field removes an electron from its host
atom, splitting the
wave function into a coherent superposition of a bound state and a free-
electron wave packet.
In the language of interferometry, ionization process acts as an effective
beam splitter. Next,
the free-electron wave packet moves in the oscillating laser field and returns
to the parent atom
during the negative half of the driving field oscillation cycle. This
effectively corresponds to
an adjustable delay line. Finally, during the re-collision, the two portions
of the wave function
overlap. The characteristics of the resulting interference (time-dependent
dipole moment) are
encoded in the output attosecond radiation pulse emitted from a generation
medium. The
amplitude, energy and phase of the re-collision electron are transferred to
the emitted radiation
pulse through the dipole moment (energy transition). The control of the
spectral properties,
temporal properties and spatial properties of the HHG process, and by
extension those of the
emitted harmonic beam, requires manipulating electron trajectories on
attosecond time-scale.
Trace diagrams 102 and 104 in FIG. 1, illustrate an electron's propagation
paths (trajectories)
106 and 107 when a host atom 105 experiences a symmetric electric field, as
illustrated by
positive and negative half-cycles 108 and 109, respectively. Half-cycles 108
and 109 represent
an electric field cycle experienced by a host atom 105 upon which a driving
laser field 110 is
incident. Hence forth, driving laser field 110 may be interchangeably
referenced as
fundamental field 110. As can be observed from trace diagram 102, electron
propagation paths
106 and 107 are symmetric in response to the
Date Recue/Date Received 2022-02-28
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symmetric profile of half-cycles 108 and 109. As such the left and right arms
of the
interferometer are balanced.
[0045] Due to the non-linear nature of the strong-field light-matter
interaction, small
perturbations in the driving laser .field 110 may result in large changes in
harmonic behavior
of a generating medium (of which host atom 105 is a part). Solid trace 114 and
116 illustrate
the expected alterations in the propagation paths (trajectories) of an
electron when an electric
field experienced by host atom 105 is altered as illustrated by the asymmetric
profile of
positive and negative half-cycles 117 and 118, respectively. The alteration is
due to the
perturbation of driving laser field 110. The perturbation, in this case, is
introduced in form of
a weak secondary control field 120 with a frequency corresponding, for
example, to the
second harmonic of the fundamental frequency coo (frequency of the driving
laser field 110).
The secondary control field 120, henceforth referred to as second-harmonic
control field,
unbalances the interferometer by increasing or decreasing the electron
propagation path
(trajectory) by a small amount, thus adding or removing a small amount of
phase to
each arm of the interferometer. As a result, the phase accumulated by the
propagating
electron (propagation path 114) is enhanced in the half cycle 117 when the
fundamental field
110 and the second-harmonic control field 120 are appropriately phased
(similarly phased).
Similarly, phase accumulated by the propagating electron (propagation path
116) is
suppressed in the adjacent half cycle 118 when the fundamental field 110 and
the second-
harmonic control field 120 are oppositely phased. The shape of the electric
field experienced
by an atom (represented by trace 108, 118 and 117, 118) is variably modulated
by changing
the relative delay (relative phase) of the second-harmonic control field 120
with respect to the
fundamental field 110. This alters the interference profile between the second-
harmonic
control field 120 and the fundamental field 110. The relative phase (relative
delay) that
maximizes the strength of the emitted harmonics carries information related to
the phase of
the interfering electron wave-packets.
100461 Amplitude and spectral phase of the emitted harmonic radiation
carries the
complete information about the harmonic generation process. By tuning the
temporal
profile of driving laser field 110 to a known state, phase and amplitude
distribution of the
generated high-order harmonics, and by extension the time-domain
characteristics of the
isolated ultrashort radiation pulse, may be predicted.
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[0047] FIG. 2 illustrates the emitted high harmonic spectrum versus the
relative phase
(delay) between the two color fields (fundamental field and the second-
harmonic control
field), with the second-harmonic control field intensity set at 9* 106 of the
fundamental
field intensity level. The delay of the second-harmonic control field is
defined in terms of
the cycles of the fundamental field. Weak even harmonics are visible between
the strong
odd harmonics. At its peak an even harmonic, for example, even harmonic 202 at
10t5
harmonic order, is approximately 15% of the adjacent odd harmonic. According
to FIG.
2 the even harmonic intensity modulates with the delay between the fundamental
field
and the second-harmonic control field, at every half cycle of the fundamental
field. The
odd harmonics intensity is also modulated, but the modulation is not readily
observed
because they saturate the color scale of the display instrument used in the
measurement.
