阅读说明：本技术 光学频率梳偏移频率的量子干涉检测 (Quantum interference detection of optical frequency comb offset frequency ) 是由 史蒂文·T·坎迪夫 约翰·希佩 王凯 罗德里戈·穆尼兹 于 2018-05-10 设计创作，主要内容包括：提出了用于确定频率梳的偏移频率的方法。该方法包括：生成具有在时域中有规律地重复并且在频域中呈现频率梳的波形的光束；将光束指向材料上的入射点；以及检测由光束引起的材料中的光电流的振荡。值得注意的是,光束具有包括以第一频率传播的光和以第二频率传播的光的光学带宽,其中,第一频率小于第二频率,并且第二频率与第一频率之比为n∶m,其中,n＝m+i,m为大于1的整数,以及n和i为正整数。另外,材料具有带隙并且带隙不大于第一频率的n倍。(A method for determining an offset frequency of a frequency comb is presented. The method comprises the following steps: generating a light beam having a waveform that regularly repeats in the time domain and exhibits a frequency comb in the frequency domain; directing a light beam at a point of incidence on a material; and detecting an oscillation of the photocurrent in the material caused by the light beam. Notably, the optical beam has an optical bandwidth that includes light propagating at a first frequency and light propagating at a second frequency, wherein the first frequency is less than the second frequency and a ratio of the second frequency to the first frequency is n: m, wherein n ═ m + i, m is an integer greater than 1, and n and i are positive integers. In addition, the material has a bandgap and the bandgap is no greater than n times the first frequency.)

1. A method for determining an offset frequency of a frequency comb, comprising:

generating a light beam having a waveform that repeats regularly in the time domain and presents a frequency comb in the frequency domain, wherein the light beam has an optical bandwidth comprising light propagating at a first frequency and light propagating at a second frequency, wherein the first frequency is less than the second frequency and a ratio of the second frequency to the first frequency is 3: 2;

directing the beam of light at a point of incidence on a material, wherein the material has a band gap and the band gap is no greater than three times the first frequency; and

detecting an oscillation of a photocurrent in the material caused by the light beam.

2. The method of claim 1, wherein the waveform of the light beam is defined by a series of light pulses in the time domain.

3. The method of claim 1, further comprising: a first beam is generated using a mode-locked laser.

4. The method of claim 1, wherein the repetition rate of the beam is in the range of 10 megahertz to 10 gigahertz.

5. The method as set forth in claim 1 wherein the material is further defined as one of a semiconductor or an insulator.

6. The method of claim 1, wherein the material has a bandgap that is greater than two times the first frequency but less than three times the first frequency.

7. The method of claim 1, further comprising: the oscillation of the photocurrent is detected by measuring a frequency of the oscillation of the photocurrent.

8. The method of claim 7, further comprising: detecting oscillation of the photocurrent using an electrode disposed on a surface of the material.

9. The method of claim 1, further comprising: oscillations of the photocurrent flowing through the material transverse to the direction of propagation of the light are detected.

10. The method of claim 1, wherein detecting the oscillation of the photocurrent further: the material is arranged such that the light beam does not propagate along an axis of symmetry of the material.

11. The method of claim 10, further comprising: oscillations of the photocurrent flowing through the material parallel to the propagation direction of the light are detected.

12. The method of claim 1, further comprising: amplifying at least one of the first frequency of light and the second frequency of light in the beam of light before the beam of light is incident on the material.

13. The method of claim 1, further comprising: filtering at least one of the first frequency of light and the second frequency of light from the beam of light before the beam of light is incident on the material.

14. A method for determining an offset frequency of a frequency comb, comprising:

generating a light beam having a waveform that regularly repeats in the time domain and presents a frequency comb in the frequency domain, wherein the light beam has an optical bandwidth that includes light propagating at a first frequency and light propagating at a second frequency such that the first frequency is less than the second frequency and a ratio of the second frequency to the first frequency is n: m, wherein n +1, m is an integer greater than 1 and n is a positive integer;

directing the beam of light at a point of incidence on a material, wherein the material has a band gap and the band gap is no greater than n times the first frequency; and

detecting an oscillation of a photocurrent in the material caused by the light beam.

