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Linear Circuits

Linear Circuits

A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...

Classification of Systems-I

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

Network Function of a Circuit

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.

Lossless Lines

Lossless Lines

In electrical engineering, a lossless transmission line is characterized by a purely imaginary propagation constant and a resistive characteristic impedance. The ABCD parameters, which describe the relationship between the input and output voltages and currents, indicate an equivalent π circuit with an imaginary series impedance and a shunt admittance. This results in a transmission line that, when the product of the phase constant (beta) and the length of the line is less than pi, exhibits...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

Bewley Lattice Diagram

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.

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Related Experiment Video

Updated: May 10, 2026

Characterization of Anisotropic Leaky Mode Modulators for Holovideo

Characterization of Anisotropic Leaky Mode Modulators for Holovideo

Published on: March 19, 2016

Direct characterization of linear-optical networks.

Saleh Rahimi-Keshari¹, Matthew A Broome, Robert Fickler

¹Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia. s.rahimik@gmail.com

|June 6, 2013

Summary

We present an efficient method to fully characterize multimode linear-optical networks using only a laser and intensity measurements. This technique directly determines all network parameters, verified with two-photon interference.

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Area of Science:

Quantum optics
Photonics
Linear optical networks

Background:

Characterizing complex optical networks is crucial for quantum information processing.
Existing methods can be complex and require specialized equipment.
Understanding network properties like moduli and phases is essential.

Purpose of the Study:

To introduce an efficient and direct method for full characterization of multimode linear-optical networks.
To enable precise determination of network matrices, including moduli and non-trivial phases.
To provide a practical approach using standard laboratory tools.

Main Methods:

Utilizing a standard laser source for optical network excitation.
Performing direct intensity measurements to gather network data.
Applying a novel algorithm to uniquely determine the network's transformation matrix.

Main Results:

Successfully characterized a 6x6 fiber-optic network.
Directly and uniquely determined all moduli and non-trivial phases of the network matrix.
Independently verified the characterization results using nonclassical two-photon interference.

Conclusions:

The developed method offers an efficient and direct approach for complete optical network characterization.
This technique simplifies the process, requiring only standard equipment.
The results demonstrate the method's accuracy and applicability in quantum optics experiments.