Comparison of the grey line 204 with the reference line 206 in FIG. 2 further
demonstrates that the phase modulation of the even harmonics (determined by
the
relative phase difference or delay between the second-harmonic control field
and the
fundamental field that maximizes the strength of the respective even
harmonic), depends
on the harmonic order. The weak second-harmonic control field modifies the
electron
wave packet between the moment of ionization and the moment of re-collision,
thus
modulating the emitted harmonic spectrum. Measuring the modulation of the even
harmonics versus phase delay (relative phase between the control field and the
fundamental field) measures the order-dependent relative phase that maximizes
the
intensity of each even harmonic as explained above. This parameter, denoted as
where N represent the harmonic order, may be used to extract the emission time
of each
even-order harmonic or equivalently, the spectral phase of the attosecond
pulses. The
emission time of odd-order harmonics may similarly be extracted by measuring
the
order-dependent relative phase that maximizes the intensity of each odd-order
harmonic.
[0048] In FIG. 3, the (1),õ2õ,(2N) parameter, extracted from the
measurements illustrated
in FIG. 2, is plotted as a function of the harmonic order up to the cut-off of
the measuring
spectrograph, and depicted as a set of circular data points 202. An unmeasured
constant
phase is used to position the experimental data (this constant phase is
measurable using
nonlinear optical methods). Trace 204 represents the theoretical values of
(I)m3,(2N), plotted
for the intra-band sources, corresponding to harmonics that arise from the
oscillatory motion
of the newly freed electron in the laser field. Trace 206 represents the
theoretical values of
Omax(2N), plotted for interband sources, corresponding to the re-collision and
recombination
CA 02912310 2015-11-19
13
of the ionizing electron with its associated "hole" (parent ion). Satisfactory
agreement
between experiment, illustrated by data points 202, and theoretical
calculation of interband
emission, illustrated by trace 206, is achieved. The disclosed measurements in
FIG. 2 and
FIG. 3 provide verification of electron re-collision as the dominant mechanism
for high-
order harmonic emission in an exemplary semiconductor medium such as, for
example, ZnO.
[0049] The slope of the curves in FIG. 3 is determined by both the
intensity of the
fundamental field and the band structure of the generating medium such as, for
example, a
dielectric crystal. The dispersion of the wave packet in a crystal medium has
two major
consequences: first, the electron-hole pair accumulates much more phase,
approximately
507-r, relative to that of the free electron wave packet in gaseous medium
which is
approximately 107. As a result, it is easier to break the symmetry of the
electron propagation
path in a crystal medium, using a control field, for example, as low as
approximately 10-5 of
the fundamental field (i.e., five orders of magnitude less that the
fundamental field intensity).
Second, it determines the duration of the high harmonic pulses. Initial
measurements produce
a harmonic chirp of approximately 0.38 fs/eV at the 16th harmonic,
corresponding to a train
of pulses with duration of 1.7 femtosecond (before dispersion compensation)
for a 2 eV
bandwidth. Wider bands and higher intensities will result in smaller chirps,
thereby allowing
attosecond pulse generation from a solid medium.2()
[0050] As the control field intensity is increased the action moves from
perturbing to
controlling of the high harmonic generation process and the harmonic
emissions. FIG. 4
illustrates how the harmonic emission spectrum is modified when the intensity
of the second-
harmonic control field is increased to approximately 10-4 of the fundamental
field. At this
intensity of the control field, even and odd harmonics modulate out of phase.
Alternation
between even and odd harmonics occurs when the second-harmonic control field
modulates
the re-collision electron phase by Td2.
[0051] At even higher second-harmonic control field intensity levels, high-
order harmonic
generation is substantially modified. In the highly asymmetric sum filed,
ionization only
occurs once per laser cycle. This leads to simultaneous emission (or
suppression) of even and
odd harmonics. FIG. 5 illustrates in-phase modulation of all harmonics as the
second-
harmonic control field intensity level is increased to 3x10-3 of the
fundamental field. This is
important because it simplifies the generation of isolated, ultrashort
(attosccond) pulses
which is achievable only by making use of the full high-order harmonic
spectrum.
CA 02912310 2015-11-19
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[0052] Control can rely on interference in space rather than time. By
suitable modification
of the second-harmonic control field phase front, the harmonic beam in the far
field can be
manipulate at will, effectively enabling functionalities associated with
lenses, beam splitters,
diffraction gratings and spatial light modulators. In situ optical elements
can be remarkably
useful for future studies of solid state dynamics or ex situ experiments with
the harmonic
beam. Due to the weak control field (second harmonic field) required, it is
plausible that DC
or pulsed electric fields21 applied, for instance, by electrodes on the
crystal, can perform the
same task.
