Apparatus and method for testing coupled AC circuit

Various technologies described herein pertain to a testing apparatus that enables an analog frequency response of a device under test to be analyzed. The testing apparatus includes a laser source and an optical resonator. The laser source is optically injection locked to the optical resonator. The testing apparatus also includes a modulator configured to apply a time-varying voltage to the optical resonator. The time-varying voltage causes the laser source optically injection locked to the optical resonator to generate a frequency modulated optical signal that can include time-varying chirps. The testing apparatus further includes an interferometer (e.g., variable delay, fixed length) configured to receive the frequency modulated optical signal from the laser source optically injection locked to the optical resonator. The interferometer outputs an optical test signal having a range of frequencies. The frequencies in the optical test signal are based at least in part on the time-varying chirps.

BACKGROUND

Light detection and ranging (lidar) systems are surveying systems that measure distance to a target in an environment by illuminating the target with laser light and measuring reflected light (lidar return). Differences in laser return times can be utilized to generate a three-dimensional (3D) representation of the target. Lidar systems can also be used to measure the velocity of the target with respect to the observer. Thus, lidar systems can be used in various terrestrial, airborne, and mobile applications; for instance, lidar systems can be employed in autonomous or semi-autonomous vehicles, drones, robotics, and other applications that utilize laser scanning capabilities.

When designing a lidar system, it is often desirable to test analog frequency responses of various alternating current (AC) circuits that potentially may be integrated into the lidar system. However, it typically is desirable to test such circuits before integrating them into the overall lidar system. Further, it may be desirable to be able to test the analog frequency responses of the AC circuits in a lab or other controlled environment.

A conventional approach for generating test signals utilizes a laser source and an interferometer, where the laser source provides a single frequency light beam to the interferometer. Such conventional approaches typically output an optical signal having a single frequency (or a few discrete frequency points). However, these conventional approaches may be difficult to use to investigate frequency responses of an AC circuit over a spectrum of frequencies.

SUMMARY

Described herein are various technologies that pertain to a testing apparatus. The testing apparatus can enable an analog frequency response of a device under test (e.g., an AC circuit) coupled to the testing apparatus to be analyzed. For instance, the testing apparatus and the device under test can be optically coupled or electrically coupled (e.g., an optical test signal or an electrical test signal can be outputted from the testing apparatus). The testing apparatus can include a laser source and an optical resonator that is optically coupled to the laser source. The optical resonator can be formed of an electrooptic material. Further, the laser source can be optically injection locked to the optical resonator. Moreover, the testing apparatus can include a modulator configured to apply a time-varying voltage to the optical resonator. The time-varying voltage can control modulation of an optical property of the electrooptic material to cause the laser source optically injection locked to the optical resonator to generate a frequency modulated optical signal. The frequency modulated optical signal can include time-varying chirps. The testing apparatus can also include an interferometer. The interferometer can be configured to receive the frequency modulated optical signal from the laser source optically injection locked to the optical resonator. The interferometer can further be configured to output an optical test signal having a range of frequencies. The frequencies in the optical test signal can be based at least in part on the time-varying chirps. Pursuant to an example, the interferometer can be a variable delay interferometer. According to another example, the interferometer can be a fixed length interferometer.

According to various embodiments, the interferometer can include a first beam splitter, a second beam splitter, a first optical path, and a second optical path. The first optical path can be between the first beam splitter and the second beam splitter. Likewise, the second optical path can be between the first beam splitter and the second beam splitter. The first beam splitter can be configured to split the frequency modulated optical signal received from the laser source optically injection locked to the optical resonator into a first portion of the frequency modulated optical signal and a second portion of the frequency modulated optical signal. The first portion of the frequency modulated optical signal can propagate from the first beam splitter to the second beam splitter via the first optical path. Moreover, the second portion of the frequency modulated optical signal can propagate from the first beam splitter to the second beam splitter via the second optical path such that receipt of the second portion of the frequency modulated optical signal at the second beam splitter is delayed relative to receipt of the first portion of the frequency modulated optical signal at the second beam splitter. Further, the second beam splitter can be configured to combine the first portion of the frequency modulated optical signal and the second portion of the frequency modulated optical signal as delayed to output the optical test signal.

