This invention relates generally to continuously tunable external cavity diode lasers for use in cavity-enhanced spectroscopy, and particularly to a compact, improved tuning system that avoids tuning discontinuities by maintaining a constant integral number of half wavelengths over at least a portion of the entire tuning range of the laser. The improved tuning system of the present invention suppresses mode hopping and reduces undesirable feedback.
Frequency-tunable semiconductor diode lasers are known as versatile optical tools for a variety of uses in telecommunications, metrology, spectroscopy and other applications. Many such tunable lasers use a diffraction grating with a movable reflector (mirror) to select a desired wavelength from the laser beam diffracted by the grating. Generally, a diode gain medium is employed that has an antireflection (AR) coating on one facet thereof. Light emitted from the AR coated facet is diffracted by a grating and directed to the mirror, which feeds light back to the grating and gain medium. Rotational movement of the reflector with respect to a pivot point selects the wavelength diffracted by the grating and allows the laser to be tuned to a desired output wavelength. Translational motion of the reflector is frequently employed in conjunction with the rotational motion to couple the cavity optical path length to the desired wavelength and provide mode-hop-free tuning.
Such semiconductor diode lasers are handicapped by the fact that the existing tuning mechanisms do not maintain a constant number of half wavelengths within the optical cavity. Variation in the angle of the mirror is used to select the desired wavelength, which is diffracted by the grating at the angle represented by the mirror position. While this approach provides a means for tuning the operating wavelength of the laser, it has been found that the mirror does not provide a smooth tuning action because rotation of the mirror about an arbitrary axis does not maintain the length of the tuning cavity at an integral number of half wavelengths. As the wavelength is varied and the number of waves in the cavity varies, the laser output exhibits discontinuities including large changes in output power and discontinuous changes in the emitted wavelength.
The basic principles of the operation of a tunable laser utilizing a variable-length external cavity in conjunction with a diffraction grating and a rotatable mirror are set forth in “Spectrally Narrow Pulse Dye Laser Without Beam Expander”, by M. G. Littman and H. J. Metcalf, Applied Optics, vol. 17, No. 14, pages 2224-2227, Jul. 15, 1978 and P. McNicholl and H. J. Metcalf, Applied Optics, vol. 24, no. 17, 2757-2761, Sep. 1, 1985. The Littman-Metcalf system utilizes a diffraction grating illuminated at a grazing angle with an incident collimated laser beam. The diffracted beam impinges at normal incidence onto a mirror, is reflected back onto the grating and, from there, diffracted back into the lasing medium, where it serves to determine the operating wavelength of the system. Rotation of the mirror to select the diffracted wave allows the system to be tuned to a desired output wavelength. Using this approach, a very high degree of precision in the rotation mechanism is required for mode-hop-free tuning, and additionally the tuning process is slow.
It was later recognized that simple rotation of the mirror did not provide a continuous single-mode scan over a range of wavelengths. The publication, “Novel Geometry for Single-Mode Scanning of Tunable Lasers” by Michael G. Littman and Karen Liu, (Optics Letters, Vol. 6, No. 3, pages 117, 118, March, 1981) describes a tunable laser cavity in which the mirror is rotated about a specified pivot point, to change the cavity length in correlation with the angle of the diffracted beam returned to the laser. Although the authors state that the pivot point selected by this method provides exact tracking for all accessible wavelengths, this is in fact true only for the case where there are no dispersive elements in the cavity, since the changes in optical length due to the effects of dispersion are not considered. Further information of a more general nature is available in “Introduction to Optical Electronics” by Amnon Yariv, 1976, published by Holt, Rinehart and Wilson; and “Optics” by Eugene Hecht, 1987, Addison-Wesley Publishing Co.
The shortcomings of tuning systems in which the mirror was only rotated was further discussed in “Synchronous Cavity Mode and Feedback Wavelength Scanning in Dye Laser Oscillators with Gratings” by Harold J. Metcalf and Patrick McNicholl, Applied Optics, Vol. 245, No. 17, pages 2757-2761, Sep. 1, 1985. The geometry described in this publication relates to positioning the point of rotation (pivot point) of the mirror at the intersection of the planes of the surface elements. The article suggests that for oscillators with mirrors as both end elements, a useful displaced configuration will also be synchronous. However, the displaced configurations will, again, be synchronous only in the absence of dispersive elements in the cavity.