15. The method of claim 14, wherein the waveform of the light beam is defined by a series of light pulses in the time domain.

16. The method of claim 14, further comprising: a first beam is generated using a mode-locked laser.

17. The method of claim 14, wherein the repetition rate of the beam is in the range of 10 megahertz to 10 gigahertz.

18. The method as set forth in claim 14 wherein the material is further defined as one of a semiconductor or an insulator.

19. The method of claim 14, wherein the material has a bandgap that is greater than n times the first frequency but less than m times the first frequency.

20. The method of claim 14, further comprising: the oscillation of the photocurrent is detected by measuring a frequency of the oscillation of the photocurrent.

21. The method of claim 20, further comprising: detecting oscillation of the photocurrent using an electrode disposed on a surface of the material.

22. The method of claim 14, further comprising: oscillations of the photocurrent flowing through the material transverse to the direction of propagation of the light are detected.

23. The method of claim 14, wherein detecting the oscillation of the photocurrent further: the material is arranged such that the light beam does not propagate along an axis of symmetry of the material.

24. The method of claim 23, further comprising: oscillations of the photocurrent flowing through the material parallel to the propagation direction of the light are detected.

25. The method of claim 14, further comprising: amplifying at least one of the first frequency of light and the second frequency of light in the beam of light before the beam of light is incident on the material.

26. The method of claim 14, further comprising: filtering at least one of the first frequency of light and the second frequency of light from the beam of light before the beam of light is incident on the material.

27. A method for determining an offset frequency of a frequency comb, comprising:

generating a light beam having a waveform that regularly repeats in the time domain and presents a frequency comb in the frequency domain, wherein the light beam has an optical bandwidth that includes light propagating at a first frequency and light propagating at a second frequency such that the first frequency is less than the second frequency and a ratio of the second frequency to the first frequency is n: m, wherein n + i, m is an integer greater than 1 and n and i are positive integers;

directing the beam of light at a point of incidence on a material, wherein the material has a band gap and the band gap is no greater than n times the first frequency; and

detecting an oscillation of a photocurrent in the material caused by the light beam.

28. The method of claim 27, wherein the waveform of the light beam is defined by a series of light pulses in the time domain.

29. The method of claim 27, further comprising: a first beam is generated using a mode-locked laser.

30. The method of claim 27, wherein the repetition rate of the beam is in the range of 10 megahertz to 10 gigahertz.

31. The method as set forth in claim 27 wherein the material is further defined as one of a semiconductor or an insulator.

32. The method of claim 27, wherein the material has a bandgap that is greater than n times the first frequency but less than m times the first frequency.

33. The method of claim 27, further comprising: the oscillation of the photocurrent is detected by measuring a frequency of the oscillation of the photocurrent.

34. The method of claim 33, further comprising: detecting oscillation of the photocurrent using an electrode disposed on a surface of the material.

35. The method of claim 27, further comprising: oscillations of the photocurrent flowing through the material transverse to the direction of propagation of the light are detected.

36. The method of claim 27, wherein detecting the oscillation of the photocurrent further: the material is arranged such that the light beam does not propagate along an axis of symmetry of the material.

37. The method of claim 36, further comprising: oscillations of the photocurrent flowing through the material parallel to the propagation direction of the light are detected.

38. The method of claim 27, further comprising: amplifying at least one of the first frequency of light and the second frequency of light in the beam of light before the beam of light is incident on the material.

39. The method of claim 27, further comprising: filtering at least one of the first frequency of light and the second frequency of light from the beam of light before the beam of light is incident on the material.

Technical Field

The present disclosure relates to an improved method for determining an offset frequency of an optical frequency comb.

Background

Optical frequency combs have a significant and continuing impact on a range of technologies. Optical frequency combs provide the ability to coherently link optical signals separated by arbitrarily large frequency differences and to link optical frequencies to radio frequencies. Originally, the excitement of combs was due to their application in optical frequency metrology (i.e., making absolute measurements of the frequency of light) and the inverse problem of developing optical atomic clocks. However, the use of combs has been steadily expanding. These include the development of coherent communications and double comb spectra, which can produce higher resolution faster and with smaller packets than traditional methods.