Pursuant to various embodiments, the interferometer can be a variable delay interferometer that can include a plurality of optical delay paths between the first beam splitter and the second beam splitter, where each optical delay path is configured to cause a respective corresponding delay for an optical signal propagating there through. The second optical path through which the second portion of the frequency modulated optical signal propagates can be one of the optical delay paths. Thus, one of the optical delay paths can be used as the second optical path during a particular time period, and a different one of the optical delay paths can be used as the second optical path during a differing time period to generate optical test signals having different ranges of frequencies during the different time periods. In accordance with an example, the plurality of optical delay paths can be a plurality of fibers of different lengths. According to another example, the plurality of optical delay paths can be a plurality of fibers formed of different types of materials. Pursuant to yet another example, mirrors can be utilized to provide the plurality of optical delay paths.

According to various embodiments, the optical test signal generated by the interferometer can be outputted from the testing apparatus such that the optical test signal is operable to be inputted to a device under test (e.g., to analyze analog frequency response of an optically coupled AC circuit). Pursuant to other embodiments, the testing apparatus can further include a signal converter configured to receive the optical test signal from the interferometer. In accordance with such embodiments, the signal converter can further be configured to convert the optical test signal to an electrical test signal. Moreover, the electrical test signal can be outputted from the testing apparatus such that the electrical test signal is operable to be inputted to a device under test (e.g., to analyze analog frequency response of an electrically coupled AC circuit).

DETAILED DESCRIPTION

As used herein, the terms “component” and “system” are intended to encompass computer-readable data storage that is configured with computer-executable instructions that cause certain functionality to be performed when executed by a processor. The computer-executable instructions may include a routine, a function, or the like. It is also to be understood that a component or system may be localized on a single device or distributed across several devices. Further, as used herein, the term “exemplary” is intended to mean “serving as an illustration or example of something.”

Referring now to the drawings,FIG.1illustrates a testing apparatus100. The testing apparatus100can enable an analog frequency response of a device under test (e.g., an AC circuit) coupled to the testing apparatus100to be analyzed. For instance, the testing apparatus100and the device under test can be optically coupled or electrically coupled (e.g., an optical test signal or an electrical test signal can be outputted from the testing apparatus100). The testing apparatus100includes a laser source102. The laser source102can be a semiconductor laser, a laser diode, or the like. It is contemplated that the laser source102can operate at substantially any wavelength (e.g., 1550 nm, 905 nm, etc.).

The testing apparatus100further includes an optical resonator104. The optical resonator104can be a whispering gallery mode (WGM) resonator (e.g., a high quality factor (Q) WGM resonator). The optical resonator104is formed of an electrooptic material. Examples of the electrooptic material include lithium niobate, lithium tantalate, calcium fluoride, magnesium fluoride, silicon, and so forth. The optical resonator104can include an electrode (or electrodes) to which a voltage can be applied. Application of a voltage to the optical resonator104can change an optical property of the electrooptic material of the optical resonator104. For instance, application of a voltage can change an index of refraction of the electrooptic material of the optical resonator104.

The optical resonator104is optically coupled to the laser source102. A light beam emitted from the laser source102is provided to the optical resonator104, circulates inside the optical resonator104undergoing total internal reflection, and is provided back from the optical resonator104to the laser source102. Accordingly, the laser source102is optically injection locked to the optical resonator104. Since the laser source102is optically injection locked to the optical resonator104, a voltage applied to the optical resonator104can impart a frequency change on the laser source102. Due to electrooptic properties and size of the optical resonator104, frequency of the optical resonator104can be linearly modulated with a relatively narrow linewidth. Accordingly, optical signals outputted by the laser source102optically injection locked to the optical resonator104can have low noise characteristics.