A further development of the Littman-Metcalf configuration is set forth in “External-Cavity Diode Laser Using a Grazing-Incidence Diffraction Grating”, by K. C. Harvey and C. J. Myatt, Optics Letters, Vol. 16, No. 12, pages 910-912, Jun. 15, 1991, which describes a tunable cavity system utilizing a diode laser in which the diode laser has a highly reflective rear facet and an anti-reflection coated output facet with an output window. The output beam is collimated by a lens and illuminates a diffraction grating at a grazing angle. The first order of diffraction of the grating is incident on the mirror, which reflects it back onto the grating, where the first order of diffraction passes back into the diode laser. The output of the system is the zeroeth-order reflection from the grating. In this system, no mention is made of coordinated rotation and lineal translation of the mirror, or of a specific pivot point for rotation.
Another variable-wavelength design is described by J. B. D. Soule, et al., “Wavelength-Selectable Laser Emission From A Multistripe Array Grating Integrated Cavity Case,” Applied Physics letters, Vol. 61, No. 23, 7 Dec. 1992, pp. 2750-2752. In this device, single-output/selectable-wavelength operation was obtained by blazing a single “output” stripe on a grid and injection pumping different second stripes in order to obtain lasing at different wavelengths.
Numerous patents deal with wavelength tuning using moveable lenses and/or gratings, e.g., U.S. Pat. Nos. 5,524,012; 6,108,355; 6,252,897; 6,282,213; 6,301,274; 6,285,183 and 6,788,726. Recently, a variety of novel techniques have been applied to tuning diode lasers. For example, a variety of U.S. patents exist for laser tuning with alternative configurations of the mirrors at the cavity ends. U.S. Pat. No. 4,896,325 discloses an alternative cavity configuration in which a pair of mirrors, with narrow discontinuities that provide reflective maxima, bound the active cavity. These narrow bands of reflective maxima provide means for wavelength tuning which is actively controlled by a Vernier circuit. U.S. Pat. No. 4,920,541 discloses an external laser cavity configuration of multiple resonator mirrors used to produce multiple wavelength emission from a single laser cavity simultaneously or with a very fast switching time. Various mechanical arrangements for movement of the mirror have been devised to introduce simultaneous rotation and longitudinal translation in attempts to maintain the physical length of the laser cavity at a constant number of half wavelengths. One such a system is shown in U.S. Pat. No. 5,058,124. U.S. Pat. No. 5,319,668 discloses a tunable diode laser with a diffraction grating for wavelength separation and a movable mirror at the cavity end for wavelength selection. The pivot points are designed to provide a laser cavity length specific for the production of several wavelengths. U.S. Pat. No. 5,771,252 discloses an external-cavity, continuously tunable wavelength source utilizing a cavity end reflector movable about a pivot point for simultaneous rotation and translation for wavelength selection.
In addition, several U.S. patents disclose the use of alternative components in the laser cavity configuration in order to achieve wavelength tuning. U.S. Pat. No. 4,216,439 discloses a spectral line selection technique that utilizes a spectral line selection medium in the gain region of an unstable laser resonator cavity. U.S. Pat. No. 4,897,843 discloses a microprocessor-controlled laser system capable of broadband tuning by using multiple tuning elements, each with progressively finer linewidth control. U.S. Pat. No. 5,276,695 discloses a tunable laser capable of multiple wavelength emission simultaneously, or with a very fast switching time between wavelengths, by using a laser crystal in the cavity and fine rotation of the cavity end reflective element. U.S. Pat. No. 5,734,666 discloses a wavelength selection apparatus for a laser diode eliminating mechanical motion of a grating by utilizing a laser resonator for wavelength range selection and a piezoelectric-controlled crystal for specific wavelength selection.
Recent non-patent prior art also discloses relevant technology. In SPIE vol. 2482, pp. 269-274 by Zhang, et al., a microprocessor-controlled tunable diode laser that utilizes a stepper motor to rotate the grating for wavelength tuning is described. In addition, in SPIE vol. 3098, pp. 374-381 by Uenishi, Akimoto and Nagoka, a tunable laser diode with an external silicon mirror has been fabricated with MEMS technology and has wavelength tunability.