For mode-locked laser frequency combs, stabilizing and controlling the comb offset frequency is necessary. The most common scheme for measuring the offset frequency is f-2f self-reference. One implementation of f-2f self-referencing is quantum interference control (QuIC) that detects the photocurrent caused by simultaneous single-photon and two-photon absorption across a semiconductor gap. The QuIC self-reference scheme has been used to measure and stabilize the carrier envelope phase of a titanium sapphire laser frequency comb. However, this scheme and all other f-2f schemes require a spectrum that spans at least an octave (i.e., twice over frequency).

This section provides background information related to the present disclosure that is not necessarily prior art.

Disclosure of Invention

This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.

A method for determining an offset frequency of a frequency comb is proposed. The method comprises the following steps: generating a light beam having a waveform that regularly repeats in the time domain and exhibits a frequency comb in the frequency domain, wherein the light beam has an optical bandwidth that includes light propagating at a first frequency and light propagating at a second frequency such that the first frequency is less than the second frequency and a ratio of the second frequency to the first frequency is n: m, wherein n is m + i, m is an integer greater than 1, and n and i are positive integers; directing a beam of light at a point of incidence on a material, wherein the material has a bandgap and the bandgap is no greater than n times the first frequency; and detecting an oscillation of the photocurrent in the material caused by the light beam.

In one embodiment, the ratio of the second frequency to the first frequency is n: m, where n ═ m +1, m is an integer greater than 1, and n is a positive integer. More specifically, the ratio of the second frequency to the first frequency may be 3: 2.

The waveform of the light beam is defined in the time domain by a series of light pulses.

The first beam may be generated using a mode-locked laser.

The repetition rate of the beam may be in the range of 10 mhz to 10 ghz.

The material is further defined as one of a semiconductor or an insulator.

In some cases, the material has a bandgap that is greater than two times the first frequency but less than three times the first frequency.

The oscillation of the photocurrent may be detected by measuring a frequency of the oscillation of the photocurrent (e.g., using an electrode disposed on a surface of the material).

In some embodiments, the oscillation of the photocurrent flows through the material transverse to the direction of propagation of the light. The material is arranged such that the light beam does not propagate along the symmetry axis of the material.

In another embodiment, the oscillation of the photocurrent flows through the material parallel to the direction of propagation of the light.

Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.

Drawings

The drawings described herein are for illustration purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.

FIG. 1 is a schematic diagram of a quantum interference control process using single photon and two photon absorption;

FIG. 2 is a flow chart illustrating an improved method for determining an offset frequency of a frequency comb;

FIG. 3 is a diagram of a system for determining a shift frequency of a frequency comb exhibited by an excitation beam;

fig. 4A to 4E are diagrams illustrating different arrangements in which a photocurrent flows through a material perpendicular to the propagation direction of light;

FIG. 5 is a diagram of an arrangement in which photocurrent flows through the material parallel to the direction of propagation of light;

fig. 6 is a diagram for explaining an experimental setup of the proposed method for determining the offset frequency of a frequency comb, where DDS: a direct digital synthesizer; DM: a dichroic mirror; EDFA: an erbium-doped fiber amplifier; f0 is the comb offset frequency; FM: a folding mirror; HPF: a high-pass filter; LA: a lock-in amplifier; LPF: a low-pass filter; PBS: a polarizing beam splitter; PD: a photodiode; SCG: generating a super-continuum spectrum; SPF: a short pass filter; TS: a translation stage; and YDFA: an ytterbium-doped fiber amplifier;

FIG. 7A is a graph showing the RF spectrum of quantum interference control current induced by a 1040nm only beam, a 1560nm only beam, and both unblocked 1560nm and 1040nm beams; and

fig. 7B is a graph showing a spectrum when the offset frequency is varied from 2kHz to 60 kHz.

Corresponding reference characters indicate corresponding parts throughout the several views of the drawings.

Detailed Description

Example embodiments will now be described more fully with reference to the accompanying drawings.

