# Recovery and Characterization of Orbital Angular Momentum Modes with Ghost Diffraction Holography

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## Abstract

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## 1. Introduction

## 2. Principle and Methods

#### 2.1. Generation and Recovery of OAM Modes

#### 2.2. Experimental Design and Recovery Scheme

## 3. Results and Discussion

#### 3.1. Simulation Results

#### 3.2. Experimental Results

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Conceptual schematic of the generation and propagation of a vortex beam with specific OAM mode. The superposition of an independent random reference field with the ghost diffraction fields makes an off-axis ghost diffraction holography scheme; RGGD: rotating ground glass diffuser; SLM: spatial light modulator.

**Figure 2.**(

**a**) Schematic of the experimental system for the generation and recovery of OAM modes: He-Ne, helium-neon laser source; M, mirror; SF, spatial filter assembly; L, lens; HWP, half wave plate; A, aperture; GG, ground glass diffuser; BS, beam splitter; SLM, spatial light modulator; MO, microscope objective; and CCD, charge coupled device camera; (

**b**–

**e**) CCD recorded resultant speckle pattern for OAM modes with $l=1,4,-1-4$, respectively.

**Figure 3.**Illustration of the recovery scheme of the technique: (

**a**) step by step analysis procedure; (

**b**) vortex phase mask ($\epsilon l=+3$) encoded in the SLM; (

**c**) zero order phase mask encoded in the SLM; (

**d**,

**e**) raw intensity images recorded by the camera corresponding to (

**b**,

**c**), respectively; (

**f**) correlation hologram retrieved from cross-correlation of intensity images; (

**g**) results of Fourier transform operation on correlation hologram; (

**h**) amplitude distribution of OAM mode; and (

**i**) phase distribution of OAM mode.

**Figure 4.**Theoretical simulation results; Simulation results: (

**a**–

**d**) retrieved correlation holograms; (

**e**–

**h**) recovered amplitude distributions of the OAM modes; (

**i**–

**l**) recovered phase distributions of OAM modes; (

**m**–

**p**) OAM distribution with X-axis representing the topological charge ($\epsilon l$) and Y-axis the OAM power spectrum ($P\left(l\right)$); Scale bar: 110 µm.

**Figure 5.**Experimental results: (

**a**–

**d**) retrieved correlation holograms; (

**e**–

**h**) recovered amplitude distributions of the OAM modes; (

**i**–

**l**) recovered phase distributions of the OAM modes; (

**m**–

**p**) OAM distribution with X-axis the topological charge ($\epsilon l$) and Y-axis the OAM power spectrum ($P\left(l\right)$); Scale bar: 110 µm.

**Figure 6.**Quantitative comparison of experimental and simulation results: (

**a**) variation of inner and outer radii with the topological charge (

**r**

_{1}, inner radius and

**r**

_{2}, outer radius); (

**b**) variation of area of dark core (Ad, dark core) and area of bright annular ring (Ar, annular ring) of the recovered OAM modes.

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**MDPI and ACS Style**

Huang, Y.; R.V., V.; Chen, Z.; Sarkar, T.; Singh, R.K.; Pu, J. Recovery and Characterization of Orbital Angular Momentum Modes with Ghost Diffraction Holography. *Appl. Sci.* **2021**, *11*, 12167.
https://doi.org/10.3390/app112412167

**AMA Style**

Huang Y, R.V. V, Chen Z, Sarkar T, Singh RK, Pu J. Recovery and Characterization of Orbital Angular Momentum Modes with Ghost Diffraction Holography. *Applied Sciences*. 2021; 11(24):12167.
https://doi.org/10.3390/app112412167

**Chicago/Turabian Style**

Huang, Yanyan, Vinu R.V., Ziyang Chen, Tushar Sarkar, Rakesh Kumar Singh, and Jixiong Pu. 2021. "Recovery and Characterization of Orbital Angular Momentum Modes with Ghost Diffraction Holography" *Applied Sciences* 11, no. 24: 12167.
https://doi.org/10.3390/app112412167