Wavelength-division multiplexed (WDM) optical communications systems require compact optical sources which can be tuned to specific channel wavelengths. The telecommunications prior art has frequently utilized a distributed feedback laser (DFB). Producing a DFB laser for a specific wavelength is a low-yield, statistical process, and a single DFB cannot be broadly tuned. Although external-cavity semiconductor lasers can be widely tuned to cover the entire band with a single unit, the existing grating-based designs are typically both large and delicate.
Versatility and low cost are especially desirable aspects of a tunable laser system to be used in spectroscopic applications. All of the previously described prior art designs are limited in their performance by one or more of the following: requiring complex mechanical motion, small wavelength range tunability, and/or specified or limited wavelength selection order. Especially for applications in spectroscopy, broadband, continuous wavelength tuning, arbitrary or simultaneous precise wavelength selection, and limited mechanical motion are highly desired characteristics. None of the known prior art designs provides a singular, compact, tunable light source that emits light with variable, but stable, wavelengths and stable light intensity that is thermally and mechanically insensitive and is especially suitable for cavity-enhanced spectroscopy applications.
Tables 1 and 2 show several theoretically possible alternatives for realizing a widely tunable laser in an external-cavity configuration. However, all these designs have major shortcomings with respect to linewidth/current noise and/or modulation. Moreover, all of the currently commercially available lasers cover only the telecommunications C-band, and although some might possibly be configured to cover the L-band, none covers the spectroscopically important ranges of 1380-1420 nm and 1660-1720 nm. These considerations suggest that development of a widely and continuously tunable laser, configurable for spectroscopic analysis and, in particular for use in cavity enhanced spectroscopy, would be highly desirable in the range around 1550 nm and would constitute a truly major advance if useable in the range of about 1300 nm to 1700 nm.
Cavity-enhanced spectroscopic methods resolve the sensitivity limitation inherent in conventional spectroscopy by increasing the effective path length of the light through the sample. Cavity-enhanced optical detection entails the use of a passive optical resonator (also referred to as a cavity). Integrated cavity output spectroscopy (ICOS) and cavity ring-down spectroscopy (CRDS) are two of the most widely used cavity-enhanced optical detection techniques. ICOS, as used herein, is intended to include a recent variant called off-axis ICOS where the light is injected into the resonator at an angle to the optical axis. The teaching of U.S. Pat. Nos. 5,528,040; 5,912,740; 6,795,190 and 6,466,322, which describe these techniques, are hereby incorporated herein by this reference. Although the present invention will be described primarily in the context of CRDS, it should be understood that it is also applicable to CEAS including ICOS and off-axis ICOS.
Cavity ring-down spectroscopy (CRDS) is based on the principle of measuring the rate of decay of light intensity inside a stable optical resonator, called the ring-down cavity (RDC). Once sufficient light is injected into the RDC from a laser source, the input light is interrupted, and the light transmitted by one of the RDC mirrors is monitored using a photodetector. The transmitted light, I(t,λ), from the RDC is given by the equation:
where I0 is the transmitted light at the time the light source is shut off, τ(λ) is the ring-down time constant, and R(λ)=1/τ(λ) is the decay rate. The transmitted light intensity decays exponentially over time.
In CRDS, an optical source is usually coupled to the resonator in a mode-matched manner, so that the radiation trapped within the resonator is substantially in a single spatial mode. The coupling between the source and the resonator is then interrupted (e.g., by blocking the source radiation, or by altering the spectral overlap between the source radiation and the excited resonator mode). A detector typically is positioned to receive a portion of the radiation leaking from the resonator, which decays in time exponentially with a time constant τ. The time-dependent signal from this detector is processed to determine τ (e.g., by sampling the detector signal and applying a suitable curve-fitting method to a decaying portion of the sampled signal). Note that CRDS entails an absolute measurement of τ. Both pulsed and continuous-wave laser radiation can be used in CRDS with a variety of factors influencing the choice. The articles in the book “Cavity-Ringdown Spectroscopy” by K. W. Busch and M. A. Busch, ACS Symposium Series No. 720, 1999 ISBN 0-8412-3600-3, including the therein cited references, cover most currently reported aspects of CRDS technology.