Moreover, the testing apparatus100can include a modulator106configured to apply a time-varying voltage to the optical resonator104. The time-varying voltage can control modulation of an optical property of the electrooptic material (e.g., the index of refraction) of the optical resonator104to cause the laser source102to generate a frequency modulated optical signal comprising a series of optical chirps. Thus, the time-varying voltage can control modulation of the optical property of the electrooptic material to cause the laser source102optically injection locked to the optical resonator104to generate a frequency modulated optical signal. Further, the frequency modulated optical signal can comprise time-varying chirps (e.g., the modulation can be modulated such that chirps change over time). Accordingly, frequencies of the optical signal outputted by the laser source102optically injection locked to the optical resonator104can be a function of voltages applied by the modulator106to the optical resonator104over time.

The testing apparatus100also includes an interferometer108. The interferometer108is configured to receive the frequency modulated optical signal from the laser source102optically injection locked to the optical resonator104. The interferometer108splits the frequency modulated optical signal into two beams that travel in different optical paths; the two beams are then combined. The interferometer108is further configured to output an optical test signal having a range of frequencies. The frequencies in the optical test signal can be based at least in part on the time-varying chirps included in the frequency modulated optical signal. According to various examples, the interferometer108can be a variable delay interferometer. Pursuant to other examples, the interferometer108can be a fixed length interferometer (e.g., providing a fixed propagation delay of a portion of the frequency modulated optical signal relative to another portion of the frequency modulated optical signal).

The frequencies in the optical test signal outputted by the interferometer108can also be based on a propagation delay of a portion of the frequency modulated optical signal caused by the interferometer108. The interferometer108can be a variable delay interferometer that can include a plurality of optical delay paths; each optical delay path is configured to cause a respective corresponding delay for an optical signal propagating there through. Thus, one of the optical delay paths can be used during a particular time period, and a different one of the optical delay paths can be used during a differing time period to generate optical test signals having different ranges of frequencies during the different time periods. In accordance with an example, the plurality of optical delay paths can be a plurality of fibers of different lengths. According to another example, the plurality of optical delay paths can be a plurality of fibers formed of different types of materials (e.g., an optical signal passes through the different types of materials at different speeds). Pursuant to yet another example, mirrors can be utilized to provide the plurality of optical delay paths.

As noted above, the frequencies in the optical test signal can be based on the propagation delay of the portion of the frequency modulated optical signal. According to an illustration, the interferometer108(e.g., the variable delay interferometer) can include fibers of different lengths. Following this illustration, the portion of the frequency modulated optical signal can propagate through one of the fibers; thus, the propagation delay can be based on a length of the fiber through which the portion of the frequency modulated optical signal propagates. In accordance with another illustration, the interferometer108(e.g., the variable delay interferometer) can include fibers formed of different types of material. Pursuant to this illustration, the portion of the frequency modulated optical signal can propagate through one of the fibers; accordingly, the propagation delay can be based on a type of the material of the fiber through which the portion of the frequency modulated optical signal propagates.

The testing apparatus100can also include a controller110. The controller110can be operatively coupled with the laser source102, the modulator106, and/or the interferometer108. The controller110, for instance, can control the modulator106to apply the time-varying voltage to the optical resonator104. The controller110can control timing, waveform shape, or the like of the time-varying voltage. By way of example, the controller110can control the modulator106to apply a continuous wave sawtooth waveform, a continuous wave triangular waveform, a pulsed triangular waveform, a continuous wave sigmoid-shaped waveform, or the like. Further, the controller110can change the waveform shape or properties of a particular waveform shape over time (e.g., a voltage change of a chirp can be modified over time, a period of a chirp can be modified over time).

Moreover, in various embodiments, the controller110can be configured to selectively control operating parameters of the laser source102. For instance, the controller110can control a power level of the laser source102. By changing the power level of the laser source102, an intensity response of a device under test can be evaluated. In other embodiments, however, it is contemplated that in-line attenuation can additionally or alternatively be employed to enable evaluating the intensity response of the device under test (e.g., the testing apparatus100can include an attenuator to reduce a power level of the optical test signal and/or an electrical test signal inputted to the device under test).