[0053] Taken together, the forgoing provides strong evidence for controlled
high-order
harmonic generation in solids. The relative phase of the modulation between
even and odd
orders reveal detailed information on the time-dependent electron tunneling
rate.22 Odd
harmonics also show a weak modulation in solids. Transfer of this second in
situ method to
solids will allow the resolution of electronic sub-cycle temporal response to
strong fields.23'
24
[0054] Demonstrating the dominant role of electron re-collision in high-
order harmonic
generation in solids renders them an important medium for attosecond
technology.
For example, in gases, in situ probing allows for measurement of the field of
a light pulse.
It is the brief life of the re-collision electron in the continuum that
provides the ultrafast
gate. In accordance to one aspect of the present invention a theoretical and
empirical frame work for implementing similar in situ measurement in a solid
is
disclosed, thereby making the light-wave technology more easily transferrable
to the larger
scientific community. It should be noted that a solid medium may comprise a
crystal having a
crystalline structure, a dielectric material, polymer material, biological
material or it may
comprise a thin slice of biological material as a sample.
[0055] In summary, non-linear light-matter is essential in probing
materials and their
dynamics. Until now only perturbative probing methods have been used for
solids. In
accordance to one embodiment of the present invention a methodology and a
system for
controlled generation of high harmonics from transparent solids and solid-
state medium is
disclosed. This enables the adaptation and application of well-developed non-
perturbative methods from atomic physics to condensed matter. For example, a
re-collision
electron inevitably carries information about its origin5 and the band
structure of the
material through which it travelled. This information is encoded in the
emitted harmonic
CA 02912310 2015-11-19
spectrum. This will enables, for example, the reconstruction of a material's
3D momentum-
dependent band structure from measurements of (1)max(2N) as a function of
crystal
orientation.
[0056] The ease of delivery and application of the attosecond XUV pulse
that is generated
and controlled directly in a semiconductor substrate can significantly
simplify and enhance
analysis, diagnostic and metrology for a large array of solid-state integrated
systems.
Furthermore, realization of controlled HHG in semiconductor medium enables co-
integration
of these complex functionalities in the same substrate as optical and
electronic processing and
readout modules, thus enhancing the capabilities of the current solid-state
based applications
while creating avenues for entirely new applications and novel technological
solutions.
[0057] One embodiment of the present invention discloses a method for high
resolution
dynamic imaging of integrated circuits. Semiconductor circuits are grown on
semiconductor
materials. High harmonics generated and measured in these materials can be
used to spatially
image the circuit. When the circuit is off, the measured pattern reflects the
shape and
location of the semiconductor devices in the circuit. The circuit geometry can
be
reconstructed from the pattern by employing available algorithms. When the
circuit is on, the
electric fields modify the pattern. Subsequently comparison of this pattern to
the "off pattern"
allows the algorithm to reconstruct the distribution and magnitude of the
electric fields in the
circuit. The spatial resolution of the method is limited by the wavelength of
the harmonics,
approximately 100 nm. Those skilled in the art will realize that imaging can
be made active
as follows: The harmonic generation process (which is much faster than any
electrical
switching speed) can be delayed frame by frame to make a movie of the field as
a function of
time. Hence, this method allows the direct 2D imaging of the instantaneous
magnitude and
temporal/spatial propagation profile of electric fields in an active circuit.
Presently, there is
no method that can measure the chip internal fields. It is potentially
relevant for gaining
greater insight into operation of integrated circuits and for developing more
precise electronic
simulation tools and models. Additionally, direct observation of charge
transfer and
electronic dynamics in photovoltaic cells and transistors through monolithic
integration of
attosecond spectroscope in semiconductor substrate can facilitate development
of new
photovoltaic cells that are more efficient, and transistors that switch
faster.
CA 02912310 2015-11-19
16
[0058] One disclosed embodiment of the present invention provides a method
for probing
nano-plasmonic response in devices on semiconductor substrates: In a nano-
plasmonic
device, electric fields propagate along the interface between a semiconductor
and a metal,
mostly permeating the semiconductor. Harmonics generated from this substrate
and
subsequently modulated by the plasmonic electric field can be used to probe
the plasmonic
waves and measure the electric field of a propagating plasmon. These devices
can be useful
in engineering plasmonic devices or for tracking parasitic effects/losses in
circuits. No such
devices currently exist.