Single-spatial-mode excitation of the resonator is also usually employed in ICOS (sometimes called CEAS)) although not in off-axis ICOS. ICOS/CEAS differs from CRDS in that the wavelength of the source is swept (i.e., varied over time), so that the source wavelength coincides briefly with the resonant wavelengths of a succession of resonator modes. A detector is positioned to receive radiation leaking from the resonator, and the signal from the detector is integrated for a time comparable to the time it takes the source wavelength to scan across a sample resonator mode of interest. The resulting detector signal is proportional to τ, so the variation of this signal with source wavelength provides spectral information on the sample. Therefore ICOS/CEAS entails a relative measurement of τ. The published Ph.D. dissertation “Cavity Enhanced Absorption Spectroscopy”, R. Peeters, Katholieke Universiteit Nijmegen, The Netherlands, 2001, ISBN 90-9014628-8, provides further information on both ICOS/CEAS and CRDS technology and applications. CEAS is also discussed in a recent article entitled “Incoherent Broad-band Cavity-enhanced Absorption Spectroscopy by S. Fiedler, A. Hese and A. Ruth, Chemical Physics Letters 371 (2003) 284-294. The teaching of U.S. Pat. No. 6,795,190 which describes ICOS and off-axis ICOS are also incorporated herein.
In cavity-enhanced optical detection, the measured ring-down time depends on the total round-trip loss within the optical resonator. Absorption and/or scattering by target species within the cavity normally account for the major portion of the total round-trip loss, while parasitic loss (e.g., mirror losses and reflections from intracavity interfaces) accounts for the remainder of the total round-trip loss. The sensitivity of cavity-enhanced optical detection improves as the parasitic loss is decreased, since the total round trip loss depends more sensitively on the target species concentration as the parasitic loss is decreased. Accordingly, both the use of mirrors with very low loss (i.e., a reflectivity greater than 99.99 percent), and the minimization of intracavity interface reflections are important for cavity-enhanced optical detection.
It is an object of the present invention to provide a piecewise continuously tunable diode laser with broadband wavelength selection capability and a compact and robust form factor.
It is also an object of the present invention to provide a piece-wise continuously tunable diode laser with fast, broadband, wavelength selection capability in an arbitrary order.
It is another object of the invention to provide a laser whose wavelength can be scanned continuously with high spectral resolution and high precision over a narrow wavelength range for the purpose of spectroscopy.
It is also an object of the invention to provide a piece-wise continuously tunable diode laser with fast, broadband and precise wavelength selection capability in an arbitrary order that allows discrete switching between a predetermined series of wavelengths by mechanical translation of a lens.
It is also an object of the invention to provide a piece-wise continuously tunable diode laser which is resistant to mode hopping and which maintains an integral number of half wavelengths in the optical cavity over at least a portion of the entire tuning range of the laser.
It is also an object of the invention to provide a laser that emits light of a variable but stable wavelength and of stable intensity.
It is a further object of the present invention to provide a broadly tunable laser configurable for spectroscopic analysis in multiple wavelength regions, including, in particular, the regions around 1400 nm to 1700 nm.
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Our experiments indicate that our novel, diffraction-grating-based, external-cavity tunable laser architecture is capable of producing excellent performance in a cavity ring-down or other cavity-enhanced spectrometer. A wavelength-tunable laser according to the present invention comprises: i) a semiconductor diode laser mounted on a base element and having one facet (end plane) of a reduced reflection factor and positioned to illuminate; ii) a lens which faces the facet; iii) a grating-type reflector for reflecting light supplied from the facet via the lens in either a Littman-Metcalf or Littrow type configuration; and iv) means for precisely shifting the lens in a direction substantially perpendicular (orthogonal) to the axis of the lens to change an incident angle of the light to the grating. Furthermore, it is preferred that the focal point of the lens be substantially coincident with the above described end plane of the semiconductor laser. Moreover, it is preferred that the light emitted from the above described end plane be converted into parallel light. Also, it is preferred that the above described lens be an aspherical lens. The grating may be of either the holographic or blazed (ruled) type. In a particularly preferred embodiment of our invention, the cavity lens is linearly actuated by a piezoelectric element, resulting in angular sweeping of the beam emitted by the laser incident on the grating, thereby tuning it to the desired wavelength. This particular embodiment provides reduced size, higher speed, and enhanced wavelength stability. Other suitable means for translating the lens include, as an alternative to a PZT, an arcuate voice coil, a MEMS, thermal expansion and a manual or motorized micro-positioning screw. By piece-wise, mode hop free continuous tuning is meant that the cavity can access any wavelength within the tuning range of the laser but that the total tuning range must be considered as an overlapping series of segments and the laser is mode hop free, continuously tunable only within a given segment. To access another segment the laser must switch to another longitudinal mode corresponding to the longitudinal mode of the particular segment.