It is further contemplated that the controller110can control the interferometer108in various embodiments. As noted above, the interferometer108can be a variable delay interferometer that can include a plurality of optical delay paths. The controller110can cause a particular one of the optical delay paths to be utilized for generating the optical test signal for a particular period of time. Thus, the controller110can enable switching between the optical delay paths over time.

The testing apparatus100can be comprised in a housing. Accordingly, elements described herein in various examples as being part of the testing apparatus100can be housed within the housing. For instance, the housing can be rack-mountable.

Now turning toFIG.2, illustrated is an exemplary testing apparatus200(e.g., the testing apparatus100ofFIG.1). The testing apparatus200includes the laser source102, the optical resonator104, the modulator106, and the interferometer108. As described above, the laser source102is optically injection locked to the optical resonator104, and the modulator106is configured to apply a time-varying voltage to the optical resonator104. The time-varying voltage causes the laser source102optically injection locked to the optical resonator104to generate a frequency modulated optical signal, which is received by the interferometer108. Although not shown inFIG.2, it is to be appreciated that the testing apparatus200can also include the controller110.

The interferometer108depicted inFIG.2is a variable delay interferometer that includes a first beam splitter202, a second beam splitter204, a first optical path206, and a plurality of optical delay paths208. The first optical path206is between the first beam splitter202and the second beam splitter204. The plurality of optical delay paths208are likewise between the first beam splitter202and the second beam splitter204. In the example ofFIG.2, the plurality of optical delay paths208are a plurality of fibers. The fibers can have differing lengths and/or can be formed from different types of materials.

The first beam splitter202is configured to split the frequency modulated optical signal into a first portion of the frequency modulated optical signal and a second portion of the frequency modulated optical signal (e.g., the frequency modulated optical signal is split into two beams). According to the depicted example, the first beam splitter202can be a 1×2 beam splitter (e.g., one beam is inputted into the first beam splitter202and two beams are outputted out of the first beam splitter202). The first beam splitter202can split the frequency modulated optical signal such that the first portion of the frequency modulated optical signal and the second portion of the frequency modulated optical signal are each at approximately 50% of the power of the frequency modulated optical signal inputted to the first beam splitter202. However, the first beam splitter202need not equally divide the power of the frequency modulated optical signal in other embodiments.

The first portion of the frequency modulated optical signal (e.g., a first beam) can propagate from the first beam splitter202to the second beam splitter204via the first optical path206. Moreover, one of the plurality of optical delay paths208can be a second optical path (e.g., during a particular period of time, the optical delay path from the optical delay paths208used as the second optical path can change to alter a delay). Accordingly, the second portion of the frequency modulated optical signal (e.g., a second beam) can propagate from the first beam splitter202to the second beam splitter204via the second optical path. By way of example, an optical delay path210from the plurality of optical delay paths208can be the second optical path during a particular period of time (also referred to herein as the second optical path210). The optical delay path210can be selected from the plurality of optical delay paths208as the second optical path. While the optical delay path210is described as being the second optical path in many of the examples set forth herein, it is contemplated that these examples can be extended to the other optical delay paths208alternatively being the second optical path (e.g., during a given period of time).

Further, the optical delay paths208can delay a beam propagating there through as compared to the first optical path206. Each optical delay path208is configured to cause a respective corresponding delay for an optical signal propagating there through. Accordingly, the second portion of the frequency modulated optical signal propagates from the first beam splitter202to the second beam splitter204via the second optical path210such that receipt of the second portion of the frequency modulated optical signal at the second beam splitter204is delayed relative to receipt of the first portion of the frequency modulated optical signal at the second beam splitter204(e.g., the first portion propagates via the first optical path206).