[0059] One disclosed embodiment of the present invention provides a method
for
measuring the time-dependent field of an optical pulses such as, for example,
a laser pulse, if
the optical pulse is used as the perturbing electric field, i.e., the control
field is another optical
pulse. The field of the optical pulse can then be measured by the measurements
of emitted
harmonics. To date, only one alternative method can perform a similar action,
but it is much
slower, operationally more expensive requiring instruments such as, for
example, vacuum
chambers and electron energy analyzers more expensive, and requires
approximately hundred
to a thousand times more laser energy. On the other hand, a device based on a
semiconductor
generating medium will be compact, cheap, fast (possibly even capable of
measuring single
pulses) and will require much less laser power. No other methods currently
exist that can
measure the electric field of light pulses. The semiconductor device will find
utility in
application requiring generation of short laser pulses. Additionally,
measuring the electric
field of the light will be increasingly relevant for the telecommunication
industry with growth
towards optical communication and transport.
[0060] One disclosed embodiment of the present invention provides a method
to control
high-harmonic emission in space and time. Accordingly control field may be
applied through
internal terminals such as, for example, a surface of a semiconductor medium
may be
patterned with thin electrodes that convey DC or AC fields into the
semiconductor-laser
interaction region of intense ionizing pulse (i.e. intense laser pulse),
thereby suitably
modifying the propagation of the harmonics. The control field may comprise DC
or AC
pulsed electrical signals, applied through internal or external terminals.
This presents an
extremely powerful and convenient method to control harmonic light to use, for
example, for
probing other systems and/or implementing functionalities such as, for
example,
focusing/defocusing, raster scanning and beam splitting. Although conventional
optical
CA 02912310 2015-11-19
17
mirrors are available to steer visible light, vacuum-ultraviolet radiation
requires costly
solutions. Furthermore, each mirror is often designed to perform one single
operation such as,
for example, specular reflection, focusing, beam splitting. The disclosed
method, in
accordance to one embodiment of the present invention may perform multiple
tasks at once.
I00611 One disclosed embodiment of the present invention provides a laser
source
delivering ultraviolet frequency comb by means of high-harmonic generation in
a
semiconductor substrate. Controlling the spectral properties of the laser beam
enables tuning
the period of the harmonic frequency comb, thus offering operational
flexibility.
Furthermore, due to the low laser energy required to produce the harmonics,
nano-antennas
deposited directly on the semiconductor may further reduce the threshold to
laser intensities
available with laser frequency combs. Much effort has been devoted to produce
soft X-ray
frequency combs with high-harmonic generation in gases. The methods disclosed
in
accordance to one aspect of the present invention enable the generation of
optical, ultraviolet
and vacuum ultraviolet frequency comb directly in a semiconductor medium. This
opens the
possibility of co-integration of an ultra-precise metrology and diagnostic
functionalities with
optical, electronic and microfluidic components monolithically fabricated in a
single
microsystem.
[00621 One disclosed embodiment of the present invention enables monolithic
integration
of ultra-precise XUV spectroscopic functionality with micro fluidics and lab-
on-chip
components.
EXAMPLES
Example 1
Experimental setup
[0063] A disclosed embodiment provides an experimental set up for
generating high
harmonics in semiconductor crystal using, for example, a MIR laser source
centered around
approximately 3.7 nm (central wavelength of 3.7 nm) and with approximately 19
nJ energy.
The pulse duration of approximately 85 fs is measured with a dispersion-free
SHG FROG. In
accordance to one embodiment, the beam is spatially filtered with a pin-hole
and focused
with, for example, a f/30 spherical Ag mirror onto an epitaxially grown 500 nm
thin film of a
single crystal of wurtzite Zn0(0001) deposited on a 0.5 mm Sapphire(0001)
substrate. The
18
optical axis of both crystals is aligned parallel to the laser k-vector. The
focus size is measured
with knife-edge technique. The generated harmonics are refocused with a Al
mirror onto a VIS-
UV spectrometer. The second-harmonic control field is generated in a 300 gm
AGS2 crystal
optimized for Type-I SHG right after the pin-hole to exploit the high
intensity and high beam
quality. It is separated and then recombined before the focusing mirror with
dichroic beam
splitter that reflects the second-harmonic control field. Its polarization is
rotated with a
broadband 2/2 before recombination. The delay between the two color fields is
scanned with a
PZT stage on the second-harmonic control field arm.
[0064]
Having described the various embodiments of the present invention in detail,
it will
be apparent that modifications and variations are possible without departing
from the scope of
the invention defined in the appended claims. Furthermore, it should be
appreciated that all
examples in the present disclosure, while illustrating many embodiments of the
invention, are
provided as non-limiting examples and are, therefore, not to be taken as
limiting the various
aspects so illustrated.
Date Recue/Date Received 2022-02-28
19
References
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technology that may
be used with the present invention:
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