As above indicated, the external cavity laser suitable for the practice of the present invention can be in either the Littrow or Littman-Metcalf configuration. In the “Littrow” arrangement, the retroreflective dispersive element (grating) itself serves as a resonator end mirror, and in the “Littman-Metcalf” arrangement, the retroreflective dispersive element is positioned between the end mirrors of a folded resonator cavity. The end mirror and/or retroreflective dispersive element are varied in angle with respect to each other to control tuning or selection of desired laser output wavelengths.
It is desirable for spectroscopic applications that the system include additional means for finely adjusting the wavelength output of the laser. Suitable techniques include altering the temperature of the semiconductor chip by means such as thermoelectric (e.g., Peltier) units, resistive heaters and/or circulating air of variable temperature. Additional fine-tuning capability is normally achieved by providing a variable current source for altering the input current to the electrically pumped semiconductor diode laser chip.
The fundamental working principle of a diffraction grating is that interference between waves scattered from each illuminated groove of the grating will be constructive only when:
a(sin θm−sin θi)=mλ, Eq. 2
wherein a is the groove spacing, θm the diffracted angle, θi the incidence angle, m the diffraction order, and λ the wavelength of the incident light.
In the context of the present invention as shown in
The diffraction formula for the Littrow configuration therefore becomes
2a sin θi=λ. Eq. 3
For example, for a grating having a density of 1000 grooves/mm (a=1 μm) and an incident light wavelength of 1550 nm, θi=50.8°.
An alternative embodiment of the present invention (
There are three requirements for a grating to work effectively as a dispersive element in an external cavity laser:
(1) the diffracted beam must be of sufficient power;
(2) the angular dispersion needs to be sufficiently high, and
(3) the transfer function needs to be sufficiently narrow.
The first requirement is to ensure that there will be enough feedback to cause lasing; the second and third conditions ensure that lasing will occur in a single longitudinal mode. To satisfy the first condition, the grating must be biased to diffract most of the incoming light into the desired order, since all other orders are unused. This can be achieved by using either a blazed or a holographic grating. In either case the diffraction efficiency can be very high (˜90% diffraction into first order).
In order to satisfy the second and third requirements, it is useful to consider a practical reference point to derive a performance benchmark. Such guidance can be obtained from external-cavity lasers, and particularly those constructed having a semiconductor optical amplifier (SOA) as the gain medium and an etalon-based wavelength-selective cavity element. The figure of merit to consider is the subthreshold side-mode suppression ratio (SMSR), which represents the relative loss experienced in the subthreshold state by the nearest-neighbour longitudinal modes compared to the dominant mode. For a laser to operate stably in the single-mode regime, the SMSR will preferably be greater than about 0.3 dB.
One can translate the SMSR requirement to the case of a grating. In order to do so, two quantities need to be defined. For a grating in the Littrow configuration and such that the optical beam waist is coincident with the grating, the full-width half-maximum (FWHM) instrumental broadening Δθ−1, where a is the groove spacing and N is the number of grooves illuminated, is:
and the angular dispersion is
An analytical model, designed to explore the relationships between component specifications and performance parameters and informed with empirical data points, provides insight.
In Eq. 4, the denominator Na cos θi is the beam diameter, assuming that the entire beam diameter fits on the grating at angle θi. For a fixed wavelength, the instrumental broadening will be a function only of how wide the beam can be made. On the other hand, if other constraints fix the beam diameter, one can affect side-mode rejection by increasing the groove density a and simultaneously increasing the grating angle θi (Eq. 3) to keep the system in Littrow retroreflection. Then, as seen from Eq. 5, the separation of neighboring modes will increase, due to the increased angular dispersion.
Table 3 shows the result of simulations for a variety of cavity configurations. As indicated, the figure of merit is the side mode suppression ratio expressed in dB. For example, consider three cavity lenses that span two octaves in 1/e2 beam diameters; and also consider two cavity lengths: 20 mm, for a mode spacing of 0.05 nm, and 2 mm, yielding a mode spacing of 0.16 nm. A groove density of 750 mm−1 was chosen. Tests were performed using this grating in conjunction with a C-band laser. The laser was configured to leave the cavity lens intact (a Geltech 350140), but a Littrow grating was inserted at two different grating-to-lens distances (20 mm and 2 mm). The resulting spectral purity was observed.