As shown in the example ofFIG.2, the optical delay paths208can include four fibers. Moreover, the fibers can be coiled to allow for maintaining a relative compact size of the testing apparatus200. For instance, a particular fiber from the plurality of fibers can be selected as the second optical path (e.g., for a particular period of time). According to an example, the fibers (e.g., the optical delay paths208) can have different lengths. Pursuant to an illustration, the fibers can include a first fiber having a length of 25 m, a second fiber having a length of 50 m, a third fiber having a length of 100 m, and a fourth fiber having a length of 200 m; yet, other fiber lengths are intended to fall within the scope of the hereto appended claims. Pursuant to another example, the fibers (e.g., the optical delay paths208) can be formed of differing types of material. In accordance with yet another example, the fibers can have different lengths and can be formed of differing types of materials. Moreover, it is contemplated that more than or less than four fibers can alternatively be included in the interferometer108(e.g., the interferometer108can include one fiber and thus can be a fixed length interferometer). It is also to be appreciated that mirrors can alternatively be used to provide the optical delay paths208.

The second beam splitter204is configured to combine the first portion of the frequency modulated optical signal and the second portion of the frequency modulated optical signal as delayed to output an optical test signal. In various embodiments, the second beam splitter204can be a 2×2 beam splitter. Accordingly, the second beam splitter204can be configured to combine the first portion of the frequency modulated optical signal and the second portion of the frequency modulated optical signal as delayed to generate an optical test signal. The second beam splitter204can split the optical test signal into a first portion of the optical test signal and a second portion of the optical test signal such that the first portion and the second portion of the optical test signal are outputted by the second beam splitter204.

Moreover, the testing apparatus200(e.g., the interferometer108) can include a fiber input212and two fiber outputs, namely, a fiber output214and a fiber output216. The fiber input212can be a connector between the laser source102optically injection locked to the optical resonator104and the beam splitter202. For instance, the frequency modulated optical signal generated by the laser source102optically injection locked to the optical resonator104can be in free space. The frequency modulated optical signal can be incident on an end of the fiber input212. It is also contemplated that a collimator or some other type of optical element can take the frequency modulated optical signal from free space and input the frequency modulated optical signal into an end of the fiber input212.

As noted above, the second beam splitter204can split the optical test signal. Thus, the second beam splitter204can output the first portion of the optical test signal via the first fiber output214and the second portion of the optical test signal via the second fiber output216. The fiber outputs214-216can be at a set spacing. For instance, the fiber outputs214-216can be laterally offset on the order of 350 μm. Moreover, the fiber outputs214-216can be aligned. According to an example, the fiber outputs214-216can be oriented vertically to output to the optical test signal from the testing apparatus200. The fiber outputs214-216provide a phase delay, which enables mitigating a direct current (DC) part of the optical test signal (which can mitigate saturation of component(s) of the device under test).

In the example set forth inFIG.2, the testing apparatus200is configured to output the optical test signal (e.g., via the fiber outputs214-216). The optical test signal can be outputted from the testing apparatus200such that the optical test signal is operable to be inputted to a device under test. As shown in the example ofFIG.2, the optical test signal from the testing apparatus200can be inputted to a transimpedance amplifier (TIA) device under test (DUT)218. According to an example, the transimpedance amplifier device under test218can generate a voltage signal responsive to the optical test signal received from the testing apparatus200. The voltage signal from the transimpedance amplifier device under test218can be inputted to a radio frequency (RF) board220(e.g., an RF circuit). Moreover, an output of the radio frequency board220can be inputted to a spectrum analyzer222, which can generate a Fast Fourier Transform (FFT) data output224.

The testing apparatus200enables an analog frequency response of an optically coupled AC circuit (e.g., the transimpedance amplifier device under test218) to be analyzed using the low noise, frequency modulated laser source102(optically injection locked to the optical resonator204) and the interferometer108. Moreover, alignment onto photodiodes (e.g., of the optically coupled AC circuit) can be provided via the fiber outputs214-216. According to an example, modulation of the laser source102(as provided by the modulator106applying the time-varying voltage to the optical resonator104) can be altered to provide a continuous spectrum of frequencies in the optical test signal. Further, an intensity response of the optically coupled AC circuit can be evaluated using an in-line attenuator and/or by reducing power of the laser source102(e.g., as controlled by the controller110). The foregoing can allow a lidar return at range to be simulated in the testing apparatus200(e.g., in fiber) to test and/or screen receiver circuitry (e.g., the transimpedance amplifier device under test218) without having to test in an integrated system outside.

