FMCW Laser (FMCWL) - INTERCONNECT Element

The FMCW laser model generates a frequency modulated continuous wave (FMCW) optical signal

Keywords

electrical, optical, unidirectional

Ports

Properties

General Properties

Standard Properties

Standard/Frequency Modulation Properties

Polarization Properties

Waveguide/Mode 1 Properties

Waveguide/Mode 2 Properties

Enhanced Properties

Numerical Properties

Simulation Properties

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Implementation Details

The Frequency-Modulated Continuous-Wave (FMCW) Laser element is designed to generate an optical signal whose frequency changes over time, making it ideal for applications that require frequency modulation. This model is based on the Continuous Wave (CW) Laser model, and properties unrelated to frequency modulation is identical as those described there.

Frequency Modulation

The frequency of the optical signal in the FMCW Laser is modulated by the input electrical signal. The overall optical output signal can be described by the following equation

$$
s\left(t\right)=A \cdot e^{2\pi i\phi\left(t\right)} \cdot e^{i2\pi f_0t}
$$

where \( s(t) \) is the output optical signal in the time domain, \( A \) is the amplitude of the output, which is calculated by \( \sqrt{\text{power}} \) (specified under “Standard Properties”), \( f_0 \) is the center frequency (specified under “Standard Properties”), and \( \phi(t) \) represents the frequency modulation.

In the FMCW Laser, the frequency modulation \( \phi(t) \) is determined by the integration of the input electrical signal, scaled by the FM Sensitivity. This is described by the following equation:

$$
\phi\left(t\right)=\int_{0}^{t}{K\left(V_{in}\right)V_{in}\left(\tau\right)d\tau}
$$

where \( K \) is the FM Sensitivity, in units of \( \text{Hz/V}, \) and \( V_{in}(\tau) \) is the input electrical signal as a function of time \( \tau. \) In general, \( K \) could be a function of \( V_{in}, \) and this is described in the section below. In the limiting case where \( K\left(V_{in}\right)=0, \) the output of the FMCW Laser is equivalent to that of the CW Laser.

FM Sensitivity

An important setting in the FMCW Laser is the Frequency Modulation (FM) sensitivity parameter. FM sensitivity measures how effectively the frequency modulation responds to changes in the driving electrical signal. This parameter can be specified as a constant value or as a table (or text file) where the first column represents the input voltage, and the second column represents the corresponding FM sensitivity. Using a table format is particularly useful for nonlinear chirp signals, where the relationship between the input voltage and the frequency deviation is not linear. This non-linear relationship could be caused by either experimental nonidealities, such as those induced by manufacturing variations, thermal fluctuations, or inherent nonlinearities in lasers. Alternatively, it can be an intentional design for better system performance.

Similar Elements

• CW Laser (CWL): The CW laser is the same element as the FMCW laser, except it does not have frequency modulation.
• Multimode CW Laser (MMCW): The MMCW element is similar to the CW Laser, but it can create optical signals in multiple orthogonal modes.
• Directly Modulated Laser (DML): The DML element can be used to model a laser that is directly modulated by an electrical signal. A simple laser model is used to determine the output signal based on the electrical signal input. 
• Traveling Wave Laser Model (TWLM): The TWLM element implements a more complex laser model compared to the DML element.

Examples

Basic Example

A basic example of the FMCW Laser element is attached as fmcw_source_basic_example.icp. The FMCW Laser element in this case is driven by a ramp source with a slope of 100 MV/s, the FM sensitivity parameter is set to be 50 GHz/V, with a starting frequency of 193.1 THz.

Note: The starting frequency for frequency modulation is set under “frequency” in the “Standard Properties” section of the FMCW element. While this frequency is used as the starting frequency for frequency modulation, it is used as the center frequency for other calculations such as RIN.

After simulation of 10 ns, the script plot_fmcw_source.lsf can be used to visualize key results of the FMCW Laser. The frequency-time spectrogram shows a linear increase in frequency from 193.1 THz to 193.15 THz, which is consistent with the parameters set and the formulas provided above.

Similarly, the spectrum of the output signal of the FMCW Laser shows a frequency range between the expected values.

Finally, the optical oscilloscope displays a time-domain chirp signal characterized by a linear increase in frequency over time.

Application Gallery Example

The FMCW Laser element is used in the following examples:

• LiDAR Application Using Frequency Modulation Continuous Wave