By way of background, quantum interference control (QuIC) of injected photocurrent can be used to determine the offset frequency of the frequency comb. In this method, photo-carriers are generated in the conduction band of the semiconductor by both single photon and two photon absorption, as seen in fig. 1. The quantum interference of these two paths depends on both the momentum of the electrons and the relative phase of the light. The net effect is a phase-dependent imbalance of the electron distribution in momentum space, which is equivalent to a phase-dependent photocurrent. Photocurrent exists even without bias, and thus is directly injected through the QuIC process. Specifically, the current injection rate for the octave crossover pulse is

Wherein E is_f(E_2f) Electric field of light at frequency f (2f), and_CEis the carrier envelope phase of the pulse. For a pulse train with an evolving carrier envelope phase, the current will oscillate at the offset frequency of the corresponding comb.

In this disclosure, a new two-photon-three-photon (2p-3p) self-referencing QuIC scheme to measure comb offset frequency is proposed. This approach is based on photocurrent induced by quantum interference of two-photon absorption processes and three-photon absorption processes. One advantage of this scheme is that, similar to the optical 2f-3f self-reference, the required bandwidth is reduced. Furthermore, in 2p-3pQuIC, the absorption length of both f-field and 3/2 f-field is greater than tens of microns because the photon energy of both light fields is lower than the band gap energy, compared to a one-photon-two-photon QuIC scheme where the absorption length of both fields is mismatched due to strong beyond band gap one-photon absorption of light at 2 f. Therefore, single photon absorption is greatly suppressed, allowing the design of an integrated device using a waveguide.

Fig. 2 further shows the proposed method for determining the offset frequency of the frequency comb. At 21, a light beam is generated having a waveform that repeats regularly in the time domain and exhibits a frequency comb in the frequency domain. In one embodiment, the waveform of the light beam is defined by a series of light pulses in the time domain. The repetition rate of the pulses is preferably in the range of 10 mhz to 10 ghz. Note that the optical beam has a sufficiently large optical bandwidth such that the optical beam includes light propagating at a first frequency and light propagating at a second frequency, wherein the first frequency is less than the second frequency.

In general, the ratio of the second frequency to the first frequency is n: m, where n is m + i, m is an integer greater than 1, and n and i are positive integers. In one embodiment, the ratio of the second frequency to the first frequency may be n: m, where n ═ m +1, m is an integer greater than 1, and n is a positive integer. In another embodiment, the ratio of the second frequency to the first frequency is substantially 3: 2 (or 1.5). For example, the light beam may include 1040nm and 1560nm light. These values are merely illustrative and are not intended to be limiting. Other ratios are contemplated within the general rules.

The light beam is directed (and incident) to the sample, as shown at 22. The sample includes a material having a bandgap, and the bandgap is no greater than n times the first frequency. More specifically, the band gap of the material is preferably greater than twice the first frequency but less than three times the first frequency. In the case where the first frequency corresponds to light having a wavelength of 1040nm, the sample may comprise aluminum gallium arsenide having a bandgap of 1.912eV (648.4 nm). I.e. the bandgap is no more than three times the first frequency. Again, these values are merely illustrative and are not intended to be limiting. It should be understood that different types of materials may be used, including semiconductors and insulators, depending on the application.

The light beam induces a photocurrent in the sample. At 23, oscillation of the photocurrent is detected. The present disclosure contemplates different detection methods. For example, the frequency of oscillation of the photocurrent may be measured electrically using electrodes placed on the surface of the sample.

In another example, radiation due to the photocurrent may be detected and an indication of the frequency of the oscillation provided. The injection of current by the quantum interference process is equivalent to the rapid acceleration of electrons in the material. The basic result of electromagnetic theory is that accelerated charges (here electrons) radiate electromagnetic waves. Therefore, the injection of current by quantum interference causes radiation of electromagnetic waves. The frequency of these waves is determined by the time scale of the current acceleration. For a single pulse, the timescale is sub-picoseconds, the radiation is at terahertz frequencies, but with a very large bandwidth that has been detected. However, the cumulative effect of many pulses (or repetitions of the waveform) will increase the component of the radiated electromagnetic wave to the comb offset frequency, and an integer multiple thereof. In any case, the frequency of the oscillation corresponds to the offset frequency of the frequency comb exhibited by the excitation beam.