The results conform to the expectations drawn from an etalon-based external-cavity laser benchmark and from the analytical investigation of a grating-based external-cavity laser. For the beam diameter given by the existing cavity lens, the 20-mm cavity did not go single-mode (second row in Table 3: SMSR=0.01 dB which is rather low), but the 2-mm cavity did support single-mode operation (also second row: SMSR=0.14 dB approximates the benchmark of 0.3 dB). Additional tests with angle tuning of the grating showed that the C-band laser was capable of supporting lasing across a ˜150-nm band, from 1425 to 1575 nm.
The tuning mechanism introduced in this invention involves linear translation of the cavity lens in the X direction (the direction perpendicular to the direction of the beam and in the plane of diffraction) to bring about angular displacement of the cavity beam, and therefore wavelength tuning in a Littrow cavity. There are practical advantages to such an arrangement, e.g., the feasibility of using a piezoelectric driver to translate the lens (since lens motion is linear) instead of the prior art approach of a galvo driver to pivot the grating (where motion must be angular). It also proved possible to arrange the cavity parameters so that translation of the lens automatically results in mode-hop-free tuning across the operating range.
The results of the analysis are shown in Table 4. The approach followed was to calculate the minimum groove density necessary to yield a sufficiently high SMSR (i.e., SMSR>0.3 dB) for use with each of the three cavity lenses under consideration, and in each case to calculate the associated tuning parameters (total angular displacement, linear-to-angular conversion for each lens, and resulting linear displacements) necessary to yield a 40-nm tuning range. The three configurations show the results of optimization for each of the three listed cavity lenses.
What should be noted is that the total linear travel necessary to cover 40 nm is substantially invariant (approximately 55 μm): a shorter-focal-length (FL) lens has a higher efficiency in converting linear translation into angular displacements, but the associated smaller cavity beam requires a higher groove density and larger grating angle to achieve a similar SMSR, which in turn increases the necessary angular displacement requirement. This extent of linear translation is achievable with commercially available piezoelectric units. The third row in Table 4 shows calculations for a configuration that was found to be particularly advantageous in practice. Here the cavity lens (Geltech 350390) was translated, while the grating was kept fixed. The SMSR for such a configuration (0.49 dB) is well above that needed for robust single-mode operation (0.3 dB). The results of a practical embodiment of such a configuration are shown in
The prior art describes an external-cavity Littrow configuration (
In one preferred Littrow-configuration embodiment of the present invention (
One embodiment of the present invention, as shown in
The prior art also describes a variation of the Littman-Metcalf configuration (
An embodiment of the present invention, shown in
An alternative embodiment of the invention, is shown in
Major remaining components of a spectrometer in accordance with the present invention are shown in
In any of the embodiments of the invention described above, it is often advantageous either to tune the wavelength continuously and without mode hops, or to hold the wavelength fixed without mode hops. In either case, the wavelength is selected primarily by translation of the lens, and mode hops are prevented by adjusting the wavelength of the longitudinal mode of the external cavity laser, so that the diffraction efficiency function 310 remains substantially centered with respect to the incident angle 301 as shown in
In the Littrow configuration, if and only if the function 310, as indicated in
A second lens location, shown in
A dipole detector may be added to the Littman-Metcalf configuration shown in
The Littman-Metcalf grating configuration shown in
The Littman-Metcalf configuration shown in
Alternatively, as shown in
The foregoing detailed description of the invention includes passages that are chiefly or exclusively concerned with particular parts or aspects of the invention. It is to be understood that this is for clarity and convenience, that a particular feature may be relevant in more than just the passage in which it is disclosed, and that the disclosure herein includes all the appropriate combinations of information found in the different passages. Similarly, although the various figures and descriptions herein relate to specific embodiments of the invention, it is to be understood that where a specific feature is disclosed in the context of a particular figure or embodiment, such feature can also be used, to the extent appropriate, in the context of another figure or embodiment, in combination with another feature, or in the invention in general. Figures are schematic only and are not intended to constitute an accurate geometric portrayal of the location of the elements shown. Further, while the present invention has been particularly described in terms of certain preferred embodiments, the invention is not limited to such preferred embodiments. Rather, the scope of the invention is defined by the appended claims.