With reference toFIG.3, illustrated is another exemplary testing apparatus300(e.g., the testing apparatus100ofFIG.1). Again, the testing apparatus300includes the laser source102, the optical resonator104, the modulator106, and the interferometer108. Further, although not shown, it is to be appreciated that the testing apparatus300can include the controller110. Moreover, similar to the example set forth inFIG.2, the interferometer108of the testing apparatus300(e.g., a variable delay interferometer) includes the first beam splitter202, second beam splitter204, the first optical path206, and the plurality of optical delay paths208. The testing apparatus300can further include the fiber input212.

In the example set forth inFIG.3, the testing apparatus300includes a signal converter302configured to receive the optical test signal from the interferometer108(e.g., from the second beam splitter204). The signal converter302is further configured to convert the optical test signal to an electrical test signal. Pursuant to an example, the signal converter302can be a transimpedance amplifier; however, the claimed subject matter is not so limited. The electrical test signal is outputted from the testing apparatus300such that the electrical test signal is operable to be inputted to a device under test. Accordingly, as shown, the electrical test signal can be outputted from the testing apparatus300and inputted to an RF device under test304. An output from the RF device under test304can be provided to the spectrum analyzer222, which can generate a Fast Fourier Transform (FFT) data output224. Thus, the testing apparatus300can be utilized to analyze an analog frequency response of an electrically coupled AC circuit (e.g., the RF device under test304).

Now turning toFIG.4, illustrated is another exemplary testing apparatus400(e.g., the testing apparatus100ofFIG.1). The testing apparatus400again includes the laser source102, the optical resonator104, the modulator106, and the interferometer108(e.g., a variable delay interferometer, a fixed length interferometer). Moreover, the testing apparatus400includes the controller110and the signal converter302.

As described herein, the interferometer108can output an optical test signal. Further, the optical test signal can be inputted to the signal converter302, which can convert the optical test signal to an electrical test signal. In the example ofFIG.4, the controller110can include an output controller402. The output controller402is configured to cause the testing apparatus400to switch between outputting an optical test signal404(e.g., generated by the interferometer108) and an electrical test signal406(e.g., generated by the signal converter302).

Referring now toFIG.5, illustrated is yet another exemplary testing apparatus500(e.g., the testing apparatus100ofFIG.1). The testing apparatus500again includes the laser source102, the optical resonator104, the modulator106, the interferometer108, and the controller110. The testing apparatus500ofFIG.5further includes one or more variable attenuators (VAs). In particular, in the example shown, the testing apparatus500can include a variable attenuator502, a variable attenuator504, a variable attenuator506, and a variable attenuator508. It is contemplated that the testing apparatus500need not include all of the variable attenuators502-508shown inFIG.5. Additionally or alternatively, the testing apparatus500can include other variable attenuator(s). For instance, rather than including the variable attenuator504between the plurality of optical delay paths208and the second beam splitter204, each of the optical delay paths208can include a respective variable attenuator. According to another illustration, the variable attenuators506and508can alternatively be between the second beam splitter204and the fiber outputs214-216.

Each of the variable attenuators502-508can reduce power of a signal propagating through the respective variable attenuator502-508. Moreover, a loss caused by each of the variable attenuators502-508can be controllable (e.g., to enable analyzing various properties of a device under test coupled to the testing apparatus500). For example, the controller110can control the loss of each of the variable attenuators502-508; however, the claimed subject matter is not so limited.

The variable attenuators502-508can enable analyzing various properties of an AC circuit (e.g., a device under test) coupled to the testing apparatus500. For example, one or more of the variable attenuators502-508can be used to evaluate how a noise floor of an AC circuit is influenced by various components. According to another example, the variable attenuator502on the first optical path206can be utilized to detect a minimum local oscillator power to be used for the AC circuit. Pursuant to another example, the variable attenuator504after the variable delay (e.g., after the optical delay paths) can be employed to provide different power levels of a signal (variable target reflectivity) that can be monitored with the AC circuit. In accordance with another example, the variable attenuators506and508can be used to test how well photodiodes of the AC circuit are balanced.