FIG. 3 depicts a system 30 for determining a shift frequency of a frequency comb exhibited by an excitation beam. System 30 generally includes a frequency comb light source 31, a sample 32, and a detector 33. It should be understood that only relevant components are discussed with respect to fig. 3, but that other components may be required to implement the overall system.

In an exemplary embodiment, the frequency comb light source 31 is a fiber-based femtosecond laser source that employs a nonlinear optical ring mirror mode-locking mechanism. For further details regarding exemplary femtosecond laser sources, reference may be made to C-fiber femtosecond fiber lasers commercially available from Menlo Systems. It is readily understood that other arrangements of light sources and modulators may be used to implement the frequency comb light source, and such other arrangements fall within the scope of the present disclosure.

The light beam generated by the frequency comb light source 31 is directed to a point of incidence on the sample. As shown in fig. 4A-4D, different waveguide arrangements may be used. In these examples, the point of incidence 41 is at one end of the elongated waveguide 40. Waveguide 40 includes an aluminum gallium arsenide layer supported on top of a gallium arsenide layer. In fig. 4A and 4B, the rail 42 is integrally formed from a top layer of aluminum gallium arsenide, and protrudes upward from the top surface of the waveguide. In fig. 4A, two electrodes 43 are formed on the top surface of the waveguide 40; however, in fig. 4B, two pairs of electrodes are formed on the top surface of the waveguide. In fig. 4C and 4D, rail 42 is formed from multiple aluminum gallium arsenide layers deposited on top of the gallium arsenide layer. In fig. 4C, two electrodes 43 are formed on the exposed top surface of the gallium arsenide layer; however, in fig. 4D, two pairs of electrodes are formed on the exposed top surface of the gallium arsenide layer. The present disclosure contemplates other arrangements of electrodes.

In operation, light incident on the waveguide propagates in the direction of the rail 42 from one end of the waveguide to the other end of the waveguide. A photocurrent induced by light flows between two adjacent electrodes 43. That is, the photocurrent flows through the sample transverse to the direction of propagation of the light. To detect the oscillation of the photocurrent, the detector 33 is electrically coupled to the electrode 43. In one embodiment, detector 33 is a lock-in amplifier.

Fig. 4E is another arrangement in which the photocurrent flows through the sample transverse to the direction of propagation of the light. In this example, an electrode 43 is placed on the top surface of the material, and light 44 is incident from above the surface. In particular, the light 44 is incident between two electrodes 43 placed on the surface of the material. The material may be a uniform block sample with the properties described in 017 or it may have a layer with tailored properties as shown in figure 4E. The photocurrent flows between the electrodes and is therefore transverse to the direction of downward propagation of light in the sample. To detect the oscillation of the photocurrent, the detector 33 is electrically coupled to the electrode 43.

Fig. 5 is a variation in which the photocurrent flows through the sample parallel to the direction of propagation of the light. The electric field vector (polarization) of the incident light is always transverse to the direction of propagation. If the polarization is along the symmetry axis of the material, the induced current flows parallel to the polarization and thus transverse to the direction of propagation. However, if the polarization direction is not parallel to the axis of symmetry, the current flow will not necessarily be parallel thereto, but may have a component in the direction of propagation. The optimal direction is when the polarization is oriented at 45 degrees with respect to the 3 axes of symmetry, although some parallel current flow will occur for any deviation from alignment along the axes of symmetry. Because light is always incident on the surface, the most common way to achieve these conditions is by cutting the crystal, i.e., how the surface is oriented with respect to the crystal lattice. The best case is called "111" cutting.

In this example, the light beam is incident on the top surface of the sample. When the sample material is arranged such that the light beam does not propagate along the symmetry axis or symmetry plane of the material, the generated photocurrent flows parallel to the propagation direction of the light. That is, the photocurrent flows from the top to the bottom. Likewise, the electrode 43 is arranged on top of and below the sample material. These are just some exemplary arrangements that may be used in the proposed system.