FIGS.6-8illustrate various exemplary chirps of the frequency modulated optical signal generated by the laser source102optically injection locked to the optical resonator104. These examples are intended to depict how changes between chirps can cause the interferometer108to output different frequencies in the optical test signal (e.g., beat frequencies resulting from combining a portion of a frequency modulated optical signal with a delayed portion of the frequency modulated optical signal). Yet, it is to be appreciated that the claimed subject matter is not limited to the depicted examples.

Now referring toFIG.6, illustrated is a chart600depicting a first portion of a frequency modulated optical signal602and a delayed second portion of the frequency modulated optical signal604. More particularly,602represents a first portion of the frequency modulated optical signal as received at an output (e.g., the second beam splitter204) that has propagated through the first optical path206. Moreover,604represents a second portion of the frequency modulated optical signal as received at the output that has propagated through the second optical path210(e.g., one of the optical delay paths208). Receipt of the second portion604at the second beam splitter204is delayed relative to receipt of the first portion602. Further,

n*Rc
is a time delay between receipt of the first portion602and the second portion604. As set forth below, R is a physical path difference between a length of the second optical path and a length of the first optical path, c is the speed of light, and n is the index of refraction of the interferometer108. The first portion602and the second portion604are combined (e.g., coherently interfere, at the second beam splitter204), resulting in the interferometer108outputting the optical test signal that is representative of beat frequencies over time (e.g., a carrier frequency of the laser source102is removed by combining the first portion602and the second portion604).

In the example depicted inFIG.6, a linear modulation scheme is used to generate triangular chirps as part of the frequency modulated optical signal, each with a period T (e.g., two chirps are shown). A first waveform of a time-varying voltage applied by the modulator106to the optical resonator104(e.g., time0to time T) can cause the laser source102optically injection locked to the optical resonator104to generate the first chirp, and a second waveform of the time-varying voltage applied by the modulator106to the optical resonator104(e.g., time T to time27) can cause the laser source102optically injection locked to the optical resonator104to generate the second chirp. A first voltage change of the first waveform differs from a second voltage change of the second waveform. In the example ofFIG.6, the second voltage change is greater than the first voltage change resulting in bandwidth B2of the second chirp being greater than bandwidth B1of the first chirp (e.g., due to the frequency of the beam emitted by the laser source102optically injection locked to the optical resonator104being proportional to the voltage applied to the optical resonator104).

f0is the carrier frequency of the laser source102. In the example shown, the first chirp can have a first slope

ξ1=2⁢B1T
and the second chirp can have a second slope

ξ2=2⁢B2T.
Moreover, a beat frequency f is related to the slope ξ of a chirp as follows:

f=n*Rc⁢ξ.
R is a physical path difference between a length of the second optical path and a length of the first optical path, c is the speed of light, n is the index of refraction of the interferometer, and is a slope of a chirp. It follows that n*R is an optical path difference between the second optical path and the first optical path. Thus, the beat frequency f has a linear relationship that is proportional to the slope of the chirp ξ. Accordingly, a beat frequency f1of the first chirp is

f1=n*Rc⁢ξ1
and a beat frequency f2of the second chirp is

f2=n*Rc⁢ξ2.
In view of the foregoing, modulating the voltage change between chirps (e.g., in a continuous manner) can result in the optical test signal having a range of frequencies.

Turning toFIG.7, illustrated is a chart700depicting a first portion of a frequency modulated optical signal702and a delayed second portion of the frequency modulated optical signal704. Similar to above,702represents a first portion of the frequency modulated optical signal as received at an output (e.g., the second beam splitter204) that has propagated through the first optical path206. Further,704represents a second portion of the frequency modulated optical signal as received at the output that has propagated through the second optical path210(e.g., one of the optical delay paths208). Receipt of the second portion704at the second beam splitter204is delayed relative to receipt of the first portion702

(e.g.,n*Rc
is a time delay between receipt of the first portion702and the second portion704). The first portion702and the second portion704are combined (e.g., coherently interfere, at the second beam splitter204), resulting in the interferometer108outputting the optical test signal that is representative of beat frequencies over time.