Fig. 6 depicts the experimental setup. The laser system is a custom C-fiber laser system commercially available from Menlo Systems. The laser outputs two femtosecond pulse trains with different wavelengths: one (400mW) was centred at 1560nm and the other (740mW) was centred at 1040 nm. The pulse duration of the two beams is about 70fs and the repetition rate is 250 MHz. The offset frequency of the laser comb was measured optically using heterodyne beat tones generated in a 2f-3f self-referencing interferometer, where the frequency of the 1040nm beam was doubled with a BBO crystal and the frequency of the 1560nm beam was tripled with a PPLN crystal (PPLN was designed for second harmonic generation, but it also produces a weak third harmonic). The line width of the 2f-3f beat note (beat note) is about 400 KHz. A feed forward technique is used to reset the offset frequency with a narrower linewidth. The feed forward arrangement also enables control of the offset frequency.

The light is then focused on an AlGaAs device between two gold electrodes separated by about 10 μm. Both field polarizations are oriented along the [010] crystal axis. The current is detected by the electrode in the [010] direction. The device is made of AlGaAs epitaxially grown on a GaAs substrate. The bandgap of AlGaAs is at wavelengths <700nm, suppressing linear absorption at 1040nm and two-photon absorption at 1560 nm. Photocurrent is injected into AlGaAs by quantum interference between two-photon absorption of 1040nm beam and three-photon absorption of 1560nm beam.

Fig. 7A shows the spectrum of the photocurrent induced in AlGaAs under three different conditions: the 1560nm light beam is blocked, the 1040nm light beam is blocked, and both the 1040nm light beam and the 1560nm light beam are not blocked. The QuIC signal in the semiconductor is used as a current source rather than a voltage source; the observed photocurrent signal was 2nA with a signal to noise ratio of 15dB at 30KHz bandwidth. The same signal measured using lock-in detection was greater than 0.3mV (using a 150k Ω load resistor) and the average powers (spot size) at 1040nm and 1560nm were 7mW (4.11. + -. 0.4. mu.m, FWHM) and 30mW (3.16. + -. 0.3. mu.m, FWHM), respectively. An additional degree of freedom that can be manipulated is the CEO frequency, which is controlled by the feed forward setting. By changing the CEO frequency from 2KHz to 60KHz, a change in beat note in the spectrum can be observed.

In conclusion, quantum interference control of injected photocurrent due to two-photon absorption process and three-photon absorption process of interference is detected in AlGaAs. Using the quac photocurrent, the carrier offset frequency of the fiber laser frequency comb is measured. This approach is promising since the required bandwidth is reduced and waveguide detection in an integrated structure will lead to a more compact device for comb biasing. It is envisaged that this technique may be employed to implement a direct on-chip digital optical combiner.

The foregoing description of the embodiments has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but are interchangeable if applicable and can be used in even selected embodiments that are not specifically shown or described. The various elements or features of a particular embodiment may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises," "comprising," "including," and "having," are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Unless specifically identified as an order of execution, the method steps, processes, and operations described herein are not to be construed as necessarily requiring their execution in the particular order discussed or illustrated. It should also be understood that additional or alternative steps may be employed.

When an element or layer is referred to as being "on," "engaged to," "connected to" or "coupled to" another element or layer, it can be directly on, engaged, connected or coupled to the other element or layer or intervening elements or layers may be present. In contrast, when an element is referred to as being "directly on," "directly engaged to," "directly connected to" or "directly coupled to" another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a similar manner (e.g., "between … …" versus "directly between … …", "adjacent" versus "directly adjacent", etc.). As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another region, layer or section. When terms such as "first," "second," and other numerical terms are used herein, no order or sequence is implied unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.

Spatially relative terms, such as "inner," "outer," "below," "lower," "upper," and the like, may be used herein for ease of description to describe one element or feature's relationship to another element or feature as illustrated. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "below" or "beneath" other elements or features would then be oriented "above" the other elements or features. Thus, the example term "below" can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.