In the example ofFIG.7, triangular chirps having differing periods are generated (e.g., two chirps are shown). A first waveform of a time-varying voltage applied by the modulator106to the optical resonator (e.g., time0to time T1) can cause the laser source102optically injection locked to the optical resonator104to generate the first chirp, and a second waveform of the time-varying voltage applied by the modulator106to the optical resonator104(e.g., time T1to time T1+T2) can cause the laser source102optically injection locked to the optical resonator104to generate the second chirp. A first period of the first waveform T1differs from a second period of the second waveform T2. As shown inFIG.7, the second period T2is greater than the first period T1. Moreover, bandwidth B of the first and second chirps is substantially similar in this example (e.g., the first waveform and the second waveform can have a substantially similar voltage change during the respective time periods). Thus, in the example ofFIG.7, the first chirp can have a first slope

ξ1=2⁢BT1
and the second chirp can have a second slope

ξ2=2⁢BT2.
Similar to above, a beat frequency f1of the first chirp is

f1=n*Rc⁢ξ1
and a beat frequency f2of the second chirp is

f2=n*Rc⁢ξ2.
In view of the foregoing, modulating the period between chirps can result in the optical test signal having a range of frequencies.

With reference toFIG.8, illustrated is a chart depicting a first portion of a frequency modulated optical signal802and two delayed portions of the frequency modulated optical signal, namely, a delayed portion804and a delayed portion806. More particularly,802represents a first portion of the frequency modulated optical signal as received at an output (e.g., the second beam splitter204) that has propagated through the first optical path206. Further, the delayed portion804represents a second portion of the frequency modulated optical signal as received at the output having propagated via a first optical delay path (e.g., from the optical delay paths208) and the delayed portion806represents the second portion of the frequency modulated optical signal as received at the output having propagated via a second optical delay path (e.g., from the optical delay paths208). As depicted, different beat frequencies result depending upon which optical delay path of a variable delay interferometer is used.

As shown, if the second portion of the frequency modulated optical signal propagates via the first optical delay path having a length R1, then a beat frequency f1resulting from a chirp can be

f1=n*R1c⁢ξ.
Alternatively, if the second portion of the frequency modulated optical signal propagates via the second optical delay path having a length R2, then a beat frequency f2resulting from a chirp can be

f2=n*R2c⁢ξ.
Similarly, if the optical delay paths are fibers formed of different materials, then the speed of light c in such fibers can differ, which can lead to different beat frequencies.

Reference is generally made again toFIGS.6-8. It is to be appreciated that a combination of the techniques set forth in these examples can be utilized (e.g., both period and voltage change used to generate chirps can be altered over time).

FIG.9illustrates an exemplary methodology relating to generating an optical test signal for analyzing an analog frequency response of a device under test. While the methodologies are shown and described as being a series of acts that are performed in a sequence, it is to be understood and appreciated that the methodologies are not limited by the order of the sequence. For example, some acts can occur in a different order than what is described herein. In addition, an act can occur concurrently with another act. Further, in some instances, not all acts may be required to implement a methodology described herein.

FIG.9illustrates a methodology900for generating an optical test signal. At902, a time-varying voltage can be applied to an optical resonator that is optically coupled to a laser source. The laser source is optically injection locked to the optical resonator. The time-varying voltage causes the laser source optically injection locked to the optical resonator to generate a frequency modulated optical signal. Moreover, the frequency modulated optical signal comprises time-varying chirps. At904, the frequency modulated optical signal can be split into a first portion of the frequency modulated optical signal and a second portion of the frequency modulated optical signal. The first portion of the frequency modulated optical signal propagates via a first optical path and the second portion of the frequency modulated optical signal propagates via a delayed second optical path. At906, the first portion of the frequency modulated optical signal and the second portion of the frequency modulated optical signal as delayed can be combined to output the optical test signal.